METHODOLOGY Open Access

Modeling methodology and faultsimulation of distribution networksintegrated with inverter-based DGLongchang Wang, Houlei Gao* and Guibin Zou

Abstract

The increasing penetration of inverter-based distributed generations (DGs) significantly affects the fault characteristicsof distribution networks. Fault analysis is a keystone for suitable protection scheme design. This paper presents themodelling methodology for distribution networks with inverter-based DGs and performs fault simulation based on themodel. Firstly, a single inverter-based DG model based on the cascaded control structure is developed. Secondly, asimulation model of distribution network with two inverter-based DGs is established. Then, different fault simulationsare performed based on the Real Time Digital Simulator (RTDS). Theoretical analyses are conducted to justify thesimulation results, including the equivalent circuit of distribution networks with inverter-based DGs and the solutionmethod for loop currents.

Keywords: Distribution network, Inverter-based distributed generation (DG), Simulation model, Fault analysis, Real timedigital Simulator (RTDS)

1 IntroductionIn recent years, different kinds of distributed gener-ation (DG) are being connected in distributionnetworks, such as wind generation and photovoltaic(PV) generation. A great number of power elec-tronic devices are connected to distribution net-works due to the integration of inverter-based DGs.Therefore, compared with traditional distributionnetwork, planning and design, control and protec-tion, simulation and analysis for distributionnetworks with inverter-based DGs are more compli-cated. This has motivated a considerable number ofstudies [1–5].Simulation model plays an important role in the

research of power system. As a real-time simulationtool designed for power system, Real-Time DigitalSimulator (RTDS) are widely used for power systemsimulation and analysis [6–9]. One important advan-tage of RTDS is that it can interface electrical andcontrol signal with physical devices and achievehardware-in-loop simulation. Thus, the simulation

models based on RTDS can be used to test realequipments.Fault characteristics of distribution networks with

DGs are quite different from traditional distributionnetworks. How to model DG under fault conditionsis a prerequisite for fault analysis of the distributionnetworks with DGs. Researchers have put forwarddifferent equivalent models of inverter-based DG toanalyze their fault characteristics, such as thecurrent source with a parallel changeable impedance[10], the voltage source with a series changeable im-pedance [11], and the current source controlled bypositive sequence voltage at common coupling point(PCC) [12]. In the previous researches, their simula-tion models contain only one DG. However, in real-ity, there may be several DGs placed in differentlocations.In this paper, single inverter-based DG is modeled

firstly based on RTDS. Then, a simulation model fora distribution network with two inverter-based DGs isdeveloped. After that, fault simulations are performedusing the simulation model and the results are ana-lyzed briefly. Theoretical analyses are conducted tojustify the correctness of simulation results and the* Correspondence: houleig@sdu.edu.cn

School of Electrical Engineering, Shandong University, Jinan, China

Protection and Control ofModern Power Systems

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 DOI 10.1186/s41601-017-0058-9

effectiveness of control strategy for inverters underfault conditions. A brief summary is presented in theend.

2 Modeling of inverter-based DGAs one kind of green energy, PV generation has beenwidely integrated in power supply systems. Since PVgeneration output direct current, there must be invertersto connect it to AC grid. Therefore, PV is chosen as anexample to introduce the modeling process of inverter-based DG in this study.As shown in Fig. 1, the single-stage gird-connected PV

generation system is composed of primary equipmentsand control system. The primary equipments include thePV array, inverter, filter inductor, filter capacitor andgrid-connected transformer. The control system gener-ates firing pulse for inverter according to specified con-trol strategy. The PV generation system can be builtbased on the supporting software RSCAD in RTDS.The commonly used constant P-Q control strategy

based on dq synchronous reference frame is adoptedin this study. Two different control modes are de-signed for different operation conditions. Under thenormal conditions, DGs only have the active poweroutput. However, during fault conditions, DGsprovide extra reactive power support to mitigate thevoltage sag at the PCC [13].In Fig. 1, the relationship between output voltage and

current of DC/AC converter can be expressed as:

VTabc ¼ Riabc þ Ldiabcdt

þ V Sabc ð1Þ

The equation can be transformed into the dq syn-chronous reference frame:

VTd ¼ Rid þ Ldiddt

þ V Sd−ωLiq

VTq ¼ Riq þ Ldiqdt

þ V Sq þ ωLid

8><>: ð2Þ

Let the d-axis and grid voltage vector be in the samedirection in dq synchronous reference frame. The activeand reactive power output of the inverter can beexpressed as [14]:

