634 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

Fault Current Contribution From SynchronousMachine and Inverter Based Distributed Generators

Natthaphob Nimpitiwan, Student Member, IEEE, Gerald Thomas Heydt, Fellow, IEEE, Raja Ayyanar, Member, IEEE,and Siddharth Suryanarayanan, Member, IEEE

Abstract—There are advantages of installing distributed gen-eration (DG) in distribution systems: for example, improvingreliability, mitigating voltage sags, unloading subtransmissionand transmission system, and sometimes utilizing renewables.All of these factors have resulted in an increase in the use ofDGs. However, the increase of fault currents in power systemsis a consequence of the appearance of new generation sources.Some operating and planning limitations may be imposed by theresulting fault currents. This paper discusses a model of inverterbased DGs which can be used to analyze the dynamic performanceof power systems in the presence of DGs. In a style similar toprotective relaying analysis, three-dimensional plots are used todepict the behavior of system reactance ( ) and resistance ( )versus time. These plots depict operating parameters in relationto zones of protection, and this information is useful for thecoordination of protection systems in the presence of DG.

Index Terms—Distributed/dispersed generation, fault calcula-tion, inverters, power distribution, power system protection.

I. INTRODUCTION

ACCORDING to the demands of clean energy, high relia-bility, and enhanced power quality for sensitive loads, the

demand of distributed resources is gradually rising. Moreover,the distributed resources may decrease or defer the investment ofsystem upgrades (i.e., transmission line and transformer ratings)due to increasing power demand. There are many technologiesfor distributed resources beyond the conventional synchronousmachine DGs such as fuel cells, wind turbines, solar cells, andmicroturbines. These DGs often require power electronic inter-faces to interconnect with the utility grid.

Installing DG at a customer site enhances certain aspects ofthe power quality of the owners by mitigating the voltage sagduring a fault. Moreover, DG improves the owner reliability asthe back up generator can often be started within 2 minutes. Al-though there are many advantages of installing DGs, a few op-erating conflicts cannot be ignored. Conflicts from installationof DGs, such as changes in coordination of protective devices,

Manuscript received September 22, 2005. This work was supported in partby the Salt River Project (SRP), Phoenix, AZ and in part by the Power SystemsEngineering Research Center (PSerc). Paper no. TPWRD-00559-2005.

N. Nimpitiwan was with the Department of Electrical Engineering at ArizonaState University, Tempe, AZ 85287-5706 USA. He is now with the Departmentof Electrical Engineering at Bangkok University, Pratumthani, Thailand (e-mail:natthaphob.n@bu.ac.th).

G. T. Heydt and R. Ayyanar are with the Department of Electrical Engineeringat Arizona State University, Tempe, AZ 85287-5706 USA (e-mail: heydt@asu.edu; rayyanar@asu.edu).

S. Suryanarayanan is with the Center for Advanced Power Systems atFlorida State University, Tallahassee, FL 32306 USA (e-mail: sid.surya-narayanan@ieee.org).

Digital Object Identifier 10.1109/TPWRD.2006.881440

TABLE IINTERCONNECTION SYSTEM RESPONSES TO ABNORMAL VOLTAGE [4]

nuisance trip, safety degradation and changes in the reach ofprotective relays, are discussed in [1]–[3]. Installing a small ormedium DG may not have a significant impact on the powerquality indices at the feeder level. The main reason for this ob-servation is that IEEE Standard 1547 [4] requires that the DGshould be disconnected from the supply feeder after a specifiedperiod of time shown in Table I. The DG will, after the citeddisconnection, have no impact on the supply feeder.

Fault calculations in power systems are used to determine theinterrupting capability of circuit breakers and the settings of pro-tective relays. The calculation of fault current at system busesis done conventionally by applying the system matrix. Theeffects of merchant plants, such as independent power producers(IPPs), must be augmented to the classical fault current cal-culation. New developments in deregulation have brought newgeneration sources to the system. The appearance of DGs is acause of increasing fault currents that may not have been pre-viously envisioned. Analysis of fault current by modifying thetraditional algorithm (i.e., analysis of bus impedance matrix) isdiscussed in [5] . However, fault current calculation by applyingthe conventional matrix in the presence of inverter basedDGs may be complicated due to the difficulty of estimating theimpedance of the electronic inverter.

