Allocating armonic emission to MV customers in long feeder systems V.J. Gosbell and D. Robinson Integral nergy Power Quality Centre University of Wollongong Abstract Previous work as attempted to find satisfactory metods for te allocation of armonic current emission MV subsystems containing long feeders. It as been proposed tat best use of te network's armonic absorption capacity is made if te allocated current varies wit te inverse square root of te armonic impedance at te point of connection. It as been sown tat an eact solution following tis principle requires an impracticably large amount of data. Here it is assumed tat eac feeder supplied from a given substation as its load distributed uniformly and continuously along it, giving equations requiring only a modest amount of data. It is demonstrated by means of a suitable eample tat te metod is sufficiently accurate for practical situations were loads are lumped non-uniformly.. INTRODUCTION A/NZ 6000.3.6 (based on IC 6000-3-6 and referred to subsequently as te tandard gives a procedure for utilities to allocate armonic current emission to MV customers []. One possible allocation strategy is to give an equal sare of te armonic voltage absorption capacity of te local network to all installations of equal maimum demand. Te allocated current is ten given by te allocated voltage divided by te armonic impedance at te point of common connection (PCC. Wen tese installations are spread out on a long feeder, for eample or more km in lengt, tere can be a : or more cange in fault level. Hence installations at te far end will be allocated a comparatively lower armonic current. Anoter option is tat installations of equal maimum demand are allocated an equal sare of te armonic current absorption capacity of te local network. Tis as te difficulty tat equally sized installations close to te supply point are limited to te same current as te most distant load, greatly restricting te armonic absorption capacity of te system. Te tandard recommends an intermediate option, te allocation of equal sare of te armonic voltamperes, equivalent to varying te armonic current wit te inverse square root of te armonic impedance at te PCC. An eample is given in te tandard to sow te application of te metod. Te particular case given involves all feeders being equally loaded, and as sown in [], tis leads to a great reduction in te data required and te analysis can be made eactly. Practical cases require an impractical amount of data for an eact solution. [] sows some metods for estimating upper and lower bounds for te armonic allocation, but te metod requires engineering eperience and judgement for reliable application. Tis paper proposes a new metod wic will provide more accurate analysis of te armonic allocation problem for a wide range of system types. Te key step is te replacement of te several lumped loads distributed along a feeder by a uniform continuous load. Tis leads to a system wic is capable of eact matematical solution and requiring only a modest amount of data. A couple of eamples will sow tat te uniform load model is accurate enoug for typical armonic application studies. In order to present te approac witout undue compleity, two simplifications will be made. (i Te contribution from LV loads will be ignored. (ii All numerical calculations will be restricted to te t armonic. Te correction of te teory to allow for te effect of LV loads is simple in concept but leads to cumbersome equations [3]. Calculation of armonics oter tan te t are seldom required as tey are usually small and insignificant [].. OVRVIW OF A/NZ 6000.3.6 Te tandard is applicable to MV systems (MV defined by te IC as -3kV line-line drawing distorting current wit armonics in te range -0. It outlines bot utility and customer responsibilities. Utilities ave to ensure teir net armonic voltage levels are less tan teir Planning Levels, wit typical values at kv of % at te t armonic, falling to 0.% at ig armonics. It needs to be noted tat Planning Levels are reduced at eac successively iger voltage level, wit % t armonic being common at transmission voltage levels. Customers ave to limit teir armonic current emission to te values allocated by utilities and stated in connection agreements. Te utility is a distribution company at MV. It as a major difficulty in assessing a particular customer's
