Aggregated Rooftop PV Sizing in Distribution Feeder Considering Harmonic Distortion Limit

Aggregated Rooftop PV Sizing in Distribution Feeder Considering Harmonic Distortion Limit Mrutyunjay Mohanty Power Research & Development Consultant Pvt. Ltd., Bangalore, India Student member, IEEE mrutyunjay187@gmail.com Shekhar Kelapure Power Research & Development Consultant Pvt. Ltd., Bangalore, India Senior member, IEEE shekhar.kelapure@prdcinfotech.com Abstract With the global green initiatives, agencies dealing with the renewable energy are coming with lucrative schemes to promote consumers for opting solar photovoltaic (PV) source as an alternative source of energy. The aggregated impact of the growing number of dispersed rooftop PV source may originate many power system related problems, power quality problem being one of them. This paper presents the methodology to determine the maximum PV solar capacity that can be allocated in a distribution feeder keeping harmonic distortion within acceptable limit as per IEEE-519 standard. The proposed approach also gives additional aggregated PV solar size at any location for future PV penetration, provided the harmonic injection does not raise voltage distortion above specified limit. A case study is carried out on a distribution feeder consisting 5 distribution transformers (s) to validate the approach and results are published. Power system simulation tool MiPower TM is used for network modeling and for verifying the result. Keywords Dispersed PV solar source; PV penetration; aggregated PV source; PV sizing; harmonic analysis; voltage distortion. I. INTRODUCTION As power distribution companies are providing subsidies for rooftop solar panels, a large number of consumers are now opting for PV sources as a secondary source of energy. Though this is considered as clean energy source, many research areas are continuously evolving to identify and improve the impact on flexibility, reliability and power quality issues due to large penetration of these PV sources which use power electronics based DC-AC converters[1-2]. There are some constraints, which limits the net PV penetration capacity, such as, overvoltage in system, equipment overloading, harmonic distortion, etc. The practical problem area for sizing aggregated PV source in a distribution feeder with respect to harmonic distortion is discussed in detail in section II. The methodology is also explained as a strategic solution for the same. II. PROBLEM DESCRIPTION Multiple guidelines are followed by the power distribution companies for approving rooftop PV capacity based upon consumer category. Normally the consumers are allowed to install rooftop PV source in first come first serve basis, after feasibility study is done related to available transformer capacity, harmonic distortions, etc. For deciding maximum PV penetration without violating harmonic distortion limit violation, an approach has been analyzed [3], which is limited to few typical distribution patterns, such as, in case PV sources are allocated across feeder in equal distribution / uniformly increasing / uniformly decreasing manner. In [4] location based PV optimization using particle swarm optimization (PSO) technique gives the ideal size of PV without violating harmonic distortion limits. But in case of distribution system, location based optimization can t be used, as the location of the rooftop solar is fixed at consumer premise. Though with the guidelines for rooftop PV approval process, over voltage and transformer overloading issue can be avoided. But in case of heavily loaded and long feeder, harmonic distortion crosses the limit specified by IEEE-519 [5], because of aggregated harmonic injection from PV sources. Available power system simulation software can help in finding harmonic distortion level in a distribution feeder with specific PV injection points. But it would be a