One of the requirements of the IEEE Standard 1547 [4] is thatthe installation of DGs should not cause the network equipmentloading and interrupting capability (IC) of protection equip-ment, such as fuses and circuit breakers, to exceed the ratedIC. Also, the coordination of the protection system of the net-work should not be disrupted. This paper accesses the impact ofinstallation of DGs (i.e., synchronous machine DGs as well asinverter based DGs) on coordination of protection devices in asubtransmission system.

The organization of this paper includes sections on the modelof an inverter based DG with associated controls, the simulationstrategy, case studies and results from the simulation model, anda discussion on the effect of DGs on protection coordination.

0885-8977/$20.00 © 2006 IEEE

NIMPITIWAN et al.: FAULT CURRENT CONTRIBUTION FROM SYNCHRONOUS MACHINE 635

Fig. 1. Inverter based DG connecting to a grid system.

II. MODEL OF INVERTER BASED DISTRIBUTED GENERATIONS

Not all DGs are conventional synchronous generators. SomeDGs employ energy sources that produce dc voltage which isused as an input to an inverter and is ultimately interfaced withthe ac system. The controls of that inverter and the electronictopology of the inverter determine how the inverter is ‘seen’by the network. A full detailed treatment of inverter based DGsmay be quite complex, but the approximate response of the in-verter in the 2 to 60 cycle time frame may suffice for fault cur-rent analysis. DG controls are not standardized and control mod-eling may be problematic. References [6]–[9] discuss the mod-elling of the inverter based DGs and their connection to the gridsystem.

For the purpose of fault analysis in subtransmission systems,the model of inverter based DG is accomplished under the as-sumption that the input voltage from dc sources to the pulsewidth modulation (PWM) inverter is regulated and essentiallyfixed in the time frame 0–1.0 s. Inverter based DGs operate ascontrolled voltage sources connected to the grid through a stepup transformer. The step up transformer with delta—delta con-nection (e.g., 4 kV/12.47 kV) eliminates the zero sequence com-ponents from the inverter to the grid. Fig. 1 shows the assumedconnection of inverter based DG to the grid system.

The control strategies are to generate the balanced three phasevoltage and to control the power output of the inverter. The con-troller consists of two control loops: the amplitude controllerand the angle difference controller. The amplitude and angledifference controller provide the modulating signal to the PWMsignal generator. The harmonics from the PWM inverter are fil-tered by an LC low pass filter. The cutoff frequency, , shouldbe set low enough to pass the fundamental power signal but highenough to provide the attenuation of harmonics of the invertervoltage. Fig. 2 shows the generalized control model for an in-verter based DG.

The amplitude controller is shown in Fig. 3. The outputvoltage of the DG, , is transformed via a time dependenttransformation. The transform used is the transformation.This transformation has the property of frequency domainshifting the input phase voltages to a low frequency voltage.

Fig. 2. Control model for an inverter based DG.

Fig. 3. Amplitude controller of an inverter based DG.

Also, high frequency terms occur as a result of the transforma-tion. The input of the transformation is the power frequency ofthe grid system which is detected by a phase locked loop (PLL)at the point of common coupling (PCC). The advantage of the

to transformation is the ability to obtain low frequencycontrol signals and rapid calculations. In this discussion, it isassumed that the high frequency terms that occur in thetransformed variables are filtered out.

The time domain variables , , and mainlyconsist of “power frequency” components (i.e., 60 Hz com-ponents). The transformation is time varying with dc andpower frequency components. Therefore, , , and

generally contain dc, 60 Hz, and 120 Hz components.This is a consequence of the property that the Fourier transform(FT) of a product is the convolution of the FTs of the com-ponent multipliers. If a low pass filter is applied to the vector

, then results. The latter vectoris nearly dc, under near balanced sinusoidal steady state con-ditions. For purposes of designing and modeling a controller,rms voltages of , , , , , andare used. These rms values are denoted as , , , ,

, and . The same notation is used for rms current.A proportional plus integral (PI) controller minimizes the

error signal , the difference between the reference signaland the instantaneous voltages and .