allocation since te armonic voltage at any point is made up from te time-varying contribution of many loads, most of wic will not be known in detail. Distributors often do not ave complete records of teir system parameters, for eample te impedance seen by eac of teir MV customers. Te tandard as developed a metod based on a statistical average view of te system and te customers. Time-variation is accounted for by te specification of all armonic currents and voltages by teir 9% values. Te relationsip of te armonic voltage and current of one customer are given by armonic impedances, were resistances are ignored. Te combined effect of many armonic sources is approimated by te tandard's econd ummation Law wic as been partially establised by teory and by observation []. In te case of two armonic voltages aving 9% values V and V, te 9% value of te resultant voltage is V V + ( V were varies wit te armonic order and is. for te t armonic and accounts for time and pase diversity. Te allocation of armonic current to one customer cannot be made witout some assumptions about te operation of te system and te armonic injection of all oter customers connected to neigbouring parts of te subsystem. In te simple case were all customers are connected to te busbar of te zone substation (zero lengt feeders te recommended assumptions are (i Te system is operating wit all present and future customers connected. (ii All customers are using teir full armonic allocation rigts. (iii Te upstream supply as armonic distortion at its full Planning Level. (iv All contributions combine according to te econd ummation Law. (v Te igest voltage in te system just reaces te local Planning Level. uppose now tat te local and upstream Planning Levels are L and L U. Application of te econd ummation Law will give a voltage (te so-called global emission voltage in te tandard to be distributed to te local MV loads given by G L L U ( An additional assumption is required regarding te relative allocation to all customers. Te tandard adopts wat is sometimes called te "equal rigts premise" - all customers of equal maimum demand connected to te same supply point are to receive equal armonic current (and terefore equal armonic voltage allocations. uppose now tat te total supply capability is t and tat an allocation is to be made to a customer "i" aving maimum demand i. Because of te non-linear nature of te econd ummation Law, te voltage allocation is given by Ui (3 Te current allocation is ten determined by te armonic impedance at te supply busbar. Ui Ii ( Tis approac proves unsatisfactory wen te customers are distributed along a long feeder (one or more km long were tere are significant canges in fault level. If customers wit equal maimum demand are allocated equal armonic voltage, te current allocation given by eqn( will be muc smaller for customers near te far end of a feeder. Alternatively, if customers wit equal maimum demand are allocated equal armonic current, te allocation will need to be small to reduce te impact of customers at te far end. Tis will lead to a great reduction in te capacity of te system to absorb armonics. Te tandard recommends te allocation of equal volt-amperes in suc cases. Te approac is sound but it is not detailed and is illustrated wit a poorly cosen eample in wic all feeders and all loads are identical. Altoug it is not clear from te eample, te metod can only be applied to more practical cases if every load and te impedance at its point of connection is known. MV systems generally consist of about 0 feeders, eac aving a conductor type wic canges trougout its lengt. Tere can be 00 or more MV loads connected to te various feeder for eac zone substation. It is inconvenient, wit present database systems, to find all te information required for armonic allocation purposes. [, 6] represent attempts to develop metods of analysis aving sufficient accuracy and requiring considerably less data. Te starting point is to use a modified allocation policy i t i k Ii ( were k, te allocation constant, is determined by te need to keep te far end of te weakest feeder at te Planning Level. Tis will be te feeder wose far end voltage will first reac te planning level as te system is loaded up. Tis is most likely to be te system aving te largest l product ( being load supplied and l is lengt. everal metods ave been developed, none of wic can be guaranteed to be accurate in all cases. However, te various approaces do serve to bracket te correct solution. i
