A new approach to harmonic allocation for medium-voltage installations

Transcription

1 University of Wollongong Researc Online Faculty of ngineering and Information Sciences - Papers: Part A Faculty of ngineering and Information Sciences 03 A new approac to armonic allocation for medium-voltage installations ictor J. Gosbell University of Wollongong, vgosbell@uow.edu.au R A. Barr lectronic Power Consulting, rbarr@uow.edu.au Publication Details. J. Gosbell & R. A. Barr, "A new approac to armonic allocation for medium-voltage installations," Australian Journal of lectrical and lectronics ngineering, vol. 0, () pp , 03. Researc Online is te open access institutional repository for te University of Wollongong. For furter information contact te UOW ibrary: researc-pubs@uow.edu.au

2 A new approac to armonic allocation for medium-voltage installations Abstract Distributors need to allocate a maimum allowed level of armonic current to medium-voltage customers to eep voltage distortion acceptable. Tlie paper describes a new approac, based on te concept of voltage droop, requiring muc less calculation and data tan required by te present approac based on an IC tecnical report. Te discrepancy between te new metod and te present is studied by comparing some carefully selected scenarios. It is sown tat te proposed metod gives results witin 0% of te standardsbased approac wic maes it a very attractive alternative for armonic allocation. Institution of ngineers Australia, 03. Keywords armonic, allocation, medium, voltage, installations, approac Disciplines ngineering Science and Tecnology Studies Publication Details. J. Gosbell & R. A. Barr, "A new approac to armonic allocation for medium-voltage installations," Australian Journal of lectrical and lectronics ngineering, vol. 0, () pp , 03. Tis journal article is available at Researc Online: ttp://ro.uow.edu.au/eispapers/49

3 A New Approac to Harmonic Allocation for M Installations.J. Gosbell, ife Member, I University of Wollongong Wollongong, Australia v.gosbell@uow.edu.au R.A. Barr, Member, I lectric Power Consulting Culburra, Australia rbarr@epc.com.au Abstract Distributors need to allocate a maimum allowed level of armonic current to M customers to eep voltage distortion acceptable. Te paper describes a new approac, based on te concept of voltage droop, requiring muc less calculation and data tan required by te present approac based on an IC tecnical report. Te discrepancy between te new metod and te present is studied by comparing some carefully selected scenarios. It is sown tat te proposed metod gives results witin 0% of te standards-based approac wic maes it a very attractive alternative for armonic allocation. Keywords- distribution systems, armonics, IC standards, armonic allocation, voltage droop Symbol Ii SCR S i d i i α I. NOMNCATUR Meaning mission allocation of current at armonic "" for load "i" Harmonic order Harmonic allocation constant armonic voltage limit oad sort-circuit ratio; fault level divided by maimum demand Ma demand of load "i" oltage droop Harmonic voltage caused by load "i" at its point of connection Harmonic reactance seen by load "i" Summation law eponent II. INTRODUCTION Distributors are required, under Australian armonic standard AS/NZS [], to eep armonic voltage levels on teir networ below te acceptable limits. Te main concern is armonic levels in M distribution systems wic depend mainly on te armonic current drawn by te M installations. Te standard gives some principles by wic eac M installation's armonic current allowance can be determined as will be detailed in Section III. Reference [] is largely based on an IC document aving te status of a tecnical report because te international community could not come to final agreement on ow armonic allocation sould be done. Te IC counterpart sould be viewed as a list of ideas and guidelines rater tan a final normative statement of ow te allocation process sould be carried out. Tis as caused difficulties in Australia were [] as been called up by te National lectricity Rules and as legal autority. Consequently tere as been muc wor in Australia to find satisfactory analytical tecniques and tis as led to te publication of [] wic details some aspects of M armonic allocation, i.e. radial distribution systems