JET  11
JET Volume 15 (2022) p.p. 11-24
Issue 3, 2022
Type of article: 1.01 
www.fe.um.si/si/jet.html
 
ℜ Corresponding author: Eva Tratnik, Tel.: +386 (0)2-220-7086, University of Maribor, Faculty of Electrical Engineer-
ing and Computer Science, Koroška cesta 46, 2000 Maribor, Slovenia, E-mail address: eva.tratnik@um.si
1
 University of Maribor, Faculty of Electrical Engineering and Computer Science, Koroška cesta 46, 2000 Maribor, 
Slovenia
2
 Elektro Celje d.d., Vrunčeva ulica 2a, 3000 Celje
The use of differential evolution to determine maximum generation and load values in the distribution network
Uporaba diferenčne evolucije za določitev največje proizvodnje ter porabe v distribucijskem omrežju
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković
THE USE OF DIFFERENTIAL 
EVOLUTION TO DETERMINE MAXIMUM 
GENERATION AND LOAD VALUES IN 
THE DISTRIBUTION NETWORK
UPORABA DIFERENČNE EVOLUCIJE ZA 
DOLOČITEV NAJVEČJE PROIZVODNJE 
TER PORABE V DISTRIBUCIJSKEM 
OMREŽJU
Eva Tratnik
ℜ1
, Janez Ribič
1
, Matej Pintarič
1
, Miran Rošer
2
, Gorazd Štumberger
1
, Miloš Beković
1
Keywords: distribution network, renewable energy sources, optimisation method, voltage pro-
file
Abstract
By integrating renewable energy sources into the existing distribution network, the characteris-
tics and local stability of the network is highly impacted. The network, which was built with the 
goal of a directed energy flow from large conventional sources connected to the transmission 
network via the distribution network to consumers, can change the direction of the energy flow. 
The adoption of environmental commitments and directives encourages the integration of local 
dispersed energy sources, which can worsen voltage conditions in the distribution network. To 
avoid excessive local production, distribution network operators must limit the installation of 

12 JET 12 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
new generation units, as it is necessary to take into account the quality of power supply by mon-
itoring its network parameters, such as the appropriate voltage profile and the ratio between ac-
tive and reactive power. On the other hand, excessive loads due to the mass transition of house-
hold heating and transport towards electricity can also pose a problem for high-quality electricity 
supply due to the excessive voltage drop. The article presents an algorithm for determining the 
maximum size of unit production and the maximum load at a node in the distribution network. 
Also demonstrated is the use of variable tap transformer technology, which adjusts the tap of 
the transformer to provide an appropriate voltage profile in the network. The entire analysis was 
performed on a model of a real medium-voltage network, in which solar and hydropower plants 
are already included. The model was verified by comparing its calculated values with actual 
measurements. The goal was to determine the size of the unit’s maximum production, as well as 
the size of the maximum load, by using the differential evolution algorithm, while keeping volt-
age profiles within the permissible limits. The results of the analysis are presented in the article.
Povzetek
Z vključevanjem obnovljivih virov energije v obstoječe distribucijsko omrežje vplivamo na karak-
teristike in lokalno stabilnost omrežja. Omrežje, ki je bilo zgrajeno s ciljem usmerjenega pretoka 
energije od velikih konvencionalnih virov, priklopljenih na prenosno omrežje preko distribucijs-
kega omrežja do porabnikov, lahko spreminja usmerjenost pretoka energije. Sprejetje okoljskih 
zavez in direktiv spodbuja integracijo lokalnih razpršenih virov energije, ki lahko poslabša nape-
tostne razmere v distribucijskem omrežju. V izogib čezmerni lokalni proizvodnji želijo operaterji 
distribucijskih omrežij omejiti priklapljanje novih proizvodnih enot, saj je treba upoštevati kakov-
ostno oskrbo s spremljanjem parametrov omrežja, kot sta ustrezen napetostni profil ter razmerje 
med delovno in jalovo močjo. Prevelika bremena pa zaradi množičnega prehoda ogrevanja in 
transporta na električno energijo prav tako prestavljajo težavo za kakovostno oskrbo z električno 
energijo. V članku je predstavljen algoritem za določitev največje velikosti proizvodnje enote in 
največjega bremena v vozlišču v distribucijskem omrežju. Prikazana je tudi uporaba tehnologije 
transformatorja s spremenljivo prestavo, ki prilagodi prestavo transformatorja tako, da zagotovi 
ustrezen napetostni profil v omrežju. Celotna analiza je bila narejena na modelu realnega sredn-
jenapetostnega omrežja, v katerega so že vključene sončne in hidroelektrarne. Model je bil verif-
iciran tako, da smo izračunane vrednosti modela primerjali z dejanskimi meritvami. Cilj je določiti 
velikosti maksimalne proizvodnje enote in bremena z uporabo algoritma diferenčne evolucije, pri 
tem pa ohraniti napetostne razmere znotraj dopustnih meja. V članku so predstavljeni rezultati 
opravljene analize.
1 INTRODUCTION
With the development of dispersed sources of production and environmental protection com-
mitments, the distribution network has undergone a major transformation in recent years. If in 
the past it was considered a passive part of the power grid with a consumer character, with the 
integration of distributed sources it is turning into an active one. As a result of the change in net-
work activity, new requirements for network operation and the need for advanced planning algo-
rithms and optimisation of network operation arise. To analyse operating conditions and energy 
flows in the network, it was necessary to develop appropriate models that describe conditions in 
the network. These algorithms need to be adapted, since distribution networks are mostly radial 
in nature, while transmission networks are closed-looped. By including distributed sources and 

JET  13
The use of differential evolution to determine maximum generation and load values in the distribution network
larger loads in the distribution network, the voltage profiles are heavily influenced. The main 
problem with distributed sources of electricity is that the production of electricity depends on 
meteorological conditions and/or the time of day. Due to unreliable and unpredictable current 
production from scattered sources, it is difficult to coordinate current consumption. Therefore, 
local power surges may occur in the network, where voltages in the lines may exceed the permis-
sible values in the case of excessive production, and at the same time voltages may drop sharply 
below the permissible value in the case of excessive loads. Adequate voltage conditions can be 
ensured by several methods and measures, such as: changing the topology of the network or 
even by replacing conductors with ones of larger cross-sections. These measures are passive, 
usually very expensive and sometimes not the most optimal; sometimes the optimal placement 
of distributed resources in the network is sufficient.
Chapter 2 presents the creation of the network model and verification; Chapter 3 presents the 
results of the analysis. The analysis is divided into several parts: the first part consists of the 
analysis of the current situation in the network, the second part consists of the analysis of deter-
mining the maximum production and the maximum load for a summer and winter day, and the 
third part consists of the introduction of OLTC, when we include production units in the network 
that cause an increase in voltage in a network that is larger than allowed. Chapter 4 presents the 
conclusion.
2 DESCRIPTION OF METHODS AND MODEL VERIFICATION
The article discusses a practical example of the operation of a radial medium-voltage distribu-
tion line. Data about the network topology and the parameters of the network elements were 
obtained from the distribution company. The data was processed as shown in Figure 1, where 
the original shp data is converted to Excel using the Qgis program and imported into the Matlab 
environment, where all further network analysis and later optimisations are carried out.
The use of differential evolution to determine maximum generation and load
values in the distribution network
3
----------
Figure 1: Conversion of data from the distribution operator into a structure for resolving electrical networks
To create the network model, a Matlab environment was used, where a network model for the calculation of voltage
conditions for the planned topology and parameters of the lines was created. The model of the considered network
with thirty-six nodes is shown symbolically in Figure 2, where nodes in which solar or hydro power plants already
connected are marked in red. For the purposes of the analysis, any node could be changed arbitrarily.
Figure 2: Renumbered topology of considered radial distribution network 
The three solar power plants (PV) and five hydroelectric power plants (HPP) are included in the network. Data on the
nominal generated power P gen and the type of individual production of the unit are shown in Table 1.
Table 1: Rated power and type of power plant included in the specific node
Node P gen [kW] Type
TP 1 30 22 PV
TP 2 31 0 /
TP 3 14 276 HPP
TP 4 35 11 PV
TP 5 10 169 HPP
TP 6 26 1316 HPP
TP 7 18 287 HPP
TP 8 7 0 /
TP 9 4 160 HPP
TP 10 8 0 /
TP 11 25 207 HPP
TP 12 6 49 PV
TP 13 19 205 HPP
TP 14 29 0 /
TP 15 22 0 /
TP 16 28 0 /
The created network model, which has been built, was also verified before further analysis. Several types of load flow
methods are known [2,3,5], but in this case the BFS algorithm has been used [1] . Verification of the calculation was
Figure 1: Conversion of data from the distribution operator into a structure for resolving electri-
cal networks
To create the network model, a Matlab environment was used, where a network model for the 
calculation of voltage conditions for the planned topology and parameters of the lines was creat-
ed. The model of the considered network with thirty-six nodes is shown symbolically in Figure 2, 
where nodes in which solar or hydro power plants already connected are marked in red. For the 
purposes of the analysis, any node could be changed arbitrarily.