cumbersome process form network planning perspective, to determine the maximum aggregated rooftop solar capacity in a feeder with different PV penetration level for transformers. the feasible capacity of aggregated rooftop PV sources to be connected at specific location (under any ) for future PV penetration. Considering these above requirements, a methodology is explained in section III, to find out maximum capacity of aggregated PV sources can be allocated in a feeder or in other words, to find out penetration factor for each in any feeder without exceeding harmonic distortion limit. Thus a chart can be made available for network planners on total numbers of s with a range of penetration factors. penetration factor = Aggregate installed PV capacity under the rated capacity Also another practical challenge comes related to determining the available PV source capacity for future penetration, under any with respect to harmonic distortion limit. In such scenario, though network is having enough capacity to carter additional PV plant, but same can bring

harmonic distortion issues. Instead of repetitively checking the feasibility with different PV capacity, an approach is explored in section IV to compute feasible PV capacity directly. III. MATHEMATICAL FORMULATION FOR MAXIMUM PV PENETRAION A feeder can get PV penetration near to the substation or at tail end or at middle of the feeder or combination of all. Allowable PV source capacity diverges [6] based upon it s distance from substation along the feeder. Generally all distribution feeders are operated radially, hence current harmonics, injected from converters get accumulated in feeder and flows towards substation, unless feeder is equipped with mid-span filter banks. So using the mathematical logics of radial load flow solution, total maximum allowable harmonic current can be computed keeping the voltage distortion below limit. Then based upon the harmonic current magnitude, a meaningful estimation can be concluded for deciding aggregated wise PV penetration capacity. Of course due the phase cancellation, there would be reduction in net harmonic current[7-8], this deviation is not much to be worried about, at the planning level. A typical distribution system shown in fig.1 consisting number s connected to grid through a feeder is used for deriving nodal equations to calculate voltage distortion. Aggregated distribution loads as well as PV sources are connected at secondary side. Grid 1 2 3 n Lumped Load Solar Panel Fig. 1. A typical distribution system with aggregated load and PV sources A. Penetration from tail end in feeder When PV penetration starts from feeder tail end, current harmonics accumulated at primary side sees maximum impedance. So when PV sources are installed from feeder tail end towards substation, voltage harmonic distortion at tail end gets the maximum impact and increases gradually. So PV sources can be added, till voltage distortion at tail end of main trunk line remains below acceptable limit. And to check the feasibility related to harmonic distortion, no need to compute distortion at other buses, as distortion at those areas will be always less than farthest bus from substation. The derivation for harmonic voltage at the farthest bus from grid using driving point impedance is explained here in a 3 bus radial system network, taken from the fig. 1. If harmonic current injections are considered from Bus 1, 2 and 3 are, and respectively, harmonic voltage at Bus 3 is as in (1): = + + + + _ + _ Where, = Grid impedance for h order, _ and _ are the branch impedance between Bus 1-2 and Bus 2-3 for h order. If bus wise h order driving point impedance at Bus 1, 2 and 3 are considered to be Z _, Z _ and Z _ respectively, ignoring load impedance, the difference between driving point impedance of two consecutive bus will be the line impedance, so, Z _ = (Z _ Z ), Z _ = (Z _ Z _ ) and