The phase controller provides a phase difference, , be-tween and (see Fig. 2). A model of the phase controlleris shown in Fig. 4. Inputs to the phase controller, and , aretransformed to reference frame. The phase of and canbe calculated as,

In the phase controller, a PI controller is applied to minimizethe error of specified power output value, . The output av-erage power of the inverter based DG is measured as the outputfrom a low pass filter.

636 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

Fig. 4. Phase controller of an inverter based DG.

TABLE IICHARACTERISTICS OF AN INVERTER BASED DG FOR SIMULATIONS

The cut-off frequency of the low pass filter has to be set at theappropriate value to attenuate measurement noise. However, thevalue must be high enough to provide a good transient responseof the phase controller. The output of the PI controller is addedto the phase of and used to calculate the required amplitudeand phase of the modulating signal. The last step in the phasedifference controller is to transform the modulating signal backto the reference frame. The transformed modulating signalis used to control the PWM signal generator.

A simulation of stand-alone operation is utilized to demon-strate the cited model, and this simulation assumes a local loadand an inverter based DG. The inverter based DG is discon-nected from the grid system (Fig. 1) to show the transient re-sponse of the DG due to changes in load. In the case of stand-alone operation, the inverter requires only the amplitude con-troller to set the voltage at the reference point. For purposes ofthis demonstration, the output power of the inverter varies de-pending on the load. The inverter based DG parameters used inthe simulation are shown in Table II.

The demonstration of the stand-alone simulation time is fromto 0.3 s with simulation time step, . The three

Fig. 5. Output current of the inverter based DG (stand alone) with a load changeat t = 0:15 s.

Fig. 6. Output voltage of the inverter based DG (stand alone) with a loadchange at t = 0:15 s.

Fig. 7. Modulation index (m ) of the inverter based DG (stand alone) with aload change at t = 0:15 s.

phase output voltage is set at 1.0 p.u. or 12.47 kV. To demon-strate the dynamic performance of the inverter based DG, afterreaching the steady state, the load is changed from 3 MW/0.1MVAr to 5 MW/0.1 MVAr at . Figs. 5 and 6 show thecurrent of the inverter based DG and the output line to neutralvoltage, respectively. Note that, in Fig. 6, a voltage swell occursduring the change of the load. In this case, the voltage swellis approximately 5% of the nominal operating voltage. Fig. 7depicts the modulation index in the amplitude controllerwhich is used to control the switching of PWM generator.

NIMPITIWAN et al.: FAULT CURRENT CONTRIBUTION FROM SYNCHRONOUS MACHINE 637

Fig. 8. Harmonic content of the output current from inverter based DG in stand-alone operation.

Fig. 9. Active power output of inverter based DG in stand-alone operation.

According to the specific design and the indicated operatingcondition, after reaching the steady state, the total harmonic dis-tortion ( and ) are 1.36 and 0.66%, respectively.Fig. 8 depicts the harmonic content of the output current of in-verter based DG. Note that the plots are shown in semi loga-rithmic scale. The average active power output (average overone cycle) is shown in Fig. 9. The active power changed from 3MW to 5 MW at . Note that the inverter output fol-lows the load demand and the transient response time is in therange of 20–30 ms.

III. SIMULATION STRATEGY

As discussed in the previous section, the analysis of fault cur-rent of the system with the presence of inverter based DGs maybe complicated because the inverter effectively has a nonlinearV-I characteristic in the 2 to 60 cycle time range. A dynamicsimulation technique is proposed to analyze the consequences ofthe installation of DGs. The major advantage of the simulationtechnique is the ability to evaluate the response of the systemwith complex elements (e.g., power electronic elements). Sincethe inverter is a dynamic element, it appears that the only ac-curate method to characterize fault currents in the presence ofinverter based DGs is through the use of dynamic simulation.The simulation of the power system is accomplished by cre-ating a dynamic model state space representation of the system.The simulation is performed by applying numerical differential

equation solvers in both the time domain and in the domain(e.g., trapezoidal method, Adams method, modified Rosenbrockmethod and the Runge–Kutta method). This approach allowsone to accurately model the effects of electronic switching. Theresults of simulations, such as voltages and currents measuredin the system, can be recorded for further analysis.

