Application of PandaPower Tool in Evaluating the Potential of Using PV Distributed Generation

for Voltage Regulation in Electrical Power Networks

N. Bogunović*, S. Vlahinić**, D. Franković** and V. Komen* * HEP Distribution System Operator, Elektroprimorje Rijeka, Rijeka, Croatia

** University of Rijeka, Faculty of Engineering, Rijeka, Croatia nikola.bogunovic@hep.hr, sasa.vlahinic@riteh.hr, dubravko.frankovic@riteh.hr, vitomir.komen@hep.hr

Abstract - Traditional electrical power systems were designed with an assumption of unidirectional power flows through electrical networks. For many years power plants had been the only sources of electrical energy, and the energy had been delivered to the consumers by the means of transmission and distribution networks exclusively.

With the emergence of distributed generation units, power flows have become bidirectional, which has made it impossible to estimate the voltages and currents in substation feeder nodes by measuring only the values at the beginning of the feeder. As the aforementioned estimation process is the basis of traditional voltage regulation techniques, it is obvious that under the new circumstances existing methods have to be upgraded.

The article demonstrates how the open source tool PandaPower along with the Python programming language was utilized to analyze and evaluate several different scenarios of using photovoltaic distributed sources inverters for voltage regulation in low voltage electrical power networks.

Keywords – PandaPower; voltage regulation; voltage stability; photovoltaic; distributed generation

I. INTRODUCTION The emergence of distributed generation units has

transformed the traditional electrical power distribution networks from passive to active. Power flows through the networks have become bidirectional, which has added more complexity to the process of bus voltage estimation. Since the aforementioned estimation process is the basis for traditional voltage regulation techniques, it is obvious that, under the new circumstances, these techniques have to be upgraded.

As the inverters used in photovoltaic (PV) distributed generation (DG) units are designed to operate with different power factors, they can be utilized to support voltage regulation in the networks [1].

The aim of this article is to analyze the influence of reactive power injected by DG units on voltage stability in

a typical Croatian low voltage (LV) electrical distribution network.

The analysis was performed with the PandaPower package for the Python programming language, since it is a scriptable electrical power networks calculation tool.

II. VOLTAGE REGULATION IN ELECTRICAL POWER NETWORKS

A. Voltage Drop on LV Distribution Lines Typical low voltage electrical distribution line can be

approximated with a series connection of resistance R and reactance X, as it is shown in Figure 1.

The voltage difference Δ�̅� along the line can be expressed as

Δ�̅� = �̅�1 − �̅�2 = 𝐼�̅� + 𝑗𝐼�̅�, (1)

where 𝐼 ̅is the current flowing through the line and �̅�1 and �̅�2 are the voltages at the beginning and the end of the line respectively.

Equation (1) can be transformed to take the active power 𝑃1 and reactive power 𝑄1 transferred by the line into account:

Δ�̅� =𝑃1𝑅 + 𝑄1𝑋

𝑉1+ 𝑗

𝑃1𝑋 − 𝑄1𝑅

𝑉1. (2)

Since the 𝑅 / 𝑋 ratio in LV distribution networks is relatively high (usually above 10) [1], the imaginary part of (2) is usually neglected. Therefore, the approximate equation for voltage drop along the LV line can be stated as:

Δ𝑉 ≈𝑃1𝑅 + 𝑄1𝑋

𝑉1. (3)

V1 V2

I R X

Figure 1. Low voltage distribution line model

MIPRO 2020/CTS 1135

As the higher voltage drops are correlated to the higher power losses in distribution networks, it is desirable to keep the voltage drops as low as possible, and that is where the voltage regulation comes in place.

From (3), it is easily observed that the voltage drop can be reduced in three ways: by using conductors with lower impedance levels, by raising the voltage at the beginning of the line, or by reducing the reactive power flow. Active power flows are usually dictated by consumers’ demand and they are in general not easy to control.

The aim of voltage regulation is to keep the voltages in all nodes of a network as close as possible to the nominal voltage of a feeder, thus reducing the overall power losses of the network.

