1 Sizing of and Ground Potential Rise Calculations for Grounding Transformers for Photovoltaic Plants M. Ropp, Member, IEEE, D. Schutz, Member, IEEE, C. Mouw, Member, IEEE Abstract Due to concerns about ground fault overvoltage, increasing numbers of North American utilities are requiring that PV plants be effectively grounded before an interconnect permit can be issued. This generally equates to a requirement that a grounding transformer be installed, because most PV inverters are not inherently grounded. This requirement creates two challenges. First: there is uncertainty amongst PV plant designers as to how to correctly specify these grounding transformers in terms of impedance and current-handling capability. The grounding transformer impedance must balance the concerns of maintaining effective grounding while not desensitizing utility protection. The ratio-ofimpedances method described in IEEE 142 cannot be applied to inverter-based sources because the inverter impedances are not well defined. A new recommendation for the grounding transformer impedance is being proposed in IEEE 1547.8, but many developers and field engineers are either unaware of it, or are not clear on how to use it, and in any case this recommendation does not address how to find the short-duration and steady-state current ratings. Second: ground potential rise calculations are also needed often in this situation, but for PV grounding transformers there is uncertainty regarding proper quantification of the current that leads to the ground potential rise. The existence of this problem is acknowledged in IEEE 367 Clause 4.4, but in the case of PV grounding transformers, there is no clear guidance on how to solve it. This is especially true in the case in which the PV distribution or GSU transformer H and X neutrals, along with the grounding transformer neutral, all share the same grounding electrodes, which is the most common configuration in the field. This paper provides background on these problems, and presents: a) a simple, fundamentally-based procedure for sizing PV grounding transformers that utilizes the IEEE 1547.8 recommendation and yields defensible but not Manuscript received September 11, 2014. This work was supported by Advanced Energy Industries and Gerlicher Solar. M. Ropp, D. Schutz and C. Mouw are with Northern Plains Power Technologies, Brookings, SD 57006 USA (phone: 605-692-8687; email: michael.ropp@northernplainspower.com). excessively overdesigned results; and b) quantitative recommendations for calculating the correct current to be used in IEEE 367 ground potential rise calculations, again based on fundamental considerations. The procedures presented are demonstrated via examples, and vetted by testing against simulation results from a detailed 4-wire feeder model. Index Terms Ground fault overvoltage, effective grounding, photovoltaics, inverter, distributed generation, grounding transformer. DG GFO GPR GSU M I. NOMENCLATURE Distributed Generation Ground Fault Overvoltage Ground Potential Rise Generator Step-Up (transformer) II. INTRODUCTION ANY US utilities are starting to require that PV power plants be effectively grounded so that these plants will not cause a ground fault overvoltage (GFO) on a threephase four-wire feeder after the utility breaker opens. GFO is a phenomenon that can occur if an ungrounded voltage source feeds an ungrounded feeder containing a single-phase to ground fault, resulting in a phase-to-ground overvoltage on the unfaulted phases. The GFO phenomenon is well-known in rotating generators [1], but there is an ongoing debate about how to think of this phenomenon with inverter-based distributed generation that acts as a current source [2]. Until that debate is resolved, utilities are understandably erring on the side of caution, meaning that increasing numbers of interconnect permits for inverter-based distributed generation (DG) will run into utility policy requiring effective grounding. There is thus a need for a grounding transformer design procedure that is simple and minimally situationally-specific, and that requires a minimum of input data from the utility, but that still results in a grounding transformer specification that is rigorously defensible. This paper proposes such a procedure. Inclusion of a grounding transformer also gives rise to the possibility of ground potential rise (GPR) becoming an issue at the DG site. This paper also suggests a method for determining the fault current for use in GPR calculations.