P ¼ 32udid

Q ¼ −32udiq

8><>: ð3Þ

If we set P and Q as the active and reactive powerreference, the corresponding current reference id andiq under dq synchronous reference frame can be calcu-lated according to (3).In normal condition, make DG only output active

power, so i�q is 0. But in fault conditions, current refer-

ence of q-axis will be adjusted according to the voltagesag under the constraint that output current of DGcannot exceed 1.2 times the rated value [15]:

iq� ¼0;

−2 1−u1ð Þ;−1:2;

8<:

u1 > 0:90:4≤u1≤0:9u1 < 0:4

id� ¼ min id0�;ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:22−iq�2

q� � ð4Þ

where u1 is the amplitude of positive sequence voltage(p.u.) at PCC, id0 is current reference of d-axis beforethe fault.The main structure of the control system is shown in

Fig. 2.

Fig. 1 Single-stage grid-connected PV system

Fig. 2 Main structure of the control system

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 2 of 9

3 Modeling of distribution networks withinverter-based DGsOn the basis of Section 2, the simulation model of aneutral point ungrounded distribution network contain-ing two inverter-based DGs, as shown in Fig. 3, can bedeveloped.In Fig. 3, the DG1 and DG2 represent the two

single-stage grid-connected PV systems. The TB,K1 to K4, Kdg1 and Kdg2 are circuit breakers atdifferent locations. The feeders in the networkadopt PI model. To simulate different fault condi-tions, four fault locations, f1 to f4, are set at themiddle of L1 to L4, respectively. Load1 and load2are inductive loads modeled by series resistanceand inductor.The reference power for DG1 and DG2 is set to

1 MW and 2 MW, respectively. Table 1 shows the pa-rameters of the main components in Fig. 3.

4 Fault simulation and calculationBased on the proposed simulation model in Section 3,large numbers of fault simulations are performed at dif-ferent locations of the system model. The typical simula-tion results for three-phase faults and phase-to-phasefaults at location f4 are presented in this section.

4.1 Three-phase faultSet three-phase fault with 0.2 s duration at location f4.The current waveforms flowing through each line areshown in Fig. 4. The output current and voltage wave-forms of the main source and two DGs are shown inFig. 5.

From Fig. 5, it can be seen that the current suppliedby main source increased greatly, while current suppliedby DGs increased slightly under the fault condition,which means that the control strategy for inverter-basedDGs can effectively limit the output current of DG.

4.2 Phase-to-phase fault (A-B)Set A-B fault with 0.2 s duration at location f4. Thecurrent waveforms flowing through each line are shownin Fig. 6. The output current and voltage waveforms ofthe main source and two DGs are shown in Fig. 7.From Fig. 7, it can be observed that the current of

main source has the traditional fault characteristics, suchas current of phase A and B increased greatly and theoutput current became unsymmetrical. However, faultcurrent characteristics of DGs are obvious different. Theoutput current increased slightly and maintained sym-metrical under the A-B fault condition.

4.3 Current and voltage phasor calculationIn order to present the fault characteristics clearly,current and voltage phasors (steady state componentsunder fault condition) are calculated based on one-cycleFourier algorithm. The calculation results of the currentof phase A flowing through line L2, L3, L4 and the volt-age of phase A at PCC (M and N) are presented in thissubsection.For the three-phase fault at location f4, calculation

results are as follows:

I L2A ¼ 1:515∠−78:4∘kA

I L3A ¼ 1:603∠−80:7∘kA

I L4A ¼ 1:838∠−82:4∘kA

VMA ¼ 4:902∠−31:9∘kV

VNA ¼ 2:051∠−33:1∘kV

8>>>>>>>><>>>>>>>>:

ð5ÞEquation (5) show that due to the fault current injec-

tions from DG1 and DG2, the magnitude of _IL3A is

greater than that of _IL2A, while the magnitude of _IL4A is

Fig. 3 A distribution network with inverter-based DGs

Table 1 Parameters of main components

Components Parameters

Main source Voltage magnitude: 10.5 kVPositive impedance: 1∠80°Ω

Transmission line L1 to L4 Positive impedance: (0.270 + j0.335) Ω/kmLength: 5 km, 4 km, 4 km,5 km, respectively

Loads Load1: 1MVA, power factor is 0.9Load2: 4MVA, power factor is 0.9

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 3 of 9

greater than that of _IL3A . The phase angle differences

among _IL2A,_IL3A and _IL4A are quite small. The magni-

tude of _V MA is greater than that of _V

NA , and _V MA

leads _V NA in phase angle.