The simulation of synchronous machine DGs is derived fromvoltage equations and flux linkage equations, expressed in a ro-tational reference frame. Details of the synchronous machinemodel are discussed in [10]. In general, simulation time steps inthe 50 microsecond range are recommended for a 60 Hz system.The simulation interval in the illustrative examples shown is 0–1second. Longer simulation times are unlikely to be needed forfault current analysis, but could be easily accommodated.

To demonstrate the impact of DGs in a subtransmissionsystem, a test bed representative of an actual distributionsystem is produced for illustrative purposes and this test systemis shown in Fig. 10. Characteristics of the test bed are shownin Table III. The test bed system is connected to a 230 kVtransmission system at Bus1 which itself is modeled as aThevenin equivalent obtained from conventional short circuitanalysis. The voltage level at the 230 kV supply is steppeddown to 69 kV. The taps of the 230 kV substation transformerand the 12 kV distribution transformers usually operate higherthan 1.0 p.u. to mitigate the effect of voltage drop in thedistribution primary system. The Thevenin equivalent posi-tive and negative sequence impedance of the 230 kV bus is

ohms per phase for the demonstration below.Note that capacitors are installed at the load sites to improvethe power factor. The per unit base used in all illustrative casesis 100 MVA.

IV. SIMULATION RESULTS

In this section, the simulation technique is used to investigateand compare the impact of the presence of both synchronousmachine DGs and the inverter based DGs in the subtransmissionsystem. The subtransmission system (Fig. 10) is used as a testbed to illustrate the simulation technique.

Assume that DGs are installed at 12.47 kV buses at four lo-cations: Bus16, Bus24, Bus25 and Bus27 (Fig. 10). Illustrativecases are separated into three parts: no DGs in the system inCase 1, the system with synchronous machine DGs in Case 2and the system with inverter based DGs in Case 3. The gener-ation capacity of each synchronous machine DG in Case 2 andinverter based DG in Case 3 are 5 MW. Parameters of all syn-chronous machine DGs applied in the simulations (in Case 2)are identical and shown in Table IV. Similar to the synchronousmachine DGs, all machine parameters of the inverter based DGs(in Case 3) are identical and are described in Table II. Summaryof the illustrative cases is provided in Table V. In these partic-ular cases, the penetration level in the system is approximately7% based on the total load of the test bed system (300 MVA).The intent is to illustrate a modest penetration of DGs and theresultant fault current response.

After analyzing the results of simulation with various faultsituations (i.e., various type of faults, fault locations), it is foundthat the installation of DGs (at the specific locations in the testbed system) may disrupt the operation of the protective relays

638 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

Fig. 10. Sample 69 kV transmission system.

TABLE IIICHARACTERISTIC OF THE TEST BED SYSTEM

located at Bus16 (12.47 kV bus). For this particular case, misop-eration of the protective relay can be illustrated by a three phasebolted fault at the midpoint of the subtransmission line betweenBus14 and Bus23 (69 kV). Assume that the fault occurs at

and is cleared at 500 ms or 100 ms after fault occurs. This100 ms fault is a commonly selected duration time for fault anal-ysis. The impedance , resistance , and reactance(i.e., “seen” from the line terminals) are measured at various lo-cations to monitor the consequences of the installation of DGs.

For the purposes of this presentation, the notation and proce-dures of power system protective relaying are used with regardto , , and . These quantities are ratios of rms volts to rmsamps, and the rms is carried out over one cycle (i.e., 1/60 s).The measurement at Bus16 is detected at the PCC or the pointof DG connection on the secondary side of 69/12.47 kV distri-bution transformer. Note that these measurements are the inputto the protective relays at Bus16 (12.47 kV). The analysis isperformed by assuming that all the DGs have constant poweroutput. Loads in the system at 12.47 kV buses are considered asconstant impedance loads.

Fig. 10 shows the one line diagram of the test bed system usedfor the simulation case studies. The several plots in Fig. 11 willbe discussed.

