Journal of ENERGY TECHNOLOGY mm !■ Mkt University of Maribor Faculty of Energy Technology Volume 10 / Issue 4 DECEMBER 2017 www.fe.um.si/en/jet.html 2 JET Journal of ENERGY TECHNOLOGY ✓_____ JET 3 VOLUME 10 / Issue 4 Revija Journal of Energy Technology (JET) je indeksirana v bazah INSPEC© in Proquest's Technology Research Database. The Journal of Energy Technology (JET) is indexed and abstracted in database INSPEC© and Pro-quest's Technology Research Database. 4 JET /_____ ra JOURNAL OF ENERGY TECHNOLOGY Ustanovitelj / FOUNDER Fakulteta za energetiko, UNIVERZA V MARIBORU / FACULTY OF ENERGY TECHNOLOGY, UNIVERSITY OF MARIBOR Izdajatelj / PUBLISHER Fakulteta za energetiko, UNIVERZA V MARIBORU / FACULTY OF ENERGY TECHNOLOGY, UNIVERSITY OF MARIBOR Glavni in odgovorni urednik / EDITOR-IN-CHIEF Jurij AVSEC Souredniki / CO-EDITORS Bruno CVIKL Miralem HADŽISELIMOVIC Gorazd HREN Zdravko PRAUNSEIS Sebastijan SEME Bojan ŠTUMBERGER Janez USENIK Peter VIRTIČ Ivan ŽAGAR Uredniški odbor / EDITORIAL BOARD Zasl. prof. dr. Dali DONLAGIČ, Univerza v Mariboru, Slovenija, predsednik / University of Maribor, Slovenia, President Prof. ddr. Denis DONLAGIČ, Univerza v Mariboru, Slovenija / University of Maribor, Slovenia Doc. dr. Željko HEDERIČ, Sveučilište Josipa Jurja Strossmayera u Osijeku, Hrvatska / Josip Juraj Strossmayer University Osijek, Croatia Prof. dr. Ivan Aleksander KODELI, Institut Jožef Stefan, Slovenija / Jožef Stefan Institute, Slovenia Prof. dr. Milan MARČIČ, Univerza v Mariboru, Slovenija / University of Maribor, Slovenia Prof. dr. Greg NATERER, University of Ontario, Kanada / University of Ontario, Canada JET 5 Prof. dr. Enrico NOBILE, Université degli Studi di Trieste, Italia / University of Trieste, Italy Prof. dr. Brane ŠIROK, Univerza v Ljubljani, Slovenija / University of Ljubljana, Slovenia Doc. dr. Luka SNOJ, Institut Jožef Stefan, Slovenija / Jožef Stefan Institute, Slovenia Prof. dr. Mykhailo ZAGIRNYAK, Kremenchuk Mykhailo Ostrohradskyi National University, Ukrajina / Kremenchuk Mykhailo Ostrohradskyi National University, Ukraine, Tehnični urednik / TECHNICAL EDITOR Sonja Novak Tehnična podpora / TECHNICAL SUPPORT Tamara BREČKO BOGOVČIČ Izhajanje revije / PUBLISHING Revija izhaja štirikrat letno v nakladi 150 izvodov. Članki so dostopni na spletni strani revije -www.fe.um.si/si/jet.html / The journal is published four times a year. Articles are available at the journal's home page - www.fe.um.si/en/jet.html. Cena posameznega izvoda revije (brez DDV) / Price per issue (VAT not included in price): 50,00 EUR Informacije o naročninah / Subscription information: http://www.fe.um.si/en/jet/ subscriptions.html Lektoriranje / LANGUAGE EDITING Terry T. JACKSON Oblikovanje in tisk / DESIGN AND PRINT Fotografika, Boštjan Colarič s.p. Naslovna fotografija / COVER PHOTOGRAPH Jurij AVSEC Oblikovanje znaka revije / JOURNAL AND LOGO DESIGN Andrej PREDIN Ustanovni urednik / FOUNDING EDITOR Andrej PREDIN Izdajanje revije JET finančno podpira Javna agencija za raziskovalno dejavnost Republike Slovenije iz sredstev državnega proračuna iz naslova razpisa za sofinanciranje domačih znanstvenih periodičnih publikacij / The Journal of Energy Technology is co-financed by the Slovenian Research Agency. 6 JET JET l Spoštovani bralci revije Journal of energy technology (JET) Jedrska energetika omogoča učinkovito proizvodnjo električne in toplotne energije. V svetu je trenutno delujočih približno 450 jedrskih reaktorjev za proizvodnjo električne energije, razen tega deluje v svetu še približno 225 raziskovalnih reaktorjev, cca. 180 jedrskih reaktorjev je uporabljenih za pogon ladij in podmornic. Na ta način se v svetu pridobi približno 11 % električne energije ter dobršen del toplotne energije in energije potrebne za pogon ladij ter podmornic. Absolutno največ električne energije s pomočjo jedrskih reaktorjev pridobijo v ZDA, Rusiji in Franciji. V Franciji je delež proizvedene električne energije z jedrsko energetiko približno 75 %. Slovenija spada v skupino šestnajstih držav z vsaj 25 % deležem elektrike proizvedene v jedrskih elektrarnah. Razvoj jedrskih tehnologij na področju fuzije in fisije je zelo intenziven. Z novejšimi generacijami jedrskih reaktorjev bo možno še učinkoviteje in varneje pridobivati toplotno, električno energijo ter vodik. V predstavljenem izvodu revije je objavljen tudi članek, ki obravnava omenjeno tematiko. Jurij AVSEC odgovorni urednik revije JET 8 JET Dear Readers of the Journal of Energy Technology (JET) Nuclear energy enables the efficient production of electricity and heat. There are currently approximately 450 nuclear reactors operating in the world, with an additional approximately 225 research reactors in the world. Furthermore, about 180 nuclear reactors powered ships and submarines. In this way, around 11% of the electricity is supplied to the world as well as a good part of the heat and energy needed for the propulsion of ships and submarines. Overwhelmingly, most of the electricity generated by nuclear reactors is in the USA, Russia, and France. In France, the share of electricity produced by nuclear energy technology is approximately 75%. Slovenia belongs to a group of sixteen countries in which at least 25% of the electricity is produced in nuclear power plants. The development of technologies in fusion and fission is very intense. With newer generations of nuclear reactors, it will be possible to generate heat, electricity and hydrogen more efficiently and safely. An article published in this issue is dealing with this topic. Jurij AVSEC Editor-in-chief of JET JET 9 Table of Contents / Kazalo A Straightforward Analytical way of Evaluating the Single-phase Inverter SPWM Frequency Spectrum Analitičen postopek ocenitve frekvenčnega spektra SPWM izhodne napetosti enofaznega razmernika Alenka Hren, Franc Mihalič.......................................11 Hydraulic transient control of new and refurbished Kaplan turbine hydropower schemes in Slovenia Blaženje prehodnih pojavov v slovenskih novih in obnovljenih hidroelektrarnah s Kaplanovimi tur- binami Jernej Mazij, Anton Bergant.......................................29 The calculation of high-pressure viscosity for refrigerant mixtures Izračun viskoznosti pri visokih tlakih za zmesi hladil Jurij Avsec, Urška Novosel........................................45 Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine Mehanska analiza rotorjev dvostranskega sinhronskega stroja z aksialnim magnetnim pretokom Franjo Pranjic, Peter Virtič........................................57 Future Generation IV SMR reactors: assessment and possibility of integration in closed nuclear fuel cycles Prihajajoča IV. generacija SMR reaktorjev: evalvacija in možnost integracije v zaprte jedrske gorivne kroge Aleš Buršič, Tomaž Žagar........................................71 Instructions for authors.........................................93 10 JET im Journal of JET v°iume 10 (2°1?) p.p. n-2? Issue 4, December 2017 Type of article 1.01 Technology www.fe.um.si/en/jet.html A STRAIGHTFORWARD ANALYTICAL WAY OF EVALUATING THE SINGLE-PHASE INVERTER SPWM FREQUENCY SPECTRUM ANALITIČEN POSTOPEK OCENITVE FREKVENČNEGA SPEKTRA SPWM IZHODNE NAPETOSTI ENOFAZNEGA RAZMERNIKA Alenka Hren1R, Franc Mihalič2 Keywords: Fourier analysis, sinusoidal pulse-width modulation (SPWM), over-modulation phenomenon, single-phase inverter, total harmonic distortion (THD) Abstract For a DC-AC converter (inverter), a key element in renewable power supply systems, an output voltage of sinusoidal shape is required to assure a high-quality sustainable energy flow. Thus, through the modulation process, this property must be "incorporated" into the output voltage. This operation incurs some harmonic distortion into the inverter output voltage, which can have an undesired influence on the load. In the single- or three-phase systems (grid-connected, uninterrupted power supply systems (UPS) or motor drives), the high quality Total Harmonic Distortion (THD) factor must be considered; the voltage harmonic content also must be limited. This paper provides a comprehensive spectrum analysis of a three-level output voltage in singlephase inverter. The output voltage is generated by triangular Sinusoidal Pulse-Width Modulation (SPWM) and, by using the Fourier analysis, Bessel functions and trigonometric equality, the high Corresponding author: dr. Alenka Hren, Tel.: +386 2 220 7332, Mailing address: University of Maribor, Faculty of Electrical Engineering and Computer Science, Koroška cesta 46, 2000 Maribor, E-mail address: alenka.hren@um.si 2 dr. Franc Mihalič, University of Maribor, Faculty of Electrical Engineering and Computer Science, Koroška cesta 46, 2000 Maribor, E-mail address: franc.mihalic@um.si JET 11 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 harmonic components are extracted in a straightforward analytical way. Finally, the overmodulation phenomenon is also considered, and the procedure is experimentally validated. Povzetek Za zagotavljanje visokokakovostnega trajnostnega pretoka energije iz obnovljivih virov, mora razmerniško vezje, ki je ključni sestavni element pretvorniških sistemov, na izhodu zagotavljat sinusno obliko napetosti. To lastnost oz. obliko "vgradimo" v izhodno napetost razsmernika z izbranim modulacijskih postopkom, ki pa ob osnovni harmonski kompenenti vnaša v izhodno napetost tudi višje harmonske komponente. Te negativno vplivajo na breme razsmerniškega vezja in njegov izkoristek delovanja. V enofaznem ali trifaznem sistem (omrežne povezave, sistemi neprekinjenega napajanja ali motorni pogoni), mora razmerniško vezje delovati tudi z ustreznim, dovolj majhnim, faktorjem popačitve (Total Harmonic Distortion - THD), ki pa je odvisen prav od vsebnosti višjih harmonskih komponent v izhodni napetosti. V članku je opisan postopek celovite analize harmonskega spektra trinivojske izhodne napetosti enofaznega razsmernika, pri čemer izhodno trinivojsko napetost generiramo s pomočjo sinusne trikotne modulacije (Sinusoidal Pulse-Width Modulation - SPWM). Z uporabo Fourierjeve analize, Besselovih funkcijin trigonometričnih enakosti lahko posamezne višje harmonske komponente izračunamo analitično. Opisan je tudi način delovanja razmernika in postopek izračuna harmonskih komponent v področju nadmodulacije. Pravilnost postopka analitičnega izračuna je eksperimentalno verificirana. 1 INTRODUCTION The efficiency and stable operation of switching mode power inverters are of crucial importance for the sustainable production of the renewable energy sources connected to the utility grid, [1], [2], or that are a part of the standalone multifunctional power systems, [3], and are both closely related to the used modulation strategy. The Pulse-Width Modulation (PWM) strategy has been in a focus of research for many decades, [4], and remains an active research topic, [5], [6], due to its widespread usage in many fields of applications. Its usage is the most popular in the control of switching mode power converters for which it continues to represent a state-of-the-art solution. Although, PWM has been used for many years and is well-described in many textbooks, [7]-[10], the PWM algorithms for switching power converters have been the subject of intensive research, [11]-[15], and some initiations of the analytical approach have been established, especially in [11]. Some PWM research work has been dedicated to the analytical way to understand the ac-ac converter modulation strategies, [12], [16], [17]. The necessity of the analysis of the PWM strategies in single-phase inverters began with the exploitation of the back-up systems (UPS) and with taking advantage of acoustics equipment in home appliances, [18]-[23]. Single-phase inverters in back-up systems are designed to adapt to the changing needs of load and input voltage sources, and the filter function can be solved by using passive filters, [7]. To minimize the filters' weight and size, it is also important to know the harmonic components of the inverter output voltage. Finally, it is generally accepted that the performance of an inverter that operates with arbitrary switching strategy is closely related to the frequency spectrum of its output voltage, [11]. 12 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum PWM can be implemented in many different forms. Pulse frequency is the most important parameter related to the PWM method and can be either constant or variable. A constant frequency PWM signal is obtained by comparing the modulation function with the carrier signal that can be in a sawtooth or a triangular shape. The most commonly used PWM form for a single-phase inverter is a naturally sampled PWM with a triangular (double-edge) carrier signal and a sinusoid as a modulation function, known as SPWM, since this kind of PWM improves the harmonic content of the pulse train considerably, [24]. In many textbooks, the authors only describe the "modern" approach for frequency spectrum evaluation based on Fast Fourier Transformation (FFT), probably due to the comfortability of this sophisticated mathematical tool. Understanding the PWM process using FFT was explored as a short-cut due to its spread appearance in many computer software tools, such as Matlab, LabVIEW SPICE, EWB, Simplorer, among others. These algorithms are also available in some electronic measuring instruments. This paper presents a step-by-step analytical approach to the exact evaluation of single-phase inverter frequency spectrum obtained by naturally sampled SPWM. The proposed analytical way of evaluating SPWM frequency spectrum gives a comprehensive and deep insight into the mechanism of the harmonic components generation as well as a better foundation for understanding or even designing the SPWM devices in inverters. The main goal is to follow the SPWM procedure exactly by using the Fourier analysis, Bessel functions, and trigonometric equality in order to extract the high harmonic components in an analytical way. The switching (existing) function introduced by Wood, [9], is used for a mathematical description of the modulation function. Additionally, the over-modulation phenomenon in a single-phase inverter and its analysis are considered and are presented in Section 3, where the obtained results were also experimentally verified in order to prove the procedure's correctness. Conclusions are summarized in Section 4. 2 SINGLE-PHASE FULL-BRIDGE INVERTER When the high-efficiency, low-cost, and compact structure are of primary concern, the transformer-less inverter's topologies based on bridge configuration are the primary choice. Fig. 1 shows a single-phase full-bridge inverter circuit with a DC input voltage (vin) and AC output voltage (voet), the semiconductor switches' structure and the load structure. The inverter consists of two legs (half-bridges) with two semiconductor switches (IGBTs or MOSFETs and diode as indicated in Fig. 1), voltage sources indicated by (V/2) and current source (indicated by Load), representing the inverter output filter consisting of inductor L, capacitor C, and load resistance R. The SPWM processes can generally be divided into two groups with respect to the inverter output voltage that can be either in two-level (+ Vd and -Vd) or three-level shape (with +Vd, 0 and -Vd). Since it is well known that the three-level output voltage has better spectrum properties, this kind of SPWM process will be considered in detail in this paper. Moreover, the first harmonic magnitude can be increased over Vd when over-modulation is applied, which means that the modulation index must exceed 1. With over-modulation, an increased magnitude of the first harmonic component is welcome in those situations in which the input voltage is decreased, but as a consequence of this phenomenon, [10], additional spectrum lines appear, which also increases the Total Harmonic Distortion (THD) of the output signal. JET 13 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 Figure 1: Single-phase inverter structure; the semiconductor switch structure; the (current source) load structure. Figure 2: (e) Output volteges: vA0(t), vB0(t) eed vAB(t) with appropriate modulation functions eed (b) Spectrel lines for three-level output voltege. 