14 JET 14 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
The use of differential evolution to determine maximum generation and load
values in the distribution network
3
----------
Figure 1: Conversion of data from the distribution operator into a structure for resolving electrical networks
To create the network model, a Matlab environment was used, where a network model for the calculation of voltage
conditions for the planned topology and parameters of the lines was created. The model of the considered network
with thirty-six nodes is shown symbolically in Figure 2, where nodes in which solar or hydro power plants already
connected are marked in red. For the purposes of the analysis, any node could be changed arbitrarily.
Figure 2: Renumbered topology of considered radial distribution network 
The three solar power plants (PV) and five hydroelectric power plants (HPP) are included in the network. Data on the
nominal generated power P gen and the type of individual production of the unit are shown in Table 1.
Table 1: Rated power and type of power plant included in the specific node
Node P gen
 [kW] Type
TP 1 30 22 PV
TP 2 31 0 /
TP 3 14 276 HPP
TP 4 35 11 PV
TP 5 10 169 HPP
TP 6 26 1316 HPP
TP 7 18 287 HPP
TP 8 7 0 /
TP 9 4 160 HPP
TP 10 8 0 /
TP 11 25 207 HPP
TP 12 6 49 PV
TP 13 19 205 HPP
TP 14 29 0 /
TP 15 22 0 /
TP 16 28 0 /
The created network model, which has been built, was also verified before further analysis. Several types of load flow
methods are known [2,3,5], but in this case the BFS algorithm has been used [1] . Verification of the calculation was
Figure 2: Renumbered topology of considered radial distribution network
The three solar power plants (PV) and five hydroelectric power plants (HPP) are included in the 
network. Data on the nominal generated power P
gen
 and the type of individual production of the 
unit are shown in Table 1.
Table 1: Rated power and type of power plant included in the specific node
Node P
gen
 [kW] Type
TP 1 30 22 PV
TP 2 31 0 /
TP 3 14 276 HPP
TP 4 35 11 PV
TP 5 10 169 HPP
TP 6 26 1316 HPP
TP 7 18 287 HPP
TP 8 7 0 /
TP 9 4 160 HPP
TP 10 8 0 /
TP 11 25 207 HPP
TP 12 6 49 PV
TP 13 19 205 HPP
TP 14 29 0 /
TP 15 22 0 /
TP 16 28 0 /
The created network model, which has been built, was also verified before further analysis. Sev-
eral types of load flow methods are known [2,3,5], but in this case the BFS algorithm has been 
used [1]. Verification of the calculation was carried out by calculating on an arbitrary day and at 
any measurement point, where the two years of measurement data were available with nine-