For the purposes of illustration and comprehension, twographic devices are used: a two-dimensional plot of versus

and three-dimensional plots of versus time. Athree-dimensional plot can be used to depict the behavior of

TABLE IVSYNCHRONOUS MACHINE PARAMETERS

TABLE VSUMMARY OF THE ILLUSTRATIVE CASES

and versus time. The three-dimensional plots in some com-mercial software are equipped with the ability to “zoom-in,”“zoom-out” and rotate graphs to any desired orientation. Thisability cannot be completely demonstrated in a paper document.However, the plots of , versus time are illustrated fromtwo distinct vantage points in Fig. 11. Although interesting inappearance, these plots may be difficult to interpret and, there-fore, a two-dimensional plot may be used, namely versus

. The concepts and applications of graphical illustrations onprotective relaying evaluation and testing are discussed in [11].

NIMPITIWAN et al.: FAULT CURRENT CONTRIBUTION FROM SYNCHRONOUS MACHINE 639

Fig. 11. Plots ofX �R andX �R-time at Bus16 (12.47 kV) illustrating the visualization afforded by rotation around the vertical (reactance) axis. (a) Plots ofX �R andX �R versus time at Bus16 (12.47 kV) of the test bed system without DG, Case 1. (b) Plots ofX �R andX �R versus time at Bus16 (12.47 kV)of the test bed system with synchronous machine DGs, Case 2. (c) Plots of X � R and X � R-time at Bus16 (12.47 kV) illustrating the visualization affordedby rotation around the vertical (reactance) axis.

In Fig. 11, the cylinder in the plots of versus timerepresents the characteristic of the impedance relay (e.g., con-stant ). The impedance relay operates when the impedancemeasured at the bus falls within the cylinder (80% of theline impedance for protection zone 1 and 120% for zone 2).Also note that the circle in the plots represents thecharacteristic of the impedance relay. The rotating graphiccapability appears to be useful to conceptualize thecharacteristic.

For example, if only the plane is needed (i.e., the timeof entry of a trajectory into a zone of protection of a relay isa parameter that evolves in this plot), the plot may be rotatedso that t is perpendicular to the page (or computer screen). Ifthe time dial setting is needed, the plot is rotated 45 , so that

the entry of the trajectory into the zone of protection is plainlyvisible. Other interpretations of rotated plots are also possible.

The results of calculating root-mean-square voltages and cur-rents for relaying applications are shown in the plots of -and versus time. In Fig. 11, the plots of and

versus time are separated into three durations: prefault( –0.4 s), during the fault ( 0.4–0.5 s) and after thefault is cleared ( –1.0 s). All three time intervals areshown on every graph in Fig. 11. With reference to Fig. 11(a),note that the primary and secondary protection loci are depicted,and the trajectory of versus is shown in the left most plot asa “dot” situated near , . The versus trajectory“motion” is better noted in the center plot of Fig. 11(a). In Case2 [Fig. 11(b)], the versus trajectory is the irregular locus

640 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 22, NO. 1, JANUARY 2007

Fig. 12. Comparison of the fault currents (p.u.) from three phase to groundbolted fault at the middle of the line between Bus14–Bus23 (69 kV), Cases 1–3(per unit base: 100 MVA, 69 kV).

Fig. 13. Plot of time to operation of the distance relay at bus Bus16 (12.47 kV)versus reach of the relay, Case 2 and 3 (per unit base: 100 MVA, 12.47 kV).

seen to start at , and “move” toward the secondaryprotection boundary [see the leftmost plot of Fig. 11(b)]. Theoperational trajectory is seen also in the center and rightmostplots of Fig. 11(b). Fig. 11(c) depicts similar results for Case 3.

Conclusions can be drawn from the simulations as: installa-tion of DGs in the distribution system increases the fault cur-rent throughout the system. This situation may change the wayprotective relays react to the faults. Circuit breakers, fuses andsetting of relays may need to be adjusted to the new appropriaterange. For a person skilled in the interpretation of the three-di-mensional plots, the rotational and zoom features may be usedto quickly determine protective relay settings.

The simulation results show that the increase of fault cur-rent from synchronous machine DGs is higher than that of in-verter based DGs of identical ratings. Fault currents from thethree-phase to ground bolted fault in Cases 1–3 are shown inFig. 12. In order to compare fault currents with and without DG,let the “no DG” case for the test bed system result in a fault

current of . The installation of four 5 MVA DGs in thetest bed system results in for synchronous DGs, or

for inverter based DGs. Thus, one concludes thatif the indicated study is representative of deployment of DGs indistribution systems, the synchronous machine design results in

or 1.2 (i.e., 20%) higher fault cur-rent for the synchronous machine design.