Z _ = Z _. Because, if load impedance is ignored (generally taken as parallel combination of resistance and harmonic order times fundamental reactance), the driving point impedance at each bus sees the impedance in direction towards the substation[9-10]. This consists of branch line impedance and substation impedance. = + + + + + (2) = ( )+ ( )+( )( ) (3) In (3) harmonic voltage is represented in terms of harmonic injections (, and ) and driving point impedance (, and ). Similarly voltage distortion at bus is computed using multiplication two matrices, these are: [1 ] matrix, filled with bus wise driving point impedance [ 1] matrix, filled with bus wise current injections at those buses. As PV penetration is initiated from tail end, impedance matrix gets filled from [1, ] to [1,1], whereas current injection matrix gets filled from [, 1] to [1,1] in arrow mark direction shown in (4). In case of no harmonic injection, corresponding fields gets filled with zeros. Harmonic voltage at tail end (at bus) is computed using below matrix: = _... (4) _, _, are the driving point impedance calculated at each buses and, _, are the harmonic currents injected at each bus. Harmonic voltage at bus is as in (5): = ( )+ + + ( ) (1) (5)

B. Penetration from substation end in feeder Unlike last matrix filling as explained in last sub-section A, as PV penetration is initiated from substation end, current matrix gets filled from [1,1] to [1, ] and impedance matrix gets filled from [1,1] to [, 1] in arrow mark direction shown in (6). = (6) Equation for computing harmonic voltage at bus remains same as in (5). C. Procedure to compute maximum feasible PV solar capacity To compute the total overall Solar capacity, step-by-step procedures are described as follows. Step 1) Model distribution network including elements, such as, feeder branches, s, aggregated lumped load (summated value of all consumer load) using any power system simulation tool. Step 2) Initialize IEEE specified voltage distortion limits and allowable PV penetration limit for s. Step 3) Compute driving point impedance at each bus for the interested harmonic order ignoring the load impedance. Step 4) Decide the PV penetration direction, such as: starting from feeder towards tail end of feeder or in a reverse manner. Step 5) Accordingly formulate the matrix as shown in (4) or (6) based upon penetration directions. Step 6) Based on the desired penetration factor, allocate the PV capacity. Assuming harmonic characteristics of all inverters are same irrespective of their size, a fixed percentage can be considered on a total PV capacity connected under. Step 7) Execute equations formulated in step-5. Find the individual and total voltage distortion at farthest bus from substation. Step 8) If computed voltage distortion is above IEEE specified limit, stop and total PV capacity in that feeder with the considered penetration factor is concluded as: penetration factor capacity Where n is the last included without violating distortion. Go to step 10. Step 9) If voltage distortion is below specified limit, go to step-7 to update matrices in (4) or (6) by including adding next for voltage distortion calculation. Step 10) Perform detailed analysis from various aspects with finalized PV capacity. All the steps explained above are shown in the flow chart in fig.2. Continue addition of next in selected PV installation direction Fig. 2. Flow chart for computing maximum PV penetration This approach is applied on a test system and result is published in sub-section A and B of section V. IV. Inputs: Network model( including lines, s and lumped load) Interested harmonic orders (h= i,, j) Fix PV penetration level for s Fix voltage distortion limits Compute driving point impedance at each bus Select PV penetration direction, from substation end / from feeder tail end Calculate harmonic voltage at farthest location where PV