B. Traditional Voltage Regulation Techniques Traditional voltage regulation techniques were

designed with an assumption of unidirectional power flows (i.e. from power plants to consumers) in electrical networks. In such networks it is relatively easy to estimate the voltages and currents in all nodes on a feeder by measuring the values at its beginning. As the loads in distribution networks are mainly inductive, the voltage drops along a feeder and reaches the lowest value at its end.

In medium voltage (MV) distribution networks, voltage is commonly regulated by installing transformers with automatic tap changers in HV/MV and MV/MV substations. The tap changer keeps the voltage on the secondary coil of a transformer high enough to compensate for voltage drops in a feeder, i.e. to keep all the voltages along the feeder within allowable tolerances.

Similar technique is used in LV distribution networks, with the difference that the tap changers are usually manual, so they will have to be switched by the operator once the conditions on a feeder change.

Along with regulation transformers, shunt capacitor banks for reactive power compensation are usually installed in substations and in industrial plants.

C. Distributed Generation as a Voltage Stability Support With the emergence of DG units, power flows have

become bidirectional, and under that circumstances traditional voltage regulation techniques have to be upgraded.

The most common DG type connected to LV networks in Croatia is photovoltaic (PV) generation, which makes almost 86% of total DG installed power [2]. As the PV

inverters can easily operate with different power factors, they can be used to support voltage stability by either injecting (if the voltage is too low) or absorbing (if the voltage is too high) the reactive power from a connection point in LV network [3].

Maximum amount of reactive power 𝑄𝐺,𝑀𝐴𝑋(𝑡) that the PV inverter can produce at certain moment 𝑡 is limited by its rated apparent power 𝑆𝐼𝑁𝑉 and the active power 𝑃𝐺(𝑡) generated at the same moment [4]:

𝑄𝐺,𝑀𝐴𝑋(𝑡) = √𝑆𝐼𝑁𝑉2 − 𝑃𝐺

2(𝑡). (4)

Furthermore, the produced reactive power level is usually limited by country specific regulations, i.e. the Distribution Network Grid Code. In Croatia, all grid-connected generation units must support the operation with a power factor from 0.9 to unity [5]. That requirement leads to the following maximal reactive power injection amount:

𝑄𝑅,𝑀𝐴𝑋(𝑡) ≈ 0.484 ⋅ 𝑃𝐺(𝑡). (5)

Therefore, the maximum theoretical amount of reactive power that can be produced by PV generation unit inverter is given by [6]:

𝑄𝑀𝐴𝑋(𝑡) = min[𝑄𝐺,𝑀𝐴𝑋(𝑡), 𝑄𝑅,𝑀𝐴𝑋(𝑡)]. (6)

The limiting values defined by (4) and (5) are shown in Figure 2 [6].

D. PV Inverter Reactive Power Control Approaches There are different approaches to controlling the

amount of reactive power produced by PV inverters. Some of the most common are [7,4]:

1. Reactive Power Management (RPM)

2. Power Loss Minimization (PLM)

3. Voltage Rise Minimization (VRM)

4. Power Curtailment Strategy (PCS)

In this article the RPM strategy is analyzed, since it does not require any communication infrastructure for transferring measurement data from network nodes to a centralized controller.

Basically, the RPM strategy is based upon a predefined relation between PV inverter power factor and LV bus voltage, which is stored in the PV inverter controller. The

Figure 2. PV inverter reactive power generation limits

Figure 3. Typical reactive power control characteristic [8]

P

Q

QG,MAX

QR,MAX

PG

SINV

1136 MIPRO 2020/CTS

inverter controller sets the required power factor according to the voltage measurements at the DG point of connection, and the inverter produces the reactive power which supports the voltage stability [7,4].

A typical RPM 𝑄(𝑉) relation shape used for small PV distributed generation units is shown in Figure 3.

E. Test Cases Comparison Methodology It is usually not possible to minimize voltage drops and

power losses at the same time [7]. Therefore, a modified maximum voltage deviation and loss reduction index introduced in [9] was used to compare different test cases and scenarios.

