HARMONIC ALLOCATION TO MV CUSTOMERS IN RURAL DISTRIBUTION SYSTEMS

Transcription

1 HARMONIC ALLOCATION TO MV CUSTOMERS IN RURAL DISTRIBUTION SYSTEMS V Gosbell University of Wollongong Department of Electrical, Computer & Telecommunications Engineering, Wollongong, NSW 2522, Australia Abstract Te armonic management of power systems in Australia is governed by AS/NZS Tis document is limited to a discussion of principles wit little advice on detailed calculation. A Standards Australia andbook sows ow te standard can be applied to find customer armonic allocations for city and urban power systems. Tis paper furter extends tis work to rural power systems aving te features of isolated lumped loads and radials wit spurs. A general armonic allocation equation is developed containing an allocation coefficient wic is required to be found for eac MV system. It is sown tat te computation to find tis coefficient can be simplified so tat a small spreadseet can be used. 1. INTRODUCTION International armonic surveys sow tat THD voltages are generally increasing at about 1% per decade and tere are many sites in Europe were armonic levels already exceed limits, also known as Planning Levels, for some armonics [1]. It is important tat utilities ave effective policies for ensuring tat te armonic loads being connected to teir system do not exceed teir system s capacity to absorb distortion. At LV, equipment armonic emission is controlled by equipment standards suc as [2], wile at MV, armonic current is allocated to eac customer s installation guided by te principles of AS/NZS [3]. Unfortunately, tis document is unclear in places, and is particular difficult for occasional users. Standards Australia commissioned a andbook [4] to give a guide to applying te standard. Tis guide was limited in application to MV distribution systems wit uniformly distributed loads and a simple radial topology, based on a correction factor as developed in [5]. Wit a growt in mining loads remote from towns, tere is now a need to extend te procedure to rural systems aving te following additional features of lumped loads and spur lines. Tis paper proposes an approac wic can be applied to rural systems and is illustrated wit a particular test system wic will be used to confirm te usefulness of te suggested approac. It allows te determination of te armonic current to be allocated to an installation under Stage 2 of te standard. It is assumed tat pfc capacitors are fitted wit series detuning reactors so tat te armonic impedance can be determined from simple fault level considerations. LV installations are ignored in tis paper since teir armonic effects on MV systems are not usually of great significance [4]. Te treatment of diversity given in Section 2.1 is based on a combination of experience and teory and is necessarily approximate. Hence little is to be gained by an attempt at an exact approac, especially as tis leads to te need for an enormous amount of data. Engineering judgement need to be exercised in most armonic allocations were te accuracy required is about 10%. A list symbols is given after te References section. 2. STAGE 2 OVERVIEW Tis section gives te main aspects of Stage 2 as given in [3, 4]. It identifies te basic principles tat will be used in te paper for te development of analytical tecniques wic can address rural systems. 2.1 Representation of time-varying quantities Under normal conditions, power system armonics are due to te interaction of many time-varying distorting loads. Te following principles are recommended for representing voltages and currents in tis situation [3]: 1. Time-varying voltages and currents are represented by teir 95% probability values. 2. Te 95% values of voltages and currents can be found from te 95% value of te independent contributions using te Summation Law to account for diversity. Tis law is V tot = V 1 + V V n were varies wit te armonic order. A value of = 1.4 is used for 5 10 and 2 for > 10. (1) 122