JET  15
The use of differential evolution to determine maximum generation and load values in the distribution network
ty-six measurement samples per day at 15-minute time intervals, therefore giving over 70,000 
measurement points in total. The goal of verification is to check the accuracy of the calculation 
of the built model by comparing the results with measurements.
In Figure 3, a comparison for the selected day is presented, where a comparison between the 
measured voltage value and the calculated voltage values in each phase can be seen. A minor 
asymmetry is visible in phase L1, whilst in phases L2 and L3 correspondence with the measure-
ments is satisfactory. Based on many selected currents and several days, we can conclude that 
the built model realistically describes the voltage situation and that it can be used for the study 
of potential new loads as well as new dispersed sources.
In Figure 3, on the left, it can be seen that the same P and Q values as were used for the measure-
ments were used for the model calculation. The graph on the right shows the voltages, where it 
can be seen that in the case of phases L1 and L2 there is a relatively good match, while in phase 
L3 there is a smaller deviation, but this model cannot take this into account.
4
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
----------
carried out by calculating on an arbitrary day and at any measurement point, where the two years of measurement
data were available with ninety-six measurement samples per day at 15-minute time intervals, therefore giving over
70,000 measurement points in total. The goal of verification is to check the accuracy of the calculation of the built
model by comparing the results with measurements.
In Figure 3, a comparison for the selected day is presented, where a comparison between the measured voltage value
and the calculated voltage values in each phase can be seen. A minor asymmetry is visible in phase L1, whilst in phases
L2 and L3 correspondence with the measurements is satisfactory. Based on many selected currents and several days,
we can conclude that the built model realistically describes the voltage situation and that it can be used for the study of
potential new loads as well as new dispersed sources.
In Figure 3, on the left, it can be seen that the same P and Q values as were used for the measurements were used for
the model calculation. The graph on the right shows the voltages, where it can be seen that in the case of phases L1 and
L2 there is a relatively good match, while in phase L3 there is a smaller deviation, but this model cannot take this into
account. 
00:00 06:00 12:00 18:00
Jun 22, 2020   
-600
-400
-200
0
200
400
Q [kvar], P [kW]
P - Calc.
Q - Calc.
P - Meas.
Q - Meas.
00:00 06:00 12:00 18:00
Jun 22, 2020   
11.6
11.8
12
12.2
12.4
U [kV]
Calc.
L
1
 - Meas.
L
2
 - Meas.
L
3
 - Meas.
a) b)
Figure 3: Comparison of calculations and measurements for selected day
After the verification of the model, the next step was to utilise an optimisation, which is a process of finding the
parameters of the function so that the final value of the function cannot be improved. This means that, using
optimisation methods, the optimum that gives either the lowest or the highest function value was found. Several types
of optimisation methods are known [4,6,7], but in this case the differential evolution algorithm has been used. The
differential evolution flow chart is shown in Figure 4. The optimisation process starts with the generation of NP
randomly selected vectors of dimension D. Then the following operations are performed: mutation, crossover and
selection [8].
The optimisation seeks the minimum of the criterion function, which is defined as (2.1 ) in the case where only one
parameter is sought:
2.1
When two parameters are sought, the criterion function is written by (2.2), and similarly the optimisation can be
extended to more parameters. 
2.2
In the context of the discussed issue of adding production units or additional loads, let's say that in the first case we
were only looking for a single-criteria optimisation using equation (1), and in the case of a dual-criteria optimisation
using equation (2) we were simultaneously looking for P L and P G in different nodes. In both equations, the variable p
represents penalties or penalty functions, which are designed in such a way that by including additional production or
load, we do not exceed the voltage limits.
Figure 3: Comparison of calculations and measurements for selected day
After the verification of the model, the next step was to utilise an optimisation, which is a pro-
cess of finding the parameters of the function so that the final value of the function cannot be 
improved. This means that, using optimisation methods, the optimum that gives either the low-
est or the highest function value was found. Several types of optimisation methods are known 
[4,6,7], but in this case the differential evolution algorithm has been used. The differential evo-
lution flow chart is shown in Figure 4. The optimisation process starts with the generation of 
NP randomly selected vectors of dimension D. Then the following operations are performed: 
mutation, crossover and selection [8].
The optimisation seeks the minimum of the criterion function, which is defined as (2.1) in the 
case where only one parameter is sought:
4
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
----------
carried out by calculating on an arbitrary day and at any measurement point, where the two years of measurement
data were available with ninety-six measurement samples per day at 15-minute time intervals, therefore giving over
70,000 measurement points in total. The goal of verification is to check the accuracy of the calculation of the built
model by comparing the results with measurements.
In Figure 3, a comparison for the selected day is presented, where a comparison between the measured voltage value
and the calculated voltage values in each phase can be seen. A minor asymmetry is visible in phase L1, whilst in phases
L2 and L3 correspondence with the measurements is satisfactory. Based on many selected currents and several days,
we can conclude that the built model realistically describes the voltage situation and that it can be used for the study of
potential new loads as well as new dispersed sources.
In Figure 3, on the left, it can be seen that the same P and Q values as were used for the measurements were used for
the model calculation. The graph on the right shows the voltages, where it can be seen that in the case of phases L1 and
L2 there is a relatively good match, while in phase L3 there is a smaller deviation, but this model cannot take this into
account. 
00:00 06:00 12:00 18:00
Jun 22, 2020   
-600
-400
-200
0
200
400
Q [kvar], P [kW]
P - Calc.
Q - Calc.
P - Meas.
Q - Meas.
00:00 06:00 12:00 18:00
Jun 22, 2020   
11.6
11.8
12
12.2
12.4
U [kV]
Calc.
L
1
 - Meas.
L
2
 - Meas.
L
3
 - Meas.
a) b)
Figure 3: Comparison of calculations and measurements for selected day
After the verification of the model, the next step was to utilise an optimisation, which is a process of finding the
parameters of the function so that the final value of the function cannot be improved. This means that, using
optimisation methods, the optimum that gives either the lowest or the highest function value was found. Several types
of optimisation methods are known [4,6,7], but in this case the differential evolution algorithm has been used. The
differential evolution flow chart is shown in Figure 4. The optimisation process starts with the generation of NP
randomly selected vectors of dimension D. Then the following operations are performed: mutation, crossover and
selection [8].
The optimisation seeks the minimum of the criterion function, which is defined as (2.1 ) in the case where only one
parameter is sought:
2.1
When two parameters are sought, the criterion function is written by (2.2), and similarly the optimisation can be
extended to more parameters. 
2.2
In the context of the discussed issue of adding production units or additional loads, let's say that in the first case we
were only looking for a single-criteria optimisation using equation (1), and in the case of a dual-criteria optimisation
using equation (2) we were simultaneously looking for P L and P G in different nodes. In both equations, the variable p
represents penalties or penalty functions, which are designed in such a way that by including additional production or
load, we do not exceed the voltage limits.
(2.1)
When two parameters are sought, the criterion function is written by (2.2), and similarly the 
optimisation can be extended to more parameters.
4
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
----------
carried out by calculating on an arbitrary day and at any measurement point, where the two years of measurement
data were available with ninety-six measurement samples per day at 15-minute time intervals, therefore giving over
70,000 measurement points in total. The goal of verification is to check the accuracy of the calculation of the built
model by comparing the results with measurements.
In Figure 3, a comparison for the selected day is presented, where a comparison between the measured voltage value
and the calculated voltage values in each phase can be seen. A minor asymmetry is visible in phase L1, whilst in phases
L2 and L3 correspondence with the measurements is satisfactory. Based on many selected currents and several days,
we can conclude that the built model realistically describes the voltage situation and that it can be used for the study of
potential new loads as well as new dispersed sources.
In Figure 3, on the left, it can be seen that the same P and Q values as were used for the measurements were used for
the model calculation. The graph on the right shows the voltages, where it can be seen that in the case of phases L1 and
L2 there is a relatively good match, while in phase L3 there is a smaller deviation, but this model cannot take this into
account. 
00:00 06:00 12:00 18:00
Jun 22, 2020   
-600
-400
-200
0
200
400
Q [kvar], P [kW]
P - Calc.
Q - Calc.
P - Meas.
Q - Meas.
00:00 06:00 12:00 18:00
Jun 22, 2020   
11.6
11.8
12
12.2
12.4
U [kV]
Calc.
L
1
 - Meas.
L
2
 - Meas.
L
3
 - Meas.
a) b)
Figure 3: Comparison of calculations and measurements for selected day
After the verification of the model, the next step was to utilise an optimisation, which is a process of finding the
parameters of the function so that the final value of the function cannot be improved. This means that, using
optimisation methods, the optimum that gives either the lowest or the highest function value was found. Several types
of optimisation methods are known [4,6,7], but in this case the differential evolution algorithm has been used. The
differential evolution flow chart is shown in Figure 4. The optimisation process starts with the generation of NP
randomly selected vectors of dimension D. Then the following operations are performed: mutation, crossover and
selection [8].
The optimisation seeks the minimum of the criterion function, which is defined as (2.1 ) in the case where only one
parameter is sought:
2.1
When two parameters are sought, the criterion function is written by (2.2), and similarly the optimisation can be
extended to more parameters. 
2.2
In the context of the discussed issue of adding production units or additional loads, let's say that in the first case we
were only looking for a single-criteria optimisation using equation (1), and in the case of a dual-criteria optimisation
using equation (2) we were simultaneously looking for P L and P G in different nodes. In both equations, the variable p
represents penalties or penalty functions, which are designed in such a way that by including additional production or
load, we do not exceed the voltage limits.
(2.2)

16 JET 16 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
In the context of the discussed issue of adding production units or additional loads, let’s say that 
in the first case we were only looking for a single-criteria optimisation using equation (1), and 
in the case of a dual-criteria optimisation using equation (2) we were simultaneously looking for 
P
L
 and P
G
 in different nodes. In both equations, the variable p represents penalties or penalty 
functions, which are designed in such a way that by including additional production or load, we 
do not exceed the voltage limits.
The use of differential evolution to determine maximum generation and load
values in the distribution network
5
- --- -- -- --
START
Model of distribution 
network
LOAD FLOW
Direct approach
Selection of F, CR , NP and x
p
LOAD FLOW analysis
Evaluation of fitness function
Max. Number 
of iteration 
exceeded
NO
YES
RESULT
Max. P
gen
and P
load
END
Mutation
Crossover
selection
Optimization
Figure 4: Flowchart of the proposed procedure for the optimisation of network operation
Voltage quality problems can occur in the network, meaning the voltage in the network is too low or too high. The
permissible limits between which the voltage can fluctuate are prescribed in the SIST EN 50160 standard and are usually
±10%. There are several ways to solve the problems of too low or too high voltages. One possibility is to replace long-
distance cable connections of smaller cross-sections with cables of larger cross-sections, change the network topology,
and other such changes. Although these solutions are technically easy to implement and bring an additional benefit in
terms of reduced electricity losses, they have a high investment cost. In the distribution network, voltage regulation is
also possible using OLTC (On Load Tap Changer). A medium voltage/low voltage transformer with OLTC can have 9 taps
and is able to regulate the voltage in steps of ±3%. The selected transformer can decrease or increase the voltage by a
maximum of 12% of the nominal voltage [9].
3 RESULTS
On the built and verified model, the maximum network limits for adding new elements to any node of the network can
be checked on the real network parameters.
3.1 Analysis of the current situation in the network
Figure 5 shows the analysis of non-zero load nodes. Six such nodes exist with a unique loading profile, with the largest
load being in node 27. A similar analysis is also done for the production units for the selected day in January, where out
of every thirty-five nodes, only seven are generating energy, the others being negligible. Figure 6 shows that some
production units are independent of the time of day, considered as production from small hydropower plants, while
production from solar power plants depends on the time of day.
Figure 4: Flowchart of the proposed procedure for the optimisation of network operation
Voltage quality problems can occur in the network, meaning the voltage in the network is too 
low or too high. The permissible limits between which the voltage can fluctuate are prescribed in 
the SIST EN 50160 standard and are usually ±10%. There are several ways to solve the problems 
of too low or too high voltages. One possibility is to replace long-distance cable connections of 
smaller cross-sections with cables of larger cross-sections, change the network topology, and 
other such changes. Although these solutions are technically easy to implement and bring an 
additional benefit in terms of reduced electricity losses, they have a high investment cost. In 
the distribution network, voltage regulation is also possible using OLTC (On Load Tap Changer). 
A medium voltage/low voltage transformer with OLTC can have 9 taps and is able to regulate 