For A-B fault at location f4, calculation results are asfollows:

I L2A ¼ 1:331∠−112:5∘kA

I L3A ¼ 1:415∠−111:7∘kA

I L4A ¼ 1:623∠−112:0∘kA

VMA ¼ 6:221∠−103:2∘kV

VNA ¼ 4:629∠−124:2∘kV

8>>>>>>>><>>>>>>>>:

ð6Þ

It can be seen from (6) that the calculation resultsshow the similar characteristics as the above three-phasefault results.

5 Theoretical verificationIn this section, the theoretical derivations and cal-culations are presented to verify the simulationresults.

5.1 Fault equivalent circuitTo analyze fault characteristics of distribution networks withDGs, the fault equivalent circuit should be established firstly.The output of inverter-based DG is determined by its con-trol strategy. Under fault conditions, the PV generation canbe equivalent to a current source controlled by the ampli-tude of positive sequence voltage at PCC according to (4):

I dg;f ¼ f u1ð Þ ð7Þwhere u1 is the amplitude of positive sequence voltage atPCC and f(u1) is a nonlinear function. For a given valueof u1, f(u1) can be calculated according to (4).

For example, suppose the output current of PV is _Idg;f

¼ Idg;f∠θdg, and the full-voltage at PCC is _Upcc ¼ Upcc∠

θpcc. Idg , d and Idg , q can be calculated from (4), and then

Idg;f ¼ffiffiffiffiffiffiffiffiffiffiffiIdg;d2

qþ Idg;q2. Let Δθ be the phase angle differ-

ence between _Upcc and _Idg;f , which equals to the power

factor angle of PV, φ. Considering (3), the angle φ can bederived from the output active and reactive power:

φ ¼ arctan Q=Pð Þ ¼ arctan −Idg;q=Idg;d� �

ð8Þ

then

(a)

(b)

(c)

(d)

Fig. 4 Current waveforms flowing through each line for a three-phase fault at f4. a Current through line L1, b Current through line L2, c Currentthrough line L3, d Current through line L4

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 4 of 9

θdg ¼ θpcc−φ ð9Þ

In this paper, the fault equivalent model under A-Bfault at location f4 is taken as an example. There arepositive and negative sequence components under A-Bfault. The positive network contains main source andtwo PVs, but the negative network has no sourcebecause the main source and PV only output positive se-quence voltage and current.The positive sequence network and negative se-

quence network are illustrated in Fig. 8(a) and (b), re-spectively. Here, we suppose that each positive

sequence impedance (PSI) equals its negative se-quence impedance.

Where.

_Es: Voltage of the main source;

Zs: Equivalent PSI of the main source;ZL1, ZL2, ZL3: PSI of L1, L2, L3, respectively;ZL41: PSI of the line from fault point to busbar N;ZL42: PSI of the line from fault point to the end of

L4;ZLoad1: Equivalent PSI of the load1;ZLoad2: Equivalent PSI of the load2.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 5 Output current and voltage waveforms of each source for a three-phase fault at f4. a Output Current of main source, b Output voltage ofmain source, c Output Current of DG1, d Output voltage of DG1, e Output Current of DG2, f Output voltage of DG2

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 5 of 9

The simplified positive and negative sequence net-works are illustrated in Fig. 9.In Fig. 9, the equivalent voltage source and each im-

pedance can be expressed as:

Eequ;s ¼ kEs

Z1 ¼ ZS⋅Ztem1ð Þ= ZS þ Ztem1ð Þ þ ZL2

Z2P ¼ Z2

P1⋅Z2

P2

� �= Z2

P1 þ Z2

P2

� �8>>><>>>:

ð10Þ

where Ztem1 = ZL1 + ZLoad1, k = Ztem1/(Zs + Ztem1), Z2 ∑ 1

= (ZsZtem1)/(Zs + Ztem1) + ZL2 + ZL3 + ZL41, Z2 ∑ 2 = ZL42

+ ZLoad2.According to the boundary conditions, the compound

sequence network and its simplification can be drawn inFig. 10.In Fig. 10(b), the equivalent impedance Z2 and Z3 are

expressed as:Z2 = ZL3, Z3 = ZL41 + (Z2∑ ⋅ Z2 ∑ 2)/(Z2∑ + Z2 ∑ 2).