2 2.2 Allocation principles Te Standard adopts tese principles for armonic allocation under Stage 2: 1. Te armonic allowance to an installation increases wit maximum demand. 2. Te armonic allowance sould be suc tat te igest armonic voltage in te local power system just reaces te Planning Level wen te system is fully loaded and all installations are taking teir maximum allocation. [3] discusses te coice of quantity to be allocated. In distribution systems wit long feeders, as is usually te case in Australia, armonic VA is sown to be a more suitable quantity tan voltage or current since it gives a useful allocation to customers at points of low fault level. Tis allocation quantity will be adopted ere. 2.3 Interaction wit oter parts of te distribution system 33kV 11kV 3. HARMONIC ALLOCATION IN RURAL DISTRIBUTION SYSTEMS 3.1 Overview Te system of Figure 2 will be used to discuss te details of te allocation process. It as been cosen because it is simple but as all te features wic need to be treated to apply to rural system armonic allocations: Feeders 1 and 2 wit distributed loads. Feeders 2 and 3 wit lumped loads. Feeder 3 wit spurs 3A and 3B. V US S t, x t V MV impedance x s S D, x D S A (x sa to x da ) S B (x sb to x db ) Feeder 1 Feeder 2 Feeder 3A S E, x E S C, x C Feeder 3B S F, x F Figure 1-11 kv power system wit study installation aving maximum demand S i In te local power system sown in Figure 1, te armonic voltages are influenced by loads connected elsewere wit armonic effects propagating via te 33kV system. Similarly, te local power system influences armonic voltages upstream. Assumptions need to be made wic allow te user to avoid making any detailed study of upstream effects due to te 33kV system and oter more remote interconnected parts. It is assumed tat tat te wole power system is armonically fully loaded so tat te 33kV bus reaces its Planning Level. Te 33kV bus is represented as a constant voltage source equal to te Planning Level for eac armonic being studied. Tis is an approximation because some part of te 33kV bus armonic voltage is due to downstream effects of te local power system and it is incorrect to use a voltage source representation for tis contribution. However te assumption is pessimistic and gives some safety margin for te allocation calculation. If L MV is te MV Planning Level and L US te Planning Level at te next voltage level upstream, te armonic voltage available to local MV loads is, making use of (1), G MV MV US = L L (2) S i Figure 2 - Example system One as to consider future as well as present loads in te allocation process (Section 2.2, point 2), ence not all te loads sown in Figure 2 need be connected at present. In some cases, te position of future loads is uncertain and engineering judgment needs to be made. Te allocation principles lead to an allocation law given in Section 3.2. Te armonic current drawn by MV loads is determined as sown in Sections 3.3, 3.4. Harmonic voltage can ten be calculated as sown in Section 3.6, owever tis calculation need only be done for te weakest feeder as defined in Section 3.5. Te value of k is ten determined by simple proportion as given in Section Te allocation equation A load wit maximum demand S i is connected to te system at a point were te armonic impedance is x i. It is sown in [6] tat te principles of armonic allocation are followed if te load S i is given te following current allocation: 1/ k Si E Ii = (3) x k is te allocation constant for all MV loads in te local power system and varies wit te armonic order. i 123

3 3.3 Lumped MV loads If resistance is small at armonic frequencies, te armonic impedance at te point of connection of load S i is given closely by x i = x i1 (4) were x i1 is te fundamental reactance determined from fault level considerations. Te armonic current for installation i is taken as its full allocated emission from (3) I i = k 1/ Si 3.4 Uniformly distributed MV loads Te metodology requires tat all loads are represented as lumped quantities. We ave sown in Appendix A tat uniformly distributed MV loads drawing equal armonic VA can be replaced wit adequate accuracy, for armonic calculations, by a lumped loads aving a somewat increased value of total MVA and situated at te appropriate pcc using (A.9, A.10). Te loads S A, S B are replaced by: Feeder 1: S Aeq is concentrated at x Aeq. Feeder 2: S Beq is concentrated at x Beq. Te system of Figure 2 becomes transformed to tat of Figure 3, wic also sows node numbers for future reference. x s 1 2 x i S Aeq, x Aeq Feeder Feeder 2 (5) Te fundamental loading