JET  17
The use of differential evolution to determine maximum generation and load values in the distribution network
the voltage in steps of ±3%. The selected transformer can decrease or increase the voltage by a 
maximum of 12% of the nominal voltage [9].
3 RESULTS
On the built and verified model, the maximum network limits for adding new elements to any 
node of the network can be checked on the real network parameters.
3.1 Analysis of the current situation in the network
Figure 5 shows the analysis of non-zero load nodes. Six such nodes exist with a unique loading 
profile, with the largest load being in node 27. A similar analysis is also done for the produc-
tion units for the selected day in January, where out of every thirty-five nodes, only seven are 
generating energy, the others being negligible. Figure 6 shows that some production units are 
independent of the time of day, considered as production from small hydropower plants, while 
production from solar power plants depends on the time of day.
6
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
5
10
15
20
P
L
 [kW]
node
5
node
7
node
9
node
25
node
27
node
28
 
Figure 5: Loading profile of selected nodes for a winter day, January 5th
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
50
100
150
200
P
G
 [kW]
node
3
node
9
node
13
node
17
node
21
node
24
node
29
Figure 6: Generation profile of selected nodes for a winter day, January 5th
The analysis of voltage conditions does not change significantly over a single day in all 15-minute intervals, so the
results for a working day of the year are presented for a selected part of the day, because the values deviate the most
from the average profile. Figure 7 shows an analysis of the voltage profiles at an individual node, where either the
minimum values or the maximum values for the month are presented. The highest voltage occurs in the month of
February, while the lowest occurs in September. From this it can be concluded that for all 365 days and all ninety-six 15-
minute interval measured values each day, only those of potential concern are plotted. Based on permissible voltage
limits, it can be concluded that there are no problems with the voltage profile in the considered network. On the other
hand, the effects of additional elements in the network can be analysed and their maximum values can be estimated so
that the values are still within the prescribed limits. 
0 5 10 15 20 25 30 35 40
node
0.95
1
1.05
1.1
Nodal voltage [p.u.]
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Lower limit Upper limit
Figure 7: Voltage profile throughout the year for a worst case scenario
Figure 5: Loading profile of selected nodes for a winter day, January 5th
6
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
5
10
15
20
P
L
 [kW]
node
5
node
7
node
9
node
25
node
27
node
28
 
Figure 5: Loading profile of selected nodes for a winter day, January 5th
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
50
100
150
200
P
G
 [kW]
node
3
node
9
node
13
node
17
node
21
node
24
node
29
Figure 6: Generation profile of selected nodes for a winter day, January 5th
The analysis of voltage conditions does not change significantly over a single day in all 15-minute intervals, so the
results for a working day of the year are presented for a selected part of the day, because the values deviate the most
from the average profile. Figure 7 shows an analysis of the voltage profiles at an individual node, where either the
minimum values or the maximum values for the month are presented. The highest voltage occurs in the month of
February, while the lowest occurs in September. From this it can be concluded that for all 365 days and all ninety-six 15-
minute interval measured values each day, only those of potential concern are plotted. Based on permissible voltage
limits, it can be concluded that there are no problems with the voltage profile in the considered network. On the other
hand, the effects of additional elements in the network can be analysed and their maximum values can be estimated so
that the values are still within the prescribed limits. 
0 5 10 15 20 25 30 35 40
node
0.95
1
1.05
1.1
Nodal voltage [p.u.]
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Lower limit Upper limit
Figure 7: Voltage profile throughout the year for a worst case scenario
Figure 6: Generation profile of selected nodes for a winter day, January 5th
The analysis of voltage conditions does not change significantly over a single day in all 15-minute 
intervals, so the results for a working day of the year are presented for a selected part of the day, 
because the values deviate the most from the average profile. Figure 7 shows an analysis of the 

18 JET 18 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
voltage profiles at an individual node, where either the minimum values or the maximum values 
for the month are presented. The highest voltage occurs in the month of February, while the 
lowest occurs in September. From this it can be concluded that for all 365 days and all ninety-six 
15-minute interval measured values each day, only those of potential concern are plotted. Based 
on permissible voltage limits, it can be concluded that there are no problems with the voltage 
profile in the considered network. On the other hand, the effects of additional elements in the 
network can be analysed and their maximum values can be estimated so that the values are still 
within the prescribed limits.
6
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
5
10
15
20
P
L
 [kW]
node
5
node
7
node
9
node
25
node
27
node
28
 
Figure 5: Loading profile of selected nodes for a winter day, January 5th
2 4 6 8 10 12 14 16 18 20 22 24
time [h]
0
50
100
150
200
P
G
 [kW]
node
3
node
9
node
13
node
17
node
21
node
24
node
29
Figure 6: Generation profile of selected nodes for a winter day, January 5th
The analysis of voltage conditions does not change significantly over a single day in all 15-minute intervals, so the
results for a working day of the year are presented for a selected part of the day, because the values deviate the most
from the average profile. Figure 7 shows an analysis of the voltage profiles at an individual node, where either the
minimum values or the maximum values for the month are presented. The highest voltage occurs in the month of
February, while the lowest occurs in September. From this it can be concluded that for all 365 days and all ninety-six 15-
minute interval measured values each day, only those of potential concern are plotted. Based on permissible voltage
limits, it can be concluded that there are no problems with the voltage profile in the considered network. On the other
hand, the effects of additional elements in the network can be analysed and their maximum values can be estimated so
that the values are still within the prescribed limits. 
0 5 10 15 20 25 30 35 40
node
0.95
1
1.05
1.1
Nodal voltage [p.u.]
Jan Feb Mar Apr
May Jun Jul Aug
Sep Oct Nov Dec
Lower limit Upper limit
Figure 7: Voltage profile throughout the year for a worst case scenario Figure 7: Voltage profile throughout the year for a worst case scenario
3.2 Determination of maximum load and maximum production unit
On the left in Figure 8, the voltage distribution when additional production units are added to the 
selected node 9 is shown. For the selected day and the selected moment of the day, a relatively 
large generating unit can be added to the node and at the same time the voltage profile is kept 
within the permissible limits of +10%. When the limit is exceeded, as in the case of +50 MW, the 
voltage in a larger number of nodes is exceeded, and nodes are immune to addition depending 
on the network topology. A similar analysis is made for adding loads to the node, as shown on 
the right in Figure 8. More than 80 MW of load can be added to node 9 without worsening the 
voltage profile, but in the case of 100 MW the values exceed the permissible limits.
The use of differential evolution to determine maximum generation and load
values in the distribution network
7
----------
3.2 Determination of maximum load and maximum production unit
On the left in Figure 8, the voltage distribution when additional production units are added to the selected node 9 is
shown. For the selected day and the selected moment of the day, a relatively large generating unit can be added to the
node and at the same time the voltage profile is kept within the permissible limits of +10%. When the limit is exceeded,
as in the case of +50 MW, the voltage in a larger number of nodes is exceeded, and nodes are immune to addition
depending on the network topology. A similar analysis is made for adding loads to the node, as shown on the right in
Figure 8. More than 80 MW of load can be added to node 9 without worsening the voltage profile, but in the case of
100 MW the values exceed the permissible limits. 
0 10 20 30 40
node
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
initial +10 MW
+20 MW +30 MW
+40 MW +50 MW
Lower limit Upper limit
+P
G
 node 9
 