3. NW APPROACH UNIFORM LOADING APPROACH It is assumed tat eac feeder is loaded uniformly and continuously, altoug eac feeder can ave a different lengt and total loading. uppose a feeder as a total load of, an impedance at te supply end, and an impedance R at te far end. Let be te eponent used in te econd ummation Law. Ten it is sown in te Appendi tat te armonic current allocated to te feeder is approimated by I k (/ / ( R -0.3 (6 were k is an allocation constant required to be determined. It is also sown tat te armonic voltage at te far end of te feeder due to its MV loads is approimated by V k ( (/ R 0.33 (7 Fig. sows a system in wic a feeder wit total MV load is te weakest. Oter feeders, not sown individually, carry total MV loads. Let us determine te total voltage at te sending end busbar due to te armonic contributions of tese loads. Te upstream fundamental reactance at te busbar is. Fig. - tudy feeder Te voltage at te far end of te weakest feeder due to its load can be found from (8 V k ( (/ 0.33 R (8 Te currents at te sending end bus due to can be found from (9 I k (/ -0.3 / ( R (9 Te corresponding armonic voltage due to is V k ( (/ R -0.3 (0 It is recommended tat R be cosen to be te average value of te ratio of te sending end to far end fault levels for all te feeders connected to te upstream bus, oter tan te weakest. Were tere is some uncertainty, values for individual feeders can be combined weigted according to te MVA supplied. Te armonic voltage at te far end of te feeder is found from combining eqns(8, 0 wit te upstream component L U using te power law V L U + (k ( R 0.33 + (k ( R -0.3 L U + (k ( ( R 0.33 + R -0.3 ( If te planning level for te far end of te feeder is L, we find k U 0.33 0. 3 ( R + R L L ( We can now eamine for wat feeder lengts te correction terms become significant. Te terms R 0.33 and R -0.3 cange from unity by 0% for R about.. Hence a feeder is considered long wen te ratio of te fault levels at te two ends eceeds.. Now consider an kv feeder wit a typical upstream fault level of 0MVA. Using a base of MVA, Z B V / B / Ω. /FL 0.0067 pu. 0.0083 pu feeder 0.007 pu feeder (Ω feeder Z B 0.0 Ω. Assuming a typical reactance per km value of 0.3Ω/km Lengt feeder (Ω/ 0.6km. Hence an kv feeder more tan 0.6 km sould be considered as long.. XAMPL Two specific case studies will be investigated to illustrate te use of te new metod of allocating acceptable armonic emissions to an MV customer. Te case studies will be completed for te t armonic only, as mentioned in ection. Te customer allocations will be compared wit metods previously described in [, ]. For bot cases an upstream contribution of L U % and a planning level of L % will be assumed. All metods are based on an allocation policy using eqn. (, i.e. an equitable armonic volt-ampere allocation.. Homogenous study system Te first study system is derived from an eample system provided in []. A 0kV distribution network consists of si identical feeders all km in lengt. ac feeder contains si 00kVA MV customers, equally spaced along te feeders as sown in Fig.. 0kV 0MVA XT% km km km km km PCC0 PCC PCC PCC3 PCC PCC 3kV 3 3 6 6 feeders i00kva Fig. - Homogenous study system from []
Te armonic emission allocation according to te metod described in ection 3 is completed as follows. A base of base 0MVA will be used. Te fault level at te sending and receiving ends of eac of te feeders is 3MVA and 38MVA respectively. From te fault levels te impedance ratios are as follows R R (X feeder +X trans /X trans 6.83 Also from eqn. ( we ave te allocation constant k 0. 0.08 0.0 0.0 0.33 0.3 ( 0.06 6.83 + 0.30 6.83 From eqn. ( te individual armonic emission allocated to eac customer can be determined. Table I compares te allocated armonic emissions using te principles outlined in [] to obtain an eact solution, an alternative metod proposed in [], and te metod described in ection 3. As can be seen from Table I te metod proposed in tis paper produces emission allocations to eac customer tat are comparable to te eact, but more comple, solution provided in te tandard. Tis is in spite of te fact tat te proposed metod requires muc less information tan te eact solution and even less information tan te more conservative metod from []. Table I - mission allocation for customers according to metods in [], [], and tis paper Customer Ii [] (eact Ii [] (altern Ii (proposed 37.