2 A. Procedure III. GROUNDING TRANSFORMER SIZING 1) Fundamental considerations Consider the generic distribution feeder shown schematically in Figure 1. The utility source is at the left, and it serves the feeder through a substation transformer that grounds the feeder, marked here as a delta-yg. For simplicity, no loads are shown. At the right end of the distribution feeder is an inverter-based DG (a PV plant in this case), assumed here to be tied to the feeder through a Yg-Yg distribution transformer. The PV plant has a grounding transformer, shown here as a Yg-delta but which could also be a zigzag. However, for consistency with standard practice, that factor is not considered here, and its exclusion will lead to a conservative design recommendation for the grounding transformer. There are several ways of obtaining the needed zerosequence path. One way is to connect the DG to the feeder using a Yg-delta distribution transformer, with the Yg on the feeder side and probably grounded through a grounding reactor to control the fault current contribution. When viewed from the Yg (feeder) side, this transformer provides a zerosequence path to ground through its delta winding [3] and prevents GFO for faults on the distribution feeder. In this configuration, a ground fault on the 480 V bus will result in a GFO driven by the utility source. Thus, in this case it might still be necessary to include a grounding transformer on the distribution transformer LV bus. Figure 1. One-line diagram of a generic 15 kv class feeder circuit, with a PV plant and a Yg-delta grounding transformer. The situation of concern to utilities occurs when a single phase fault to ground occurs. To understand this situation, consider Figure 2, which shows the sequence networks for Phase A of the feeder in Figure 1 under a single-phase fault on the PV plant 480 V bus, before opening of the substation breaker. The top loop is the positive sequence network, the middle loop is the negative sequence, and the bottom loop is the zero sequence. The variables used in Figure 2 are listed in Table 1. Derivation of the sequence networks and interconnecting them to represent the single-phase fault is explained in [3-5]. When unfaulted, the sequence networks are decoupled, and since there are no sources in the negative or zero sequence networks there are no currents in those loops. When the single-phase fault occurs, the sequence networks become coupled at the fault point through the fault impedance Z F. Figure 2 shows that the inverter s zero-sequence shunt impedance is infinite. This is true for most (but not all) DG inverters. While the utility is still connected, the substation transformer provides a path for zero-sequence currents, through the substation grounding impedance Z 0,gnd,sub. However, when the utility s overcurrent protection detects the fault and opens, the feeder is cut off from the substation transformer and Z 0,gnd,sub. If the grounding transformer impedance Z 0,g were not present in Figure 2, the DG would not provide a path for the zero-sequence current, which would then have to flow through the zero-sequence impedance of the phase-ground connected load, the charging capacitances of the feeder conductors, and any other phase-ground connected impedances, such as arrestors. These phase-ground connected loads and elements are not included in the sequence network diagram. This is standard practice, but this exclusion can cause an interpretation problem when dealing with inverterbased DGs acting as current sources, because after opening of the utility breaker it is these elements that provide the path for the DG currents. The phase voltages and any resulting GFO will then be determined by the DG phase currents and the current-voltage relationship of the Yg-connected load. Figure 2. The sequence networks of the generic feeder in Figure 1, including a single-phase fault on the PV plant 480 V bus. Table 1. Variable names used in Figure 2. I PVa1 Positive-sequence PV output current V a1 Positive-sequence utility source voltage Z 1,source; Z 2,source; Z 0,source Positive, negative and zero-sequence utility source impedances Z 1,line; Z 2,line; Z 0,line Positive, negative and zero-sequence impedances of the distribution feeder between the substation and the fault Z 1,disttx; Z 2,disttx; Z 0,disttx Positive, negative and zero-sequence impedances of the distribution transformer Z 1,inv,s; Z 2,inv,s; Z 0,inv,s Positive, negative and zero-sequence series impedances of the inverter Z 1,inv,sh; Z 2,inv,sh; Z 0,inv,sh Positive, negative, and zero-sequence shunt impedances of the inverter Z 1,g; Z 2,g; Z 0,g Positive, negative and zero-sequence impedances of the grounding transformer Z 0,gnd,sub Substation grounding impedance (if not includes in Z0,source) Fault impedance Z f If a Yg-Yg distribution transformer is used to connect the DG to the feeder, then a separate grounding transformer can be used to effectively ground the PV plant, and this configuration is the topic of the present paper. Grounding transformers are either Yg-delta or zigzag types, both of which