10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial +20 MW
+40 MW +60 MW
+80 MW +100 MW
Lower limit Upper limit
+P
L
 node 9
Figure 8: Voltage profile in all thirty-five nodes while adding generation unit into node 9 (left) and adding load (right)
10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial P
G
=+4 MW P
G
=+ 8 MW
P
G
=+12 MW P
G
=+16 MW Lower limit
Upper limit
+P
G
 node 28
0 10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial P
L
 =+10 MW P
L
 =+20 MW
P
L
 =+30 MW Lower limit Upper limit
+P
L
 node 28
Figure 9: Voltage profile in all thirty-five nodes while adding generation unit into node 28 (left) and adding load (right)
A similar analysis can be performed for any node, as presented for the example of node 28 in Figure 9. The graph on the
left shows that adding generating units again raises the voltage, and the limit is exceeded for the added 16 MW. It can
also be observed that when adding loads, the voltage decreases, as shown in the graph on the right, where the limit is
exceeded at an added load of 30 MW. In the rest of the article, the simultaneous addition of loads and generators is
presented, but before that, an annual analysis of the situation in the network is presented.
As presented so far, changes to both loads and production are conducted manually, and only for the selected moment
of the selected day. If the goal is to give a definitive answer about the maximum values of additional elements, it is
necessary to perform a substantial number of calculations. It is simpler to use the optimisation algorithm from Figure 4,
where calculations can be performed arbitrarily for each non-balance node.
On the left in Figure 10, the calculation of the maximum unit production for nodes 2 to 36 for both summer and winter
days is shown. On the right-hand side, the calculation of the maximum load for nodes is shown. The calculation of the
maximum production or load is calculated so that the voltage remains within the permissible limits. Since the network
is radial, larger unit productions can be included at the beginning of the lines, and the closer we get to the nodes at the
end of the lines, the smaller the calculated maximum unit production size is. The optimisation process is similar to the
graphs in Figures 8 and 9, except that in a maximum of 50 iterations the result converges to the satisfactory value.
Figure 8: Voltage profile in all thirty-five nodes while adding generation unit into node 9 (left) 
and adding load (right)

JET  19
The use of differential evolution to determine maximum generation and load values in the distribution network
The use of differential evolution to determine maximum generation and load
values in the distribution network
7
----------
3.2 Determination of maximum load and maximum production unit
On the left in Figure 8, the voltage distribution when additional production units are added to the selected node 9 is
shown. For the selected day and the selected moment of the day, a relatively large generating unit can be added to the
node and at the same time the voltage profile is kept within the permissible limits of +10%. When the limit is exceeded,
as in the case of +50 MW, the voltage in a larger number of nodes is exceeded, and nodes are immune to addition
depending on the network topology. A similar analysis is made for adding loads to the node, as shown on the right in
Figure 8. More than 80 MW of load can be added to node 9 without worsening the voltage profile, but in the case of
100 MW the values exceed the permissible limits. 
0 10 20 30 40
node
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
initial +10 MW
+20 MW +30 MW
+40 MW +50 MW
Lower limit Upper limit
+P
G
 node 9
 
10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial +20 MW
+40 MW +60 MW
+80 MW +100 MW
Lower limit Upper limit
+P
L
 node 9
Figure 8: Voltage profile in all thirty-five nodes while adding generation unit into node 9 (left) and adding load (right)
10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial P
G
=+4 MW P
G
=+ 8 MW
P
G
=+12 MW P
G
=+16 MW Lower limit
Upper limit
+P
G
 node 28
0 10 20 30 40
node
0.9
1
1.1
U [p.u.]
initial P
L
 =+10 MW P
L
 =+20 MW
P
L
 =+30 MW Lower limit Upper limit
+P
L
 node 28
Figure 9: Voltage profile in all thirty-five nodes while adding generation unit into node 28 (left) and adding load (right)
A similar analysis can be performed for any node, as presented for the example of node 28 in Figure 9. The graph on the
left shows that adding generating units again raises the voltage, and the limit is exceeded for the added 16 MW. It can
also be observed that when adding loads, the voltage decreases, as shown in the graph on the right, where the limit is
exceeded at an added load of 30 MW. In the rest of the article, the simultaneous addition of loads and generators is
presented, but before that, an annual analysis of the situation in the network is presented.
As presented so far, changes to both loads and production are conducted manually, and only for the selected moment
of the selected day. If the goal is to give a definitive answer about the maximum values of additional elements, it is
necessary to perform a substantial number of calculations. It is simpler to use the optimisation algorithm from Figure 4,
where calculations can be performed arbitrarily for each non-balance node.
On the left in Figure 10, the calculation of the maximum unit production for nodes 2 to 36 for both summer and winter
days is shown. On the right-hand side, the calculation of the maximum load for nodes is shown. The calculation of the
maximum production or load is calculated so that the voltage remains within the permissible limits. Since the network
is radial, larger unit productions can be included at the beginning of the lines, and the closer we get to the nodes at the
end of the lines, the smaller the calculated maximum unit production size is. The optimisation process is similar to the
graphs in Figures 8 and 9, except that in a maximum of 50 iterations the result converges to the satisfactory value.
Figure 9: Voltage profile in all thirty-five nodes while adding generation unit into node 28 (left) 
and adding load (right)
A similar analysis can be performed for any node, as presented for the example of node 28 in 
Figure 9. The graph on the left shows that adding generating units again raises the voltage, and 
the limit is exceeded for the added 16 MW. It can also be observed that when adding loads, the 
voltage decreases, as shown in the graph on the right, where the limit is exceeded at an added 
load of 30 MW. In the rest of the article, the simultaneous addition of loads and generators is 
presented, but before that, an annual analysis of the situation in the network is presented.
As presented so far, changes to both loads and production are conducted manually, and only 
for the selected moment of the selected day. If the goal is to give a definitive answer about the 
maximum values of additional elements, it is necessary to perform a substantial number of cal-
culations. It is simpler to use the optimisation algorithm from Figure 4, where calculations can be 
performed arbitrarily for each non-balance node.
On the left in Figure 10, the calculation of the maximum unit production for nodes 2 to 36 for 
both summer and winter days is shown. On the right-hand side, the calculation of the maximum 
load for nodes is shown. The calculation of the maximum production or load is calculated so that 
the voltage remains within the permissible limits. Since the network is radial, larger unit pro-
ductions can be included at the beginning of the lines, and the closer we get to the nodes at the 
end of the lines, the smaller the calculated maximum unit production size is. The optimisation 
process is similar to the graphs in Figures 8 and 9, except that in a maximum of 50 iterations the 
result converges to the satisfactory value.
8
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
0 10 20 30
node
0
50
100
150
200
250
P
G
 [MW] 
Summer
Winter
0 10 20 30
node
0
50
100
150
200
250
300
350
P
L
 [MW] 
Summer
Winter
Figure 10: Values of P G and P L for nodes 2 to 36 over two seasons
However, we can conclude that the values calculated in the latter analysis are not necessarily final if the described OLTC
device is installed in the network. The continuation presents an analysis of what can happen in the network when a
production unit is connected to the network, which, due to its operation, causes the voltage to rise above the permitted
l i m i t . A s m a ny a s t w o p ro duc tio n un it s i n no des 21 an d 22 ar e inc lu de d in t he n et w ork . Figure 11 displays the
topography of the network, on which the location of the OLTC is visible (node 16, in red) and the nodes in which
additional production units are added are marked with P gen, node 21 and 22.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
P
gen
P
gen
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Figure 11: Topology of considered radial distribution network with marked node with OLTC and nodes of additional
generation units
Figure 12a shows the additional production unit for node 21 over time. A 20 MW generating unit is connected to the
grid, which operates at a constant power throughout the day, and at 11:00 a 20 MW generating unit is added to it.
Figure 12b shows the same for node 22, except that the additional generating unit is connected later.
Node 21
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
P
generation
 [MW] 
Node 22
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
50
P
generation
 [MW] 
a) b)
Figure 12: Change adding production unit to two nodes after OLTC operation
Figure 10: Values of P
G
 and P
L
 for nodes 2 to 36 over two seasons