% 7.8% 39.%.% 8.9% 6.6% 3 0.6%.3%.% 7.7% 3.% 8.%.8%.7% 6.% 6.% 0.7%.0% Allocation constant for eac metod k 9.7% 7.3% 0.8% Using te acceptable armonics emissions levels presented in Table I te resultant armonic voltages along eac feeder were determined for eac metod and are illustrated in Fig. 3. It can be seen tat te proposed allocation metod produces armonic voltages tat approimately matc te eact allocation metod. However, te proposed solution is sligtly more generous to te customers tan te eact solution, and tus results in armonic voltages sligtly above te planning level at te end of te feeder. Te precision of te proposed metod can be improved by more accurately calculating te contribution from te weakest feeder used in determining te allocation constant k. Tis involves additional data consisting of te loading and impedances along te weakest feeder, as is required for te metod outlined in []. However, for tis eample system an error of 3% in te calculated armonic voltage at te end of te feeder is considered well witin te accuracy limitations of te summation law. Harmonic Voltage (%..8.6.. 3.8 3.6 3. act Metod [] Proposed 3. 0 3 Customer location on feeder Fig. 3 - Harmonic voltages due to different allocation metods for omogenous eample (note suppressed zero wit vertical scale. treme study system To test te proposed metod furter a system containing two distinctively different feeders, as illustrated in Fig. was used. Te system contains one weak feeder wit ten 00kVA MV customers, and one strong feeder wit five MVA MV customers. kv 0MVA XT7% 3kV Overead feeder km long 3 6 7 8 9 0 Underground feeder km long 3 Fig. treme study system i00kva imva Te overead line reactance and underground cable reactance is assumed to be 0.3Ω/km and 0.06Ω/km respectively. All loads are equally distributed along te feeders. Using te impedance values of te overead line of te weakest feeder te value of R.63 is obtained. imilarly for te strong feeder te value of R.7 is obtained. Tus k 0.88 0.36 0.0 0.0 0.33 0.3 ( 0..63 + 0..7 Te armonic allocation constant for te eact metod and te metod outlined in [] for te etreme study system were.% and.83% respectively. Te resulting armonic voltages on te strong and weak feeders are illustrated in Fig.. It can be seen tat te proposed metod again provides results in armonic voltages eceeding te planning levels. As wit te omogenous study system tis is due to
underestimating te contribution of te weakest feeder. For tis etreme case te error in te resulting armonic voltage is approimately 8%. Tis error may still be deemed acceptable due to te limitations of te summation law. Harmonic Voltage (%.. 3. 3 act Metod [] Proposed. 0 0 Customer location on feeder Fig. - Harmonic voltages due to different allocation metods for etreme eample (note suppressed zero wit vertical scale Te armonic voltage at te end of te weakest feeder due to its contribution alone in te proposed metod is estimated by eqn (8. As te loads in MV systems will usually be lumped rater tan continuously distributed te eact contribution from te weakest feeder can be more accurately calculated using eqn (3 n V k (3 i / i X i Tis correction requires more data, but gives results wic precisely matc te eact metod, as illustrated in Fig. 6.. CONCLUION A refined metod of armonic emissions allocations as been proposed wic aderes to te guiding principles of te A/NZ 6000.3.6 standard. Te new metod requires muc less data tan te detailed approac suggested in standard but produces te same level of relative accuracy. Te metod improves on a simple tecnique suggested in [], requiring muc less data in most cases, and producing less pessimistic allocations closer to te comple eact solution. Harmonic Voltage (%.. 3. 3 act Metod [] Proposed. 