witout spurs. Reference [3] sows tat implementing te IC guidelines in a rigorous manner requires a detailed armonic study, requiring data on te maimum demand and impedance at te point of connection for all locally connected M loads. Assumptions need to be made regarding te effect of loads connected to te system and M loads wic may be connected in future. Tis involves guesswor and judgement and tere is muc scope for utility/customer conflict. Te autors ave developed an alternative approac based on te concept of "voltage droop" wic is te fundamental voltage drop between a load and a ypotetical upstream Tevenin voltage source [4]. We can define te voltage droop due to a particular load or te voltage droop at te end of a particular feeder due to all loads in te local power system. Our particular interest is te maimum voltage droop wic can occur in te power system. Tis is liely to be at te end of a long feeder. Since eac upstream transformer can regulate over a range of about 0%, and tere are about tree effective suc levels, one would epect tat te maimum voltage droop in a power system (to be given te symbol d ) is limited to be about 30%. Te approac can be used for armonic allocation in distribution systems of any topology providing te armonic impedance at armonic "" is "" times te fundamental reactance. Tis requires tat transmission lines are sufficiently sort for line capacitance to be negligible and all suntconnected capacitors to be detuned. It sould be noted tat if tese assumptions do not old, tere are major issues for all armonic allocation scemes presently used. Te role of te present paper is to estimate te accuracy in te proposed approac and to investigate if it is acceptable for practical systems. Sections III and I summarise te IC guidelines and te new armonic allocation approac respectively. Te net section studies te difference or "margin" between a strict IC allocation and te new metod. Section I gives te application of te new approac to bot a omogenous system (all feeders and loads identical) and a more realistic system wit a mi of strongly and wealy loaded feeders.

4 III. IC GUIDINS Te major IC guidelines for armonic allocation ave been adopted witout cange in []. (a) Under time-varying conditions, armonic quantities are to be caracterised by teir 95% values. (b) Diversity between independent armonic sources can be represented by an eponential summation law. tot = + () were α depends on te armonic order. (c) All present and projected customers are assumed to be drawing teir full armonic allocation wic sould be suc tat, wen te system is fully loaded, te maimum armonic voltage reaces te limit. Reference [] suggests tat te allocation in distribution systems sould give eac installation a armonic A proportional to te maimum demand, wit an allowance for diversity and tis approac as been followed in []. Tis is acieved for a load wit maimum demand S i by a armonic current allocation of / Si I i = () i were is called te Allocation Constant and needs to be determined for eac supply substation. Guideline (c) above requires a complete armonic study of te substation load wit every significant connected customer needing to be represented and varied until te armonic voltage limit is just reaced. Tis requires nowledge etensive nowledge of all relevant present day loads, including upstream and loads, information wic can be difficult to assemble. Guesses need to be made regarding te magnitude and point of connection of all future loads in te subsystem. It is unsatisfactory tat a standard could lead to a result wic is so poorly defined. I. NW APPROACH A. Summary of teory Te proposed new approac, presented in [4] will be summarised ere. It is best introduced by neglecting diversity, tat is taing α =. Suppose every customer is allocated te same percentage armonic current. At te t armonic, all M power system impedances are "" times larger tan te corresponding fundamental reactances and te IX drop at te "" armonic is simply proportional to te fundamental voltage drop. Te maimum armonic voltage in te subsystem will occur at te end of te most eavily loaded feeder and can be sown to be equal to te voltage droop limit, scaled up by "" (because of te increase in system reactance) and scaled down by te fraction of armonic current to fundamental