can be estimated for eac feeder by computing te sum Σx i S i and finding te one aving te largest value see Table I for te calculations for te system in Figure 3. Uniform loads are given an impedance value corresponding to te average connection point. Tis is not exactly te same as te impedance of te equivalent lumped load used for armonic calculations (A.10). Table I - Fundamental loading for eac feeder in Figure 2 Feeder 1: x Aav S A Feeder 2: x Bav S B + x C S C Feeder 3A: x D S D + x D S F + x E S E Feeder 3B: x D S D + x D S E + x F S F Notice tat for Spur 3A, it is necessary to allow for te impact of te load on Spur 3B at te common impedance x D. A similar remark applies to te impact on Spur 3B of te load on Spur 3A. Were tere is uniform construction trougout te local system (eiter overead open-wire, ABC or underground), reactances can be replaced by line lengts. 3.6 Determination of armonic voltages We determine te armonic voltage appearing at te end of te weakest feeder as identified in Section 3.5. Te following steps are necessary: (a). Harmonic currents are determined for MV loads (5) wit k initially set to unity. (b). Harmonic impedances are cosen for eac load at te pcc wit te weakest feeder. For te Figure 2 example, if Feeder 3A is te weakest, impedances are cosen as Load S Aeq : te supply impedance x s Load S F : te impedance to D, tat is x D Load S E : te impedance to E, tat is x E S Beq, x Beq S C, x C 3.7 Determining te allocation constant S D, x D 5 6 Feeder 3A S E, x E S F, x F Feeder 3B 7 Figure 3 - Lumped model equivalent of Figure Determination of weakest feeder It is not necessary to calculate te igest voltage at te end of eac feeder. Harmonic loading is related to fundamental loading since armonic currents relate to maximum demand and armonic impedance is related to fundamental impedances as given in (4). It is usually only necessary to determine te value of armonic voltage at te end of te feeder wit te igest fundamental loading. Te armonic voltage contribution of MV loads to te armonic voltage at te end of te weakest feeder, wit k equal to unity, can be found by summing te separate contributions using te Summation Law (Section 2.1). For oter values of k, linearity applies and te MV contribution will be V MV.weakest = k V MV.weakest ' (6) were te das ' indicates a value determined for k = 1. Hence, G k = MV V ' (7) MV.weakest 3.8 Extension to oter frequencies We note tat tat k in (7) is te ratio of two quantities. Te numerator, G MV will need to be determined for eac frequency. Te denominator quantity only needs 124

4 to be determined in detail at two armonic frequencies as discussed below. Te weakest feeder as been defined in terms of fundamental quantities (Section 3.5) and will not cange wit frequency. Te armonic voltage is determined using te Summation Law as te sum of terms suc as (I x ) wit k initially at unity. From te allocation law (3), tese terms are of te form Sx /2 = S /2 x 1 /2. Wen te resultant V is ten found by taking te root, we find Hence V ' (8) G k MV (9) For a given value of, if k 5, as been determined, oter values (for 10) can be found by proportion G 5 k = MV k 5 G (10) 5MV At = 11, is cosen as 2, and k 11 cannot be found from (10) it needs to be determined from a detailed calculation, as for k 5. Once determined, oter values (for 11) can be found from G 11 k = MV k11 G (11) 11MV 4. EXAMPLE CALCULATION 4.1. System Data We now consider te case of Figure 2 were te data in Table II applies. Te aim is to determine te allocation constant k for te 5 t armonic. Table II - Data for first example V US V MV S t x t L US5 L MV5 x/km 33kV 11kV 25MVA 15% Ω/ km Load A B C D E F Type Uniform Uniform Lumped Lumped Lumped Lumped S- MVA Posn km 4.2. Outline of calculations Te full calculation is given in Appendix B. A base of 1MVA is cosen for per unit calculations. System armonic impedances are found in Section B.1, including equivalent impedances for lumped equivalents to S A and S B. Te igest armonic voltage is seen to occur at te end of Feeder 3B. In Section B.3, for te Planning Levels given in Table II, G MV, te armonic voltage available for local MV loads is found as 3.1%. Wit k = 1, MV loads would cause a voltage rise of 158% (Section B.4). Te ratio of G MV to tis voltage