3 provide the finite zero sequence shunt impedance needed to mitigate GFO. It is assumed that the grounding transformer is connected on the LV side of the distribution transformer. The grounding transformer must have sufficient currenthandling capability to survive three sets of conditions: the fault current that flows after the fault strikes but before the utility breaker opens, the fault current that flows after the utility breaker opens but before the PV trips, and the steadystate circulating current that will flow in the grounding transformer due to phase-phase voltage imbalance under normal unfaulted operating conditions. Inverter fault current contributions are limited; during the fault, the inverter current will typically be on the order of 1.2 times the inverter s rated current [6], meaning that the PV fault current contribution will be much smaller than the utility-driven fault current that flows before disconnection. Thus, the fault current flowing after initiation of the fault but before the utility breaker opens will be the current that determines the short-term current handling capability the transformer must possess. The steady-state circulating current can also be sizeable, depending on the transformer impedance and the level of phase-phase voltage imbalance expected on the feeder. 2) Grounding transformer electrical specification To electrically specify the grounding transformer, one must specify six parameters: the transformer s nominal terminal voltage (assumed here to be 480 V LL,RMS), the zero-sequence current required and its duration (taken here to be 2 sec), the continuous circulating current the transformer must endure due to steady-state phase-phase voltage imbalance on the feeder, and the transformer s zero-sequence impedances R 0 and X 0. The strategy used here is to first find the transformer impedances, and then use those to calculate the transformer s needed fault current and continuous current withstand capabilities. There are two methods by which the transformer impedance is commonly specified. One is from IEEE-142 [7] and involves setting the grounding transformer impedances (R 0 and X 0) so that the ratios of R 0/X 1 and X 0/X 1 of the circuit without the utility connected result in a TOV of 120% or less. This process involves drawing the sequence network circuit, and the R 0, X 0 and X 1 values referred to in the ratios are those of the circuit, again with the utility disconnected. Usually, the recommended values for the ratios are X 0/X 1 3, and R 0/X 1 1. However, this definition can be difficult to use with inverters because it is difficult to properly define the inverter s positive- and negative-sequence impedances. The other means for finding the transformer impedances appears in an appendix to draft standard IEEE 1547.8 [8]. In this approach, one first finds the impedance base of the inverter, Z base,pv, as follows: where V PV is the line-to-neutral PV plant terminal voltage and S PV is the plant s rated output apparent power per phase in VA. Note that 1) S PV usually equals P PV because PV plants normally operate at unity power factor; and 2) if one uses the line-line voltage and total three-phase S PV, the same numerical (1) result is obtained. Then, the grounding transformer reactance and resistance, X g and R g, are found using these relationships: For example, a 500 kva (500 kw) inverter connected at 480 V has a Z base,pv of 0.4608, so the required X g of the grounding transformer would be 0.276, and the grounding transformer s R g value can be anything less than or equal to 69.1 m. The value of 60% of Z base,pv corresponds to a steady-state fault current contribution of about 167% of the PV nominal current, which is a conservative value. In this document, we will assume that R g = X g/4 (i.e., the maximum allowed R g value), because this minimizes the grounding transformer size without violating the requirements for TOV prevention. In general, one should also allow for a tolerance band on these impedances, so in this paper a ±10% tolerance on the impedance values is assumed. Figure 1 shows a representation of a generic distribution feeder with a PV plant and a grounding transformer on the PV plant s 480 V bus. This is the configuration that will be considered throughout this document. This basic configuration is the same whether a zigzag or Yg-delta grounding transformer is used. B. Grounding Transformer Sizing Results 1) Calculation of the steady-state circulating current rating The steady-state circulating current in the grounding bank arises because of the zero-sequence component of the unbalanced distribution feeder phase voltages. Denote the circulating current by I g. Looking at Figure 2, the DG appears on the right of each of the sequence networks. It is usually assumed that the DG current is entirely positive sequence, so the DG current source becomes an open circuit in the negative and zero sequences. Because we are concerned with the time period between the initiation of the fault and opening of the utility breaker, we will assume that the DG inverter s shunt impedances in the sequence domain, Z 1,inv,sh and Z 2,inv,sh, are large enough at 60 Hz relative to the other impedances in the circuit that the currents through them can be neglected while the utility is still connected. Because of the open circuit at the far right of the zerosequence network, the DG s zero-sequence impedance is entirely determined by the impedance of the grounding transformer. Also, notice that the grounding transformer only appears in the zero sequence network. Because the grounding transformer is not serving load on its secondary windings (which is usually, but not always, true), there is an open circuit on the secondary side of the grounding transformer s positive and negative sequences, so only zero sequence currents can flow in the grounding transformer. Because the impedance of the grounding transformer is known from Equations (2) and (3), it is now possible to find the circulating current I g by determining the zero-sequence voltage across the grounding bank as a function of the phase- (2) (3)