2.1 Generation of Three-Level Output Voltage The whole inverter shown in Fig. 1 is divided into two half-bridge structures (legs). By using the first leg (switches Su and S21) the voltage vA0(t) ("first leg" voltage) and by using the second one (switches S12 and S22) the voltage vB0(t) ("second leg" voltage) are generated at the inverter output, both with respect to the neutral point (shown in Fig. 1 and Fig. 2(a), respectively). If voltage vA0(t) precedes vB0(t) for an appropriate phase angle the inverter output voltage vAB(t) that equals the difference between voltages vA0(t) and vB0(t) will have the desired magnitude and desired three-level waveform, as indicated in Fig. 2(a). Voltages vA0(t) and vB0(t) are described as two switching events: VA0(t) = dA(t)(Vd/2) + de(t)(-Vd/2), (2.1) vBo(t) = ds(t)(Vd/2) + db(t)(-Vd/2), (2.2) where the switching functions (see Fig. 3(a) and 3(b)) are: 14 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum Figure 3: Thraa-laval switching functions generation (a,b) and, oetpet voltages on tha interval TS (c): VAo(t), VBo(t) and VAB(t). da = db = 1, S11 = ON, (1, S21 = ON, 0, S11 = OFF, a = [0, S21 = OFF, 1, S12 = ON, 0, S12 = OFF, db = 1, S22 = ON, 0, S22 = OFF. (2.3) (2.4) In order to avoid the short circuit between the battery terminals P and N, the following conditions must be fulfilled: dA(t) + da(t) = 1, (2.5) dB(t) + db(t) = 1. (2.6) Applying the above conditions in (2.1) and (2.2) follows to: VAo(t) = (2dA(t) - 1)(Vd/2), (2.7) VBo(t) = (2dB(t) - 1)(Vd/2). (2.8) Referring to Fig. 3(c) (up and in the middle), the average value of the voltages vA0(t) and vB0(t) over the interval [0,Ts] can be evaluated as: va0 = -I1VA0(t)dt = (2Da(t)- 1)Vd /2, ' c (2.9) B0 =1 It6VB0(t)dt = (2Db(t)- 1)Vd /2, (2.10) where DA(t)=tonA/Ts and DB(t)=tonB/Ts represent the corresponding duty cycle functions. If Ts << T = 2n/u>o holds, the following approximation can be introduced: JET 15 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 VA0 ev (t) T = VoutA (t), (2.11) 's VB0 (t) T_ = VoutB(t). (2.12) Functions voutA[t) and voutB(t) represent the desired inverter output voltages for each half-bridge that can be expressed as: V VoutA (t) = + -cos(®ot), (2.13) VoutB (t) = - i2cos(®ot). (2.14) Now, the duty cycle functions Da(0 and Db(0 can be evaluated from (2.9) to (2.14), respectively: 1 1 V/2 1 1 Da(t) = - + -,.. ,cos(®ot) = - + -mi cos(®ot), (2.15) 2 2 (vd / 2) 22 1 1 V/2 1 1 Da (t) =----cos(®0t) =---m, cos(®ot), (2.16) A 2 2(id/2) o 2 2 1 ' 0 " ' 1 where m, =V/ id is modulation index. An auxiliary triangular carrier signal vcarr(t) needs to be introduced in order to transform the duty cycle functions DA(t) and DB(t) into a switching function dA(t) and dB(t). Fig. 3(a) and 3(b) show the triangular carrier signal, and both switching functions signal, respectively. The switching functions dA(t) and dB(t) were obtained by a comparison of duty cycle functions DA(t) and DB(t) with vcarr(t) as follows: d [1, Da (t) > Vcarr (t), d = |1, Db (t) > V^ (t), [0, Da (t) < V carr (t), B [0, Da (t) < v carr(t). The above-described procedure enables the generation of the triggering pulses in electrical circuits for all the semiconductor switches in the inverter. When referring to Fig. 4, the comparators (comp) compare the duty cycle functions DA(t) and DB(t) with triangular carrier signal (vcarr) and the signals dA(t), da(t), dB(t) and db(t) are obtained according to (2.5), (2.6) and (2.17). Figure 4: Moduletor block-scheme. 16 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum The switching signals generated according to (2.17) can be considered to be periodic signals on the time interval [0,7s]. When they are provided to the inverter switches, the three-level voltage (as shown in Fig. 2(a) and Fig. 3, respectively) appears at the inverter output: vAB(t) = +Vd, dA (t) = 1, dB (t) = 0, Da (t) > Db (t), 0, dA (t) = 0, dB (t) = 0 v dA (t) = 1,dB(t) = 1, (2.18) -Vd, dA (t) = 0, dB (t) = 0,Da (t) < Db (t). It is well known that any periodic signal of period Ts can be expanded into a trigonometric Fourier series form: a m dA (t) = -° + ^ (an cos(naTt) + bn sin(n®Tt)), (2.19) 2 n=1 where wT is the frequency of the triangular carrier signal (wT = 2n/Ts), and the coefficients a0, an and bn form a set of real numbers associated uniquely with the function dA(t): 2 t0+Ts ao = — J dA (t)dt, Ts to 2 t0+Ts an = — J dA (t)cos(n®Tt)dt, (2.20) Ts f0 2 t0+Ts bn =— J dA (t)sin(na>Tt)dt. Ts t0 Each term an cos(nuiTt) + bn sin(nuiTt) defines one harmonic function that occurs at integer multiples of the triangular carrier signal frequency nuiT. According to the signal waveform of the pulse train shown in Fig. 3(a), the Fourier coefficients can now be evaluated as: dA (t) = 1, t0 - MEl < t < Da (t)Ts 0 2 t0 + s , (2.21) ' elsewhere. In order to simplify the coefficient's calculation, the initial time to = 0 is chosen, so the coefficient ao is: +DA (t)Ts 2 2 °0 = — J 1dt = 2Da (t) (2.22) Ts -Da (t)Ts 2 Coefficients an are also calculated from (2.20): +da (t)Ts 2 2 , > , 2 sin(n*DA (t)) a0 = — J 1cos(n®Tt)dt =----^ (2.23) Ts da (t)Ts * n 2 and all coefficient bn are equal to 0. According to (2.19) the Fourier series of dA(t) is: JET 17 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 , , 2 ® sin(exDA (t)) dA (t) = Da (t) + -X—-— (2.24) " e=1 and also for the switching function dB(t): ,, 2 ® sin(exDA (t)) dB (t) = Db (t) + -£ —-^ (2.25) X e=1 e 2.2 The Output Voltage Spectrum Calculation The output voltage vAB(t) can be constructed simply by subtracting outputs vA0(t) and vB0(t). In practice, when the load is connected between terminals A and B, the voltage difference vAB(t) appears on it. When (2.8) is subtracted from (2.7) it follows to: Vab (t) = (dA (t) - dB (t))Dd (2.26) The switching functions dA(t) and dB(t) can be expanded by the Fourier series in (2.24) and (2.25), respectively, and after applying (2.26) the inverter output voltage vAB(t) can be expressed by using the Bessel function as described in [7], [8], [10]: 4Vd ® 1, vab(t) = mVd cos(®0t) + —!L 2 -[ X e=1e P7T cos(—)J1(a)[cos((emT +mo)t) + cos((emT -mo)t)] flTT - cos(—)J3(a)[cos((emT + 3mo )t) + cos((emT - 3m o)t)] flTT cos(—)J5(a)[cos((emT + 5mo)t) + cos((emT - 5mo)t)]... ] where a = emn/2. The structure of the spectral line's appearance is evident from (2.27). The SPWM signal vAB(t) has a fundamental component that appears at the frequency uio and, in addition to at the triangular carrier signal frequency 2ewT, also contains the sideband harmonics at frequencies ewT + kwo, e = 1,2,3,...k = ±1/±2/±3/...~. Since the value of cos(en/2) is zero for every odd e, the spectral lines only appear around even multiples of the carrier frequency fT = wT/(2n), which is indicated in Tables 1 and 2, respectively. Fig. 2(b) shows the spectrum lines for the single-phase inverter's three-level output voltage for the Vd = 330 V and mi = 1, line frequency fo = 50 Hz and fT= 2 kHz. From all the analyses above and the obtained results, the following conclusions can be made: • The spectrum lines appear only for every even multiplier of fr, • The triangular carrier signal frequency fr = 2 kHz is present in the half-bridge voltages (Vyio(t) and VBo(t) not considered separately), but the synthesized inverter's output voltage VAB(t) switching frequency is doubled, so the first higher harmonic component appears next to the 4 kHz, and • Filter components are needed at the inverter output to extract the first harmonic component at the fundamental frequency and reject the high switching frequency components of the output voltage vAB(t). The doubled switching frequency allows reduction of the size and weight of the filter components. (2.27) 18 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum Table 1: Spattral lines aroend tha satond seltipliar of triangle carrier signal frequency 2fT. a2i 4Vd 1 2T 2T --cos(—)Ji(—s) T 2 2 2 -63.4 V a23 4Vd 1 2T. , 2T ----cos(—)J3(—sI) T 2 2 2 74.3 V a25 4Vd 1 ,2t. , 2T . --cos(—)J5(— s,) t 2 2 5 2 -11.6 V Table 2: Spattral lines aroend tha satond seltipliar of triangle carrier signal frequency 4fT. a41 4Vd 1 4T . ,4T cos(—)J1(—s,) T 4 2 1 2 -23.7 V a43 4Vd 1 4T . M --7 cos^)J3^ s,) T 4 2 2 -3.2 V a45 4Vd 1 4t . ,4T . --cos(—)J5(— sI) t 4 2 2 41.4 V 3 OVER-MODULATION PHENOMENON IN A SINGLE-PHASE INVERTER The first harmonic magnitude for three-level output voltage (see (2.27)) is defined by af = sIVd and has a position at the angular frequency uio (or frequency fo). Obviously, the maximum magnitude of the first harmonic equals Vd due to the range of sI £ (0,1). The first harmonic magnitude can be increased over Vd when over-modulation is applied, which means that the modulation index must exceed sI £ (0,1). With over-modulation, an increased magnitude of the first harmonic component is welcome in some applications but, as a consequence of this phenomenon, the additional low-frequency spectrum lines appear. (a) (b) Figure 5: Ovar-sodelation protadera (sI = 1.2): (a) Triangle tarriar signal and dety tytla fenttion DA(t), switthing fenttions dA(t) and dB(t) wavaforss. (b) Ovar-sodelatad dasirad half- bridga voltages VA0os(t) and VB0os(t). JET 19 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 The three-level output voltage signal at the inverter output and over-modulation's influence on the frequency spectrum will be considered in the following subsections. Over-modulation appears when the duty cycle function DA(t) exceeds the magnitude of the high-frequency triangular carrier signal (mI > 1). Fig. 5(a) shows a relationship between the triangular carrier signal and duty cycle function DA(t) and its influences on the switching functions dA(t) and dB(t) when a 20% over-modulation is applied, respectively. 3.1 The Duty Cycle Function Evaluation Duty cycle functions can be evaluated in over-modulation as follows from (2.15) and (2.16) by applying vA0om(t) and VB0om(t) instead of vAo(t) exceeds VBo(t): „ _ tA 11 y/2 DA (t) = ^ = - + VAoom Ts 2 2Vd/2 (t) Db (t) = -B = tB 1 1 V/2 vB0om (t) Ts 2 2Vd/2 where of vA0om(t) and vB0om(t) are shown in Fig. 5(b) and are defined as follows: V and vA0om (t) = 2 -sinwot, .Vl 2 ' 0 < wot < ß, ß< wjt < (x —ß), V sin wot, (x — ß) < mot < (x + ß) .Vi 2 (x + ß) < Wot < {2k —ß) V —sin wot, (2x — ß) < wot < 2x, vB0om(t) = V —sinwot, 2o Vd 0 < wot < ß, ß< Wot < (x —ß), (3.1) (3.2) (3.3) --sinwot, (x —ß) < wot < (x + ß) (3.4) , (x + ß) < wot < (2x — ß) V --sinwot, (2x —ß) < wot < 2x. The voltages described by (3.3) and (3.4) can be expressed using Fourier series. The functions are odd, and due to this, the coefficients cn = 0, so the voltages vA0om(t) and vB0om(t) are only 20 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum expressed by coefficients bn, yielding: œ vA0om (t) = Zbk sin(k®0i), (3.5) k œ vB0om (t) = "Zbk sin(k®ot), (3.6) k where k = 1,3,5,... and the Fourier coefficients bk can be evaluated from (3.3) by taking the symmetry of the signal during the half of the period: 2 T/2 bk = t J [/KO " f(-®ot)]sin(k®ot)dt, (3.7) T 0 where T = 2n/u>o, so it follows: b = 2Vd bk =- K sin[(k -1)^] sin[(k +1)^] (k -1) (k +1) where 6 is computed as follows from Fig. 5(b): 1 —cos(kfi)dt k (3.8) P = arcsinl = arcsinl — I (3.9) I V J { si Substituting (3.5) and (3.6) into (3.1) and (3.2), respectively, the duty cycle functions become: 1 1 ® Da (t) = - + —2 bk sin(k®0t), 2 Vd k d k (3.10) 1 1 ® Db (t) = --—2 bk sin(k®0i), 2 Vd k 3.2 The Over-Modulated Frequency Spectrum Calculation The over-modulated output voltage can be evaluated from (2.26), (3.3) and (3.4): VABos (t) = VaOos (t) - VbOos (t) = (¿A (t) - ^ (t))Vd (3.11) where the switching functions dA(t) and dB(t) can be evaluated by Fourier series as in (2.24) and (2.25), respectively and when combined with (3.10), the line to line voltage vABos(t) can be expressed as: Vabos (t) = 2^|bk cos(k^t) J + HFSC, (3.12) LFSC where LFSC means "Low-Frequency Spectral Components" and HFSC "High-Frequency Spectral Components", which can be calculated as follows: JET 21 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 HFSC = - 4V f £ 1 en . 2 — cos—sin e=1e 2 f Vn\ 2bk cosM Vd I k sin emTt (3.13) Eq. (3.12) consists of two parts: The first describes the low-frequency spectrum lines (next to the fundamental frequency wo), and the second describes the position and magnitudes of the high-frequency spectrum lines (next to the multipliers of triangle frequency wT). The overmodulation phenomenon is used in order to increase the first harmonic magnitude over the supply voltage when VAB1 > Vd. According to (3.8) and (3.12), the output voltage's low frequency harmonic components can be evaluated as follows: VA ABk = 2bk =- 4Vd mI sin[(k -1)P] sin[(k +1)P] (k -1) (k +1) -cos(kp) (3.14) for the first, third, fifth and all odd spectral components, the (3.14) can be rewritten as (where in case of the first harmonic the division by zero can be avoided by replacing the function sinx = x for mi >>, or p <<): VAB1 =' 4Vd P- sin(2P) cos(P) (3.15) VAB3 = " 4V, 4Vd mI sin(2P) sin(4P) sin(4P) sin(6P) -cos(3P) -—cos(5P) (3.16) (3.16) Figure 6: (e) Over-moduleted output voltege vABom(t) eed its first hermoeic compoeeet vAB1(t). (b) The low eed high hermoeic compoeeets spectrum liees. K Fig. 6(a) shows the three-level output voltage vAB(t) for Vd = 350 V, mI = 1.2, line frequency fo = 50 Hz and fT= 2 kHz, while its spectrum lines are presented in Fig. 6. From all the analyses above and the obtained results for spectrum evaluation the following conclusions can be made: • The HFSC spectrum lines calculated by (3.13) appear only for every even multiplier of fT, 22 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum • The LFSC spectrum lines calculated by (3.12) are zoom-out in Fig. 6, while the calculated values for the magnitude as well as the normalized values VABkn for the first, third and fifth harmonic components are given in Table 3 for the case of 20% overmodulation. The magnitude of the first harmonic component VaS1 that exceeds the DC-voltage Vd by 10.4% was calculated by (3.15). Table 3: Spattral lines aroend tha satond seltipliar of triangle carrier signal frequency 4fT. VAB1 4Vd K sI _ 2 _ sin(2B) 1 B--— + cos(B) 2 386.6 V VABln 1.1046 VAB3 _ 4VL K "m, \sin(2B) sin(4B)], 1_„(3B)" —---+— cos(3B) _ 2 L 2 4 J 3 _ -25.1 V VAB3n 0.0717 VAB5 4Vd K mL _ 2 rsin(4B) _ sin(6B) 1+ 1cos(5B)l _ 4 6 J 5 _ -12.9 V VAB5n 0.0369 Fig. 7(a) shows the calculated first, second and third harmonic components versus modulation index changed from 0 to 2. When sI exceeds 1, the magnitudes of harmonic components start to increase as follows from the presented over-modulation analysis. (a) (b) Figure 7: (a) First, third and fifth harsonit tosponants varses sodelation index sI E(0,2). (b) THD varses sodelation index sI E(1,2). To validate the presented procedure's correctness, a single-phase low-voltage (Vd = 20 V) inverter experimental set up based on the DRV8870DDAR integrated circuit was built in the laboratory. The described SPWM strategy was implemented using a Texas Instruments TMDSCNCD28335 control card that can be programmed in MATLAB SIMULINK and is ideal to use for initial evaluation and system prototyping. Output voltage over ohmic load was measured with a RIGOL DS2102A Digital storage oscilloscope. Fig. 8(a) presents the measured output voltage when the inverter operates in over-modulation with sI = 1.2 while Fig. 8(b) shows its normalized frequency spectrum calculated by FFT in MATLAB. The obtained results show clearly that the normalized values for the first, third, and fifth harmonic components JET 23 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 match almost perfectly the predicted values calculated with the described procedure (see Table 3). (a) (b) Figure 8: (a) Inverter output voltage at mI = 1.2 and (b) Its frequency spectrum. 3.3 The Upper Limit Calculation The upper limit is obtained when the modulation index mI goes to infinity and, according to Fig. 5(b), the angle p goes to 0. The upper limit can be evaluated as follows: " _ 4Vd VABk,max - lim - mI sin[(k - 1)ß] sin[(k + 1)ß] (k -1) (k +1) -cos(kß) (3.18) V, and after calculation through a limit process: T k It is evident from (3.19) that the upper limit for the first (fundamental, where k = 1) voltage harmonic component is: ABk ,max (3.19) V 4V ABk ,max d (3.20) and is indicated as the upper limit line (i.e. at the square-wave output signal) in Fig. 7(a). The over-modulation operation of the inverter also has significant influence on the THD factor that is defined as: THD - Jn- V/2 2 ABk V (3.21) AB1 THD factor dependence on modulation index mI is presented in Fig. 7(b). The maximum permissible THD factor is defined for different load types, so it is possible to set the necessary modulation index mI which defines the first harmonic component magnitude VAbi and, consequently from (3.15), the appropriate DC voltage Vd can be determined. In some special cases in which the available DC voltage supply Vd does not meet the requirements regarding the % 24 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum magnitude of the output voltage V/abi (Vd < Vabi ^ V4B1max), this over-modulation property allows us to omit the DC-DC boost converter in the power supply system. 