5.2 Solving methodThe mesh current method is used to analyze the simpli-fied compound sequence network in Fig. 10(b). There

are three meshes, and the corresponding mesh currents

are _Im1 ,_Im2 and _Im3 , respectively. The three mesh

current equations are as follows:

I m1Z1 þ UM1 ¼ E equ;s

I m2Z2 þ U N1 ¼ UM1

I m3Z3 ¼ UN1

8>><>>:

ð11Þ

Write complimentary equations by considering (7):

I m2−I m1 ¼ I dg1;f ¼ f um1ð ÞI m3−I m2 ¼ I dg2;f¼ f un1ð Þ

(

ð12Þ

There are five equations in (11) and (12) with five

unknown complex variables, _Im1 , _Im2 , _Im3 , _UM1

and _UN1 . Each complex variable has the real part

and imaginary part. Thus, the equations can be re-written as:

(a)

(b)

(c)

(d)

Fig. 6 Current waveforms flowing through each line for a phase A-to-phase B fault at f4. a Current through line L1, b Current through line L2,c Current through line L3, d Current through line L4

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 6 of 9

f1¼Im1Z1 cos θm1 þ θZ1ð ÞþUM1 cosθUM1 ‐Eequ;s cosθE ¼ 0

f2¼ Im1Z1 sin θm1 þ θZ1ð ÞþUM1 sinθUM1−Eequ;s sinθE ¼ 0

f3 ¼ Im2Z2 cos θm2 þ θZ2ð Þ þ UN1 cosθUN1 ‐UM1 cosθUM1¼ 0

f4 ¼ Im2Z2 sin θm2 þ θZ2ð Þ þ UN1 sinθUN1 ‐UM1 sinθUM1¼ 0

f5 ¼ Im3Z3 cos θm3 þ θZ3ð Þ‐UN1 cosθUN1 ¼ 0

f6 ¼ Im3Z3 sin θm3 þ θZ3ð Þ‐UN1 sinθUN1 ¼ 0

f7 ¼ Im2 cosθm2‐Im1 cosθm1‐Idg1;f cosθdg1 ¼ 0

f8 ¼ Im2 sinθm2‐Im1 sinθm1‐Idg1;f sinθdg1 ¼ 0

f9 ¼ Im3 cosθm3‐Im2 cosθm2‐Idg2;f cosθdg2 ¼ 0

f10 ¼ Im3 sinθm3‐Im2 sinθm2‐Idg2;f sinθdg2 ¼ 0

8>>>>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>>>>:

ð13Þ

Especially, there are four nonlinear equations relatedto f(um1) and f(un1). The Newton-Raphson algorithm isused to solve the equation group in (13).During every iteration, the amplitude and phase angle

of full-voltage at position M and N need to be calcu-lated. Then Idg1 , f can be calculated according to (4) andθdg1 can be calculated according to (8) and (9). Idg2 , fandθdg2 can be derived in the same way.

5.3 Comparisons with simulation resultsFor three-phase fault, the theoretical analysis results areas follows:

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7 Output current and voltage waveforms of each source for a phase A-to-phase B fault at f4. a Output Current of main source, b Output voltageof ma in source, c Output Current of DG1, d Output voltage of DG1, e Output Current of DG2, f Output voltage of DG2

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 7 of 9

I L2A ¼ 1:512∠−82:8∘kA

I L3A ¼ 1:610∠−82:8∘kA

I L4A ¼ 1:758∠−87:3∘kA

VMA ¼ 4:659∠−33:5∘kV

VNA ¼ 1:891∠−36:1∘kV

8>>>>>>>><>>>>>>>>:

ð14Þ

For A-B fault, the theoretical analysis results are asfollows:

I L2A ¼ 1:340∠−104:0∘kA

I L3A ¼ 1:429∠−104:4∘kA

I L4A ¼ 1:609∠−107:3∘kA

VMA ¼ 5:621∠−100:7∘kV

VNA ¼ 4:354∠−125:3∘kV

8>>>>>>>><>>>>>>>>:

ð15Þ

The comparisons between simulation and theoreticalresults are shown in Table 2 and Table 3.It can be seen from Table 2 and Table 3 that the theor-

etical results are consistent with simulation results. Therelative errors of most quantities are within 5%. All theabsolute errors of phasor angles are within 5° underthree-phase fault condition, and within 10° under A-Bfault condition. The comparisons have shown the effect-iveness of the simulations results.

6 ConclusionsTo investigate the fault characteristics of distributionnetworks with inverter-based DGs, this paper proposes acomplete simulation model for a typical distribution net-work integrated with PV generators based on the RTDS.The comparisons between the simulation results and

the theoretical analysis proved the feasibility of the pro-posed modeling methodology. Both the fault simulation

(a)

(b)

. . ..

.

Fig. 8 Positive and negative sequence networks. a Positivesequence network, b Negative sequence network

. . . .

..