4 phase imbalance. Using that voltage, Ohm s Law will give I g. The first step in this process is to determine an expression for the zero-sequence voltage across Z 0,g that results from a given level of phase-phase voltage imbalance. To obtain this relationship, we first write expressions for the phase voltages expressing the level of unbalance. For generality, we will allow for different levels of imbalance on each phase. We will assume the Phase A voltage V a to be the reference, so that it has a magnitude of 1 per unit and a phase of zero. Then, let the ratio of V b to V a be x and the ratio of V c to V a be y. This can be written: where a is the 120 o phase shift operator. The symmetrical components of this unbalanced set of voltages are: (4) (5) and. Substituting these relationships into Equation (9) and performing the indicated algebra, the following result is obtained: (10) Equation (10) gives the zero-sequence voltage as a function of the percent imbalance, under the assumptions described above. Now the circulating current can be found using the circuit in Figure 2 by setting the voltage across the grounding transformer impedance equal to the zero-sequence voltage at that point and using Ohm s Law: (11) Substituting Equations (4) and (5) into (6) and carrying out the top line of the matrix multiplication to get V a0, the following expression results: Note that the general form of Equation (7) for arbitrary x and y and for arbitrary phase shifting between phases, would be: where b and c are the Phase B and Phase C phase shifts relative to Phase A. Equation (8) will become important shortly, but for the time being, we rewrite Equation (7) in rectangular form, making use of the fact that This gives: and. Equation (9) is a generalized expression for the magnitude of V a0 for arbitrary values of x and y but for b = 120 o and c = - 120 o. An additional simplifying assumption can be made: for planning calculations, the phase-phase voltage imbalance is often approximated by assuming that the Phase B and C voltages are equally spaced from the Phase A voltage. For example, if the total imbalance is 5%, then Phase B would be assumed to be 2.5% above Phase A and Phase C would be 2.5% below. Define P to be the percent imbalance between the phases. Then, (6) (7) (8) (9) However, empirical data, along with simulation results performed using the MATLAB/Simulink model in Figure 3 and a well-validated manufacturer-specific inverter model [2], suggest that Equation (11) consistently underpredicts the continuous current expected to flow in the grounding transformer. The reason is that two of the assumptions that were used to simplify Equation (8) to Equation (10) are not entirely valid. First, in the real world, the phase imbalance is not symmetrical. For example, for x = 1 and y = 1.05, the magnitude of V a0 from Equation (9) becomes 15% larger than for the symmetrical case of x = 0.975, y = 1.025 (P = 5% in both cases). Figure 4 shows a surface plot of the magnitude of V a0, relative to the P = 5% case, as a function of x and y. Note that for feeder imbalances up to 10%, which is a larger value than expected in practice, the largest value seen in the surface plot in Figure 4 is 2.0. Second, under unbalanced conditions, the phase voltages are not necessarily spaced by 120 o. Simulations conducted using the MATLAB model shown in Figure 3 suggest that for 5% imbalance or greater, b and c may be shifted by two or three degrees on each phase. The primary impact of the phase separation being different than 120 o is imperfect cancellation of terms in Equation (8). Figure 5 shows a surface plot of the magnitude of V a0, relative to the case of P = 5% and normal phase shifts, as a function of b and c. Figure 5 suggests that Equation (8) is quite sensitive to changes in the phases, with the change in the magnitude of V a0 approaching a factor of 4, but fortunately in practice the phase changes are rarely such that the change in V a0 is very large, and this factor can be neglected. To get an exact value, one should use Equation (8) directly, but in the planning stage one does not know the values of x, y, b or c. Thus, to arrive at an equation that gives a realistic value but maintains the simplicity of Equation (11), based on the results in Figures 4 and 5, the proposed procedure is to double Equation (11), resulting in Equation (12). (12)