4 CONCLUSION In this paper, a straightforward, step-by-step SPWM frequency spectrum analysis has been presented for a single-phase inverter as an indispensable part of renewable energy source systems. The precise, analytical approach to SPWM signal analysis is rather unpopular among many engineers due to the relatively long and complicated procedure but, to understand these processes, it is necessary to take advantage of it. The additional reason that the analytical approach is not widely used in practice is due to the widespread usage of the MATLAB Software package. This program enables FFT numerical analysis of the PWM processes but, by using FFT, engineers do not gain an in-depth insight into the connections between the different quantities appearing in the formulas. For three-level inverter output voltage, and over-modulation, principles of modulation algorithms have been developed here in a traditional analytical way. The electronic circuit of an SPWM modulator can be realized from the described algorithms by using new microcomputer technology and in the paper presented knowledge is also a good base for further investigation into SPWM switching strategies. The over-modulation phenomenon can help engineers to speculate using the inverter's parameters; for example, it can decrease the DC input voltage Vd and the output voltage will still have the necessary magnitude of the first harmonic component Vb . The obtained results were experimentally verified in order to prove the procedure's correctness. This analysis could be easily extended to three-phase inverters intended for electrical motor drive applications or grid-connected. And finally, the results of this analysis are also appropriate for further investigation of SPWM processes with respect to higher harmonic components' influence on losses for the different types of loads, as well as for filter design in the single-phase inverters used in UPS or grid-connected back-up systems. References [1] G. Wang, G. Konstantinou, C.D. Townsend, J. Pou, S. Vazquez, G.D. Demetriades, and V.G. Agelidis: A raviaw of power electronics for grid connection of etility-stala battery anargy storage systess, IEEE Trans. Sustainable Energy, vol. 27 no. 4, pp. 1778-1790, Oct. 2016 [2] R. Theodorescu, M. Liserre, P. Rodriguez: Grid Converters for Photovoltaic and Wind PowerSystess, West Sussex: IEEE Press/John Wiley & Sons, Inc., 2011 [3] F. Mihalic and A. Hren: Isolated bi-directional DC-DC converter, Journal of Energy Technology, vol. 3, no. 3, pp. 27-40, Aug. 2010 [4] H.S. Black: Modulation Theory, New York: Van Nostrand Reinhold Company, 1953 JET 25 AlenkaHren, Franc Mihalic JETVol. 10 (2017) Issue 4 [5] M. Odavic, M. Summer, P. Zanchetta, and J.C. Clare: A theoretical eeelysis of the harmonic content of PWM waveforms for multiplefrequency modulators, IEEE Trees. Power Electronics, vol. 25, no. 1, pp. 131-141, Jan. 2010 [6] G. Fudulu and D. Frascinv: Spectral analysis of cless of dc-ec PWM inverters by Kepteyn series, IEEE Trans. Power Electronics, vol. 25, no. 4, pp. 839-849, April 2010 [7] N. Mohan, E.M. Unduland, W.P. Rvbbins: Power Electronics, Devices, Converter, Application end Design, second ed., New York: John Wiley & Sons., 1995 [8] R.W. Jricsvn, D. Maksimvvic: Fundamentals of Power Electronics, Dordrecht: Kluwer Academic Publisher, 2001 [9] P. Wood: Switching Power Converters, New York: Van Nostrand Reinhold Company, 1981 [10] D.G. Hvlmus, E.A. Lipo: Pulse Width Modulation for Power Converters: Principles end Practice, New York: IEEE Press/John Wiley & Sons, Inc., 2003 [11] H.S. Patul and R.H. Hvft: Generalized technique of harmonic elimination end voltege control in thyristor inverters: Pert I - Harmonic elimination, IEEE Trans. Industry Applications, vol. IA-9, no. 3, pp. 310-317, May/Jun. 1973 [12] A. Alusina and M.G.B. Vunturini: Solid-stete power conversion: e Fourier analysis approach to generalised transformer synthesis, IEEE Trans. Circuits Systems, vol. CAS-28, no. 11, pp. 319-330, April 1981 [13] J. Hvltz: Pulsewidth modulation - A survey, IEEE Trans. Industrial Electronics, vol. 39, no. 5, pp. 410-420, Oct. 1992 [14] V.G. Agulidis, A.I. Balvuktsis, and C. Cvssar: On attaining the multiple solutions of selective harmonic elimination PWM three-level waveforms through function minimization, IEEE Trans. Industrial Electronics, vol. 55, no. 3, pp. 996-1004, Mar. 2008 [15] S.A. Saluh, C.R. Mvlvnay, and M. Azzizur Rahman: Analysis end development of wevelet modulation for three-phase voltege source inverters, IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3330-3348, Aug. 2011 [16] A. Alusina and M.G.B. Vunturini: Analysis end design of optimum-emplitude nine-switch direct ec-ec converter, IEEE Trans. Power Electronics, vol. 4, no. 1, pp. 101-112, Jan. 1989 [17] M. MilanvviC and B. Dvbaj: Unity input displacement factor correction principle for direct ec to ec matrix converters besed on modulation strategy, IEEE Trans. Circuits Systems I, vol. 4, no. 2, pp. 221-230, Feb. 2000 [18] H. Koizumi, K. Kurvkawa, and S. Mvri: Analysis of cless D inverter with irreguler driving patterns, IEEE Trans. Circuits Syst. I, vol. 53, no. 3, pp. 677-687, Mar. 2006 [19] K.M. Cho, W.S. Oh, Y.E. Kim, and H.J. Kim: A new switching strategy for pulse width modulation (PWM) power converters, IEEE Trans. Ind. Electron., vol. 54, no. 1, pp. 330337, Feb. 2007 [20] S.R. Bowus and D. Holliday: Optimal reguler-sempled pwm inverter control techniques, IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1547-1559, Jun. 2007 [21] Q. Li, P. Wolfs: A review of the single phese photovoltaic module integrated converter topologies with three different DC link configurations, IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1320-1332, May 2008 [22] R.H. Gruun and J.E. Boys: Implementation of pulsewidth modulated inverter modulation strategies, IEEE Trans. Ind, Appl., vol. IA-18, no. 2, pp. 138-145, Mar./Apr. 1983 26 JET A Straightforward Analytical way ofEvaluating the Single-phase Inverter SPWM Frequency Spectrum [23] R.O. Caceres and I. Barbi: A boost dc-ac converter: analysis, design, and extesisnntation, IEEE Trans. Power Electron., vo l. 14, no. 1, pp. 134-141, Jan. 199 9 [24] Z. Song and D.V. Sarwate: The frequency spectres of pelse width modulated gignals, ¡signal Processing, vo l. 83, no. 10, pp. 2227-2258, 2003 Nomenclature (Symbols) (Symbol meaning) bk Fourier series coefficients ß cross-section angle in the ovnr-moUulanoo dA(t) switching fungtioo DDt) duty-cycle fuugtion J (a) BBssel funnting mi moUulation innux m triangular carrier signnl frequungy Ok fungumentaleurput veeage ^querny FFT fast Feurier tragsfeematien HFSC eige-freuuengy sppctralcemppnsnts LS low-freuuensy sppctralcemppnsnts CCWM siggrolUul p^se-width moUulation THD tetaleirmonic Uistostieu UCC uuigterruetiOle ppwer suuply JET 27 28 JET im Journal of JET v°lume 10 (2°1?) p.p. 29-43 Issue 4, December 2017 Type of article 1.01 Technology www.fe.um.si/en/jet.html HYDRAULIC TRANSIENT CONTROL OF NEW AND REFURBISHED KAPLAN TURBINE HYDROPOWER SCHEMES IN SLOVENIA BLAŽENJE PREHODNIH POJAVOV V SLOVENSKIH NOVIH IN OBNOVLJENIH HIDROELEKTRARNAH S KAPLANOVIMI TURBINAMI Jernej MazijR, Anton Bergant1 Keywords: hydraulic transient regimes, Kaplan turbines, Slovenia, hydropower potential, field test Abstract As a natural resource, water is abundant in Slovenia, and its exploitation for electricity generation has a long history. The construction of Kaplan-type turbines is preferred due to topographical and environmental conditions. Water hammer control strategies, including issues of axial hydraulic thrust calculations, are presented in this paper. The case studies include new and refurbished hydropower plants located on all three major river basins in Slovenia. Povzetek Slovenija ima dolgo zgodovino izrabe vodnih virov za proizvodnjo električne energije. Zaradi topografskih in ekoloških omejitev je gradnja hidroenergetskih objektov z visokimi pregradami omejena. V Sloveniji prevladujejo pretočne hidroelektrarne z vgrajenimi kaplanovimi turbinami. R Corresponding author: Jernej Mazij, BSc, Litostroj Power d.o.o., Litostrojska 50, 1000 Ljubljana, Slovenia, jernej.mazij@litostrojpower.eu 1 Anton Bergant, PhD, Litostroj Power d.o.o., Litostrojska 50, 1000 Ljubljana, Slovenia, anton.bergant@litostrojpower.eu JET 29 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 V tem prispevku so predstavljene strategije nadzora negativnih posledic prehodnih pojavov, vključno s problemi pri izračunih aksialnih hidravličnih sil. Praktični pristop je predstavljen na novih in prenovljenih hidroelektrarnah, ki se nahajajo na povodjih rek Save, Drave in Soče. 1 INTRODUCTION Together with forests, water is the only true natural resource in abundant supply in Slovenia. With an annual quantity of 17,000 m3 of water per capita, the country is ranked third in Europe, after Switzerland and Norway, [1]. Two water regions divide the country; the Danube River (Black Sea) and the Adriatic seawater region. There are three major river basins (catchment areas): Drava, Sava, and Soča. They are characterized by a combination of nival and nival-pluvial regimes. The gross hydropower potential is estimated at 19,440 GWh/year. Thus far, 45% of the total technically available potential has been exploited: 4,115 GWh/year. Hydropower plants generate approximately 30% of the total installed capacity. Conditions for the construction of high-head hydropower schemes or conventional reservoirs with high dams are not favourable. Most of the corresponding potential sites are in environmentally sensitive areas or sites where construction would not be economically feasible. Electricity generation in Slovenia using hydropower started at the end of the 19th century with the first turbine installed in Škofja Loka, [2]. Construction of the Završnica hydropower plant in 1914 and the Fala hydropower plant in 1918 marked a turning point in terms of the electrification of the country. Major developments were made after 1945 with the return of to Primorska region to Slovenia with its hydropower plants on the Soča River and the systematization of electricity distribution. In the 1960s, the construction of hydropower plants on the Sava and Drava Rivers began, to meet basic demands for electricity and continued through the 1970s. The post-independence period saw interconnection of the Slovenian power grid to the common European network. Construction of the chain of hydropower plants on the lower Sava River began, as did the start of refurbishment of existing facilities. Regarding the river basins, the Sava River basin is the largest and represents more than 50% of the total country area but is the least utilized in terms of hydropower, with a total installed capacity of 230 MW. Completion of the chain on the lower Sava River is underway, and the start of the procedure for the design of the middle Sava River chain with 10 hydropower plants is foreseen. Unfortunately, political, economic, and environmental issues are hindering the project. The Drava River basin is the most important and the most developed, with an installed capacity of 600 MW. A comprehensive refurbishment programme has been completed with the replacement of all obsolete electromechanical equipment. The Drava is a border river, and the operating regime of the chain must be co-ordinated with the operation of the chain on the Austrian side for a daily run-of-river storage regime. The Soča River basin is ideal for hydropower production due to its high annual rainfall in the southern Alpine mountains. Three major hydropower plants have a total capacity of 142 MW and a pump-storage plant at Avče (the only one in Slovenia) completes the Soča River basin utilization with additional 180 MW capacity. 30 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia There ie also the Mura River, but it ie not currently being exploited for hydroelectric production due to environmental restrictions. The river has a nival regime of discharge as the waters are fed from the central Alpine mountains, and maximum annual discharges occur in late spring. This is favourable in comparison with other catchment areas which lack water during the summer. The possible foreseen installed capacity is 158 MW based on the principle of flow-of-the river, which has less influence on natural habitats, [1]. 2 HYDRAULIC TRANSIENTS General issues related to hydraulic transients have already been presented, [3, 4]. These issues include transient operating regimes, transient control, and modern approaches to transient modelling. Specific transient issues relating to Kaplan turbines the will be covered in this paper are: • relatively short inlet and outlet conduits and the usage of rigid column water hammer theory, • check for water column separation under the turbine head cover, • calculation and measurement of axial hydraulic thrust, • installation of a surge tank for a low-head Kaplan development. Modelling will be performed using commercial computer packages [5, 6]. The EPFL SIMSEN commercial software package, [5], is based on modular structure, composed of objects, in which each object represents a specific network element. Hydraulic elements are modelled as RLC electrical circuits according to the impedance method, [7]. Momentum and mass conservation equations provide the basis for an equivalent electrical circuit modelling. The transient behaviour of a hydraulic machine can be modelled using the steady-state characteristics (hill chart). Turbine characteristics are given in forms of unit speed, unit discharge and unit torque (nil, Qn, Mu) for different guide vane openings A0 and for different runner blade angles (blade pitch angle) 6 are used. Due to the traditionally relatively short inlet and outlet conduits (length of the conduit is of the same order as the cross-sectional dimensions) and complex cross-sectional shapes, the rigid column water hammer theory is the basis for the MISI TRANK software package, [6]. The rigid water hammer is described by the one-dimensional Bernoulli equation for unsteady flow, which is solved simultaneously with the dynamic equations of the turbine unit rotating masses, taking into account the turbine characteristics. In addition to unit discharge and unit torque, the unit axial hydraulic thrust characteristics (Fau) are implemented in the turbine model. JET 31 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 2.1 Water column separation and axial hydraulic thrust Transient regimes must be controlled in such a way that the operation of the turbine is safe and reliable. One of the most severe transient regimes is the emergency shut-down triggered by the over-speed device, which is set to operate in the event of an excessive speed rise, [8]. Attention should be paid to reverse water hammer, which can occur in hydropower plants with long outlet conduits. Water column separation can occur under the turbine head cover and the draft tube inlet during the closing of the turbine (guide vanes and runner blades). Two approaches are used in the estimation of the potential danger of full column separation, [9]. Turbine head cover pressure criterion. Based on model measurements, the absolute pressure under the turbine head cover is calculated. Pressure is measured at several locations in the space between the guide vanes and runner blades. The pressure under the turbine head cover is then calculated using measured axial hydraulic thrust characteristics. The computed absolute pressure should be larger than the vapour pressure pa > Pvp. Axial hydraulic thrust criterion. The potential danger of full column separation and turbine unit lifting during transient events are estimated using the measured model axial hydraulic thrust characteristics. Full column separation under the head cover and subsequent cavity collapse induces large axial hydraulic thrust acting upwards. If the absolute value of the acting hydraulic thrust is greater than the total weight of the rotating parts of the unit, then the unit may be lifted from the thrust bearings causing structural damage. The following expression is valid: F a,max = mini \F~ad\,Wu\ (2. 1) The damaging axial hydraulic thrust is calculated by the following equation in which the full water column separation under the head cover is assumed to occur: (  2 1 V D , 10 - ^ 1 + ^ (Hs-AH, ) 900 J 4 v s ' 77- xD 1 F ad = -Pg — (2) The dynamic head is calculated with the following equation: AH, = QSt (2. 2) gtSc The installation of air valves has limited influence on the application of the above criterion and cannot prevent damaging reverse water hammer. 