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1、HARMONIC ALLOCATION CONSTANT FOR IMPLEMENTATION OF AS/NZS 61000.3.6 D.A. Robinson, V.J. Gosbell, B.S.P. Perera Integral Energy Power Quality Centre School of Electrical, Computer and Telecommunications Engineering University of Wollongong NSW 2522 Australia Abstract Allocation of equal harmonic emis
2、sion rights to MV customers having the same maximum demand is a key concept in the new Australian harmonic standard AS/NZS 61000.3.6 1. Some difficulty can arise with the application of the standard when customers are spread out along a feeder with significantly different fault levels. One proposed
3、method of overcoming this problem is to reduce the allocation as the square root of the fault level 2. This method requires the calculation of an allocation constant that is applied to all customers connected to the same zone substation. This paper gives a methodology for calculating the harmonic al
4、location constant when there is incomplete data, and discusses some simplifying assumptions that can be made to optimise calculations. 1. INTRODUCTION In January 2001 Australia adopted a new harmonic standard governing emission limits of distorting loads in MV and HV power systems. The new standard
5、AS/NZS 61000.3.6 is an adaptation of the international technical report IEC 61000-3-6 3. AS/NZS 61000.3.6 comprises a number of stages and tests to determine harmonic emission allowances for customers connected to MV or HV networks. Stage 1 has three tests that base acceptance on load size as compar
6、ed to the short circuit level at the connection point. Stage 2 contains three tests of increasing complexity depending on the amount of information known about the system. There is also a Stage 3 where excessively distorting loads are allowed connection on a temporary and precarious basis. It is per
7、ceived that most distorting loads will be assessed under Stage 2 of the standard. The Integral Energy Power Quality Centre has been involved in producing and implementing practical methods for applying AS/NZS 61000.3.6. Of particular importance is the section of the standard concerning loads distrib
8、uted along a feeder having significant variation in fault level. AS/NZS 61000.3.6 briefly covers this section in Stage 2, Test 3. The application of the principles suggested by the standard for this section is poorly described and only a non- practical trivial example is provided. A more general app
9、roach follows. 2. PRINCIPLES OF AS/NZS 61000.3.6 The guidelines specified in the new standard are somewhat more difficult to apply than in the previous harmonics standard AS 2279.2 4. These guidelines attempt to ensure allocation of harmonic emission rights to customers is more equitable. A key conc
10、ept is that customers with the same agreed power and the same Point of Common Coupling (PCC) are entitled to equal harmonic emission rights. The PCC is defined as the nearest point in the power system to which another consumer might be connected. To account for time variation, customer harmonic cont
11、ributions and utility harmonic levels are assessed generally by the 95% Cumulative Probability (CP) level. As the 95% levels are statistical quantities direct summation is inadequate for combining contributions from a number of customers. Two summation laws are proposed by the standard: (i) The firs
12、t summation law makes use of diversity factors that require knowledge of the load type and is suited to more individual cases. (ii) The second summation law is a more general method that accounts for time diversity of the individual loads on a larger scale, and is given by Equation (1) i hih UU =(1)
13、 Where the exponent depends on the harmonic order h. The recommended value for the 5th harmonic is 1.4. The second summation law provides the basis for the proposed methodology for allocating harmonic emission rights to customers within an MV distribution system. The standard encourages an equitable
14、 allocation of harmonic rights to all customers having the same maximum demand. Where customers see different fault levels the question arises as to whether these rights are to equal harmonic voltage, equal harmonic current, or some other right. It can be shown that allocating equal harmonic voltage
15、 rights allows greater use of the systems harmonic absorption capability, but customers towards the end of a weak feeder receive lower current. The allocation of equal current is fairer but underutilises the harmonic absorption capability. The standard recommends a mid-way policy of equal harmonic p
16、ower, which can be shown to be equivalent to a harmonic current allocation varying with the square root of the fault level. AS/NZS 61000.3.6 assumes that the harmonic voltage at the MV level is a combination of the emissions from the MV loads and the background distortion of the HV transmission syst
17、em. Thus a fraction ThMV of the HV harmonic planning level LhHV must be included in the MV harmonic voltage planning level LhMV. Using the second summation law the acceptable global harmonic contribution GhMV from the MV distribution system alone can be calculated using Equation (2) hHVhHM hMVhMV )L
18、(TLG=(2) The fraction ThHM is assumed here as unity. For the purpose of this work only the 5th harmonic is considered as it has been shown to be the most predominant and problematic for most MV distribution systems 5-6. A full description of the principles behind the proposed methodology can be foun
19、d in 2. 3. THE ALLOCATION CONSTANT k When loads are spread out along a feeder and connected to points having different fault levels, allocation of harmonic current emissions becomes difficult. To achieve the constant harmonic power policy recommended in Section 2, the harmonic current emissions need
20、 to be allocated in proportion to agreed power Si and inversely proportional to the square root of the harmonic impedance Zhi at the PCC. A suitable strategy from 2 is to allocate harmonic current emissions EIhi using Equation (3) hi i Ihi Z kS E 1 =(3) Where k is called the allocation constant. The
21、 same value of k is used for all loads supplied from a common substation. Its value is chosen such that when the substation reaches load saturation, and all loads are contributing their maximum permitted harmonic contribution, the magnitude of the considered harmonic voltage will have a value not ex