current. Wen tere is diversity, te lin between armonic voltage drop and voltage droop can be maintained very closely, as discussed in [4], by an allocation law wic is also dependent on impedance at te point of connection / i i S Ii = (3) Ii is te allocated current, S i is te maimum demand of load "i" being assessed, i te upstream fundamental impedance at its point of connection and an allocation constant to be determined. In order to limit te maimum armonic voltage at te far end of feeders, sould be cosen from = (4) / d were is te armonic limit. It is sometimes convenient to use epressions involving te load sort-circuit ratio or SCR defined as te fault level at te point of load connection divided by te load maimum demand. Reference [4] sows I Ii i i = SCR (5) B. ample Consider a MA load connected to a point were te fault level is 0MA, giving a SCR of 0. Assume for te 5 t armonic, for wic α =.4, an limit of 5.5%. Step (i) determine from (4) = = Step (ii) / determine SCR = 0MA/MA = 0. Step (iii) determine.4 Ii I 5 as a fraction of I from (5) = = 0.0. I i Hence te allocated 5 t armonic current is 0% of te fundamental current. C. Discrepancy between strict IC and new approaces Te metod is eact wen all loads are supplied from te one feeder as demonstrated by te eample in Fig. involving tree installations. Te reactance values are given so tat te fundamental reactance to node "i" is i. First we estimate te fundamental voltage droop, wit te assumption tat te fundamental current is equal to te maimum demand in per unit. For armonic order "" we sall tae te limit to be. d = d + d + d3 = S + S + 3 S 3 (6) From (4) = = (7) / ( ) / d S + S + 3S3 Te allocated armonic currents wic can be injected by () () (3) S S S 3 Fig. Single feeder distribution system

5 loads S -S 3 are ten / S I / =, / S I / =, / S3 I3 / 3 = (8) As a cec we compare te total armonic voltage produced against te limit. Te armonic voltages produced by eac load at te point of connection and terefore at te end of te feeder are = ( S ) /, = ( S ) /, ( S ) / 3 = (9) 3 3 Taing eac term to te power of α and adding ( ) ( S + S + 3S3 ) = S + S + 3S3 = = (0) ( S + S + 3S3 ) sowing tat te allocation metod is eact in tis case. Wen tere is more tan one feeder, tere is a need to distinguis between te combination of different sources acting at one point, and te addition voltages from a single current source acting troug impedances in series. Te first follows te summation law and is correctly accounted for wile te second add aritmetically (K) and are not. Te practical outcome is te incorrect representation of a source connected to one feeder and acting on anoter. Tis can be demonstrated by means of a two feeder system Fig.. Te voltage droop at te end of feeder is d = S + 0 S () wile for feeder d = 0 S + S () We sall assume witout loss of generality tat d d, so tat ( - 0 )S ( - 0 )S (3) = = / S + S (4) d.ma / S I / =, ( ) / / S I / 0 = (5) Wit more tan one feeder, we do not determine te armonic voltage at te point of load connection, but tat imposed on te feeder wit te largest armonic voltage (or voltage droop), tat is te armonic voltage imposed at node () in tis case. ( S ) / =, / 0S = (6) / Taing eac term to te power of α and adding 0-0 S () - 0 () S Fig. Two feeder system 0 S S + 0 S = S + = (7) ( S + 0S ) / 0 S + 0S Hence = (8) S + 0S wic is always less tan, sowing tat te allocation metod is not eact in tis case. For eample, if 0 =, = 5, = 4, S =, S =, and α =.4, = pu te inequality (3) is met and = 0.95 pu. However, if tere is no diversity (α = ), te above epression becomes pu. for any combination of values of te oter parameters. Ideally, we would lie a metod wic gives a armonic voltage reacing te armonic limit wen all loads are connected and taing teir full allocation. In te above eample, te metod is said to "underallocate", since te armonic voltage only reaces 95% of te limit. Te reserve armonic capacity, 5% in tis case, we sall call te "margin". It is desirable tat te margin is not too large so tat customers are given most of te armonic capacity of te system. In practice, some margin is desirable to allow for contingencies suc as te presence of embedded generation wic can contribute to armonic emission but is not considered in te voltage droop figure. We wis to demonstrate