32 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia Eight run-of-the-river hydropower plants form a chain on the Slovenian part of the Drava River extending from the Austrian to the Croatian border. Over the last twenty years, seven HPP have been fully refurbished and upgraded. These include Fala HPP (1991), Dravograd HPP (1997), Mariborski otok HPP (1997), Vuzenica HPP (1997), Ozbalt HPP (2004), Vuhred HPP (2004), and Zlatolicje HPP (2012). A total of twenty Kaplan units were replaced with a new runner design with larger diameters (+5%) increasing the discharge capacity in the existing flow-passages by about 25-30%. Zlatolicje HPP is designed as a channel-type power plant. It is the largest Kaplan type turbine in Slovenia and generates more than a fifth of all the electric power generated by its parent company DEM (Dravske Elektrarne Maribor). Constructed in 1966, the two units made use of 33-m head at a threshold capacity of 136 MW (160 MW after refurbishment in 2011). The plant is connected to a 17.2-km long trapezoidal profile inlet channel, see Figure 1. The outlet channel is 6.2 km long and joins the Drava River at Ptuj Lake, the largest artificial lake in Slovenia and the headwater level of the Formin HPP, the last hydropower plant on the Drava river. Each of the two units is equipped with a pressure-regulating valve (PRV) comprised of five vertical vanes connected via a rod to a servomotor and controlled by the turbine governor. During transient operating regime, the PRV is designed to completely attenuate free surface waves in the inlet and outlet channels. The continuous measurements of the channel water levels at the turbine inlet and outlet have indicated that water level oscillations in the channels are small and within the prescribed limits during transient regimes. The dimensions of the inlet conduit, scroll casing, and the draft tube are expressed as geometric characteristics. The polar moment of generator inertia is I = 3.375 x 106 kgm2. Figure 1: Zlatolicje HPP (photo www.dem.si.) JET 33 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 Emergency shut-down of the Kaplan turbine from 75 MW output or 94% of full-load is considered to be one of the most severe normal operating regimes with respect to large transient pressure heads, turbine rotational speed and surges in open channel. The turbine is disconnected from the electrical grid followed by the complete closure of the wicket gates while the runner blades open to their fully open position (Figure 2(a)). The PRV blades first open to about 90% opening synchronously with the wicket gate closure and then start to close at a very slow rate to its fully closed position. The PRV linear full-stroke closing time is tc, PRV = 1200 s. The continuous measurement of the channel water levels at the turbine inlet and outlet indicates that water level oscillations in the open channel are small and within the prescribed limits during the transient event. Figure 2(b) shows measured headwater level variations (ZHWL) during the period of the turbine closure. During this period of the transient operating regime, the pressure regulating valve completely attenuates free surface waves in the inlet channel. This is practically true for the oscillations in the outlet channel too (Figure 2(d)). Therefore, the constant water levels at the turbine inlet and the turbine outlet are assumed in water hammer calculations. Analysis of free surface waves in the inlet and outlet channel is beyond the scope of this paper. 34 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia cN O O (a) Guide vanes Runner blades PRV vanes 0 10 20 30 40 50 60 70 Time (s) 0 10 20 30 40 50 60 70 (b) Time (s) 50 40 ?3° 20 10 0 (c) 0 - Computation Measurement 10 20 30 40 Time (s) 20 n 10-^ 0-10- (d) 0 Computation Measurement 10 20 30 40 Time (s) 175 150 £ 125 o 100 01 75 50 25 0 (e) 10 20 30 Time (s) 150 g 100 g 50 r0 0-1 r « E^ -50 t^ -100 -150 0 (f) 10 20 30 40 Time (s) Figure 2: Emergency shut-down in Zlatolicje HPP (P = 75 MW): Guide vane and runner blade servomotor strokes (a), headwater level at the turbine inlet (b), scroll case (c) draft tube heads(d), unit rotational speed (e) and axial hydraulic thrust (f) The assumed flow-passage system used for rigid water hammer analysis is comprised of relatively short inlet scroll case and outlet (draft tube) conduits. Figure 2(c-f) shows results of rigid column water hammer analysis for the considered emergency shut-down of the unit. The agreement between the computed and measured maximum rotational speed rise of 35% and 36.5%, respectively, (Figure 2(e); n0 = 125 min-1) is good. The computed maximum momentary scroll case pressure head (Hsc) of 35 m practically coincides with the averaged measured one (Figure 2(c); there is a reasonable agreement between the calculated and measured draft tube pressure head too (Figure 2(d)). The maximum scroll case pressure head and the maximum speed rise are within the prescribed limits. The calculated and the measured maximum momentary negative axial hydraulic thrusts (absolute values) of 3500 kN and 1600 kN, respectively are less than the JET 35 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 permissible thrust IF'a,max | = 5370 kN (Figure 2(f); Fa,0 = 5680 kN). There is a large discrepancy between the magnitudes of the negative axial hydraulic thrust. The maximum calculated axial hydraulic thrust is based on model measurements. It is difficult to measure hydraulic quantities in the model at smaller wicket gate openings (large uncertainties), in particular at an increased rotational speed of the turbine. There is also a large uncertainty in the measured axial hydraulic force on the prototype. However, the general trace of calculated and measured axial hydraulic thrust is similar. 4 CASE STUDY 2: KRŠKO HYDROPOWER PLANT Construction on the lower Sava river reach is currently one of the largest infrastructure projects in Slovenia. Krško HPP is the fourth in a chain of six planned run-of-the-river hydropower plants. Upstream projects include Vrhovo HPP (1993), Boštanj HPP (2006), and Arto-Blanca HPP (2010). On the downstream side, Brežice HPP has been recently put into operation, and Mokrice HPP is under design review. Three Kaplan units with a total installed capacity of 39 MW are in a powerhouse constructed on the right side of the river bank (looking downstream), see Figure 3. Limited construction space, inaccessibility, the vicinity of the main road and the railway with deep excavations due to locally heavily fractured dolomite rock hindered construction in comparison to the other stages on the chain, [10]. Figure 3: Krško HPP (photo Litostroj Power archive) In an effort to lower construction and maintenance costs, the mechanical and civil engineering designs are as uniform as possible. After completion, all hydropower plants in the chain will operate fully automated and unmanned. The polar moment of generator inertia is I = 700 x 106 36 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia Emergency shut-down of the unit 11.7 MW output is observed. Figure 4 shows results of rigid column water hammer analysis for the considered emergency shutdown. The agreement between the computed and measured maximum rotational speed rise of 23% and 26.7%, respectively, (Figure 4(b); n0 = 100 min-1) is good. The same can be said for the maximum scroll case pressure; the calculated value is 14.1 m, and the measured is 14.2 m (Figure 4(c)). The maximum scroll case pressure head and the maximum speed rise are within the prescribed limits. The calculated and the measured maximum momentary negative axial hydraulic thrusts (absolute values) of 1354 kN and 641 kN, respectively, are less than the permissible thrust | F'a,max | = 1943 kN (Figure 4(d)). The general trace of calculated and measured axial hydraulic thrusts is similar. 100 80 60 40 20 0 \ Runner blades \ ........Wicked gates x1 0 0 0 10 20 Time (s) 30 150 125 100 75 50 25 0 0 (b) 14 12- - Computation ■ Measurement 10-1 x1 (c) 10 20 Time (s) 30 500-50-100-150 0 (d) 10 20 Time (s) 30 Computation Measurement 10 20 30 Time (s) Figure 4: Emergency shut-down in Krsko HPP (P = 11.7 MW): Guide vane and runner blade servomotor strokes (a), unit rotational speed (b), scroll case pressure (c) and axial hydraulic thrust (d). 0 5 CASE STUDY 3: PLAVE II HYDROPOWER PLANT The design of Plave II HPP on the Soca River basin was based on exploiting the available hydro potential and infrastructure of the existing Plave I HPP, built prior to WWII. Intakes for both HPPs are located at the Ajba dam. While the Plave I HPP uses a free-surface water underground diversion channel, Plave II HPP has a low-pressure diversion tunnel connected at the end to an expansion chamber. The tunnel is lined with prefabricated concrete elements. The complete JET 37 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 length of the tunnel is 6 km with a diameter of 6.4 m and runs parallel to the Plave I HPP channel. The TBM method for tunnel construction was used for the first time in Slovenia. The expansion chamber (tunnel) connects the low-pressure tunnel to a double-cylinder surge tank, each of 26 m diameter. The low-pressure tunnel continues to the power station as a penstock in two sections divided by a gate chamber. Two vertical Kaplan turbines, each of 20.5 MW capacity, are installed in the powerhouse; see Figure 5. Operation of both Plave I and Plave II HPP is fully unmanned and remotely operated from the control centre. Due to the long tunnel with a surge tank and relatively long penstock, an elastic column water hammer model has been used, [5]. A simplified and detailed model of the surge tank will be presented, and results compared to measured values. Attention will be given to penstock pressure, rotational speed and surge tank water levels during emergency shut-down. Figure 6(a) presents the basic or simplified model of the flow-passage. Two surge tanks are replaced in the model with a single equivalent surge tank of 37 m diameter. The value of the surge tank intake losses is kiz = 0.00125 s2/m5 and outtake losses kout = 0.00078 s2/m5. The design of the surge tank and orifice was tested in a hydraulic research laboratory. Figure 6(b) presents a more detailed model of the flow-passage system. Two surge tanks are included as well as the connecting pipe from the low-pressure tunnel. Figure 5: Plove II HPP mochize holl (photo www.sezg.si) As seen from the results presented in Figure 7, the main difference between the models is in the result for the penstock pressure; 38 m for the simplified model and 44 m for the detailed model. The difference can be attributed to the inertia of the water in the connecting pipe between the low-pressure tunnel to the penstock. A minor difference is present for the rotational speed (219 min-1 vs. 225 min-1), while there is no difference in the maximum surge 38 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia tank water level (109.6 m.a.s.l.). A comparieou of the meaeured values coufirme the detailed model. (a) Figure 6: Plave II HPP computational model JET 39 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 10080-. 60-" 402000 (a) 50 45 40 35 30 25 20 (c) 250 225 Runner blades 200 Wicked gates 'a 175 (m 150 s 125 100 10 20 Time (s) 10 20 Time (s) 30 (b) 110- C3 S. 105H 100- 30 (d) 10 20 Time (s) 30 300 600 900 Time (s) Figure 7: Emergency shutdown in Plave IIHPP: Guide vane and runner blade servomotor strokes (a), unit rotational speed (b), penstock pressure (c) and surge tank water level (d). 0 0 0 Complete tabulated measured results are not available (different measuring chains in the surge tank chamber and in the machine hall); therefore, a direct comparison is not presented. Figure 8(a) shows measured results for penstock pressure (psp) and rotational speed (n). Wicket gates and runner blades servomotor strokes are labelled y2 and y3, respectively. Figure 8(b) shows results for the surge tank water level oscillations over a prolonged interval during commissioning testing. The emergency shut-down that is taken into consideration is labelled M55. Note: Figures 8(a) and 8(b) are taken directly from the original commissioning report, [10]; therefore, the text is in its original (Slovenian) language. 40 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia Figure 8a: Emergency shutdown in Plave IIHPP (P = 18 MW): Measured results for guide vane and runner blade servomotor strokes, penstock pressure, and rotational speed So Up offs tota post ets. 0. 0V l time. 2 -trig. 0. □. ov □oh os 0. [ v ti S 5> ■vf t O WE trig Plave ger. man 2 ;H£3 0 ■J. çt. MFRlTf V NW/O. A VODE V I7RA\ /MALMlH \/nno= TAvJ 4 l^OHt OCAH bh e, 4-.10 a a. ç 00 10, to DO 3 1 10 mm ,DI'k - 0,1 ~>bar ■ AO I Hb,t .. \f «,431/ISM TA. JJOÛQ.'Slj iJA * fl h A , 51. K L. \l koC Wre IUU (, MS5 'A v r \ 'i [jniw \ HZ» NI TlELOyALA m IOHI»\ / 1 J \ 10,'OMtf V- ' h lo ' ( t ii #> w |«iT It, Sfo_li OS, 1 uzT V^ 3 lO w en s Tie Z.ÎLUSÛ vA I i fed STtoJt. il i^, ici Si le.o «3,03 3 12 two cn s + ( Mir] ) | [¿OT/> Figure 8b: Emergency shutdown in Plave II HPP (P = 18 MW): Measured results for surge tank water level oscillations JET 41 Jernej Mazij, Anton Bergant JETVoi. 10 (2017) Issue 4 6 CONCLUSIONS This paper presents three typical case studies of water hammer control strategies of Kaplan turbine hydropower plants in Slovenia. Particular design approaches, water hammer control strategies, and critical flow regimes that may induce unacceptable water hammer loads are outlined. Hydroelectric power plants with Kaplan turbines are traditionally comprised of relatively short inlet and outlet conduits; therefore, the rigid column water hammer theory is used for these cases. For systems with long penstocks, elastic column water hammer theory should be used. Acknowledgments The authors wish to thank Slovenian Research Agency (ARRS) for support of this research conducted through the project L2-5491 (ARRS). References [1] Kryzanvvsky et al.: Hydro potential ozd development opportunities iz Slovezio, Hydropower & Dams 5, 41-46, 2008 [2] I. Erselic: Lorge hydropower plozts iz Slovezio, Journal of Energy Technology 7, 21-32, 2014 [3] J. Mazij, A. Bergant: Hydroulic trozsiezt ozolysis - Issues reloted to refurbished ozd zew hydropower schemes with complex woter cozveyozce systems, Wasserkraftanlagen 2014, Vienna, 2014 [4] J. Mazij, A. Bergant, D. Dvlenc, J. Gale: From gezerol desigz to commissiozizg -hydroulic trozsiezt ozolysis iz cose of high-heod hydropower plozt Toro III, Hydro 2013, Innsbruck, 2013 [5] JPFL Computer package SISMEN version 3.0.1, Lausanne, Switzerland 2015 [6] MISI Computer package TRANK, Moscow, Russia 1984 [7] C. Nicvlet: Hydroocoustic modellizg ozd zumericol simulotioz of uzsteody operotioz of hydroelectric systems, Dissertation, EPFL, Lausanne, Switzerland 2007 [8] J. Fasalek, S. Rakcevic: Air volves ozd coztrol of the Koploz turbize durizg trozsiezts, IAHR 1986, Montreal, 1986 [9] A. Bergant, J. Sijamhvdzic: Woterhommer coztrol iz Koploz turbize hydroelectric power plozts, 8th International Conference on Pressure Surges 2000, The Hague, 2000 [10] A. Sirca et al.: Cozstructioz of the Krsko HPP oz the lower Sovo river, Gradbeni vestnik 61, 70-76, 2016 [11] Litvstrvj Power: Commissiozizg report Plove II HPP, Ljubljana, Slovenia 2001 42 JET Hydraulic transient control of new/and refurbished Kaplan turbine hydropower schemes in Slovenia Nomenclature (Symbols) D d Fa Fad F ad,max Gd Gu g H Hs Hdt Hsc AHi I K n P P Q Qsc tsc y Wu Zhwl Ztwl P (Symbol meaning) runner diameter turbine shaft diameter axial hydraulic thrust damaging axial hydraulic thrust acting upwards maximum axial hydraulic thrust acting upwards geometric characteristics of the draft tube geometric characteristics of the inlet conduit and the scroll-casing gravitational acceleration pressure head suction head draft tube head scroll case pressure dynamic head polar moment of inertia surge tank head losses (intake, outake) turbine rotational speed turbine output pressure discharge discharge at an assumed water column separation closing time from discharge Qsc to Q = 0 m3/s servomotor (guide vanes/runner blades) stroke weight of the unit rotating parts headwater level tailwater level mass density JET 43 44 JET we Journal of JET v°lume 10 (2°1?) p.p. 45-55 Issue 4, December 2017 Type of article 1.01 Technology www.fe.um.si/en/jet.html THE CALCULATION OF HIGH-PRESSURE VISCOSITY FOR REFRIGERANT MIXTURES IZRAČUN VISKOZNOSTI PRI VISOKIH TLAKIH ZA ZMESI HLADIL Jurij Avsec?, Urška Novosel1 Keywords: thermodynamics, thermomechanics, viscosity, statistical mechanics, kinetic theory, nonequilibrium mechanics Abstract This paper features a mathematical model for computing the viscosity in the fluid domain for a hy-drofluorocarbon mixture with the help of statistical thermodynamics. The viscosity pf HFC-134a (1,1,1,2-Tetrafluoroethane) and HFC-125 (Pentafluoroethane) mixtures was calculated as an example of hydrofluorocarbon mixtures. To calculate the thermodynamic properties of a real fluid, the models were applied based on the Lennard-Jones intermolecular potential. The analytical results obtained via statistical thermodynamics are compared with the experimental data and show relatively good agreement. Povzetek V članku je prikazan matematični model izračuna viskoznosti v plinastem področju za mešanico fluoroo-gljikovodikov s pomočjo statistične termodinamike. V predstavljenem članku smo izračunali viskoznost za zmes hladil HFC-134a (1,1,1,2-tetrafluoroetane) in HFC-125 (Pentafluoroetane) kot primer fluorira-nih ogljikovodikov. Za izračun termodinamičnih lastnosti realne tekočine so bili uporabljeni modeli na podlagi Lennard-Jonesovega intermolekularnega potenciala. Analitični rezultati, pridobljeni s statistično mehaniko, so primerjani z eksperimentalnimi podatki in kažejo razmeroma dobro ujemanje. R Corresponding author: Corresponding author: Prof. Jurij Avsec, Ph. D., Tel.: +386-7-620-2217, Fax: +386-2-620-2222, Mailing address: Hočevarjev trg 1, 8270 Krško, Slovenia, E-mail address: jurij.avsec@um.si 1 University of Maribor, Faculty of Energy Technology, Laboratory for Thermomechanics, Applied Thermal Energy Technologies and Nanotechnologies, Hočevarjev trg 1, SI-8270 Krško, Slovenia JET 45 JurijAvsec, UrškaNovosel JET Vol. 10 (2017) Issue 4 1 INTRODUCTION The computation of thermo-mechanical properties in the high-pressure range is vital for a large number of fluids that are essential to energy technology. Some great, even insurmountable problems remain in identifying analytical expressions for the transport characteristics of fluids at high pressures. Using super-computers and the methods of molecular dynamics, it is possible to follow each molecule in the system of particles. One drawback of numerical methods, however, is that analytical records of functions are unfortunately lost. For more than half of century, chlorofluorocarbons (CFCs) have been used as working fluids in refrigeration, heat pump and air conditioning applications. These compounds are very stable, non-toxic and non-flammable and, therefore are regarded as safe refrigerants. For several decades chlorine-fluorine-hydrocarbons were considered harmless refrigerants. Most CFCs have been replaced by hydrofluorocarbons (HFCs) which have a similar molecular structure but do not contain chlorine atoms. For example, one of the most important CFCs, R12, has been already replaced by 1,1,1,2-tetrafluoroethane (R134a) in several applications. Refrigerants 134a and R125 are alternative refrigerants, which are suitable as substitutes for R22 and R502. 