20 JET 20 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
However, we can conclude that the values calculated in the latter analysis are not necessarily fi-
nal if the described OLTC device is installed in the network. The continuation presents an analysis 
of what can happen in the network when a production unit is connected to the network, which, 
due to its operation, causes the voltage to rise above the permitted limit. As many as two produc-
tion units in nodes 21 and 22 are included in the network. Figure 11 displays the topography of 
the network, on which the location of the OLTC is visible (node 16, in red) and the nodes in which 
additional production units are added are marked with P
gen
, node 21 and 22.
8
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
0 10 20 30
node
0
50
100
150
200
250
P
G
 [MW] 
Summer
Winter
0 10 20 30
node
0
50
100
150
200
250
300
350
P
L
 [MW] 
Summer
Winter
Figure 10: Values of P G and P
L
 for nodes 2 to 36 over two seasons
However, we can conclude that the values calculated in the latter analysis are not necessarily final if the described OLTC
device is installed in the network. The continuation presents an analysis of what can happen in the network when a
production unit is connected to the network, which, due to its operation, causes the voltage to rise above the permitted
lim it . As m a ny a s t w o p ro duc tio n un i t s i n no des 21 a n d 22 a r e i nc lu de d in t he n et w ork . Figure 11 displays the
topography of the network, on which the location of the OLTC is visible (node 16, in red) and the nodes in which
additional production units are added are marked with P gen
, node 21 and 22.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
P
gen
P
gen
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Figure 11: Topology of considered radial distribution network with marked node with OLTC and nodes of additional
generation units
Figure 12a shows the additional production unit for node 21 over time. A 20 MW generating unit is connected to the
grid, which operates at a constant power throughout the day, and at 11:00 a 20 MW generating unit is added to it.
Figure 12b shows the same for node 22, except that the additional generating unit is connected later.
Node 21
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
P
generation
 [MW] 
Node 22
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
50
P
generation
 [MW] 
a) b)
Figure 12: Change adding production unit to two nodes after OLTC operation
Figure 11: Topology of considered radial distribution network with marked node with OLTC and 
nodes of additional generation units
Figure 12a shows the additional production unit for node 21 over time. A 20 MW generating unit 
is connected to the grid, which operates at a constant power throughout the day, and at 11:00 
a 20 MW generating unit is added to it. Figure 12b shows the same for node 22, except that the 
additional generating unit is connected later.
8
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
- --- -- -- --
0 10 20 30
node
0
50
100
150
200
250
P
G
 [MW] 
Summer
Winter
0 10 20 30
node
0
50
100
150
200
250
300
350
P
L
 [MW] 
Summer
Winter
Figure 10: Values of P G and P L for nodes 2 to 36 over two seasons
However, we can conclude that the values calculated in the latter analysis are not necessarily final if the described OLTC
device is installed in the network. The continuation presents an analysis of what can happen in the network when a
production unit is connected to the network, which, due to its operation, causes the voltage to rise above the permitted
lim it . As m a ny a s t w o p r o duc tio n un it s i n no des 21 an d 22 ar e inc lu de d in t he n et w or k . Figure 11 displays the
topography of the network, on which the location of the OLTC is visible (node 16, in red) and the nodes in which
additional production units are added are marked with P gen, node 21 and 22.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
P
gen
P
gen
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Figure 11: Topology of considered radial distribution network with marked node with OLTC and nodes of additional
generation units
Figure 12a shows the additional production unit for node 21 over time. A 20 MW generating unit is connected to the
grid, which operates at a constant power throughout the day, and at 11:00 a 20 MW generating unit is added to it.
Figure 12b shows the same for node 22, except that the additional generating unit is connected later.
Node 21
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
P
generation
 [MW] 
Node 22
Jun 22, 00:00 Jun 22, 12:00 Jun 23, 00:00
2020   
0
10
20
30
40
50
P
generation
 [MW] 
a) b)
Figure 12: Change adding production unit to two nodes after OLTC operation
Figure 12: Change adding production unit to two nodes after OLTC operation
Figure 13a presents the voltage conditions before and after the operation of the OLTC. The volt-
age before the activation of the OLTC has already exceeded the permissible limits, and since we 
turn on the additional generation in nodes 21 and 22 at 00:00, the OLTC level changes at the first 
moment of the day. This lowers the voltage so that it is within acceptable limits. Then, the OLTC 
rate remains the same, even though we include an additional 20 MW generating unit in node 21 
at 11:00. The OLTC rate increases only when an additional generating unit is connected to the 
grid at node 22 at 14:45, as shown in Figure 13b.