tat te new metod gives a margin wic is usually no more tan 0% of te armonic voltage limit.. TH MARGIN GIN BY TH NW APPROACH A. Metodology Te equations for armonic allocation are non-linear because of te summation law () and can only be solved eactly for some simple cases or for specific numerical cases. It would be impractical to find an eaustive set of numerical studies tat could be guaranteed to cover all situations of power system topology and reactance and load values wic could arise in practice. We ave approaced tis by carefully selecting a set of scenarios to give an estimate of te maimum margin from tis new approac. We begin wit a system aving two feeders wit single loads at te etremity of eac. Tis will demonstrate tat te maimum margin can be estimated by studying te situation wen te feeder impedances and te load maimum demands are identical. Tis case can be studied teoretically and it is ten found tat te maimum margin for a two feeder system is wen te feeder impedance is about twice te supply impedance. Te approac is ten etended to a system aving N identical feeders. B. Two feeder system Te system and its equations ave been given in Section I.C. Te equations ave been set up in a spreadseet and attempts made, using cel's Solver Add-in, to find te values

6 TAB I RSUTS OF XPORATION OF TWO FDR SYSTM Case S S / Comments Starting point All parameters canged at once & S canged from starting point & S canged from starting point & canged wile forced to be equal of input parameters giving a minimum value of / corresponding to te maimum margin. Some simplification is possible. 0 can be cosen as pu witout loss of generality. Similarly, and can be taen as. Results are summarised in Table I. Wen attempts are made to cange any of te data individually, Solver gives te starting point as te minimum (0.96). Wen all parameters are canged at once (Case ) a somewat lower value of 0.9 is acieved. If just, S togeter or, S togeter are canged, intermediate values are obtained as sown for Cases 3, 4. Solver maes no canges wen and are allowed to cange togeter. However, if and are forced to be equal to a new variable, and tat variable is canged, we obtain a minimum of 0.94 wen = =.93. It is also observed tat te minimum occurs in every case wen bot feeders ave te same voltage droop. We conclude Te minimisation problem for te -feeder system, including te voltage droop constraints, is bot teoretically and numerically very difficult. Most minimum values (Cases and 3 in particular) involve unrealistic combinations of parameters. An estimate of te margin to be epected for realistic cases can be found by eamining te case were all feeders ave te same loading and te same reactance (Case 5), corresponding to eac feeder aving te same voltage droop. C. N feeder system Te system is illustrated in Fig. 3. All loads are taen equal wit value pu, since scaling te loads sould ave no impact on te margin. A per unit system as been cosen to give a supply side reactance of pu. It is assumed tat eac feeder's load can be lumped at a point were tere is a reactance of pu to te supply bus. Using tese units, can be interpreted as te ratio of te feeder to te supply side reactance. Te load voltage droops sall be estimated from te reactance pu supply bus N identical feeders wit reactance, eac terminated wit load S Fig. 3 System wit N omogenous feeders product of te load maimum demand (equal to te fundamental current in per unit) times te fundamental reactance. Te voltage droop caused by eac load at te supply bus is pu. Te voltage caused by a load at te end of its feeder is +. Te voltage droop at te end of any one feeder is te sum of two quantities, tat from te directly connected load and te N contributions from loads connected to te remaining feeders. is d = + + (N -) = N + (9) = = / ( ) / d N + (0) For eac load te allocated current is / I = = () ( + ) (+ ) ( N + ) / Te armonic voltage caused by eac load at te supply bus.bus = ( N + ) / () (+ ) Te armonic voltage caused by eac load at its point of connection is (+ ) /.pc = (+ )I = (3) ( N + ) / Te armonic voltage at te supply bus caused by all loads is te combination of tese terms using te summation law giving ( N ) (+ ) + + ) ( N + ) ( N + ) ( + ) ( N + ) ( N ) ( + ) = = + (4) ( / ( + ) ( N ) = + (5) ( N + ) ( + ) Te