Maximum voltage deviation of a network with 𝑁𝑛 nodes can be calculated from the equation:

Δ𝑉𝐷 = max [|𝑉𝑘 − 𝑉1|

𝑉1

] , 𝑘 = 1 … 𝑁𝑛 . (7)

The total power loss of a network with 𝑁𝑏 branches is given by:

𝑃𝐿 = ∑ 𝑃𝐿,𝑖

𝑁𝑏

𝑖=1

, (8)

where 𝑃𝐿,𝑖 is the power loss of branch 𝑖.

If 𝑃𝐿0 denotes the total power loss prior to making changes in a network (e.g. by adding DG units or injecting reactive power), and 𝑃𝐿𝐶 denotes the total power loss after

the specific change in the network is applied, then the loss reduction index can be calculated as follows:

Δ𝑃𝐿𝑅 =𝑃𝐿𝐶 − 𝑃𝐿0

𝑃𝐿0. (9)

The total index for test case evaluation is calculated as a summation of (7) and (9):

𝐹 = Δ𝑉𝐷 + Δ𝑃𝐿𝑅. (10)

The lower value of 𝐹 indicates the lower voltage deviation and the lower total power loss, with a theoretical minimal value of -1.

III. DESCRIPTION OF THE MODEL CONSIDERED

A. Characteristic LV Network without DG Units The analysis has been performed on a characteristic

Croatian LV distribution network model, created from the available data [1,10]. The network model diagram is shown in Figure 4.

Characteristic LV distribution network is connected to the MV network over a 400 kVA 20/0.4 kV transformer. The substation has 4 feeders which supply 86 households with the simultaneous peak power of 1.25 kW and 9 business consumers with the simultaneous peak power of 9.9 kW. Power factor for all consumers in the network is assumed to be 0.9 inductive.

The first feeder is built with underground cables, the second one is a combination of underground cables and overhead lines, while the third and the fourth ones are

Figure 4. Characteristic LV distribution network in Croatia

MIPRO 2020/CTS 1137

entirely built with overhead lines. Total length of underground cables in the network is 1,187 m and total length of overhead lines is 2,690 m.

Without connected DG units the LV network draws 216.68 kW and 110.95 kVAr from MV network. Active and reactive power losses are 7.28 kW and 9.57 kVAr respectively. Maximum voltage drop equals 6.25 p.u.

B. Distributed Generation Units Penetration Levels According to available data [2], installed capacity of PV

generation in LV networks in Croatia equals 52,080 kW. As the number of MV/LV transformers is 26,973 with the total installed capacity of 8,954 MVA, it can be shown that the average installed capacity of PV equals 0.58% of installed capacity of a substation transformer.

Similarly, from the electrical energy production and consumption data [10], it can be derived that PV distributed generation averagely covers around 4.14% of typical LV electrical network energy requirements.

Therefore, the analysis was performed for five different PV distributed generation penetration levels: 2%, 5%, 10%, 15% and 20%.

IV. USING PANDAPOWER TOOL FOR LV NETWORK POWER FLOW AND VOLTAGE DROPS CALCULATION

A. PandaPower Tool PandaPower is an open source tool written in Python

which has the built-in capabilities for modelling, analysis and optimization of electrical power systems [11].

It is built as a Python module, and it has several advantages and a few disadvantages when compared to other electrical power systems analysis tools. The main disadvantage is that it is generally harder do enter a network model manually because the tool does not have any

graphical user interface, so every single network element has to be entered by using the Python programming language.

The scripting capabilities of the tool make its greatest advantage, because it is easily linked with existing geographical and technical information systems, so it is theoretically possible to avoid entering the network data completely.

PandaPower supports the following electrical power systems analysis modules [11]:

Power flow

Optimal power flow

State estimation

Short circuit calculation

Calculation results can be analyzed and processed with Python and then exported to several spreadsheet applications, where they can be furtherly formatted and processed.

B. Basic Alghoritm for Data Analysis and Processing The main loop of data analysis and processing

algorithm is shown in Figure 5. Generally, it creates the test network and then performs the analysis on all test cases. The results are evaluated and stored for later comparison.