2 CALCULATION OF VISCOSITY BY STATISTICAL MECHANICS Accurate knowledge of the nonequilibrium or transport properties of pure gases and liquids is essential for the optimum design of different items of chemical process plants, for the determination of intermolecular potential energy functions, and for the development of accurate theories of transport properties in dense fluids. Transport coefficients describe the process of relaxation to equilibrium from a state perturbed by the application of temperature, pressure, density, velocity, or composition gradients. The theoretical description of these phenomena constitutes that part of nonequilibrium statistical mechanics known as kinetic theory. From the semi-classical kinetic theory for polyatomic fluids the coefficients of thermal conductivity, shear viscosity and bulk viscosity can be expressed: 2k 2t 1 X= —— [A, A], —kT[B,B], K s = kT[r, r] (2.1) 3m 10 where A, B and r are complex vector, tensor and the scalar functions, [1,2,3]. The detailed description of the physical origin of bulk viscosity is explained in the literature, [2]. It arises in dense polyatomic gases and liquids. The transport properties for pure gases are represented as sums of terms for the temperature-dependent dilute-gas contributions and terms for the temperature- and density-dependent residual contributions. Contributions for the critical enhancement are not included in these background functions. From the Boltzmann equation, for mono-atomic dilute gases, transport properties not far from the Maxwellian can be calculated, [1-3]. This means that transport phenomena are treated with small temperature or velocity gradients of the molecules. On this basis, the dynamic viscosity for single-component gas can be expressed: 46 JET The calculation of high-pressure viscosity for refrigerantm ixtures Ho ( / \2 1 5kT 8Q ( 2,2 ) , 3 (Q(23) 71 1 + 49 Q( 22 > 2 (2.2) where, and Q(l,s) is the transport collision integral. With the Lennard-Jones intermodular potential, it is almost impossible to obtain collision integrals analytically. Because of the difficulty of calculating these integrals, their values are usually taken from published tables. To make computerized calculations more convenient and to improve on the accuracy obtainable by linear interpolation of the tables., the empirical formulation of Neufeld [5] et al. was used, obtained on the basis of numerical simulations and interpolation procedure. n A C E G *B *W Q =—+—+—r^s+—r-^i+RT sin(ST -p) (2.3) T*b exp\DT ) exp\FT ) exp\HT ) This equation contains 12 adjustable parameters and is developed for 16 collision integrals. The dilute gas viscosity is obtained from kinetic theory assuming that a Lennard-Jones (LJ) potential applies, and using the expression: rj0FT)= 26.69579-10-1 ^S 2 , (2.4) Q G where ^ is in Pa s, M is the molecular mass in gmol-1, T is in K, Q(2,2) is a collision integral and a is the Lennard-Jones parameter. In this paper, the Chung-Lee-Starling model (CLS) will be presented, [6]. Equations for the viscosity are developed based on kinetic gas theories and correlated with the experimental data. The low-pressure transport properties are extended to fluids at high densities by introducing empirically correlated, density dependent functions. These correlations use acentric factor ro, dimensionless dipole moment |r and an empirically determined association parameters to characterize the molecular structure effect of polyatomic molecules k, the polar effect and the hydrogen bonding effect. In this paper, new constants for fluids are determined. The dilute gas dynamic viscosity for the CLS model is written as: Ho(T) = 26.69579-10-1 2 Fc (2.5) Q1-2' 2> a The factor Fc has been empirically found to be [6]: Fc = 1 - 0.2756® + 0.059035| 4 + k (2.6) where ro is the acentric factor, |r relative dipole moment and k is a correction factor for hydrogen-bonding effect of associating substances such as alcohols, ethers, acids, and water. For dense fluids, Eq. (5) is extended to account for the effects of temperature and pressure by developing an empirically correlated function of density and temperature as shown below: H=Hk +Hp (2.7) Hk = Ho|G- + | (2.8) JET 47 Jurij Avsec, Urška Novosel JET Vol. 10 (2017) Issue 4 rjp = [36.344-10-6 ~(MTC)5/VC273]a7Y2G2 exp(A8 + A/T* + A10/T*2) Y = pVc/6 , Gi 1.0 - 0.5Y kB (1.0 - Y)3 ,VC = (0.809ct(4))3 f = 125936 v _ mana^r^a G2 = {Ai (1 - exp(- A4Y ))+A2Giexp(A5Y )+A3G1} (AiA4 + A2 + A3) (2.8) (2.9) (2.10) (2.11) The constants A1-A10 are linear functions of the acentric factor, the reduced dipole moment, and the association factor Ai = a0 (i) + al(i)m + a2 (i)pr + a3( i)K ,i=1,10 where the coefficients a0, ai, a2, and a3 are presented in the work of Chung at al., [6]. (2.12) For the determination of viscosity for fluid mixtures, a purely analytical model has been used, [2]. According to this theory, the viscosity of dense fluid mixtures containing N components can be written in the form: v = - H11 ••• H1N V1 H N1 H NN V N V1 Vn 0 H11 • H 1 N H N1 • H NN (2.13) M,Mj 2 N ... ... H = v_ 1 y V'V " * ju ( + mj )2 i 3 J= j *i 20 4M —Aj M, 3 Hij(j * 1) = - V1V j M1Mj 2 j* (Mi + Mj )2 I 3 20 4A* (2.14) (2.15) where p is the molar density, ^ and ^j are mole fractions of species I and j, and Mj and Mj are * their molecular masses. Ay is a weak function of intermolecular potential for i-j interactions. The symbol • represents the viscosity of pure component i, and • represents the viscosity of i-j interaction. We have developed the new equation for • j Vj i (2.16) 48 JET The calculation of high-pressure viscosity for refrigerantm ixtures 3 RESULTS AND DISCUSSION Figures 1-11 show the deviation of the results for ternary mixture R125+R134a in the real gas region between the analytical computation (CLS-Chung-Lee-Starling model) and experimental results, [7-9]. Table 1 shows the most important data for analytical calculation. The results for all transport properties obtained with the CLS model show relatively good agreement. Table 1: The important constants fur analytical ueluuleliuf fur R125 end R-134e R-134a R-125 8 (J) 410.04E-23 337.678E-23 ct (m) 4.76E-10 5.005E-10 m (-) 0.32684 0.3061 H-r (-) 0.15 0.6 K (-) 0 0 Temperature (K) Figure 1: Kinenatic viscosity for R125 in saturated gas region JET 49 Jurij Avsec, Urška Novosel JET Vol. 10 (2017) Issue 4 Temperature (K) Figure 2: Kinenatic viscosity for R134a in saturated gas region s a CL - 25 1 £ 25 s 8 23 ^ 2i [ | 19 O v v. 0 5 10 15 20 25 30 35 40 Volume [m3/kmol] —•— EXP —•— ANAL Figure 3: Viscosity for mixture of R125+R134a at 423 K and 75.1% of R125 50 JET The calculation of high-pressure viscosity for refrigerantm ixtures 0,1 n 0,08 0,06 0,04 0,02 0 0 -0,02 Compressibility factor Z Figure 4: Compressibility factor for mixture of R125+R134a at 423 K and 75.1% of R125 1 Figure 5: Pressure-volume diagram for mixture of R125+R134a at 423 K and 75.1% of R125 JET 51 Jurij Avsec, Urška Novosel JET Vol. 10 (2017) Issue 4 Figure 6: Viscosity for mixture of R125+R134a at 323 K and 75.1% of R125 T=323 K, 75.1%R125+24.9%R134a o Q a: -0,02 Compressibility factor Figure 7: Compressibility factor for mixture of R125+R134a at 323 K and 75.1% of R125 1 52 JET The calculation of high-pressure viscosity for refrigerantm ixtures Figure 8: Pressure-volume diagram for mixture of R125+R134a at 423 K and 75.1% of R125 Figure 9: Viscosity for mixture of R125+R134a at 423 K and 75.1% of R125 and 25.1% of R125 JET 53 Jurij Avsec, Urška Novosel JET Vol. 10 (2017) Issue 4 T=423 K, 25.08%R125+74.92%R134a Compressibility factor Figure 10: Compressibility factor frs mixture rf R125+R134a at 423 K and 25.1% rf R125 6 5 ^ 4 £ 3 IA IA (U £ 2 1 0 s 0 \ V X 5 1 01 52 Volume [ 02 m3/kmol] 53 03 54 Figure 11: Compressibility factor frs mixture rf R125+R134a at 423 K and 25.1% rf R125 54 JET The calculation of high-pressure viscosity for refrigerantm ixtures References [1] J. Millat, J.H. Dymond: C.A. Nirlu dr Castro, Transport Properties uf Fluids, Cambridge, University Press, 1996 [2] J.H. Ferziger, H.G. Kaper: Mathematical Theory uf Transport Pruurssrs if Gessrs, North-Holland Publishing Company, London, 1972 [3] F.R.W.McCourt, J.J. Beenakker, W.E. Köhler, I. Kuscer: Nufrquilibrium Phenomena if Polyatomic gases, Clarendon Press, London, 1990 [4] S. Chapman, T.G. Cowling: The Mathematical Theory of Non-Uniform Gases, Third Edition, Cambridge, University Press, 1970 [5] P.D. Neufeld, A.R. Janzen, R.A. Aziz: Empirical Equations to Calculate 16 of the Transport Collisicn Integrals for the Lennd-Jones (12-6) Purrfriel, The Journal of Chemical Physics, Vol.57, No.2, pp. 1100-1102 [6] T.-H. Chung, L.L. Lee, K.E. Starling: Ahhliueriufs of Kinetic Gas Theories and Multiparameter Correlation for Prediction of Dilute Gas Viscosity and Thermal Conductivity, Ind. Eng. Chem. Res., Vol. 27, No. 4, pp. 671-659, 1988 [7] N. Shibasaki-Kitajawa, M. Takahashi, C. Yokoyama: Viscosity of Gaseous HFC-134a Under High Pressures, International Journal of Thermophysics, Vol.19, No. 5, pp.:1285-1295, 1998 [8] M. Takahashi, N. Shibasaki-Kitajawa, C. Yokoyama: Viscosity of Gaseous HFC-125 Under High Pressures, International Journal of Thermophysics, Vol.20, No. 2, pp.:445-453, 1999 [9] C. Yokoyama, T. Nishino, M. Takahsashi: Viscosity of Gaseous Mixtures of HFC-125+HFC-134a under Pressure, Fluid Phase Equilibria, Vol. 174, pp. 231-240, 2000 JET 55 56 JET im Journal of JET v°iume 10 (2°1?) p.p. 57-?0 Issue 4, December 2017 Type of article 1.01 Technology www.fe.um.si/en/jet.html ROTOR MECHANICAL STRESS ANALYSIS OF A DOUBLE-SIDED AXIAL FLUX PERMANENT MAGNET MACHINE MEHANSKA ANALIZA ROTORJEV DVOSTRANSKEGA SINHRONSKEGA STROJA Z AKSIALNIM MAGNETNIM PRETOKOM Franjo PranjičR, Peter Virtič1 Keywords: Axial flux permanent magnet machine (AFPMM), mechanical stress analysis (MSA), rotor thickness Abstract This paper presents the mechanical stress analysis (MSA) of a rotor disk in a double-sided axial flux permanent magnet machine (AFPMM). The analysis considers the rotor of a prototype AFPMM with a double external rotor and single internal stator. Rotor disks of the prototype AFPMM are constructed of two 11.6 mm-thick steel disks and represent around 50% of the total weight of the machine. The new rotor disk thickness was determined based on a rotor axial displacement due to the attractive force between the permanent magnets on opposite rotor disks. Povzetek Članek predstavlja mehansko analizo rotorjev dvostranskega sinhronskega stroja s trajnimi magneti in aksialnim magnetnim pretokom. Analiziran je rotor prototipa stroja, ki ima dvojni zunanji rotor ter notranji stator. Rotor analiziranega stroja je izdelan iz dveh 11,6 mm debelih R Corresponding author: Franjo Pranjič, Tel.: +386 3 777402, Mailing address: Koroška cesta 62a, E-mail address: franjo.pranjic@um.si 1 University of Maribor, Faculty of Energy Technology, Hočevarjev trg 1, 8270 Krško JET 57 Franjo Pranjič, Peter Virtič JET Vol. 10 (2017) Issue 4 jeklenih diskov, kar predstavlja približno 50% skupne teže stroja. Trajni magneti na nasproti ležečih rotorskih diskih povzročajo pritezne sile med rotorskimi diski, ki se posledično upognejo. Na podlagi upogiba rotorskih diskov pa je določena nova debelina le-teh. 1 INTRODUCTION Axial flux permanent magnet machines have been becoming increasingly popular lately due to their compactness, high degree of reliability, efficiency, simple construction and high-power density, [2-6]. This type of machine is also called "a disk-type machine" and has various topologies: • Single-sided (one stator and one rotor) • Double-sided (single stator-double rotor or single rotor-double stator) • Multistage (multiple rotors and stators). nc i QZ U < c DC 1 ad 1 □ C of I < £ £ ■K □ C t£ £ I < ar s ££ I < a: i u en e it u, K K ttL 4 C) Figure 1: Basic topologies of AFPMM: a) single-sided, b) double-sided, c) multistage All the above-mentioned topologies can be constructed with or without iron cores (coreless) and with surface-mounted or buried permanent magnets (PMs). Low power permanent magnet machines are usually constructed with coreless stators and steel rotors with surface mounted PMs, [1]. Each machine topology has its own strengths and weaknesses. Topologies without stator cores are used for low- and medium-power generators and have various advantages, including the absence of cogging torque, as well as their linear torque-current characteristics, high power density, and compact construction. Due to the absence of the core losses, these types of generators can operate with a higher efficiency compared to the conventional generators, [7]. Mechanical stress analysis (MSA) has been presented in several publications. In [9], the authors present the MSA for a high-speed AFPMM and analyse the stress level of the rotor disks due to the high-speed rotation, using the three-dimensional finite element method (3D FEM). Fei et al. present the simplified 2D and 3D FEM for analysis and design of rotor disks of high-speed AFPM generators in [10]. Rani et al. present the computational method of rotor stress analysis for conventional rotors using J-MAG software in [11]. In [14], the authors presented the structural analysis of low-speed axial-flux permanent-magnet machines. Virtic, [12], analysed the rotor disk thickness of the same prototype AFPMM concerning the magnetic flux density magnitudes. This article firstly presents the double-sided AFPMM with an internal coreless stator and two external rotors and its characteristics, with a focus on the selected dimensions of rotor disks. The 58 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine prototype AFPMM was analytically analysed in [7] and optimized in [8] by using evolutionary optimization with a genetic algorithm and an analytical evaluation of objective functions. Since the thickness of the rotor disks was not included in the optimization (due to the assumed infinite permeability), this article presents the mechanical stress analysis (MSA) of the rotor disks used in the prototype machine and, based on the results, a new rotor disk thickness is determined. The mechanical stress analysis in this article is accomplished by: 1. analytically calculating the pressure caused by the PMs on opposite disks and the attractive force between them, 2. simulating the stress distribution and deflection of the disks with Solidworks software based on the calculated magnetic pressure and force, The primary reason for the rotor optimization lies in the fact that the weight of the two rotor disks represents about 50% of the total weight of the machine, [1]. 2 AFPMM PROTOTYPE The AFPMM considered in this article is a double-sided AFPMM with two external rotors and one internal coreless stator. Figure 2 shows the geometric parameters, and Table 1 shows the optimized data of the analysed prototype AFPMM. d s Figure 2, [8].- Geometric parameters of the AFPMM The PMs used in the prototype AFPMM are neodymium magnets (NdFeB). Figure 3 shows the PMs; their characteristics are presented in Table 2, where: • Br is the remanent magnetic flux density, • Hcb is the coercive magnetic field intensity of the magnetic flux density, • Hcj is the coercive magnetic field intensity of the polarization, • (BH)max is the maximum energy product, and • Tmax is the maximum working temperature of PMs JET 59 Franjo Pranjič, Peter Virtič JET Vol. 10 (2017) Issue 4 gfl Figure 3, [17]:NdFnB pnemnnnnj magnets usnd in jhn prototype AFPMM Table 1: GEOMETRY AND PARAMETERS OF ANALYSED AFPMM Symbol Quantity Value/Unit R Rotor disk radius 150 mm dFe Rotor disk thickness 11,6 mm dM Permanent magnet thickness 5 mm Tm Magnetic pole pitch 25° aL O 1- q RiPM Inner radius of PM 80 mm Cd RoPM Outer radius of PM 150 mm Br Remanent magnetic flux density 1,22 T Tp Pole pitch 36 ° P Number of pole pairs 5 i Rated phase current 12,3 A A Electrical current density 5 A/mm2 a Rated power at 1500 min-1 4,4 kW N Number of turns per coil 50 Number of coils 12 (2x6) cc dc Coil width 20 mm O 1— < ds Stator thickness 15 mm uo Tc Coil pitch 30° m Number of phases 3 dag Air-gap thickness 1mm Sw Copper wire cross section 2,46 mm2 60 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine Table 2: PROPERTIES OF PERMANENT MAGNETS USED IN PROTOTYPE AFPMM Type of Br HcB HcJ BHmax Tmax PM (kJ/m3) (T) (kA/m) (kA/m) (°C) min max min max 38SH 1,22 1,25 907 1592 287 310 150 2.1 Stator design The internal stator is constructed from non-magnetic polypropylene square plate with dimensions of 400x400x15mm. Each side of the plate has a carved space for six coils, four thermocouples, and slots for the conductors (Figure 4a). After the conductors are inserted in the slots, a varnish is applied, and the stator is ready for mounting (Figure 4b). Figure 4, [17]: a) Stator support structure, b) Stator ready for mounting 2.1 Rotor design Rotor disks are constructed from structural steel (St52), which has adequate magnetic properties and a suitable price. From the safety point of view, the thickness selected for the disks was 12 mm. After balancing, the final thickness was 11.6 mm. Figure 5, [17]/ a) Unbalanced rotor disks, b) Balanced rotor disk with au accessory for gluiug the PMs ou the rotor disk JET 61 Franjo Pranjic, Peter Virtic JET Vol. 10 (2017) Issue 4 Figure 6, [7]; n) Stntoe nnd double eojoe with the shnft, b) Rotoe disk with PMs 3 METHODS AND RESULTS The mechanical stress analysis was performed numerically and analytically, using the Solidworks simulation tool. Solidworks software simulates the magnetic pressure of the PMs on the rotor disk and determines the stress distribution and deflection using the Finite Element method (FFEPlus, i.e. Fourier Finite Element Plus algorithm). In finite element analysis, a problem is represented by a set of algebraic equations that must be solved simultaneously. FFEPlus is an iterative method that solves the equations using approximate techniques; a solution is assumed for each iteration, and the associated errors are evaluated. The iterations continue until the errors become acceptable, [13]. Since the attractive forces of PMs are high, the deflection of the disk must not be too high due to the safety reasons, such as preventing the PMs from crashing into stator surface, preventing distortion of the air gap and consequently the characteristics of the prototype AFPMM. 