JET  21
The use of differential evolution to determine maximum generation and load values in the distribution network
The use of differential evolution to determine maximum generation and load
values in the distribution network
9
----------
Figure 13a p r e s e n t s t h e v o l t a g e c o n d i ti o n s b e f o r e a n d a ft e r t h e o p e r a ti o n o f t h e O L T C . T h e v o l t a g e b e f o r e t h e
activation of the OLTC has already exceeded the permissible limits, and since we turn on the additional generation in
nodes 21 and 22 at 00:00, the OLTC level changes at the first moment of the day. This lowers the voltage so that it is
within acceptable limits. Then, the OLTC rate remains the same, even though we include an additional 20 MW
generating unit in node 21 at 11:00. The OLTC rate increases only when an additional generating unit is connected to
the grid at node 22 at 14:45, as shown in Figure 13b.
00:00 06:00 12:00 18:00 00:00
Node Jun 22, 2020   
1
1.2
1.4
Nodal voltage [p.u.]
before
after
00:00 06:00 12:00 18:00 00:00
Jun 22, 2020   
-4
-2
0
2
4
Tap position
a)
b)
Figure 13: Voltage before and after the application of the OLTC and display of the degree of OLTC taps for the selected
case over time
From the latter analysis, it is clear that optimisation algorithms can be used to check the network's limitations, which,
however, are not final, but can also be changed by adding dynamic elements such as OLTC.
3.3 Simultaneous addition of load and production units
A particularly interesting analysis is the simultaneous addition of load and production units to different nodes, where
one raises and the other lowers the voltage in the node. It is also necessary to realise that there are as many as ninety-
six different moments in time available for all 365 days of the year, which, with all the possible combinations of the
thirty-five nodes, results in an complex multitude of variants. Figure 14 shows two examples where both combinations
on the two selected nodes, 9 and 28, were made, as in the analysis above. In the graph on the left, node 9 is the
additional production unit and node 28 is the additional load, while the graph on the right it is the opposite. In the
example on the left, calculation started at the previous limits, i.e. in node 9 P G = +40 MW and P L = +30 MW, it is
noticeable that in the case of the simultaneous addition of both elements, the limit power of both units changes
disproportionately, namely the maximum production in node 9 changes to a value of 105 MW and the maximum load in
node 28 to 50 MW.
0 10 20 30 40
node
0.9
1
1.1
U [p.u.]
P
G
 40MW, P
L
 30MW
P
G
 80MW, P
L
 40MW
P
G
 105MW, P
L
 50MW
Lower limit
Upper limit
P
G
 node 9
P
L
 node 28
10 20 30 40
node
0.9
1
1.1
U [p.u.]
P
G
=100 MW, P
L
=16 MW
P
G
=120 MW, P
L
=45 MW
P
G
=110 MW, P
L
=30 MW
P
G
=130 MW, P
L
=65 MW
Lower limit
Upper limit
P
L
 node 9
P
G
 node 28
Figure 14: Voltage profile in all thirty-five nodes while adding a generation unit into node 28 (left) and adding load
(right)
Figure 13: Voltage before and after the application of the OLTC and display of the degree of 
OLTC taps for the selected case over time
From the latter analysis, it is clear that optimisation algorithms can be used to check the net-
work’s limitations, which, however, are not final, but can also be changed by adding dynamic 
elements such as OLTC.
3.3 Simultaneous addition of load and production units
A particularly interesting analysis is the simultaneous addition of load and production units to 
different nodes, where one raises and the other lowers the voltage in the node. It is also neces-
sary to realise that there are as many as ninety-six different moments in time available for all 365 
days of the year, which, with all the possible combinations of the thirty-five nodes, results in an 
complex multitude of variants. Figure 14 shows two examples where both combinations on the 
two selected nodes, 9 and 28, were made, as in the analysis above. In the graph on the left, node 
9 is the additional production unit and node 28 is the additional load, while the graph on the right 
it is the opposite. In the example on the left, calculation started at the previous limits, i.e. in node 
9 P
G
 = +40 MW and P
L
 = +30 MW, it is noticeable that in the case of the simultaneous addition of 
both elements, the limit power of both units changes disproportionately, namely the maximum 
production in node 9 changes to a value of 105 MW and the maximum load in node 28 to 50 MW.
The use of differential evolution to determine maximum generation and load
values in the distribution network
9
----------
Figure 13a p r e s e n t s t h e v o l t a g e c o n d i ti o n s b e f o r e a n d a ft e r t h e o p e r a ti o n o f t h e O L T C . T h e v o l t a g e b e f o r e t h e
activation of the OLTC has already exceeded the permissible limits, and since we turn on the additional generation in
nodes 21 and 22 at 00:00, the OLTC level changes at the first moment of the day. This lowers the voltage so that it is
within acceptable limits. Then, the OLTC rate remains the same, even though we include an additional 20 MW
generating unit in node 21 at 11:00. The OLTC rate increases only when an additional generating unit is connected to
the grid at node 22 at 14:45, as shown in Figure 13b.
00:00 06:00 12:00 18:00 00:00
Node Jun 22, 2020   
1
1.2
1.4
Nodal voltage [p.u.]
before
after
00:00 06:00 12:00 18:00 00:00
Jun 22, 2020   
-4
-2
0
2
4
Tap position
a)
b)
Figure 13: Voltage before and after the application of the OLTC and display of the degree of OLTC taps for the selected
case over time
From the latter analysis, it is clear that optimisation algorithms can be used to check the network's limitations, which,
however, are not final, but can also be changed by adding dynamic elements such as OLTC.
3.3 Simultaneous addition of load and production units
A particularly interesting analysis is the simultaneous addition of load and production units to different nodes, where
one raises and the other lowers the voltage in the node. It is also necessary to realise that there are as many as ninety-
six different moments in time available for all 365 days of the year, which, with all the possible combinations of the
thirty-five nodes, results in an complex multitude of variants. Figure 14 shows two examples where both combinations
on the two selected nodes, 9 and 28, were made, as in the analysis above. In the graph on the left, node 9 is the
additional production unit and node 28 is the additional load, while the graph on the right it is the opposite. In the
example on the left, calculation started at the previous limits, i.e. in node 9 P G = +40 MW and P L = +30 MW, it is
noticeable that in the case of the simultaneous addition of both elements, the limit power of both units changes
disproportionately, namely the maximum production in node 9 changes to a value of 105 MW and the maximum load in
node 28 to 50 MW.
0 10 20 30 40
node
0.9
1
1.1
U [p.u.]
P
G
 40MW, P
L
 30MW
P
G
 80MW, P
L
 40MW
P
G
 105MW, P
L
 50MW
Lower limit
Upper limit
P
G
 node 9
P
L
 node 28
10 20 30 40
node
0.9
1
1.1
U [p.u.]
P
G
=100 MW, P
L
=16 MW
P
G
=120 MW, P
L
=45 MW
P
G
=110 MW, P
L
=30 MW
P
G
=130 MW, P
L
=65 MW
Lower limit
Upper limit
P
L
 node 9
P
G
 node 28
Figure 14: Voltage profile in all thirty-five nodes while adding a generation unit into node 28 (left) and adding load
(right)
Figure 14: Voltage profile in all thirty-five nodes while adding a generation unit into node 28 
(left) and adding load (right)

22 JET 22 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
The graph on the right shows the opposite, as this time node 9 has a load imposed and node 28 a 
unit of production. The analysis shows that the previous limit values, such as for the case of inde-
pendent analyses, namely P
G-28node 
= 100 MW and P
L-9node
 = 15 MW, do not cause problems. When 
both values are increased, they tentatively stop at 130 MW for node 28, and 65 MW for node 9.
Such a manual analysis is not suitable, since the changes are contradictory and non-linear, so 
the use of optimisation algorithms makes sense. In addition, an exact value of the limits is also 
achieved, which can be changed at will, but in this case they are set to ±10%.
The result of employing the optimisation algorithm to the problems mentioned are displayed in 
Figure 15. The graph on the left shows the voltage distribution for all nodes where the two target 
nodes for adding additional units are selected; a production unit is added to node 35, while a 
load is added to node 25. In the graph on the left, only one in five of the thirty-five optimisation 
iterations are shown, so that it is easy to see how, when adding the two additional elements, 
the voltage values increasingly converge towards the limit values. This means that when adding 
loads, the voltages at certain nodes approach the lower limit of 90% of the nominal value (nodes 
8, 11, 15, 19 and 20), and when adding an additional generating unit to node 35, only at this node 
the voltage rises to the extreme values of 110% of the nominal value. The graph in the upper 
right shows how the search values change, and the graph below shows the convergence of the 
optimisation algorithm. It can be seen that the chosen number of iterations is thirty-five, and it 
proves to be sufficient, as the estimated error is less than 1% and the results are also satisfactory. 
Depending on the selected location of additional elements in the network, a production unit in 
node 35, size P
G-35
 = 28.68 MW, and an additional load in node 25, size P
L-25
 = 7.17 MW, can be 
connected to the network for the selected day and time.
10
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
----------
The graph on the right shows the opposite, as this time node 9 has a load imposed and node 28 a unit of production.
The analysis shows that the previous limit values, such as for the case of independent analyses, namely P G-28node
= 100 MW and P L-9node = 15 MW, do not cause problems. When both values are increased, they tentatively stop at 130
MW for node 28, and 65 MW for node 9.
Such a manual analysis is not suitable, since the changes are contradictory and non-linear, so the use of optimisation
algorithms makes sense. In addition, an exact value of the limits is also achieved, which can be changed at will, but in
this case they are set to ±10%.
The result of employing the optimisation algorithm to the problems mentioned are displayed in Figure 15. The graph on
the left shows the voltage distribution for all nodes where the two target nodes for adding additional units are selected;
a production unit is added to node 35, while a load is added to node 25. In the graph on the left, only one in five of the
thirty-five optimisation iterations are shown, so that it is easy to see how, when adding the two additional elements,
the voltage values increasingly converge towards the limit values. This means that when adding loads, the voltages at
certain nodes approach the lower limit of 90% of the nominal value (nodes 8, 11, 15, 19 and 20), and when adding an
additional generating unit to node 35, only at this node the voltage rises to the extreme values of 110% of the nominal
value. The graph in the upper right shows how the search values change, and the graph below shows the convergence
of the optimisation algorithm. It can be seen that the chosen number of iterations is thirty-five, and it proves to be
sufficient, as the estimated error is less than 1% and the results are also satisfactory. Depending on the selected
location of additional elements in the network, a production unit in node 35, size P G-35 = 28.68 MW, and an additional
load in node 25, size P L-25 = 7.17 MW, can be connected to the network for the selected day and time.
0 10 20 30 40
N
iteration
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
max value
min value
final - optymal
profile
initial profile
 