margin can be found by eamining te difference between te quantity / and one. To obtain a preliminary idea of te variation of tis multivariable function, some graps ave been given for some typical values. Fig. 4 sows te variation of / wit N for tree values of determined for α =.4. Te grap as been etended beyond te normal range of N (0-0) to sow te asymptotic variation of te function. Te variation for α = is similar, ecept tat it deviates from unity by about 50% more. For α = (no diversity), (5) is identical to one and tere is no margin. We see tat te variation gets worse wit increasing number of feeders. Te values asymptotically approac a value wic can be found from (5) by finding te limit as N / = 0. = = N Fig. 4 ariation of / wit N for tree values of

7 TAB II ASYMPTOTIC AUS OF / α =.4 α = TAB III AUS CORRSPONDING TO ARGST MARGIN FOR ACH AU OF N N (min) / approaces infinity to give Fig.5 ariation of / wit im N = (6) ( + ) Tis as been determined in te Table II. Te margin also increases wit α, being zero for no diversity (α = ). Te margin appears to increase wit because of te restricted number of points sown. Consider te variation wit for a realistic value of N = 0. Fig. 5 sows tat, for a particular value of N, tere is a value of giving te largest margin ( ~ 5 gives 0.78). Te value of giving te largest margin can be determined by te standard process of differentiating (5). Some simplification can be acieved by taing tis equation to te power of α and using 'Hospital's rule to find were te minimum occurs. Re-epressing te RHS of (5) ( + ) ( N + ) ( N ) (N )(+ ) + = ( + ) (N + ) Applying 'Hospital's rule gives + + (N )(+ ) + + (N )( )(+ ) = (N + ) Some manipulation gives - (7) + (8) - - ( + ) = ( )(+ ) + + (N )( )(+ ) (9) It is not possible to solve analytically for, but rearranging allows an epression for N (+ ) N = (30) ( -) For a given N, te value of satisfying te RHS of (30) gives te feeder reactance, relative to te supply reactance, giving te largest margin. Table III sows, for eac value of N, te value of giving te largest margin and te computed value of /. Fig. 6 sows te variation of / vs. N. A typical value of N is 0 for wic te maimum margin occurs wen te equivalent feeder impedance is = 4.8 times te supply impedance, a typical value in practice. Here te computed / is 0.77 giving a margin of 3%. Tus about 3% of te capacity of te local power system to absorb armonics is unused. Tis is not a major issue for several reasons Tis applies only wen eac feeder as te same equivalent impedance and is loaded identically. Tis is seldom te case and te margin is generally less tan given by Fig. 6. Some reserve margin is useful for contingencies e.g. (a) additional armonic contributions from embedded generation suc as rooftop P units, (b) iger emissions tan allowed by IC guidelines for some loads connected in te past under previous armonic allocation procedures, (c) some amplification due to nearby capacitors wic are not fully detuned. I. / N Fig. 6 ariation of / wit N for giving maimum margin. TYPICA DISTRIBUTION SYSTM STUDIS A. System values It would be impractical to find a power system (zone substation and its loads) tat everyone would agree was typical. We sall tae one wic as been treated for armonic allocation studies in te past [5] and wic as originally appeared in [] Appendi I see Fig. 7. Te fault level at te 0 bus is 34MA wile te reactance of te 0 feeder is 0.35Ω/m. We convert to per 0 40MA XT=5% 3 5m 5m 5m 5m 5m PCC0 PCC PCC PCC3 PCC4 PCC feeders Si=500A Fig. 7 - Homogenous study system from [,5]

8 unit using a base of 50MA as used in [5]. At 0, Z B = 0 /50 = 8Ω. Te upstream supply reactance seen at te 0 bus is 50/34 = 0.pu. Te reactance of eac 5m section = =.75Ω = 0.pu. ac load is 0.0pu. B. Homogenous power system Te system given as been set up for illustrative purposes and te voltage droop need not correspond wit 30% wic we feel is typical in Australia. It is significant tat no loads are sown. Te voltage droop from source to te end of one of te 0 feeders is te sum of te voltage droop due to te oter 5 feeders ( d ) plus tat due to te feeder under study ( d ). d = = d = 0.0 ( ) = Hence d = d + d = 0.0. For tis eample, we need to calculate our allocation.lim constant as =. For te 5 t armonic, wit an / d 0.05 assumed limit