The protection system may lose coordination upon installa-tion of DGs. This point is illustrated as follows: before installingDGs (Case 1), distance relay at Bus16 (12.47 kV) should notoperate to clear the fault. This is due to the upstream fault onthe subtransmission system. The fault should be cleared by thedistance relays of the line between Bus14 and Bus23 (69 kV).When synchronous machine DGs are installed (Case 2), the faultcurrent flows from DG at Bus16 to the fault point and the relayat Bus16 (12.47 kV) might operate [Fig. 11(b)]. This situationdepends on the coordination of the protection system before in-stalling DGs. Thus, the protection system might lose coordina-tion for the case of installed synchronous machine DGs. How-ever, in Case 3, when a three-phase fault occurs at the middleof the line between Bus14 and Bus23, the fault current from theinverter based DGs are less severe than in Case 2. Simulationresults show that the distance relay at Bus16 does not detect thefault. The protection system operates similar to Case 1 to clearthe fault.

The results of simulations can be used to analyze the settingof relays in the system with the presence of DGs. For example,Fig. 13 shows the operation time of a distance relay at Bus16(12.47 kV). Note that in Case 2, the primary protection of theprotective relay at Bus16 detects the fault in 13 ms. In Case 3,the fault is not detected by zone 1 of the protective relay. Thisplot provides useful information to analyze the coordination ofthe protection system.

V. CONCLUSIONS

This paper discusses the impact of installation of DGs in dis-tribution systems from the perspective of increase in fault cur-rent and protection coordination. The fault current calculationof the inverter based DGs by applying the matrix is com-plicated because inverters are nonlinear electronic devices. Thisproblem can be approached by applying dynamic simulationtechniques. A model of inverter based DGs based on con-trols is discussed and compared with the synchronous machinecounterpart. Simulation techniques are proposed to investigatethe operation of protection systems. Information from the dy-namic simulations is useful in protective system coordination.The use of a novel three dimensional , , depiction is illus-trated in which graphic rotation and zoom features are used.

Simulation results show that the increase in fault currentsis often greater in the synchronous machine implementationversus a comparable inverter based design.

ACKNOWLEDGMENT

The authors would like to thank J. Blevins, A. B. Cummings,and R. Thallam for their technical expertise and advice.

NIMPITIWAN et al.: FAULT CURRENT CONTRIBUTION FROM SYNCHRONOUS MACHINE 641

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Natthaphob Nimpitiwan (S’01) received the Ph.D.degree in electrical engineering from Arizona StateUniversity, Tempe.

Currently, he is a Faculty Member in the De-partment of Electrical Engineering at BangkokUniversity, Pratumthani, Thailand. His researchinterests include distributed/dispersed generation,modeling/simulation of power systems, artificialneural networks, and engineering education.

Gerald Thomas Heydt (S’62–M’64–SM’80–F’91)received the Ph.D. degree in electrical engineeringfrom Purdue University, West Lafayette, IN.

Currently, he is the Director of a power en-gineering center program with Arizona StateUniversity, Tempe, where he is a Regents’ Professor.His industrial experience is with the CommonwealthEdison Company, Chicago, IL, and E. G. & G.,Mercury, NV.

Dr. Heydt is a member of the National Academyof Engineering.

Raja Ayyanar (S’97–M’00) received the M.S. de-gree from the Indian Institute of Science, Bangalore,and the Ph.D. degree from the University of Min-nesota, Minneapolis.

Currently, he is an Assistant Professor with Ari-zona State University, Tempe. He has many years ofindustrial experience designing switch-mode powersupplies. His research interests include topologies formodern dc–dc converters, new pulsewidth modula-tion techniques for drives, and power electronics ap-plications in power systems.

Siddharth Suryanarayanan (S’00–M’04) receivedthe Ph.D. degree in electrical engineering from Ari-zona State University, Tempe.

Currently, he is an Assistant Scholar Scientist withthe Center for Advanced Power Systems at FloridaState University, Tallahassee. His research interestsinclude state estimation applications, power quality,power transmission, modeling/simulation of powersystems, and engineering education.