As it is depicted in Figure 5, PV generation units are sequentially added to the test network, and therefore the test results are easily comparable. Every PV generation unit added to the test network is defined by two parameters – its location and its installed capacity.

To simulate the inability of a distribution system operator to predict the location requirements of their customers’ distributed generation units, the location of every new unit is chosen as a random consumer node in the test network.

The installed capacity of a DG unit is calculated from a normal distribution with the mean value of 6 kW and the standard deviation of 3 kW.

Figure 6 shows the sub-process of adding DG units to the test network. When the total DG installed capacity exceeds the maximum capacity for a test case (defined by

Figure 5. The main loop of data analysis and processing algorithm

Figure 6. The sub-process for DG unit creation

CREATE NETWORK WITH TOTAL DG CAPACITY = 0

ADD PV GENERATION TO RADNOM NODES

RUN POWER FLOW ANALYSIS WITHOUT REACTIVE POWER

INJECTION

RUN POWER FLOW ANALYSIS WITH REACTIVE

POWER INJECTION

PROCESS AND STORE RESULTS

ALL PENETRATION LEVELS PROCESSED?

END

ADVANCE TO NEXT DG PENETRATION LEVEL

YES

NO

START

ADD NEW PVGENERATION UNIT

ADD NEW PV CAPACITY TO TOTAL DG CAPACITY

TOTAL CAPACITY >= MAX CAPACITY?

END

YES

NO

1138 MIPRO 2020/CTS

DG penetration level), the sub-process ends and the results are analyzed and evaluated by the main loop.

V. SIMULATION RESULTS Table I displays the installed DG units’ capacities and

their points of connection in the test network for different DG penetration levels in a single run of the algorithm shown in Figure 5. Each of the higher level test cases keeps all of the installed PV units from lower penetration levels and adds one or more new units, as shown in the table.

As the area of interest in this research has been to analyze benefits the PV distributed generation units have on voltage stability, the calculations were performed with an assumption of high irradiance levels (i.e. during a typical sunny day).

The results of the calculations are summarized in Table II. For each DG penetration level, two different sets of results are displayed – one with DG units producing only active power, and the other with reactive power injection, in accordance with RPM characteristic and limitations described in sections III.C and III.D. The test cases are compared by their respective F-index values, which are calculated by the means of (10).

Figures 7 and 8 show the voltage profiles for the lowest (case No. 1) and the highest (case No. 5) DG penetration levels compared to the base LV network without connected DG units (case No. 0).

The results indicate that PV inverters have the potential to reduce voltage drops and power losses in electrical distribution networks, provided that the DG penetration level is high enough.

Since the installed DG capacities in Croatian LV networks are still relatively low, PV inverters usually may inject the maximum possible amounts of reactive power without causing overvoltage in the network. Except for the highest irradiance levels when the inverter’s rated power is the limiting factor, these amounts are mainly dictated by Croatian Grid Codes (Equation 5).

In such circumstances, the best results could be achieved if the RPM approach is combined with one or more traditional voltage regulation techniques.

VI. CONCLUSION The emergence of distributed generation units in LV

electrical networks allow for some new approaches to voltage regulation and power loss reduction. Since the PV inverters are able to operate with different power factors,

Table I. PV units installed capacities and locations

Table II. Calculation results summary

Figure 8. Voltage profiles for high DG penetration level

Figure 7. Voltage profiles for low DG penetration level

DG

penetration

level

Node

number

DG unit

capacity

[kW]

0 - 0.00

1 30 8.44

2 104 10.44

33 5.69

64 7.13

12 4.64

94 2.48

120 2.54

7 9.30

92 6.35

3

4

5

DG

penetration

level

Total DG

installed

capacity

[kW]

Total DG

reactive

power

injection

[kVAr]

ΔV D

[%]

P loss

[kW]

Q loss

[kVAr]F -Index

0 0.00 0.00 6.25 7.28 9.57 0.063

0.00 6.22 7.02 9.01 0.026

3.52 6.16 6.96 8.88 0.017

0.00 5.23 6.41 8.27 -0.068

7.87 5.12 6.22 8.00 -0.094

0.00 4.79 5.85 7.48 -0.149

13.21 4.60 5.57 7.07 -0.190

0.00 4.75 5.51 6.92 -0.196

17.23 4.51 5.17 6.41 -0.245

0.00 4.69 5.10 6.11 -0.253

23.75 4.37 4.68 5.46 -0.313

8.44

18.88

31.70

41.37

57.02

1

2

3

4

5

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

0 6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

96

10

2

10

8

11

4

12

0

12

6

No

de

vo

ltag

e p

.u.