5 90% of V a1, if the substation grounding impedance Z 0,gnd,sub is on the order of an ohm or larger (which would be unusual in practice; for well-designed substations, this value should be in the low hundreds of milliohms). Thus, it would be prudent to simply use the worst-case value of fault current and set the fraction equal to 100%: (13) Figure 3. Generic feeder model and inverter used to test the grounding transformer design equations. Figure 4. Surface plot of the magnitude of Va0, relative to its magnitude for the symmetrical P = 5% case, as a function of x and y. The reader should bear in mind that Equation (13) neglects the PV plant s contribution to the fault current. If for a particular inverter that assumption is questionable, the inverter s fault current contribution should be added to I g, but in most cases that should be unnecessary. C. Example grounding transformer sizing results Table 2 shows the calculated X 0, I g, and I g for three sizes of PV plant and two planning levels of phase-phase voltage imbalance. The interconnection voltage is assumed to be 480 V LL, RMS. For the I g and I g results, the ±10% tolerance band on the transformer impedances has been taken into account (i.e., the currents were calculated using 90% of the transformer impedance shown in Table 2 in Equations (12) and (13)). Table 2. Example grounding transformer sizing results, assuming a 480 V interconnect voltage and 10% tolerance on the transformer impedance. PV plant size (kw) Expected imbalance 600 1400 3500 Z0 (ohms) 0.058+j0.23 0.025+j0.099 0.0099+j0.039 2.0% Ig' (A) 15 35 87 Ig (A) 1300 3025 7563 Z0 (ohms) 0.058+j0.23 0.025+j0.099 0.0099+j0.039 2.5% Ig' (A) 19 44 109 Ig (A) 1300 3025 7563 Figure 5. Plot of the magnitude of V a0, normalized to the case of P = 5% at normal phase shifts (±120 o ), as a function of b and c. If P is the expected percent imbalance expressed as a fraction, V a1 is the pre-fault positive sequence voltage (V RMS,LN), and Z g is the complex impedance (R 0 + jx 0) of the grounding transformer expressed in ohms, then I g will be the circulating current in amps. Comparison against simulation results indicates that Equation (12) consistently overpredicts the value of I g, thereby providing a conservative design. 2) Calculation of the fault current withstand rating The fault current withstand capability of the grounding transformer can be calculated using a procedure similar to that used to find the circulating current. Because the zerosequence impedance is known, if the zero-sequence voltage during a fault were known, then Ohm s Law gives the fault current withstand requirement. The key lies in determining a reasonable value for the zero-sequence voltage during a fault. We know from Figure 2 that the sequence networks create an impedance divider such that the zero-sequence voltage will be some fraction of V a1. Examples in the literature [3] and from simulation results suggest that V a0 values can be as high as A. Procedure IV. GROUND POTENTIAL RISE Once the decision is made to include a grounding transformer at a DG installation site, it may become necessary to ensure that ground potential rise (GPR) does not become a problem, particularly if there are conductive (i.e., not fiber or microwave) communications channels to the PV site. The GPR at the site is the product of the impedance to remote earth and the current that flows through it. The impedance that should be used in this calculation is typically calculated using the procedure described in IEEE-367 [9]. However, it is fairly common that engineers will use the utility s calculated single-phase fault current in this calculation, along with a fault current division factor that accounts for the division of current among the various grounding paths in the circuit (also from [9]). The problem with this practice is that the utility s fault current calculation is normally done with the fault impedance and grounding electrode impedances all set to zero. This leads to a contradiction, because the resistances that are set to zero in this calculation are part of the physical mechanism that creates GPR in the first place. Thus, using the utility s single-phase fault current as the starting point leads to GPR values that are too high. The purpose of this section is to propose a more accurate symmetrical component model for calculating the
6 fault current to be used in the GPR calculation, in cases involving a PV plant grounding transformer. Figure 6 shows a circuit diagram of a distribution feeder including the substation source, feeder impedance, a singlephase fault applied to Phase A on the MV side of the distribution transformer, a Yg-Yg generator step-up transformer, and a grounding transformer, shown here as a zigzag transformer. The phases are color-coded to make the diagram easier to read. Fault current flows from Phase A to ground through the fault, and re-enters the system via the grounding electrodes as shown. The sequence networks that correspond to this situation are shown in Figure 7. The fault impedance, Z F, and the grounding impedance seen by the fault, R Fgnd, are shown separately. For present purposes, the fault impedance Z F can be neglected because in most cases it is much less than R Fgnd. The sequence network in Figure 7 can now be solved to