is installed using (4) or (6) No Does the computed individual and total voltage distortion is above IEEE specified limit? Stop further addition and compute total feasible PV solar penetration capacity as the summation of PVs till distortion limit is not crossed. Perform detail analysis from various aspects. END MATHEMATICAL FORMATION FOR ADDITIONAL PV SOURCE FOR FUTURE PENETRATION This section explains about the methodology for determining additional PV capacity at any bus without violating voltage distortion limit. Assume in the existing network (shown in fig.3) with PV penetration, harmonic voltage at Bus 1, 2, 3, 4, and 5 are,,, and due to current harmonic injections,,, and respectively.,,, and are driving point impedance respectively. Yes

Grid Bus 1 Bus 2 Bus 3 Bus 4 Bus 5 Fig. 3. A typical distribution system with proposed PV connection at Bus3 Maximum additional PV at 3 has to be designed ensuring does not exceeds harmonic voltage limit. Voltage harmonic at 5: = + + (7) + As harmonic injection remains same at 4 and 5, (7) can be written as follows: = + (8) Where constant = ( + )( - ) + ( - ). So if changes to _, with additional PV source, new harmonic voltage at 5 changes as (9): _ = _ + (9) With an additional harmonic current injection at 3, new harmonic voltage at Bus _ are derived as follows: New harmonic voltage _ at 1: _ = + (10) New harmonic voltage _ at 2: _ = _ + + + + + ( (11) ) _ = + + + + + + (12) ( ) _ = + + + + ( (13) )+ + ( ) _ = + (14) As previous harmonic voltage at 2, = + ( + + + )( ) New harmonic voltage _ at 3: _ = _ + + + + ( ) (15) => _ = + + + + + (16) ( ) => _ = + + + ( )+ (17) + ( ) => _ = + (18) Here previous harmonic voltage at 5, = + + + ( ) Solving two equations (9) and (18) gives the _ in terms of as shown in (20) => _ =( + )+ (19) => _ = + (20) Where =( + ) Similar equation as in (20) can be formed for desired harmonic frequencies. While deciding the maximum allowed harmonic current injections, a boundary condition can be created, such that, the individual as well as total voltage harmonic distortion fall below IEEE specified limit. A case study analysis is presented in section V to validate this approach (see sub section C). V. CASE STUDY The proposed methodology is tested on a 11kV distribution feeder consisting of five 11/0.415 kv distribution transformers shown in fig. 4. Total distribution load connected under each 500kVA capacity is 350kW at 0.95 power factor. Constant PQ type loads are considered for the analysis with harmonic injections from PV sources. However, load side harmonic current injections also can be included, which would further decrease the PV capacity in order to keep the harmonic distortion below allowable limit. Weasel type conductor is considered for the analysis with 1.5 kms distance between buses, and total feeder length to be 7.5 kms. Feeder library data is provided in Table I. TABLE I. PV PV PV PV PV Fig. 4. Distribution system for case study 11KV FEEDER IMPEDANCE DATA Positive seq. R Positive seq. X Zero seq. R Zero seq. X ohm/km/phase ohm/km/phase ohm/km/phase ohm/km/phase 1.04 0.382 1.216872 1.61782 Driving point impedance computed through MiPower TM software tabulated in Table II. Bus 33/11kV Bus 1 Bus 2 Bus 3 Bus 4 Bus 5 Bus 6 11/0.415 %X= 0.052 p.u. TABLE II. HARMONIC DRIVING POINT IMPEDANCE 5 th Order 7 th Order 11 th Order Z in Angle Z in Angle Z in Angle ohm in deg. ohm in deg. ohm in deg. Bus 1 2.02 90.000 2.82 90.00 4.44 90.00 Bus 2 5.13 72.27 7.01 77.14 10.85 81.73 Bus 3 8.35 68.06 11.29 73.95 17.33 79.62 Bus 4 11.60 66.20 15.58 72.51 23.81 78.66 Bus 5 14.85 65.15 19.87 71.70 30.30 78.11 Bus 6 18.11 64.48 24.17 71.17 36.79 77.76 The current harmonic injections from PV solar inverters are assumed to be 30%, 12% and 10% for 5, 7 and 11 harmonic order respectively. Total allowable PV capacity is determined in sub-sections A and B. The 5 harmonic current injected form 200kW PV source 0.415 kv side is calculated as follows: 0.30 ( (200/( 3 0.415)) (21)