3.1 Parameter selection and calculation Maxwell stress is the link between electromagnetic and structural designs. It is represented by the magnetic attraction force acting between the rotor disks. Classical analysis of magnetic equivalent circuits can be used to determine the airgap flux density and hence the Maxwell stress is given by [14]: = Bl_ (3.1) q where Bd is the airgap flux density and jUo - permeability of free space (4n*10-7 Vs/Am) [14]. The magnetic flux density in the air gap is determined by equation (3.2) [1]: Bd =_B__<3-2> " 1 + ( + 0,5d s ))«- d M k = 1 ■ (3.3) sat (( + 0,5dFe) 62 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine M 1 A B Mo AH (3.4) where Bd is the magnetic flux density in the air gap, Br is the remenent magnetic flux density of the PM, dag is the air gap thickness, ds is the stator thickness, dFe is the rotor disk thickness, dM is the PM thickness, ksat is the saturation factor for iron, ¡j.r is the permeability of the steel, ¡j.rec is the relative recoil permeability, which is determined with the data of the magnets in Table 2. The attractive force between PMs on opposite disks can be calculated as magnetic pressure multiplied by the active surface area of all PMs SPM as shown in [1]: B 2 F = (S PM ) Spm = «, f (( " Dn ) œ = ■ aPu2V 360 (3.5) (3.6) (3.7) Where ai is the coefficient that is calculated with the angle of PMs multiplied by the number of PMs per rotor disk (poles) and divided by 360 degrees. Using the previously-described equations, data needed for the simulation was determined as shown in Table 3. Table 3: GEOMETRY AND PARAMETERS OF ANALYSED AFPMM Symbol Quantity Value/Unit q Magnetic pressure caused by the PMs 74496 Pa Spm Active area of all PMs 0,0351 m2 F Attractive force between rotor disks 2615 N dm Permanent magnet thickness 5 mm Bd Peak value of magnetic flux density in the air gap 0,4327 T dag Air-gap thickness 1mm ds Stator thickness 15 mm jrec Relative recoil permeability 1,0704 ksat Saturation factor 1,02 3.2 Simulation First, the simulation of the stress analysis and deflection was performed for the 11.6 mm rotor disk thickness. The simulation itself included the entire rotor for the accuracy of the results since in many articles the analysis includes only a segment of the rotor. JET 63 Franjo Pranjic, Peter Virtic JET Vol. 10 (2017) Issue 4 The force between PMs on opposite rotor disks was applied on each magnet on the simulated rotor disk. Figures 7a and 7b show the Von Mises stress distribution on the rotor disk and the displacement for 11.6 mm rotor thickness, respectively. It is clear that the rotor thickness can be reduced from the mechanical point of view since the maximum deflection is only 0.0053 mm. After a few simulations, it was determined that the 7 mm rotor thickness would be sufficient to withhold the forces between the adjacent PMs on opposite disks in such a way that the deflection remains acceptable. Figures 8a and 8b show the Von Mises stress distribution on the rotor disk and the displacement of 7 mm rotor disk thickness, respectively. It can be seen from Figure 8a that the simulated deflection is 0.2171mm. In [12], the author analysed the rotor disk thickness for this prototype AFPMM concerning the magnetic characteristics of the machine and determined that the characteristics are acceptable at 7 mm rotor thickness since there is practically no difference between magnetic flux density magnitudes calculated at 7 mm and 11.6 mm of rotor disk thickness. The simulation in Solidworks shows the same result for the mechanical point of view. Figure 7:11,6 mm rotor thickness: n) deflection, b) Von Mises stress distribution Figure 8: 7 mm rotor thickness: n) deflection, b) Von Mises stress distribution 64 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine 3.3 Analytical verification Equations for bending circular plates are derived in [15] and [16]. Timoshenko, [15], derived the differential equations for symmetrical bending of circular plates from observing the symmetrically distributed load acting on a circular plate. In [16], the authors presented equations for various types of loads on a circular plate. Figure 10 shows the case that is suitable for a rotor disk of AFPMM with surface mounted PMs. ya JET 65 Franjo Pranjič, Peter Virtič JET Vol. 10 (2017) Issue 4 Equations for deflection calculations are: A = Mrb DC2 + QbDC3 + qDL11 Mrb = -qa 2 i G v 2arbr (a2 - r2)" 47 Qb = (( - ro2) C2=- ■ ( w\ 1 + 2ln I (3.8) (3.9) (3.10) (3.11) ((, C, =■ 4 a r C8 =-8 2 ,2 1 + v + (1 - v)I 2 ( C 9 =■ 1 + v . ( a r | 1 - v -ln I —!- I +- 2 V br I 4 L11 = — 11 64 L17 = -17 4 1 + 41-^1 - 5 I Hl I - 4 liiL 1 + (1 + v )ln I r0 (3.12) (3.13) (3.14) (3.15) (3.16) D = Et3 12 (1 - v2) (3.17) 66 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine Table 4 presents the variables used in the set of equations (3.8)-(3.17) and their values. Values of abovementioned variables are presented in Table 4 for a 7 mm rotor disk thickness. Table 4: Variables used for deflection calculation Symbol Quantity Value/Unit ya M rb Or br ro Qb Deflection of rotor disks Bending moment Outer radius of the disk Inner radius of the disk 0.20129 mm 469 Nm 150 mm 15 mm Radial location of unit line loading or start of a 80 mm distributed load Constant termed the "flexural stiffness" or "flexural 6513 Pa mm3 rigidity", Unit shear force (force per unit of circumferential 39979 Pa mm2/mm length) q Magnetic pressure C2, C3 C9 Plate constants dependent upon the ratio a=b 74496 Pa C2 0.2425 ¿11, L17 Loading constants dependent upon the ratio a=r0 v Poisson's ratio E Elastic module of the material used for rotor disks t Thickness of the circular plate (rotor disk). C3 C9 ¿11 ¿17 0,28 210 GPa 7 mm 0.0005 0.0818 0.015994568091594 0.112680595325043 D Using the equations described above, 0.20129 mm deflection was calculated for the 7 mm thick rotor disk. Magnetic pressure q was reduced by a factor that takes into account the area of magnets (multiplied by a coefficient ai) since it is not constant over the area as marked on Figure 9. Compared to the results obtained via the simulation, we can see that there is only 2.66% difference which is acceptable. JET 67 Franjo Pranjič, Peter Virtič JET Vol. 10 (2017) Issue 4 3 CONCLUSION Using the Solidworks software and a set of analytical equations a new rotor disks thickness was determined for the analysed prototype AFPMM. MSA showed that, from a mechanical point of view, the existing rotor disks thickness can be reduced to 7 mm and maintain sufficient stiffness, so the air gap does not change significantly. By changing the thickness of the rotor disks, the weight of disks is reduced by approximately 40%. References [1] Gieras JF, Wang RJ, Kamper MJ: Axinl Flux Permanent Magnet Beushlnss Machines, Springer Verlag, 2008 [2] W. Fei, P. C. K. Luk, and K. Jinupun: Design and analysis of high-spnnd coenlnss nxinl flux pnemnjnjj magnet generator with circular magnets and coils, Electr. Power Appl. IET, vol. 4, no. 9, pp. 739-747, 2010 [3] Xue, Y., Han, L., Li, H., Xie, L.: Optimal design and comparison of different PM synchronous generator systems for wind turbines, Int. Conf. Electrical Machines and Systems, pp. 2448-2453, 2008 [4] Pinilla, M., Martinez, S.: Selection of main design variables for low-speed permanent magnet machines devoted to renewable energy conversion, IEEE Trans. Energy Convers., 26, (3), pp. 940-945, 2011 [5] M. Mirsalim, R. Yazdanpanah, and P. Hekmati: Design and analysis of double-sided slotless axial-flux permanent magnet machines with conventional and new stator core, IET Electr. Power Appl., vol. 9, no. 3, pp. 193-202, 2015 [6] H. Hatami, M. Bagher, B. Sharifian, and M. Sabahi: A New Design Method for Low-Speed Torus Type Afpm Machine for Hev Applications, IJRET, Volume: 02 Issue: 12, pp. 396406, 2013 [7] P. Virtic, P. Pisek, T. Marcic, M. Hadziselimovic and B. Stumberger: Analytical Analysis of Magnetic Field and Back Electromotive Force Calculation of an Axial-Flux Permanent Magnet Synchronous Generator with Core^s Stator, IEEE Transactions on Magnetics, vol. 44, no. 11, pp. 4333-4336, 2008 [8] P. Virtic, M. Vrazic, and G. Papa: Design of an axial flux permanent Magnet synchronous machine using analytical method and evolutionary optimization, IEEE Trans. Energy Convers., vol. 31, no. 1, pp. 150-158, 2016 [9] S. Kumar, T. A. Lipo, and B. Kwon: A 32,000 rev/min axial flux permanent magnet machine for energy storage with mechanical stress analysis, IEEE Trans. Magn., vol. 52, no. 7, pp. 1-1, 2016 [10] W. Fei, P. C. K. Luk, and T. S. El-Hasan: Rotor integrity design for a high-speed modular air-cored axial-flux permanent-magnet generator, IEEE Trans. Ind. Electron., vol. 58, no. 9, pp. 3848-3858, 2011 68 JET Rotor mechanical stress analysis of a double-sided axial flux permanent magnet machine [11] J. A. Rani, E. Sulaiman, M. F. Omar, M. Z. Ahmad, and F. Khan: Somputational Method of Rotor Stress Analysis for Vorious Flux Switching Machine Using J-MAG, IEEE Stude nt Conference on Research and Development (SCOReD), 721-726, 2015 [12] P. Virtic: Analysis of rotor dish thickness in corelest stator axial flux prrsnrnrnt mnenet synchrouous machine, PRPEGR/\D ELERTROTECHNICZNY, v/ol. ISSN 003n, d7, 12, p1, 1215, 2022 [10] 1015 SalidworEs E-lelp ICoeuonentation [1 4] M.A. Mlueller, A.E. McDonald and D.E. IMacpherson: Structural analysis oo low-speed ax-al-flux pbrmbnbnt-mubnbt machines, IEE Procaedings-Eleetric Power Appl., v/ol. 602, n7. p, 27. 2417-6426, 2000 [10] E. Timonhenko: borory of Plates dnd Shrlb, Second edition, 1181, McGraw-Hill oook Company, ICBC 0-01-414719-1 [17] W. C. Young and R. G. Bunynas: Roarh's Formulao for Stress dnd Straino vol. 1, no. 1 th Editio2. 0002 [1 1] P. PPirtic: Nacrtovanjr in analiza sin0ronshi0 strojrv s tras'nimi sutu^'i in ahsialnim mubnbtnim prrtohomo Doctoral thesis, University of Mar^o^ 0707 Nomenclature (Symbol meaning) rotor disk ra dius rotor disk th ickness permanent magnet th ickness magnetic pitch inner radius of PM outer radius of PM remanent magaetic flux density pole pitch number of pole pairs rated phase cucrent electricalnucredt density rated power at 1000 min-1 number of tu rns per coil coil wiPth (Symbols) R dFe dM Tm RiPM Ropm Br Tp P I A P N dc JET 69 Franjo Pranjič, Peter Virtič JET Vol. 10 (2017) Issue 4 "s Tc m dag Sw Sd dd ksat ^rec Spm ai q F Ya Mrb ar far ro D Qb CfrCi C9 ¿11, L17 V E t stator thickness coil pitch number of phases air-gap thickness Copper wire cross section airgap flux density permeability of free space fictitious air gap thickness saturation factor for iron permeability of the steel relative recoil permeability active surface area of all PMs coefficient that is calculated with angle of PMs multiplied by the number of PMs per rotor disk (poles) and divided by 360 degrees magnetic pressure attractive force between adjacent magnets deflection of rotor disks bending moment outer radius of the disk inner radius of the disk radial location of unit line loading or start of a distributed load stiffness factor of the material unit shear force (force per unit of circumferential length) plate constants dependent upon the ratio a=b loading constants dependent upon the ratio a=r0 Poisson's ratio elastic module of the material used, thickness of the circular plate (rotor disk) 70 JET im Journal of JET v°iume w (2017) p.p. 71-91 Issue 4, December 2017 Type of article 1.04 Technology www.fe.um.si/en/jet.html FUTURE GENERATION IV SMR REACTORS: ASSESSMENT AND POSSIBILITY OF INTEGRATION IN CLOSED NUCLEAR FUEL CYCLES PRIHAJAJOČA IV. GENERACIJA SMR REAKTORJEV: EVALVACIJA IN MOŽNOST INTEGRACIJE V ZAPRTE JEDRSKE GORIVNE KROGE Aleš Buršič R Tomaž Žagar1 Keywords: small and medium size reactors, generation IV reactors, investment cost, value analysis methodology, review and evaluation process, modular design, advanced nuclear fuel cycle, energy transition, sustainability Abstract Over the previous decade, many economic, strategic, technical, and other arguments in favour of Small and medium-size reactors (SMR), present in the nuclear industry since the beginning of its use for peaceful purposes, have become prominent. The Generation IV SMR is a next-generation design excelling in its considerable contribution to sustainability. Most favourable concepts impose high coolant temperatures and high breeding ratios and represent progress in the design of future GEN IV SMRs. This paper presents a new review and evaluation process of SMR GEN IV reactors, which seem most suitable for early implementation. Evaluation presented in this paper was performed on the basis of the Value Analysis methodology, indicating the most economically interesting technologies with the shortest time to commercial availability. The SMR GEN IV reactor integration in advanced closed nuclear fuel cycles could an play important role in the energy transition to sustainable oriented R Corresponding author: Aleš Buršič, GEN energija, d.o.o., Vrbina 17, 8270 Krško, Slovenia, Tel.:+ 386 7 49 10 250, E-mail address: ales.bursic@gen-energija.si 1 GEN energija, d.o.o., Vrbina 17, 8270 Krško, Slovenia JET 71 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 low-carbon energy future. Mass balance and material flow for nuclear fuel cycles involving SMRs were established with the NEA 1767 SMAFS model and through the webKORIGEN software. The advantages of SMRs attract embarking countries to look towards use of nuclear as domestic energy source, especially when the paradigm of energy independence is becoming strategically important. Povzetek V preteklem desetletju se pojavljajo številni ekonomski, strateški, tehnični ter ostali razlogi, ki kažejo na določene prednosti Majhnih in srednjih reaktorjev (SMR), sicer prisotnih od pričetka uporabe jedrske energije za miroljubne namene. Četrta generacija jedrskih elektrarn med katere spadajo tudi SMR GEN IV je vključena v napredne zaprte gorivne kroge in omogoča velik napredek v trajnostnem razvoju ter proizvodnji energije. Najobetavnejši SMR koncepti stremijo k visoki temperaturi hladila na izstopu iz sredice ter visokem oplodnem razmerju ter predstavljajo velik napredek v zasnovi SMR GEN IV reaktorjev prihodnosti. Ta članek predstavlja sodoben pristop k procesu pregleda in evalvacije SMR GEN IV reaktorjev, ki so glede na današnje vedenje in informacije najugodnejši za zgodnjo implementacijo. V tem članku predstavljena evalvacija bazira na metodologiji vrednostne analize ekonomsko najzanimivejših tehnologij z najkrajšim časom do njihove komercialne uporabe. Vključevanje SMR GEN IV reaktorjev v sodobne zaprte gorivne cikle predstavlja velik potencial pri energetski tranziciji v nizkoogljično prihodnost. Masne bilance in tok materiala v izbranih gorivnih ciklih, primernih za implementacijo SMR reaktorjev, so bile določene s pomočjo NEA 1767 SMAFS modela ter v nadaljevanju s pomočjo webKORIGEN programskega paketa. Predstavljene prednosti SMR reaktorjev so zanimive tudi za države, ki razmišljajo prvič o uporabi jedrske energije, sajpostaja energetska samozadostnost ter neodvisnost strateško zelo pomembna. 72 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles 1 INTRODUCTION Small and Medium Reactors (SMR) have been present in nuclear industry since the beginning of its use for electricity or heat generation in the 1950s (Figure 1). 