gives a value for k of As an example of its use, for load S C, E IC is determined from (3) as /1.4 / or pu. Relative to its fundamental current of 2.5 pu, tis is an allocated 5 t armonic current of 3.1% MATLAB verification An independent MATLAB calculation as been made to ceck te proposed metodology. Te system as been represented wit eac loads replaced by te armonic current in Section B.4 scaled up by k from Section B.5. Harmonic voltages were found as given in Table III. Te largest voltage is found at te end of Feeder 3B (Node 7) and just equals G MV as determined in Section B.3 sowing tat te approac is sound. Table III - V and fundamental loading for eac node. Nodes at te end of feeders are sown in bold. Node ΣS lengt V V as been plotted against fundamental loading in Figure 4 to ceck te metod for finding te weakest feeder. It can be seen tat tere is close relationsip between tese two parameters so tat loading is a good predictor of te weakest feeder. V Feeder 1 Feeder 2 Feeder 3A Feeder 3B Loading 4.4. Sensitivity Figure 4 - Plot of V vs ΣS lengt Te sensitivity of k on system data as been determined from te MATLAB program. For system parameters, te sensitivity is 0.3%-per-% or less. Te igest sensitivity is for load caracteristics at D and F on te weakest feeder. Tis compares wit about 2%-per-% sensitivity to parameters defined in te standards suc as and L MV. Tis demonstrates tat te proposed metod is robust. 125

5 5. CONCLUSIONS An approac as been developed to implement te basic principles of armonic standards for rural systems. Tis leads to te concept of a armonic allocation constant for a particular local power system. Calculations can be simplified by (i) determining te voltage only at te end of one feeder wic can be easily identified, (ii) making full calculations only at two armonic frequencies. Uniformly distributed MV loads can be lumped into a single equivalent load. Te calculations are sufficiently simple tat tey can be implemented by spreadseet. 6. REFERENCES [1] Euroelectric Report, February 2002 "PQ in European Electricity Supply Networks" [2] AS/NZS :1998, "Electromagnetic compatibility (EMC) Part 3.2: Limits-Limits for armonic current emissions (equipment input current less tan or equal to 16A per pase)" [3] AS/NZS , "Limits Assessment of emission limits for distorting loads in MV and HV power systems", Standards Australia [4] V.J. Gosbell, S. Perera, V. Smit, D. Robinson and G. Sanders, "Power Quality Recommendations for te application of AS/NZS and AS/NZS ", Standards Australia, HB , August 2003, ISBN [5] V.J. Gosbell and D Robinson, "Allocating armonic emission to MV customers in long feeder systems", AUPEC03, Sept-Oct, 2003, Cristcurc [6] V.J. Gosbell, D.A. Robinson and B.S.P. Perera and A. Baitc, "Te application of IEC to MV systems in Australia", ERA Conference, Tame, Feb 2001, pp LIST OF MAIN SYMBOLS Symbol E Ii G MV I i k L MV L US R SBase S eq S i V MV x av x eq x i Meaning Harmonic current emission allocation to load "i" Harmonic voltage available to local MV loads Harmonic order Harmonic current from load "i" Allocation constant Local MV Planning Level Upstream Planning Level Ratio of fault levels at supply and downstream ends of feeder Base MVA Equivalent lumped max demand for uniformly distributed load Load "i" maximum demand Voltage at end of feeder due to MV loads Average impedance at pcc for uniformly distributed load Equivalent lumped impedance at pcc for uniformly distributed load Harmonic impedance at pcc of load "i" Summation exponent APPENDIX A - UNIFORMLY DISTRIBUTED MV LOADS Tis teory used in tis section is based on results from [5]. Suppose we ave a feeder wit te following features: Total distributed load S Load distributed between points aving fundamental reactance x s at supply end and x d at downstream end Harmonic order wit Summation Law coefficient Load allocated armonic current following te principle of equal armonic VA to equal loads A specific installation S i is allocated a current I i based on te armonic VA principle and following (3). Te armonic current drawn by tis load can be closely approximated by [5]. I ~ k S (1/) R -0.3 / (x s ) (A.1) Te armonic voltage caused by tis load is igest at te far end and can be approximated by V ~ k ( x s )S (1/) R 0.33 (A.2) We now find an equivalent lumped load S eq and position x eq (given in terms of fundamental sortcircuit reactance) to give te same results. We tus need to solve te following simultaneous equations k S eq (1/) / (x eq ) = k S (1/) R -0.3 / (x s ) k ( x eq )S eq (1/) = k ( x s )S (1/) R 0.33 Multiplying (A.3) by (A.4) S eq 2/ = S 2/ R 0.03 (A.3) (A.4) giving S eq = SR 0.03/2 (A.5) Dividing (A.4) by (A.3) 1/x eq = 1/(R 0.63 x s ) Giving x eq = R 0.63 x s (A.6) Tere are approximations in tis derivation and it was cecked and furter improved by means of a spreadseet study. A model was set up were te uniformly distributed load was assumed to be accurately represented by a 10-stage discrete model. Values of armonic current and voltage were determined for combinations of R = 6, 10, 28 and = 1, 1.4, 2. Based on te above teory, te lumped model was assumed to be of te form S eq = SR x1. x eq = x s R x2 (A.7) (A.8) Values were found for te parameters x1, x2 to minimise te maximum of te percentage errors between te accurate and te lumped equivalent model. Te following modified equations gives a worst-case error of less tan 11% and an average error of 5% over te studied range of R and. 126

6 S eq = SR (A.9) x eq = x s R 0.64 (A.10) Te original equations (A.7, A.8) gave a worst-case error of 21% and an average error of 7%. APPENDIX B - NUMERICAL EXAMPLE Tese calculations ave been set out so tat tey can easily adapted to a spreadseet. Coose a base S Base = 1 MVA. Tis coice leads to eac value of S in per unit being identical to te MVA value as given in Table II. B.1 System impedances Find te relevant fundamental and armonic reactances for = 5. x s = x t = 0.15 (New base/old base) = /25 = pu x s = x s = pu At 11kV, Z Base = V 2 /S Base = 11 2 /1 = 121Ω Determine armonic reactances corresponding to eac lumped load connection point. For uniform loads, determine te quantity x d, te armonic reactance to te downstream end of te distributed load. At A: x Ad = x s + len A x/z Base = /121 = pu Similarly, x Bd = pu, x C = pu, x D = pu, x E = pu, x F = pu Determine equivalent MVA and point of connection for te distributed loads A and B. S Aeq = S A R A = = 2.79 pu S Beq = S B R B = = 2.70 pu x Aeq = x s R A 0.64 = = pu x Beq = x s R B 0.64 = = pu B.2 Weakest feeder Since in tis case line lengts are proportional to impedances, we use tem in te loading calculation for simplicity. 1: S A len Aav = /2 = : S B len Bav + S C len C = 2.5 5/ = A: S D len D + S E len E + S F len D = = 60 3B: S D len D + S E len D + S F len F = = 75 Feeder 3B is te weakest as it as te largest S lengt product. B.3 Harmonic voltage available to MV loads Determine te voltage available for MV loads. 1.4 G MV = L L = = pu MV US 031 B.4 Harmonic voltage at end of weakest feeder Determine te voltage at te end of te weakest feeder 3B wit k provisionally put to "1", using te symbol ' as a reminder. We need to determine te armonic currents injected by eac load from (5). 1/ 1/1.4 SA 2.79 Feeder A: IA ' = = = pu x Aeq Similarly, I B ' = 7.92 pu, I C ' = 3.87 pu, I D ' = 3.20 pu, I E ' = 2.36 pu, I F ' = 1.96 pu. We also need to determine te appropriate impedance for eac load to give te impact of its armonic current on te armonic voltage at te end of weakest feeder 3B. Tese are x s, x s, x s, x D, x D and x F for loads A-F respectively. Hence te armonic voltage at te end of Feeder 3B is made up of te following components wic will need to be combined by te Summation Law: A: V A ' = I A 'x s = = 0.21 pu Similarly, V B ' = 0.24 pu, V C ' = 0.12 pu, V D ' = 0.56 pu, V E ' = 0.41 pu, V F ' = 0.91 pu. Combining tese voltages = V ' = V + V + V + V + V + V A B C D E F + = 1.58 B.5 Allocation constant k is determined as te ratio of G MV from B.3 and V ' from B.4 k = /1.58 = As a quick ceck, we can compute te relative armonic current for a couple of te loads, for example B (te closest to te supply) and F (te furtest). For B: I B = k I B ' = = 0.16 pu Relative to I B1, I B = 0.16/S B = 0.16/2.5 = 6.2% For F: I F = k I F ' = = pu Relative to I F1, I F = 0.039/S F = 0.039/1.5 = 2.6%. Tese values are in te range of typical MV 5 t armonic current allocations and decrease for loads furter away from te supply as would be expected from a armonic VA allocation policy. 127