Node number

Without DG units

DG units injecting active power

DG units injecting active and reactive power

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

0 6

12

18

24

30

36

42

48

54

60

66

72

78

84

90

96

10

2

10

8

11

4

12

0

12

6

No

de

vo

ltag

e p

.u.

Node number

Without DG units

DG units injecting active power

DG units injecting active and reactive power

MIPRO 2020/CTS 1139

they make a good addition to traditional voltage regulation techniques.

When the DG penetration levels are relatively low, inverter controllers may be set to inject the maximum possible amounts of reactive power to support voltage stability in the network without causing overvoltage in the network buses.

However, for higher penetration levels some kind of controller regulation should be established to keep the voltages in allowable limits.

The article demonstrates an example of using the PandaPower tool to simulate and analyze the influence of reactive power injection from PV distributed generation controllers on voltage stability in a typical LV distribution network in Croatia. Since the PandaPower tool could be easily scripted through the Python programming language, it makes a perfect tool for analyzing and comparing many different test case scenarios.

The algorithm presented in the article is relatively simple, but it could be effortlessly upgraded to simulate and optimize the reactive power injection to achieve the minimal voltage deviations and minimal power losses in the network.

REFERENCES [1] S. Vlahinić, D. Franković, V. Komen, A. Antonić, “Reactive power

compensation with PV inverters for system loss reduction”, Energies, vol. 12, no. 21, pp. 4062, 2019.

[2] HEP ODS d.o.o., “Godišnje izvješće 2018”, HEP Operator distribucijskog sustava d.o.o., Zagreb, 2019.

[3] O. Gandhi, C. D. Rodríguez-Gallegos, W. Zhang, D. Srinivasan, T. Reindl, “Economic and technical analysis of reactive power provision from distributed energy resources in microgrids”, Applied energy, vol. 210, pp. 827-841, 2018.

[4] T. Stetz, F. Marten, M. Braun, “Improved low voltage grid-integration of photovoltaic systems in Germany”, IEEE Transactions on sustainable energy, vol. 4, no. 2, pp. 534-542, 2012.

[5] HEP ODS d.o.o., “Mrežna pravila distribucijskog sustava”, NN 74/2018

[6] M. Begović, A. Pregelj, A. Rohatgi, D. Novosel, “Impact of renewable distributed generation on power systems”, Proceedings of the 34th annual Hawaii International conference on system sciences, IEEE, pp. 654-663, 2001.

[7] R. Kabiri, D. G. Holmes, B. P. McGrath, L. Gunaruwan, “LV grid voltage regulation using transformer electronic tap changing, with PV inverter reactive power injection”, IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 3, no. 4, pp. 1182-1192, 2015.

[8] CENELEC, “Requirements for micro-generating plants to be connected in parallel with public low-voltage distribution networks”, EN 50438:2013

[9] A. M. Imran, M. Kowsalya, “A new power system reconfiguration scheme for power loss minimization and voltage profile enhancement using fireworks algorithm”, International Journal of Electrical Power & Energy Systems, vol. 62, pp. 312-322, 2014.

[10] B. Vuk et al., “Energy in Croatia – annual energy report”, Republic of Croatia, Ministry of environment and energy, 2017.

[11] L. Thurner, A. Scheidler, F. Schäfer, J. H. Menke, J. Dollichon, F. Meier, S. Meinecke, M. Braun, “PandaPower – an open-source Python tool for convenient modelling, analysis, and optimization of electric power systems”, IEEE Transactions on Power Systems, vol. 33, no. 6, pp. 6510-6521, 2018.

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