1600 Years 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020 Figure 1: Sizs af operating Nnplsar Pawsr Plants isplneisg SMRs, eata sanrps, [28] 1.1 SMR implementation goals SMR units are designed as single units that can also be accommodated as multiple SMR modules sequentially on single sites to optimize site investment costs. Economics of smaller units is planned as increasing the factory assembly manufacturing of units, shorter construction times, optimized supply chains and as mass production impact at manufacturing equipment modules could reduce construction costs and further overnight costs. SMR investment costs include the engineering, procurement and construction (EPC) costs and the owner's costs. The total capital investment cost (TCIC, defined in [2]) is equal to the sum of overnight costs, contingency and the cost of financing, [1]. According to available data for SMR overnight costs, the prices of electricity predicted per installed kW (USD/kWe) are in range from 1200 to 4000 USD/kWe, [4]. This is a rough estimate and involves many volatile factors. JET 73 Ales Bursic,Tomaz Zagar JET Vol. 10 (2017) Issue 4 1.1.1 SMR general design features SMRs are intended to fill market niches with implementation in smaller grids, or where heat production or desalinization in addition to electricity is foreseen. SMR is expected to have simpler design, optimized manufacturing costs and due to its size optimized TCIC in comparison with large ALWRs. SMRs are mainly designed with high levels of passive safety. For instance, a SMR reactor vessel with smaller thermal power (Ptherm) and higher thermal inertia can be by its design narrow and high, thus enabling more intensive natural recirculation with higher thermal dissipation with higher coolant flows along the fuel channels. With higher secondary coolant parameters, more advanced thermodynamic cycles with higher turbine efficiency rates can be implemented. It can be concluded from an American Nuclear Society report, that a major part of the active safety systems and support systems implemented in large ALWRs (Peiectr > 600 MWe) is redundant for SMRs and can be effectively replaced by passive approaches, [5]. 1. 1. 2 General GEN IV reactors classification Among next-generation design reactors, Generation IV (GEN IV) reactors generally excel in sustainability, minimal environmental impacts, better economy, and further reduced proliferation issues. Figure 2 presents six GEN IV technologies, according to their breeding ratios and coolant temperatures at reactor core exit. The most favourable concepts impose high coolant temperatures and high breeding ratio, thus most effectively implementing three fields of progress in the design of future reactors: • higher coolant temperatures when exiting reactor core enabled with the use of new materials and advanced thermodynamic cycle's higher turbine efficiency rates, • high neutron flux with 100 times better UO fuel efficiency, less radioactive waste and use of reprocessed fuel from LWRs, • favourable breeding ratio; fissile material obtained to spent fissile material after the use of a fuel mixture of fissile and fertile material in a reactor or ratio between fission and capture in actinides. 74 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles Figure 2: six mast promising GEN IV SMR technologies as snggsstse by Gsssratias IV International Farnm, eata sanrpss: [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16] 2 GENERAL APPROACH TO SMR MODULARITY A common approach to most SMR reactor designs, especially GEN IV designs is based on the elimination of postulated initiating events (PIE) and the prevention of severe accident consequences, mainly by passive means. A combination of passive and active safety systems is often used for other accident prevention approaches, similar as in today's GEN III ALWRs, such as AP1000, VVER-1000, ESBWR, etc. According to many SMR designers, general features contributing to the efficient implementation of inherent and passive safety design are: • larger surface to volume ratio at reactor vessel for larger decay heat removal, especially in case of a single-phase coolant, • solutions for a more compact Reactor Coolant System (RCS) as for instance integral compact RCS pool, suppressing certain initiating events, • reduced power density of reactor core, simplifying implementation of passive safety systems, • reduced potential hazard results from lower source term due to lower fuel inventory, lower heat and pressure energy stored in the reactor, and lower integral decay heat rate, [19]. JET 75 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 2. 1 Modularization process and improvement possibilities Customer requirements, the existence and further development of modularization at construction or manufacturing are triggered and preserved by the requirements of a short construction schedule, cost reduction, higher quality and safety at the construction site and in exploitation phase (nuclear safety). Those factors emerging mostly from market demands like investor requirements at NPP construction or vendors requirements to achieve more competitive position on market. They are integrated within the whole product lifecycle; in this case, the lifecycle of Systems Structures and Components (SSC) and for the whole NPP project from construction to decommissioning (Figure 3). In the case of SMRs, modularity is present on two levels: an SMR unit, as a whole, represents a module designed to fit and operate within multi-unit site; modules within an SMR are compatible and interchangeable within unit or within units from different vendors. Production, commissioning, operation J ^^ Module Analysis __ Figure 3: Modularization process integrated within module lifecycle 2. 1. 1 SMR SSC Modularity from the designer's point of view Since SMRs are in various design phases, it is difficult to predict to what extent particular SSCs will be interchangeable within various vendor types of SMR, as has been the case for many decades in other industries like automotive, aerospace, naval, robotics, etc. At such a modularity stage, where common SSCs were developed and licensed, a designer would have easier task to make system integration of those SSC. In the nuclear industry, in addition to functionality requirements, there is additional requirement for nuclear safety, which is distinct from other industries and of great importance in setting design basis for the plant. 76 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles The following list covers some potential SSCs that might be common for sodium-cooled fast Reactors of various vendors. SSCs of various manufacturers could be compatible, having the same functionality and operating parameters; all could be used in the same SFR or one SSC that is functionality compatible with the required operating parameters of SFRs from different vendors: • Steam Generator (SG), with which modularity/similarity is achieved with adequate heat transfer surface, SG design remains unchanged and covers wider group of this SMR type with different power outputs, e.g. with one or more same SGs; • Electromagnetic Reactor Coolant Pumps (RCP), controlled with frequency converters, enabling pre-set, project-defined optimum coolant flow through various operating states, as a single RCP or multiple-mounted, similar to AP1000 design; • RCS piping, forged according to unified codes and standards with appropriate multiple sizes, covering the range of reactors, according to safety requirements, forged as a monobloc; standardisation lowers the manufacturing costs; • Auxiliary reactor vessel cooling systems could be unified and pre-licensed for the whole range of FSR SMRs; various power ranges are handled with multiple, yet redundant systems; • Fuel Handling Building (FHB) could be assembled from the same or similar modules, varying according to requirements with modular support equipment; • Seismic resilience, small and compact dimensions at SMRs with higher eigen-frequencies are more favourable for consideration on siting in more demanding geological, geotechnical and seismic locations, with additional implementation of appropriate seismic isolators, it should be viable that site properties would not exist as limiting factor even when considering those reactors on the most demanding sites. Other equipment, such as intermediate heat exchangers, reactor protection system modules, sodium reservoirs, steam and other pipelines, and equipment for transformation to electric energy, can be similarly optimized, modularized, and unified. Experiences with the modularization process show that not many efforts in this direction have been successful, especially when the process itself has been the responsibility of developers or suppliers, without clear and strong support and collaboration from investors/operators with high requirements and particularly regulatory bodies, which may have to expand their scope and participate more proactively in order to promote the safe and peaceful use of atomic energy. 3 REVIEW AND EVALUATION OF PROMISING SMR GEN IV REACTORS A review and evaluation process of SMR GEN IV reactors that seem most suitable for early implementation is divided into two phases: preliminary elimination and secondary elimination selection. Evaluation methodology is qualitative with elements of value analysis (VA), [20], according to the methodology of Small Modular Reactor Strategic Assessment, [21], and is divided into five steps within those phases: JET 77 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 1. collecting relevant information on assessed technologies, 2. preliminary elimination, 3. determination of important functions and properties, 4. properties and relative variant value assessment, 5. optimal technology selection. The intermediate result based on VA is a ranked list of SMRs. The selection of a technology group is made among those reactors according to the most collected points for suggested ranking factors and characteristics for the most promising technology, (1st part of 4th phase). The goal of the review process by assessing the economy of different technologies is to define, by VA (2nd part of 4th phase), the group of technologies that meets the set threshold of ranking factors and characteristics (5th phase). 3. 1 Technology relevant data acquisition Data from 27 SMR GEN IV technologies (reactor designs from specific vendor) being in various design phases were gathered for the assessment: • 7 types of Gas-cooled fast reactors (GFR), • 1 very-high-temperature reactor (VHTR), • 9 types of lead-cooled fast reactors, cooled with Pb or Pb-Bi eutectic (LFR), • 3 types of molten-salt reactors (MSR), • 7 types of sodium-cooled fast reactor (SFR). The listed technologies are in development in the US, Russian Federation, Japan, China, India, South Korea, Czech Republic, and South Africa. Most R&D institutions or companies do not publish or reveal their progress regularly; therefore, this assessment is based on publicly available articles, industry societies, conferences, NRC or IAEA evaluations, interviews with design engineers or other available sources, referenced at the end of the paper. 3. 2 Preliminary elimination Preliminary elimination evaluates each of the 27 technologies according to following parameters: • commercial operation is viable only after 2030, • complex process of fuel fabrication; remark: this parameter is important, but has less influence in this preliminary evaluation due to different design phases of assessed technologies, • unreliable or non-existent sources for R&D financing, high risk for financing termination, • FOAK technology, proof-of-concept working prototype is required before final prototype, • technology in early R&D phase. Any technology fulfilling any of the above parameters is excluded (*) as an unsuitable candidate for further assessment. An exception is made when, within the whole technology group (GFR, VHTR, etc.) there is no suitable technology, in which case one technology is conditionally (0) 78 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles selected, having the best result within the group. According to these rules, the following technologies were selected and presented in Table 1. Table 1: SMR GEN IV reactor overview [1], [2], [4], [19], [21] Technology designation Selection Power (MWe) Designer Origin Parameters, Remarks GFR (Gas-cooled Fast Reactor) group Adams Engine x 1 to 100 Adams Atomic Engines, Inc. USA a, b, e EM2 x 240 General Atomic USA a, b GT-MHR x 150 General Atomic, OKBM Afrikantov, Fuji USA, Russian Federation, Japan a, b, e, igt ALLEGRO a 75 (MWt) UJV Rez, a.s., MTA EK in VUJE a.s., CEA, EURATOM Europe a, b, c, d, e MTSPNR x 2 NIKIET Russian Federation a, b, c, double reactor unit PBMR x 150 PBMR, Pty. South Africa a, c GTHTR-300 x 280 JAERI Japan a, b VHTR/AHTR (Very High Temperature Reactor) group Antares x ~288 Areva, Fuji France, Japan e, b, d HTR-PM ✓ 211 INET, Tsinghua University China LFR (Lead-cooled Fast Reactor) group ANGSTREM (Pb-Bi) x n/p TES-M soisf BREST-OD-300 x 300 Gidropress Russian Federation e ENHS x 50 University of California, Berkley USA a HPM(Pb-Bi) x 25 Hyperion Power Generation, Inc. USA e single or multiple reactor unit LSPR(LBE) x 53 RLNR TITech Japan a SSTAR (Pb-Bi) x 20 10 to 100 Argonne National Lab & Lawrence Livermore Laboratory, Toshiba USA, e STAR-LM, STAR-H2 Hydrogen x production 180 Argonne National Lab & Lawrence Livermore Laboratory USA, Japan e SVBR-100 (Pb-Bi) ✓ 100 Gidropress Russian Federation ee TWR x 300 Lawrence Livermore Lab (DOE), Terrapower USA a, b, d, e ALFRED x 300 Ansaldo nuclear with 16 European organizations Europe a, b, e MSR (Molten Salt Reactor) group Fuji MSR (LFTR) a 100 IThEMS Japan, Czech Republic a, d, e JET 79 Ales Bursic,Tomaz Zagar JET Vol. 10 (2017) Issue 4 Technology designation Selection Power (MWe) Designer Origin Parameters, Remarks LFTR X 20 to 50 Flibe Energy USA a, b, noinf PB-AHTR X 410 UC Berkley, ORNL USA a, b, d, e SFR (Sodium i-cooled Fast Reactor) group 4S V 10 Toshiba Japan dd ARC-100 X 100 Advanced Reactor Concepts, LLC USA e CEFR V 20 CNEIC China op KALIMER-600 X 600 KAERI South Korea a, b PFBR-500 V 500 IGCAR India const PRISM V 155 GE, Hitachi USA, Japan dd Rapid-L X 0.2 Toshiba, CRIEPI, JAERI Japan a, b, igt Astrid X 600 CEA with industry consortium International a, b, e Remarks: igt-integral gas turbine poses great technological challenges, noinf-non-existent or poor information on technology, dd- reactor in detail design phase, const-reactor in construction phase, op-reactor in operation phase. Technologies are conditionally selected for secondary elimination based on larger development potential, are recognized as interesting for potential investors in FOAK technologies or have broad international support on financing and R&D and have large potential for niche markets. 3. 3 Secondary elimination Eight SMR designs entered the secondary phase: Allegro, HTR-PM, SVBR-100, Fuji SMR, 4S, CEFR, PFBR-V and PRISM. The second elimination step consists of the following phases of VA: 3) determination of important functions and properties, 4) properties and relative variant value assessment (USD/kW ¡nstalled), and 5) optimal technology selection. 3. 3. 1 Determination of important functions and properties In this phase, the functions, properties and properties influence of SMR technologies enabling evaluation are selected. Results of 8 SMR technologies evaluated in greater detail on the design, licensing and construction with characteristics are: 1. Design maturity and status of development, [22], [23], 2. Designer, manufacturer experiences, [22], [23], 3. Licensing challenges, regarding current GEN III challenges at licensing, [22], [23], 4. Simplicity of design and constructability, [22], 5. Technical and technology challenges, 6. Level of participation in closed fuel cycle, HLW amount in fuel elements, possibility for the use of reprocessed nuclear fuel from other technologies like PWR, BWR, [22], [24], 7. Maturity levels for supply chain, and infrastructure for components and heavy component manufacturing and supply. 80 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles At VA, product properties, in this case technologies (variants), are evaluated. Because most of the assessed technologies are in various phases (e.g. R&D, construction, etc.), it is necessary not to assess only properties, which may be changed during process, but also the effects and influence due to conditions at project development over certain aspects, such as design or economics, etc. Instead of specific properties, the combination of group of properties as a whole (influenced properties field) are important and therefore evaluated. 3. 3. 2 Properties and relative variant value assessment 3. 3. 2. 