And current transformation ratio (0.415/11) is multiplied to get the reflected current at primary side. Similiary 7 and 11 current harmonics injections to be calculated. A. Penetration from substation end in feeder Using the flow chart in section II, both individual and total voltage harmonic distiortion are calculated as shown in Tables III to V. Shaded portion in coloumn defines the feasible number of s, those can take the allocated PV capacity keeping THD below speified limit. For example, in Table III, 200 kw of aggreagted PV source can be installed under all 5 no.s s. Whereas, as per Table IV, 225 kw capacity off aggreagted PV source can be installed under only 3 no.s s. TABLE III. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 200 KW PV CAPACITY PER 1 0.9352 0.2229 0.4751 1.0724 2 1.7022 0.4062 0.8663 1.9527 3 2.301 0.5499 1.1738 2.6410 4 2.7319 0.6539 1.3975 3.1375 5 2.9949 0.7183 1.5374 3.4423 TABLE IV. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 225 KW PV CAPACITY PER 1 1.0521 0.2508 0.5344 1.2064 2 1.5367 0.3678 0.7861 1.7648 3 2.2105 0.5294 1.1320 2.5393 4 3.0734 0.7356 1.5721 3.5296 5 3.3693 0.8081 1.7295 3.8725 TABLE V. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 250 KW PV CAPACITY PER 1 1.1690 0.2787 0.5938 1.3405 2 2.1277 0.5078 1.0829 2.4408 3 2.8763 0.6873 1.4672 3.3012 4 3.4149 0.8173 1.7468 3.9218 5 3.7437 0.8979 1.9217 4.3028 B. Penetration from substation end in feeder Tables VI to VII depict voltage distortion results in case of forward PV allocation starting from substation end. TABLE VI. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 200 KW PV CAPACITY PER 1 0.2647 0.0647 0.1401 0.3064 2 0.6956 0.1687 0.3638 0.8029 3 1.4908 1.2940 0.3123 0.6712 4 2.0604 0.4955 1.0624 2.3705 5 2.9949 0.7183 1.5374 3.4423 TABLE VII. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 225 KW PV CAPACITY PER 1 0.2978 0.0727 0.1577 0.3447 2 0.7825 0.1898 0.4093 0.9033 3 1.4557 0.3513 0.7551 1.6771 4 2.3179 0.5574 1.1952 2.6668 5 3.3693 0.8081 1.7295 3.8725 TABLE VIII. HARMONIC VOLTAGE DISTORTION AT BUS 6 WITH 250 KW PV CAPACITY PER 1 0.3309 0.0808 0.1752 0.3830 2 0.8695 0.2108 0.4548 1.0036 3 1.6175 0.3903 0.8390 1.8635 4 2.5755 0.6193 1.3280 2.9631 5 3.7437 0.8979 1.9217 4.3028 From the test results as shown in Tables III to VIII, maximum aggregated PV capacity with different penetration factor is as shown in Table IX, as a comparison between backward and forward PV penetration. TABLE IX. BACKWARD VS FORWARD PV PENETRATION Aggregated PV Backward PV penetration Forward PV penetration capacity / Total feasible capacity In kw Total feasible capacity In kw 200 kw 200*5= 1000 kw 200*5= 1000 kw 225 kw 225*3 = 675 kw 225*4 = 900 kw 250 kw 250*3= 750 kw 250*4 = 1000 kw It can be observed, when PV penetration starts from tail end, total feasible PV capacity increases as compare to forward penetration. Because of harmonic currents from PV inverters sees more impedance as compared to those installed near to substation. C. Available PV source capacity at any specific location This test case is meant to determine additional PV capacity at specific location, using the methodology explained in Section IV. Distribution network shown in fig. 4 is taken as a sample network. Aggregated roof top solar PV source under each is considered as 200kW. Current harmonic distortions from PV solar inverters are taken as, 27%, 12% and 10% for 5, 7 and 11 harmonic order respectively. In order to find the maximum available aggregated PV capacity at 4, using (20) and driving point impedance from Table II, following equations are formed: = (11.60) + (183.412), for 5 (22) = (15.58) + (109.483), for 7 (23) = (23.814) + (139.481), for 11 (24) These describe the individual voltage harmonic variation at feeder tail end (at 6 ), with respect to harmonic current.