determine the single phase to ground fault current that can be used as a starting point in a GPR calculation. Figure 8 shows the sequence networks for the situation in which the fault is on the LV side of the distribution transformer. In general, it will be easiest to solve these sequence network circuits using a circuit simulator like PSpice. The reason is because the zero-sequence networks in Figures 7 and 8 form the Wheatstone bridge configuration, and this causes the closed-form solution of this circuit to be cumbersome for byhand calculations. Figure 9 demonstrates how the zerosequence network in Figure 7 can be redrawn as a Wheatstone bridge. Figure 7. Sequence networks for an SLG fault on the MV bus, including the impedances to remote earth. Figure 6. Distribution feeder with a Yg-Yg distribution transformer, grounding transformer, and an SLG fault on Phase A. In addition, it is important to realize that when the distribution transformer s H-side and X-side neutrals share the same grounding electrode, which is commonly the case, the zero-sequence impedance of the distribution transformer, Z adisttx0, as seen from the MV side, is given by [10]: (13) where Z adisttx1 is the positive-sequence impedance of the transformer referred to the MV side, N is the turns ratio, and Z G is the impedance to remote earth along with any deliberately-added grounding impedance. Figure 8. Sequence networks for an SLG fault on the LV bus, including the impedances to remote earth. Equation (13) is obviously not a new result [10], but many of the newer reference books used today, especially by younger power engineers trying to understand transformers and symmetrical components, do not cover this case of a Yg-Yg transformer with a common H-X neutral. If the inverter-side voltage of the PV distribution transformer is 480 V and the feeder-side voltage is 12.47 kv, then N 26, so that (14)
7 Because Z G will have a value of several ohms in most cases and is multiplied by 3, neglecting this term can introduce a significant error into the calculated zero-sequence impedance. The yellow block at the far right end of the feeder contains a PV plant and grounding transformer. The contents of that yellow block are shown in Figure 11, in which the orange block at the center is the Yg-Yg generator step-up transformer, the yellow blocks at the upper left are the PV inverter modules, and the solid green block is the grounding transformer. Using switches and the red blocks at the bottom of Figure 11, an SLG fault can be applied directly to the MV or LV bus of the distribution transformer. Figure 11. Contents of the yellow block at the right in Figure 10. Table 3 compares the results obtained using the two models, using the detailed model as the reference. Results are shown for a fault on the LV side of the Yg-Yg distribution transformer, and on the MV side. According to these results, the symmetrical component model produces essentially the same results as the highly detailed model, and thus is a reasonable representation of the situation. Figure 9. Demonstration that the zero-sequence network in Figure 7 can be redrawn as a Wheatstone bridge, where Z a = Z asource0 + Z aline0 + Z adisttx0. B. Testing via simulation The use of the sequence networks to determine GPR was tested by building the sequence network model in MATLAB/SimPowerSystems, and comparing it against a highly detailed model of the feeder in Reference [11], also in SimPowerSystems. The feeder in [11] was designed to test TOV and GPR situations, and [11] includes validation data for the feeder model, so this selection of test system makes sense for present purposes. In the symmetrical component model, the GPR at the PV plant is the voltage that appears across R PVgrid in Figures 7 and 8. The detailed MATLAB/Simulink model is shown in Figure 10. The green block is the substation, and the separate feeder segments are the black and white blocks. The red-outlined blocks are locations at which faults can be applied. The solid blue blocks are measurement blocks. Table 3. RMS GPR predicted by detailed and sequence network models of the feeder model described in [11]. Case Detailed model Seq net model Percent description result (Vrms) result (Vrms) error LV-side fault 272.2 271.8-0.15% MV side fault 38.7 38.0 1.81% V. CONCLUSIONS Until there is a resolution to the ongoing debate over whether inverter-based DG requires effective grounding, there is a need for: a) a simple, robust design procedure for electrically specifying grounding transformers that does not involve excessive overdesign but still meets safety and reliability needs; and b) a means for calculating the correct current for determining GPR, especially when the GSU transformer H and X neutrals share the same ground electrodes with the grounding transformer. This paper has presented recommendations and suggestions intended to meet both of these needs, and it is hoped that these procedures will help in removing a barrier to deployment of PV in distribution systems while maintaining system safety and security. Figure 10. Model of the distribution feeder described in [11], with a PV plant and grounding transformer added in the yellow block at the far right (see Figure 11).