1 Variant properties assessment Technologies are evaluated by assessing the fulfilment level of factor K of selected group of properties for technology and influenced properties field, varying from factor value from: • 0.00 - inadequate, influence on assessment field gives unacceptable results, • e.g. 0.50 - appropriate, without significant influence on assessment field, 1.00 - most suitable, influence on assessment field exhibits excellent results. Since all assessment fields may not be equally important to the assessor, they can be weighted with a ponder value. The sum of denominated ponder relative values for assessment fields evaluated with K represents 100%; therefore, change in one ponder changes the influence of all other ponders for specific variants. Variant properties assessment was conducted on the basis of pre-prepared assessment sheets by a group of five nuclear technology experts, three of them with doctorates in nuclear technology and two with more than five decades of experience in SSC design since the deployment of GEN II NPPs. Table 2 summarizes their evaluations of selected variants. The number of points of selected property group at variant is arithmetic mean of assessor's evaluations: T = - forn = N0 of assessors (3.1) Table 2: Variant properties and influenced properties field assessment results [22] Property / Influenced Properties Field Ipi/n [%] IKi/n IT/n Ipi/n [%] IKi/n ITi/n Ip/n [%] IKi/n IT/n Ipi/n [%] IKi/n ITi/n 1 Design maturity and status of development [22] 18.2 0.6 9.9 18.2 0.8 14.9 18.2 0.9 15.3 18.2 0.3 5.9 2 II Designer, manufacturer experiences [22] 13.4 0.6 7.8 13.4 0.7 8.4 13.4 0.8 11.1 13.4 0.3 3.7 3 Licensing challenges 122] 14.2 0.5 7.0 14.2 0.7 9.2 14.2 0.8 11.5 14.2 0.3 4.4 4 Simplicity of design and constructability [22] 14.4 o.5l 7.9 14.4 0.5 6.6 14.4 0.7 9.3 14.4 0.5 7.5 5 Technical and technology challenges [22] 12.1 0.7 7.8 12.1 0.8 10.5 12.1 0.9 10.8 12.1 0.5 5.7 6 Level of participation in closed fuel cycle [24] 14.4 0.7 9.4 14.4 0.3 4.8 14.4 0.7 9.7 14.4 0.3 4.0 7 Maturity of supply chain and manuf. infrastr. 13.3 0.7 9.3 13.3 0.9 11.6 13.3 0.9 11.7 13.3 0.5 5.9 1 ■! fjUdSIBI KS93E 59.18 urn EjEBfllBiBIIBIBTBEBKBIB ■S obubUB 79.30 gH flu! HI ■B3IÜH Property / Influenced Properties Field Ref. IPi/n [%] 4S IKi/n ITi/n CEFR Ip/n [%] IK/n IT/n PFBR-500 Ip/n [%] IK/n ITi/n PRISM Ip/n [%] IK/n IT/n 1 Design maturity and status of development [22] 18.2 0.7 12.8 18.2 0.8 14.4 18.2 0.8 14.8 18.2 0.8 13.8 2 Designer, manufacturer experiences [22] 13.4 0.8 10.4 13.4 0.7 8.9 13.4 0.8 9.9 13.4 0.8 10.1 3 Licensing challenges [22] 14.2 0.6 8.4 14.2 0.7 9.7 14.2 0.8 11.0 14.2 0.6 8.6 4 Simplicity of design and constructability [22] 14.4 0.6 8.0 14.4 0.5 7.5 14.4 0.5 7.1 14.4 0.6 7.8 5 Technical and technology challenges [22] 12.1 0.7 9.0 12.1 0.8 10.8 12.1 0.8 10.9 12.1 0.8 10.8 6 Level of participation in closed fuel cycle [24] 14.4 0.6 8.5 14.4 0.6 8.5 14.4 0.6 8.8 14.4 0.6 8.9 7 Maturity of supply chain and manuf. infrastr. 13.3 0.7 9.1 13.3 0.8 11.0 13.3 0.8 10.5 13.3 0.7 9.7 SVBR-100 Fuji MSR JET 81 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 90 SVBR-100 4S HTR-PM Fuji MSR PFBR-500 CEFR PRISM Allegro Figure 4: Variant assessment results' ranking, [22] 3. 3. 2. 2 Relative value at assessed variants Collecting information on technology implementation (investment) costs is an essential part of the comprehensive assessment, although it is focused on a niche industrial field prone to ever-changing competition conditions. Collected information originates from publicly available information, [4], or from discussion with leading experts in nuclear, SMR technology-related fields. Regardless of the source of information, it can be concluded with certainty that the information is more reliable than cost calculations executed for particular SMR SSC, especially when experience shows that even partial costs given to recognized reliable investors by vendors in bidding phases for NPPs may vary from the final costs. Equipment costs may also vary according to investors requirements, since investors can prefer specific equipment suppliers due to fleet/equipment standardization and maintenance optimization, even if not recognized as standard OEM by vendors. Power generation plant costs also depend and vary on specific investor requirements, such as desalinization, hydrogen production, heat cogeneration, etc., and are not included due to multiple variants emerging from those requirements. Further costs that should be recognized in assessment are contingency, project engineering, licensing costs, various compensations costs to local community, municipality or state etc. Cost are presented separately in Table 3, ranking is conducted according to Levelized Unit Electricity Cost (LUEC) and to overnight capital costs of each technology, [4]. When assessing variant suitability, relative values are calculated, [20]: v = F/c = P/c = T/c = Properties/costs ^ 82 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles Where V represents relative value, F function, P property (group), costs (LUEC and overnight capital costs separately) and T variant properties value. Calculated V (Figure 5) provides information on property group assessment with variants relative value under costs consideration, where higher value represents better results, having lower costs. Table 3: Relative volns accoreisg to LUEC ose to oversight capital costs | HTR-PM | SVBR-100 | Fuji MSR | 4S Overnight Capital Costs (OCC) 1500 USD 1200 USD 4500 USD 1500 USD Relative tech. value/OCC 0.0440 0.0661 0.0083 0.0441 Levelized Unit Electricity Cost (LUEC) 51 USD/MWh 42 USD/MWh 29 USD/MWh 290 USD/MWh Relative tech. value/LUEC 1.2940 1.8882 1.3056 0.2283 10,00 Relative technology value/OCC Relative technology value/LUEC 1,294 1,306 1,00 0,228 0,10 0,01 0,008 0,00 in SVBR-100 4S HTR-PM Fuji MSR Figure 5: Relative value ranking from Table 3 Assessment approach with Value Analysis is reasonable and useful in case of strategic investor decisions, especially when dealing with larger lifecycles of investment, such as with NPPs. Assessment results indicate the most economically interesting technologies with the shortest times to commercial availability. JET 83 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 4 SMR GEN IV INTEGRATION IN ADVANCED NUCLEAR FUEL CYCLES Suitable for SMR GEN IV integration are examples of advanced, fully closed, nuclear fuel cycles (NFC, FC), in which all actinides are continuously recycled in fast reactors. Only two fuel cycle schemes were studied in this paper (out of several different fuel cycles possible) and are indicated as FCA and FCB. A fuel cycle based on PWR reactor and integral fast reactor concept (Fuel Cycle A (FCA)), featuring partitioning & transmutation (P&T) option, results in small waste quantities without actinides, containing only material from reprocessing losses and fission products (FP). In FCA, proliferation possibility is disabled, since there is no Pu separation from other actinides (Figure 6). A fuel cycle based on GCR concept (Fuel Cycle B (FCB)), capable of burning all actinides (U, Pu, Am, Cm, etc.) results in minimising actinides loss in process and maximizing use of uranium resources. Waste is trans-uranium elements from reprocessing efficiency losses and FP. Due to the small consumption of depleted uranium, FCB can be recognized as a sustainable energy source (Figure 8). The FCA fuel cycle features a PRISM reactor, and FCB features an ALLEGRO reactor. Material flow and mass balances originate from the characterization of advanced nuclear fuel cycles and the determination of HLW quantity for final disposal, [24], with the consideration of the Slovenian case on used nuclear fuel inventory, [27]. Mass balance and material flow for the beginning of fuel cycle was determined for each NFC through the NEA 1767 SMAFS model. With an iteration approach through webKORIGEN software, final mass balances of Used Nuclear Fuel (UNF) were established. The activity, toxicity, residual heat power, and mass balance of final high-level waste (HLW) for final disposal were also established with the same approach through webKORIGEN. Quantities in both NFCs were normalized on 1MWe year/FC, [24]. Unaturai: 114.7 kg I Enrichment T H UOX fuel 13.394 kg U irradiated: 12.389 kg Udepleted: 101.3 kg U:1518.3 g + Pu:738.1 g + MA:98.7 g FR fuel 2.536 kg FR (SFR) 36.8% Î UREX UOx PYRO metal fuel 78Ac-227Zr HLW U: 13.920 g Pu: 0.736 g Np: 0.024 g Am: 0.053 g Cm: 0.023 g FP: 1.030 kg FP, Reprocessing efficiency (HM) Disposal Figure 6: FCA fuel cycle, UOX (UREX) reprocessing, Pyrochemical reprocessing of metal fuel (PYRO)-TRU partitioning and homogenic transmutation, [24] SMR GEN IV reactors could play an essential role in the energy transition to sustainable oriented low-carbon energy future. Combining reprocessing within closed or semi-closed FCs minimizes 84 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles the quantity (volume) of material entering NFC and waste. In addition, there is notable improvement with minimizing relative residual heat generation and radioactivity reduction in comparison with open FC (Figure 7 for FCA, Figure 9 for FCB and Figure 10 for FCA, FCB, FCO comparison). All features combined contribute to reducing necessary volume in final disposal and its decay time to natural background level. Since economy of smaller HLW disposals is worse than of larger, the idea of establishing regional HLW disposal, accommodating fuel from many international reactors could be more attractive, especially when disposing of reprocessed HLW, for which the radiotoxicity timespan down to natural background could degrade under 1000 years. Actinides Helium Lanthanides Radon Total Actinides and Progenies Hydrogen Minor Actinides Rare Earths Fission Products Inert Gases Noble Metals Transuraniums 1.005e+10 Bq.-fr 400.0 kgequvalent tovitrification contgnRnttCV— Years Actinides Helium Lanthanides Radon Total Actinides and Progenies Hydrogen Minor Actinides Rare Earths Fission Products Inert Gases Noble Metals Transuraniums Years 10 10 10 Figure 7: Activity ase rssienal hsat escay avsr time far FCA fnsl cycle after eispasal, [24] JET 85 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 Udepleted: 0.757 kg i o Solid solution nuclear fuel — GCR N Cooldown U: 5.303 kg Pu: 1.306 kg Np: 7.9 g (U,Pu)C, SiC 7.442 kg 100% J i Am: 58.7 g Fuel cooldown before reprocessing: 5 years Cm: 15.8 g FP: 753.9 g i PYRO U:5298.1 g + Pu:1304.8 g + MA:82.3 g reprocessing HLW U: 5.303 g Pu: 1.306 g Np: 0.008 g Am: 0.059 g Cm: 0.016 g FP: 753.9 g I Disposal Figure 8: FCB fuel cycle, Pyrochemical reprocessing of metal fuel (PYRO)-TRU partitioning and homogenic transmutation, [24] 86 JET Future G ensmtiGnlVsMa reactors:sssensmantandpossibil(tyofistefration in ctose d nuclear fuel cycles - Actin ¡des+Progenies - Actin ides - Transuraniums - MinorActinides — Radon Light Elements — Lanthanides — Rare Earths Noble Metals Inert Gases (Ne- Ar- Kr-Xe) — Hydrogen — Helium Total 0 Years 100 200 300 400 Figure 9: Activity and residual heat decay over time for FCB fuel cycle after disposal [24] Figure 10 compares SMR-suitable FCA and FCB with open fuel cycle featuring the once-through use of UNF in PWRs designated FCO (Fuel Cycle - Open). Residual heat at FCO is generated in the disposed fuel element without any reprocessing. According to the disposed mass of material, the relative residual heat at reprocessed HLW is more favourable; however, at vitrification in universal canisters (UC-V), attention should be paid to the maximum allowable heat load for the glass matrix. In addition to residual heat generation, the heat load for the glass matrix is dependent on the environment contact conditions and exposure. 250 200 150 a100 50 FCO . ■ Residual heat after vitrification (W) 216,1 W . ■ Residual heat 50 years after reprocessing [W] 139,4 W ! ■ Residual heat 200 years ■ after reprocessing [W] ^™130,1 W 17,7 W (1) i 0,0 W (1) 15,1 W 15,1 W ^^ 1,0 W FCA Fuel cycle designation FCB 0 JET 87 Aleš Buršič, Tomaž Žagar JET Vol. 10 (2017) Issue 4 250 200 g 150 £ 100 214,5 kg Quantity of natural/depleted U, entering FC [kg] Quantity of disposed or stored HLW [kg, HM] 113,6 kg 0,8 kg 1,0 kg 0,8 kg FCO FCA FCB Fuel cycle designation 4,082E+11Bq (1) -g 4,0E+11 CO ' 3,0E+11 € 2,0E+11 1,0E+11 0,0E+00 FCO FCA Fuel cycle designation FCB Figure 10: Mass balance, Residual heat decay and Activity over time, comparing open fuel cycle FCO to closed CFA and FCB, [24] 5 CONCLUSION The main technological advantages of SMRs over large ALWRs emerge primarily out of the size of nuclear steam supply system (NSSS) and other SSCs. Size of SMRs and their potential for modularity enables factory assembly manufacturing of SMR units. This brings shorter construction times, more effective and efficient quality assurance/quality control and optimization of the project structure and management that can reduce investment capital costs. In many cases, SMR SSCs involve FOAK technology solutions, which may be extremely innovative, such as minimizing the quantity of necessary SSCs while simultaneously maintaining safety levels in comparison with large GEN II or GEN III+ reactors. In contrast, with the FOAK approach, designers implement unproven technology and increase the risk of delayed commercial availability. 88 JET Future Generation IV SMR reactors: assessment and possib ility of integration in closed nuclear fuel cycles The main contribution and novelty of this paper is its value analysis review and the evaluation of 27 different SMR GEN IV reactors design currently available. This value analysis gives insight into the commercially most promising technologies with strong implementation potential, which could be economically interesting in the next 10 to 15 years. Eight out of 27 evaluated SMR designs were shortlisted in the first phase of evaluation. Those technologies went through a more detailed assessment. The most points were collected by the SVBR-100 SMR design (lead-cooled fast reactor designed in Russia). On the second and third places are PFBR-500 and CEFR SMR designs (Sodium-cooled Fast Reactor from India and China, respectively). Among the so-called "western technologies", on the fourth place, PRISM SMR (sodium-cooled fast reactor designed by GE and Hitachi) shows potential, especially due to its multifunctionality and robust seismic design. Based on available information, despite their unfavourable economy of scale, SMR overnight investment costs put SMRs cost of electricity production in the upper band of the price range of large reactors. Since the calculated cost of electricity production is based on predictions, actual economics is yet to be proven after first SMRs are put into operation. When summarizing SMR technology could experience future growth under several conditions: • similar or lower overnight investment costs and electricity production costs in comparison to large reactors, • high level of external modularity with ability to efficiently connect several reactors on site offering several exploitation possibilities, internal modularity and standardization of SSCs of similar SMRs from different suppliers, • flexibility at siting, with no or minimal environmental impact, seismic robustness, suitability for siting close to populated areas, smart grid and distributed supply integration possibility, • unified international licensing approach implementation based on experience on SMR licensing conducted by world's most recognized regulatory bodies, such as US NRC, STUK, ASN, • large flexibility and impact at integration into existing nuclear fuel cycle schemes, consequentially leading towards closed nuclear fuel cycle, • ultimate inherent safety against internal and internal events, with minimal or no operator intervention and relying on advanced passive safety features. In case SMRs fail to deliver promised and expected features, especially at economic issues, they will remain interesting solely for research and for investors with high budgets, intent to solve energy supply issues at remote locations with poor infrastructure but high value. Energy supply independence is becoming more and more important in the focus of many environmental agreements, energy transitions towards electrification in heating, transportation and other demands. SMR technologies could deliver some of the answers for future energy needs. JET 89 Ales Bursic,Tomaz Zagar JET Vol. 10 (2017) Issue 4 References [1] OECD/NEA, Nuclear Energy Agency, Small Modular Reactors: Nuclear Energy Market Potentialfrr Near-term Deployment, OECD Publications, NEA No. 7213, Paris, France, 2016 [2] EMWG: Cost Estimating Guidelines frr Generation IV Nuclear Energy Systems, Generation IV International Forum (GIF), Economic Modelling Working Group, EMWG, 2007 [3] D. Schlissel and B. 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Žagar: Closed fuel cycle technologies, Jožef Stefan Institute, IJS-DP-9762, Issue 1, Ljubljana, 2008 [27] T. Žagar, A. Buršič et al: Recycling as an option of used nuclear fuel management strategy, Nuclear engineering and design, ISSN 0029-5493, vol. 241, no. 4, Amsterdam, North-Holland, 2011 [28] World Nuclear Association: Reactor Database, http://www.world-nuclear.org /information-library/facts-and-figures/reactor-database.aspx, accessibility check Jan 2018 JET 91 92 JET Journal of Energy Technology Author instructions www.fe.um.si/en/jet.html MAIN TITLE OF THE PAPER SLOVENIAN TITLE Author1, Author2, Corresponding author* Keywords: (Up to 10 keywords) Abstract Abstract should be up to 500 words long, with no pictures, photos, equations, tables, only text. Povzetek (Abstract in Slovenian language) Submission of Manuscripts: All manuscripts must be submitted in English by e-mail to the editorial office at jet@um.si to ensure fast processing. 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