of 5%, 5 = = Tis is about / twice te value to be epected wit a droop of 30%. Table I sows te calculation of te armonic current allocations, compared wit tat given by a more comple calculation in [5]. In reviewing tese results, we first we note tat we sould not epect te proposed metod to agree at every load point wit previous metods. Te latter are based on constant armonic A allocation giving a current variation wit te square root of fault level for equal load A as ere. In te proposed approac, te allocated currents in tis situation will vary less sensitively wit fault level, rougly as te fault level to te power of 0.3 (see (5)). Te total 5 t armonic current allocated to a feeder can be estimated from summation of te individual load currents giving 4% (relative to 500A) in te proposed approac and 33% by te former "eact" approac, illustrating te margin. Te maimum armonic voltage wic will occur wit te proposed metod as been computed as 4.3% for a limit of 5%, a margin of 4% C. Non-omogenous power system Te system of Fig. 7 as been modified to mae it nonomogenous to eplore ow te margin migt cange. Feeder number one as been replaced by a stronger one of negligible lengt wit a single load of.5 MA (0.03 pu). Feeder number two as been replaced by a longer one wit a fault level of 9MA at te far end were a load of MA is concentrated. Tese figures ave been cosen to give eactly te same voltage droop as in te omogenous eample. Te maimum TAB I COMPARISON OF AOCATD CURRNTS BY TWO MTHODS Node S F SCR Sums I 5 (%) - proposed 8% 3% 0% 9% 7% 7% 4% I 5 (%) - Ref [5] 38% 6% % 8% 6% 4% 33% voltage droop now occurs only at te end of te wea feeder. Calculation gives a armonic voltage of 4.4% at te end of feeder, giving a margin of %. We see from te above tat te system gives acceptable results for so-called typical systems, wit less margin as te system becomes less omogenous. II. CONCUSIONS Te armonic allocation principles in te IC tecnical report are difficult to apply using metods publised to date, mainly because of te data load and te need to estimate future scenarios tat are convincing to all parties. A new approac as been described based on te voltage droop concept. It as been sown to be eact only wen tere is no diversity or only one feeder connected to te supply bus. Oterwise te metod is pessimistic but tere appears to be no clear analytical metod for establising its margin and its suitability for everyday calculations. A full numerical study of a representative set of cases seems impracticable as tere are far too many possibilities. A numerical study as been made of several scenarios to obtain an estimate of te accuracy of te proposed metod for a two feeder system. Te maimum margin, for realistic parameter values, occurs wen te feeders are identical. It is assumed tat tis result applies to any number of feeders. Numerical studies ave been made for an N-feeder omogenous system wic can be also studied analytically. It is sown tat te margin increases monotonically wit te number of feeders and wit te value of α. It is also sown tat te margin is small for low and very large reactance feeders, relative to te supply impedance, wit a maimum for intermediate values. An epression as been found allowing te value of feeder reactance and te corresponding value of margin to be determined for any value of N. Wit typical values of feeder number and reactance, te margin is sown to be at most 0%. Te new metod as been demonstrated to ave sufficient accuracy for engineering use and is convenient to apply wit relatively small requirements for data. RFRNCS [] AS/NZS :00, "imits Assessment of emission limits for distorting loads in M and H power systems", Standards Australia, 00 [].J. Gosbell et al, HB , "Power Quality - Recommendations for te application of AS/NZS and AS/NZS ", ISBN , Standards Australia, 003 [3].J. Gosbell, "Harmonic Allocation to M Customers in Rural Distribution Systems", Aust Journal of lectrical & lectronics ngineering, ol. 5, No. 3, 009, pp.3-0 [4].J. Gosbell & R.A. Barr, "Harmonic Allocation Following IC Guidelines Using te oltage Droop Concept", accepted for presentation at ICHQP 00, Bergamo, September, 00. [5].J. Gosbell and D Robinson, "Allocating armonic emission to M customers in long feeder systems", AUPC03, Sept-Oct, 003, Cristcurc