0 5 10 15 20 25 30 35
0
20
40
P [MW]
P
G
-node 35 P
L
-node 25
0 5 10 15 20 25 30 35
N
iter.
0.05
0.1
Criteria fun 
X 35
Y 28. 6805
X 35
Y 7. 17854
Figure 15: Voltage profile in all thirty-five nodes while adding a generation unit into node 35 (left) and adding load to
node 25, optimisation evolution on the right 
0 10 20 30 40
N
iteration
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
minvalue
max value
initial profile
final-optimal profile
0 5 10 15 20 25 30 35
0
20
40
P [MW]
P
G
-node 25 P
L
-node 35
0 5 10 15 20 25 30 35
N
iter.
0.05
0.1
Criteria fun.
X 35
Y 13. 4339
X 35
Y 16. 0926
Figure 15: Voltage profile in all thirty-five nodes while adding a generation unit into node 35 
(left) and adding load to node 25, optimisation evolution on the right

JET  23
The use of differential evolution to determine maximum generation and load values in the distribution network
10
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer Gorazd Štumberger, Miloš
Beković
JET Vol. 15 (2022)
Issue 3
----------
The graph on the right shows the opposite, as this time node 9 has a load imposed and node 28 a unit of production.
The analysis shows that the previous limit values, such as for the case of independent analyses, namely P G-28node
= 100 MW and P L-9node = 15 MW, do not cause problems. When both values are increased, they tentatively stop at 130
MW for node 28, and 65 MW for node 9.
Such a manual analysis is not suitable, since the changes are contradictory and non-linear, so the use of optimisation
algorithms makes sense. In addition, an exact value of the limits is also achieved, which can be changed at will, but in
this case they are set to ±10%.
The result of employing the optimisation algorithm to the problems mentioned are displayed in Figure 15. The graph on
the left shows the voltage distribution for all nodes where the two target nodes for adding additional units are selected;
a production unit is added to node 35, while a load is added to node 25. In the graph on the left, only one in five of the
thirty-five optimisation iterations are shown, so that it is easy to see how, when adding the two additional elements,
the voltage values increasingly converge towards the limit values. This means that when adding loads, the voltages at
certain nodes approach the lower limit of 90% of the nominal value (nodes 8, 11, 15, 19 and 20), and when adding an
additional generating unit to node 35, only at this node the voltage rises to the extreme values of 110% of the nominal
value. The graph in the upper right shows how the search values change, and the graph below shows the convergence
of the optimisation algorithm. It can be seen that the chosen number of iterations is thirty-five, and it proves to be
sufficient, as the estimated error is less than 1% and the results are also satisfactory. Depending on the selected
location of additional elements in the network, a production unit in node 35, size P G-35 = 28.68 MW, and an additional
load in node 25, size P L-25 = 7.17 MW, can be connected to the network for the selected day and time.
0 10 20 30 40
N
iteration
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
max value
min value
final - optymal
profile
initial profile
 
0 5 10 15 20 25 30 35
0
20
40
P [MW]
P
G
-node 35 P
L
-node 25
0 5 10 15 20 25 30 35
N
iter.
0.05
0.1
Criteria fun 
X 35
Y 28. 6805
X 35
Y 7. 17854
Figure 15: Voltage profile in all thirty-five nodes while adding a generation unit into node 35 (left) and adding load to
node 25, optimisation evolution on the right 
0 10 20 30 40
N
iteration
0.85
0.9
0.95
1
1.05
1.1
U [p.u.]
minvalue
max value
initial profile
final-optimal profile
0 5 10 15 20 25 30 35
0
20
40
P [MW]
P
G
-node 25 P
L
-node 35
0 5 10 15 20 25 30 35
N
iter.
0.05
0.1
Criteria fun.
X 35
Y 13. 4339
X 35
Y 16. 0926
Figure 16: Voltage profile in all thirty-five nodes while adding a generation unit into node 28 
(left) and adding load (right)
Due to the large number of possible combinations, only one further example is presented, where 
the two mentioned nodes switched types; so now there is additional load at node 25 and addition-
al production at node 35. The result of the analysis is presented in Figure 16, where the change in 
the voltage distribution in twenty-five iterations can be seen on the left. This time, some nodes in 
front of the load node increase in voltage (compared to the results in Figure 14), and similarly, the 
voltage decreases in the last node where we add production, which is the opposite of the case 
in Figure 14. In the last iteration, when a satisfactory convergence has already been achieved, 
we can evaluate both values and conclude that in this case an additional production unit, size 
P
G-25
 = 13.43 MW, can be added to node 25, and an additional load to node 35, namely 
P
L-35
 = 16.09 MW
4 CONCLUSIONS
An inaccurate and inconsistent assessment regarding the possibility of connecting new elements 
in the distribution network can have a discriminatory effect on an individual, as their request to 
connect a new device may be rejected or permitted to a lesser extent than desired. This article 
presents an integrated approach to network analysis, which is carried out on a real example and 
verified with real measurements. The treated network already has a few production units as 
well as larger loads, both of which may increase in the future for objective reasons. The article 
presents the construction of a model for calculating voltage conditions in the network using 
standard methods. Verification of the model for any moment in the year is also carried out, so 
that different scenarios of additional elements in the network can be explored by means of sim-
ulation. By random testing and using an unsystematic approach, time-consuming procedures can 
be replaced by a comprehensive approach, including the use of an optimisation algorithm. The 
method of differential evolution was used, which finds the maximum value of the search variable 
for each node at every moment in the year, for either an additional load or an additional unit of 
production. An upgrade to this is to extend the operation of the network with an OLTC device, 
which can further improve the voltage profile within the intended limits. Finally, a dual-criteria 
optimisation is presented, where we simultaneously include both opposing elements in the net-
work, but where, due to nonlinearity and complexity, it is difficult to find the local extrema of the 
desired function. In the future work, it is possible to upgrade the model to more simultaneous 
search criteria or to use it as a model example of the entire approach.

24 JET 24 JET
Eva Tratnik, Janez Ribič, Matej Pintarič, Miran Rošer, Gorazd Štumberger, Miloš Beković JET Vol. 15 (2022)
Issue 3
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