8 VI. ACKNOWLEDGMENTS The authors gratefully acknowledge a) the financial support of Advanced Energy and Gerlicher Solar, and b) the invaluable technical assistance of Tom Yohn, Michael Beanland, Marc Johnson, Matthew Charles, and Lou Gasper. VII. REFERENCES [1] H. B-L. Lee, S. Chase, R. Dugan, Overvoltage Considerations for Interconnecting Dispersed Generators With Wye-Grounded Distribution Feeders, IEEE Transactions on Power Apparatus and Systems, vol. PAS-103 No. 12, December 1984, p. 3587-3594. [2] M.E. Ropp, M. Johnson, D. Schutz, S. Cozine, Effective Grounding of Distributed Generation Inverters May Not Mitigate Transient and Temporary Overvoltage, Proceedings of the 2012 Western Protective Relay Conference, September 2012. [3] P. M. Anderson, Analysis of Faulted Power Systems, originally published by Iowa State University Press 1973, republished by IEEE Press 1995, ISBN 9780780311459. (This book is now available online free of charge from the IEEE.) [4] J. Blackburn, Symmetrical Components for Power Systems Engineering, CRC Press 1995, ISBN 9780824787676. [5] J. Glover, M. Sarma, T. Overbye, Power System Analysis and Design, 5 th ed., Cengage Learning 2012, ISBN 9781111425777. [6] Microgrids: Architectures and Control, ed. N. Hatziargyriou, pub. IEEE Press 2014, ISBN 9781118720684. See page 123. [7] IEEE Std 142-2007, IEEE Recommended Practice for Grounding of Industrial and Commercial Power Systems (the Green Book). [8] See IEEE 1547.8, Draft 2.0, November 2011, Appendix C, pg 147. [9] IEEE Standard 367-2012: IEEE Recommended Practice for Determining the Electric Power Station Ground Potential Rise and Induced Voltage from a Power Fault. [10] Electrical Transmission and Distribution Reference Book, pub. Westinghouse Electric Corporation, 1964. See Table 7, page 804, entry A-2. [11] J. Acharya, Y. Wang, W. Xu, Temporary Overvoltage and GPR Characteristics of Distribution Feeders with Multigrounded Neutral, IEEE Transactions on Power Delivery 25(2), April 2010, p. 1036-1044. Michael Ropp (M 1999) received the BS in Music from the University of Nebraska in 1992, and the MS and PhD in EE from the Georgia Institute of Technology in 1996 and 1998 respectively. He is the President and Principal Engineer of Northern Plains Power Technologies, and is a registered Professional Engineer in SD and HI. He has 17 years experience and >50 publications in power engineering, power electronics, and photovoltaics. Dustin Schutz (M 2010) received the BS in Electrical Engineering in 2006 and MS in Electrical Engineering in 2011, both from South Dakota State University. Mr. Schutz has wide-ranging experience in power electronics, embedded control systems, and power electronics and power system simulation. His current work focuses on multi-inverter islanding scenarios and microgrid controls. Chris Mouw received the BSEE from South Dakota State University in 2008. Mr. Mouw is presently with Northern Plains Power Technologies, Brookings, SD, where he works on all aspects of modeling of electric power systems with power electronics, automation of modeling, and many types of studies for utilities.