Boundary conditions are formed considering individual as well as total harmonic distortion limits as in (25-26): 100 3%, h (25) + _ + 100 5% (26) Both THD and individual distortion for 6 are plotted against harmonic current shown in fig.5. Voltage harmonic distortion 5.0 4.5 4.0 3.5 3.0 2.5 2.0 Fig. 5. Voltage harmonic distortion for Bus 6 against harmonic current It is observed from voltage distortion plot, at 0.6A current, 5 order voltage distortion is reaching 2.998%. And at 0.62A it exceeds IEEE specified limit to 3.001% (marked in red color diamond shape). Whereas, other individual and total voltage distortions are still below IEEE specified limits 3% and 5% respectively. So maximum fundamental current is selected considering 5 harmonic current distortion level(27%), because 7 and 11 order current distortions are, 12% and 10% respectively, which are lower than 5 harmonic distortions. So the reflected fundamental current at secondary (0.415kV) side is as below: (0.62 (11/0.415))/ 0.27 = 60.86A (27) And the additional feasible PV capacity would be: 3 (0.415) = 3 (0.415) 60.86 = 43.75 (28) Harmonic analysis is performed on this network with existing PV sources and including additional PV source using MiPower TM and results are published in Table X. TABLE X. th th th HARMONIC VOLTAGE AFTER INSTALLING ADDITIONAL PV With exciting PV sources 2.998 3.001 1.5 0.5 0.52 0.54 0.56 0.58 0.6 0.62 0.64 0.66 0.68 0.7 Current harmonic in Ampere With additional PV source at Bus 4 Bus VTHD VTHD Bus 5 2.72 1.62 2.07 3.79 2.82 1.69 2.15 3.94 Bus 6 2.88 1.72 2.19 4.02 2.99 1.78 2.27 4.16 From Table X, it is observed that, with the additional feasible PV source at 4 (computed as 43.75 kw), 5 harmonic voltage at 6 is increased from 2.88% to 2.99%, which is below IEEE specified limit (3%) and voltage THD is also below IEEE specified limit (5%). So the additional PV solar capacity calculated through proposed methodology does not violate harmonic distortion limit. So without computing the feasible capacity in a repetitive manner, this methodology is able to determine the maximum future PV solar penetration at specific location. VI. CONCLUSION The proposed methodology computes maximum PV penetration capacity in a feeder with different transformer penetration level. Also in addition finds additional PV capacity at a specific location for future rooftop PV penetration without exceeding the IEEE voltage specified limit. The results demonstrate the strength of the approach and are verified using MiPower TM simulation software. The proposed methodology can be used for distribution system planning level as a preliminary approach to study the impact of rooftop solar source penetration in distribution feeder with respect to harmonic distortion. And accordingly necessary prevention measures can be taken to avoid high harmonic distortion improving the power quality. REFERENCES [1] J. H. R. Enslin and P. J. M. Heskes, "Harmonic interaction between a large number of distributed power inverters and the distribution network," in IEEE Transactions on Power Electronics, vol. 19, no. 6, pp. 1586-1593, Nov. 2004. [2] P. P. Barker and R. W. De Mello, "Determining the impact of distributed generation on power systems. I. Radial distribution systems," Power Engineering Society Summer Meeting, 2000. IEEE, Seattle, WA, 2000, pp. 1645-1656 vol. 3. [3] A. Bhowmik, A. Maitra, S. M. Halpin and J. E. Schatz, "Determination of allowable penetration levels of distributed generation resources based on harmonic limit considerations," in IEEE Transactions on Power Delivery, vol. 18, no. 2, pp. 619-624, April 2003 [4] IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, IEEE Std. 519-1992, 1993. [5] V. R. Pandi, H. H. Zeineldin and W. Xiao, "Determining Optimal Location and Size of Distributed Generation Resources Considering Harmonic and Protection Coordination Limits," in IEEE Transactions on Power Systems, vol. 28, no. 2, pp. 1245-1254, May 2013 [6] H. Anderson, B. Rebecca, H. Joshua and K.Benjamin, "Maximum Photovoltaic Penetration Levels on Typical Distribution Feeders", Journal Article, NREL/JA-5500-55094, July 2012 [7] Y. J. Wang, R. M. O'Connell and G. Brownfield, "Modeling and prediction of distribution system voltage distortion caused by nonlinear residential loads," in IEEE Transactions on Power Delivery, vol. 16, no. 4, pp. 744-751, Oct 2001. [8] H. E. Mazin, W. Xu and B. Huang, "Determining the Harmonic Impacts of Multiple Harmonic-Producing Loads," in IEEE Transactions on Power Delivery, vol. 26, no. 2, pp. 1187-1195, April 2011. [9] MiPower TM User Manual, www.prdcinfotech.com. [10] G. J. Wakileh, Power Systems Harmonics, First Ediition, Springer, 2001. J. Arillaga, N.R. Watson, Power System Harmonics, Second Edition, John Willy & Sons Ltd, 2003.