(a)

(b)

Fig. 9 Simplified sequence networks. a Simplified positive sequencenetwork, b Simplified negative sequence network

. . .

. .

...

.

(a)

(b)

Fig. 10 Compound sequence networks. a Compound sequencenetwork, b Simplified compound sequence network

Table 2 Comparison between simulation and theoretical resultsfor three-phase fault at f4Phasors Simulation

resultsTheoreticalresults

Absoluteerrors

Relativeerrors/%

I L2A Amp. 1.515 1.512 0.003 0.200

Ang. −78.4。 −82.8。 4.4。 2.458

I L3A Amp. 1.603 1.610 0.008 0.473

Ang. −80.7。 −82.8。 2.1。 1.210

I L4A Amp. 1.838 1.758 0.080 4.354

Ang. −82.4。 −87.3。 4.9。 2.689

VMA Amp. 4.902 4.659 0.243 4.961

Ang. −31.9。 −33.5。 1.6。 0.928

VNA Amp. 2.051 1.891 0.160 7.803

Ang. −33.1。 −36.1。 3.0。 1.675

Notice: Relative error of angle is compared with 180。

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 8 of 9

waveforms and the phasor calculation results show thatthe output current of inverter-based DG increasesslightly (less than 2 times of rated value) and maintainssymmetrical under different fault conditions, which arequite different from that of traditional sources.Moreover, using the proposed simulation model, RTDS

can produce analogue voltage and current signals reflectingfault characteristics of distribution network with inverter-based DGs. Then these analogue signals can be used to testactual protection devices in a close- loop manner.

AcknowledgmentsThis work was supported by Nation Natural Science Foundation of China(51377100) and the Key Scientific and Technological Project of State GridShandong Power Company (SGSDWF00YJJS1400563).

Authors’ contributionsLW investigated the modeling methodology of distribution networks integratedwith IBDGs, conducted the fault simulation and drafted the manuscript. HGproposed the equivalent circuit of distribution networks with IBDGs and thesolution method for loop current. GZ verified the simulation model and analyzedthe simulation results. All authors read and approved the final manuscript.

Authors’ informationLongchang Wang was born in Shandong Province, China, in 1990. Hereceived the B.S. degree in electrical engineering from Shandong University,Jinan, China, in 2014. He is now a Master candidate in the School of ElectricalEngineering, Shandong University. His research interest is power systemprotection and control. E-mail:longchangw@126.com.Houlei Gao (M’11) was born in Shandong Province, China, in 1963. He receivedthe B.S. and M.S. degrees in electrical power engineering from ShandongUniversity of Technology, Jinan, China, in 1983 and 1988, respectively, and thePh.D. degree in electrical power system and automation from Tianjin University,Tianjin, China, in 1997. From 2004 to 2005, he worked as senior visiting scholarwith the School of Electrical and Electronic Engineering, Queen’s University Belfast,U.K. He is currently a Professor at the School of Electrical Engineering, ShandongUniversity, China. He has authored or coauthored more than 170 technical papers.His research interests include power system protection, fault location, smartsubstation and distributed generation. E-mail: houleig@sdu.edu.cn.Guibin Zou (M’12) was born in Shandong Province, China, in 1971. He receivedthe M.Sc. and Ph.D. degrees in the automation of electric power systems fromShandong University, Jinan, China, in 2000 and 2009, respectively. Currently, heis a Professor with the School of Electrical Engineering, Shandong University. Hisresearch areas include power system protection and control, power systemsimulation and modeling, digital substations, and wind power generationtechniques.

Competing interestsThe authors declare that they have no competing interests.

Received: 23 January 2017 Accepted: 29 June 2017

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Table 3 Comparison between simulation and theoretical resultsfor A-B fault at f4Phasors Simulation

resultTheoreticalresult

Absoluteerror

Relativeerror/%

I L2A Amp. 1.331 1.340 0.009 0.676

Ang. −112.5。 −104.0。 8.5。 4.743

I L3A Amp. 1.415 1.429 0.014 0.989

Ang. −111.7。 −104.4。 7.3。 4.138

I L4A Amp. 1.623 1.609 0.014 0.863

Ang. −112.0。 −107.3。 4.7。 2.578

VMA Amp. 6.221 5.621 0.599 9.629

Ang. −103.2。 −100.7。 2.5。 1.369

VNA Amp. 4.629 4.354 0.276 5.962

Ang. −124.2。 −125.3。 1.1。 0.637

Notice: Relative error of angle is compared with 180。

Wang et al. Protection and Control of Modern Power Systems (2017) 2:31 Page 9 of 9