0 0 Customer location on feeder Fig. 6 - Harmonic voltages due to different allocation metods for etreme eample (weakest feeder contribution corrected It is suggested tat te accuracy of te proposed metod will be sufficient to be used on most practical systems. For some etreme systems owever, were feeders differ greatly in loading and impedance some correction to te metod is proposed to ensure te contribution from te weakest feeder is witin te required accuracy. Tis metod as since been adopted by a Guideline publication for application of te standard [3]. 6. RFRNC. A/NZ 6000.3.6 " Limits- Assessment of emission limits for distorting loads in MV and HV power systems", tandards Australia 00. V.J. Gosbell, D.A. Robinson and B..P. Perera and A. Baitc, " Te application of IC 6000-3-6 to MV systems in Australia", RA Conference, Tame, Feb 00, pp 7..-7..0 3. V.J. Gosbell,. Perera, V. mit, D. Robinson and G. anders, "Power Quality: Application guide to A/NZ 6000.3.6 and A/NZ 6000.3.7", to be publised by tandards Australia, late 003. V. Gosbell, D. Manni, D. Robinson &. Perera, "Harmonic urvey of an MV Distribution ystem", Proc AUPC0, Pert, eptember 00, pp.338-33. J.M. Crucq, A. Robert, "tatistical approac for armonics measurements and calculations", Proc CIRD 989, pp 9-96 6. D.A. Robinson, V.J. Gosbell and B..P. Perera, "Harmonic allocation constant for implementation of A/NZ 6000.3.6, Proc AUPC0, Pert, eptember 00, pp. -7 7. LIT OF YMBOL Ii Ui FL G k L L U R s Z B econd ummation Law eponent Current emission allocation for customer "i" Voltage emission allocation for customer "i" Fault level Global emission voltage Harmonic order Allocation constant Voltage planning level for local system Voltage planning level for upstream system Ration of far and supply end fault levels Maimum demand/km Maimum demand (VA Reactance Base VA 8. APPNDIX: QUATION FOR UNIFORMLY DITRIBUTD LOAD Let te total load on te study feeder be. It will be assumed tat te load is distributed uniformly along te feeder. Position along te feeder will be measured by, te total fundamental reactance seen looking upstream from te point in question (Fig. 7. It is assumed to vary from to as one moves from te sending end to te far end of te feeder. will
correspond to distance along te feeder if it is of uniform construction. It is to be noted tat a cange in conductor cross-section alone as only a second order effect on te variation of wit distance. ignificant canges only occur wen te construction canges from open wire to aerial bundle conductor (tree wire or underground cable. d Fig. 7 feeder wit position described by upstream reactance Let te load connected between and +d be d sd ( Integration along te feeder sows tat s /( ( As discussed in ection, wit long feeder tere are advantages in a armonic current allocation wic falls off wit te inverse of te square root of upstream impedance. We sall assume te following allocation strategy i k (/ / ( (6 were "" is te armonic order. To determine te total armonic current in te feeder, we assume tat te currents due to te many MV loads add using te power law. Te contribution between and +d is d(i [k (sd (/ / (] k ( -/ sd (7 Integrating from to and letting I be te current due to all te MV loads, I k ( -/ sd / / ( k / k / ( / / ( / ( R ( / (R / (/ I ( / R k ( ( / (R (8 (9 Altoug te RH term appears to be complicated, a grap for several values of sows tat it can be approimated by R -0.3 for in te range - (Fig. 8. Hence I ~ k (/ / ( R -0.3 (0 Tis is te same as if all te MV load was concentrated at te sending end of te feeder ecept for te correction term R -0.3. We now determine te voltage at te far end of te feeder due to all te connected MV loads. Te load sd causes a current to flow troug an upstream armonic impedance of. Hence d(v [k (sd (/ ( ] k ( / sd ( Function 0.9 0.8 0.7 0.6 0. 0. 0.3 0. 0. 0 0 6 8 0 R a a. a R^-0.3 Fig. 8 Comparison of RH term of eqn(0 wit approimation Integrating from to and letting V be te armonic voltage due to all te load V / / k s d k Hence V k / k ( + / k + / (R / ( (R + / + / ( + / ( + / + / / (R ( ( ( + / (R + / (/ (R ( + /( R (3 A grap for several values of sows tat te RH term can be approimated by R 0.33 for in te range - (Fig. 9, giving. V ~ k ( (/ R 0.33 ( Function.8.6.. 0.8 0.6 0. 0. 0 0 6 8 0 R a a. a R^+0.33 Fig. 9 Comparison of RH term of eqn(3 wit approimation Tis is te same as for all te MV load concentrated at te sending end of te feeder ecept for te correction term R 0.33.