22、ceeding the limits suggested by AS/NZS 61000.3.6. It is easy to show that this voltage will occur at the far end of the weakest feeder. Exact calculation of k is possible but complex and requires an enormous amount of data. To illustrate this process we consider a distribution system with each non-l
23、inear load modeled as an equivalent harmonic current source. At harmonic order h, the resulting voltages are related to the currents as shown in Equation (4) hhh IZV=(4) Where Vh is the unknown harmonic voltage vector, Zh is the harmonic impedance matrix, and Ih is the harmonic current vector. For a
24、 system with N nodes the expanded form of Equation (4) is as follows = hN hj h2 h1 hNNhNjhN2hN1 hiNhijhi2hi1 h2Nh2jh22h21 h1Nh1jh12h11 hN hi h2 h1 I I I I ZZZZ ZZZZ ZZZZ ZZZZ V V V V M M LL MMMM LL MMMM LL LL M M Using direct addition the harmonic voltage at node i is given by Equation (5) = N j hjh
25、ijhi IZV(5) As we are combining 95% CP level voltages using the second summation law Equation (5) must be rewritten to include the exponent as shown in Equation (6) = N j hj hij hi IZV(6) Note that the phase of the harmonic currents and voltages are not considered in Equation (6) but are assumed to
26、be included in the summation law exponent . Evaluating Equations (3) and (6) and assuming the maximum harmonic voltage to be less than the global harmonic contribution GhMV the value of k can be determined from Equation (7) 1 N j 2 hjj j hij i hMV Z SZ max G k = (7) Evaluation of Equation (7) requir
27、es the projected agreed power and system harmonic impedance at each PCC along every feeder within the local MV distribution system. To reduce the need for an extensive amount of data some assumptions can be made to determine an approximate value of the harmonic allocation constant k. 4. INCOMPLETE D
28、ATA APPROACH Although the weakest feeder is strictly defined by Equation (7) in most cases it will also be the feeder with the lowest fundamental voltage when the system is loaded to the fullest extent. Knowledge on the weakest feeder allows an approximation to k to be obtained when other data is no
29、t readily available. Three methods of approximating k when limited data is available are provided here: (i) A pessimistic approach assuming all loads other than the weakest feeder loads are connected to zone substation busbar (equivalent to assuming all other feeders to be of zero length). (ii) An a
30、pproach when all feeders are similar, i.e. all feeders are assumed to have the same loading and fault level distribution as the weakest feeder. (iii) The use of (i) incorporating correction factors. 4.1. A pessimistic approximation to k To illustrate how we can reduce the amount of data required to
31、calculate the value of the allocation constant k we consider the radial MV distribution system shown in Figure 1. Zh1Zh2ZhnZh0 S1S2Sn SF2 SF3 SFr S0 Feeder 1 Feeders 2-r Figure 1: Example radial MV distribution system (Sn in Feeder 1 is maximum expected demand at each takeoff point; SFr is the maxim
32、um expected loading on Feeder r) To simplify the expression for k given by Equation (7) we assume that all feeders other than the weakest feeder have zero harmonic impedance, i.e. all loads from the other feeders are connected at the supply busbar. This assumption simplifies the amount of data requi
33、red considerably and in addition can be justified as follows: (i) The harmonic impedance at the zone substation busbar Zh0 is generally the smallest of all the impedances and this term will not be a major part of the overall voltage drop. (ii) The assumption overestimates the current on the remainin
34、g feeders and hence will be pessimistic. Assuming that the highest harmonic voltage level will occur at the end of the weakest feeder we can estimate the value of k using the Equation (8) 1 2 2 2 n 1i h0FrF2h00hii hMV )ZS.(SZSZS G k + = (8) The approximation to k consists of three terms in the denom
35、inator. These terms are the harmonic contribution from the weakest feeder, the harmonic contribution from any local load at the zone substation busbar and the harmonic contribution from the loads on the other (2-r) feeders. This approximation requires the projected agreed power of each customer (Si)
36、 and the system harmonic impedance (Zhi) at all PCC points along the weakest feeder, and also an estimate of the total maximum agreed power from the other feeders (SF2, SF3, , SFr). Further, the approximation will always ensure a slightly pessimistic result for the value of k since it underestimates
37、 Zhi for the other feeders and therefore allocates too much current following Equation (3). 4.2. Approximation to k when all feeders are similar Various studies using the approximate value of k from Equation (8) have shown that this approach is most inaccurate when there are a number of weak feeders
38、 all of similar nature. In the case where all feeders are similar in loading and impedance a less pessimistic approximation to k may be calculated. In this case the harmonic contribution at the zone substation busbar due to each of the other feeders will be equal to that of the weakest feeder. To re
39、flect this the third term in the denominator of Equation (8) is modified to give Equation (9) 1 2 2 n 1i n 1i 2 hi h0 ih00hii hMV Z Z S1)(rZSZS G k + = (9) Less data is required to calculate k using Equation (9) than is required for Equation (8) but the application is useful only when all feeders ar
40、e of similar nature. 4.3. Correction factors for the pessimistic approximation of k By considering the relationship between the harmonic allocation constant and ratio of impedance at either end of a feeder we have been able to slightly correct the pessimistic value of k from Equation (8) if addition
41、al data is known. A good rule of thumb to optimise the value of k is to divide the contribution from the other feeders, the 3rd component of denominator in Equation (8), by the correcting factor given by Equation (10) 2 h0 hn hr Z Z F=(10) If the system impedance (Zhn) at the end of each of the othe
42、r feeders is not known a value of 2 for Fhr is usually suited to most systems. 5. CASE STUDY EXAMPLE To illustrate the application of the harmonic allocation constant k, we apply each of the above described methods to the example distribution system provided in Appendix I of AS/NZS 61000.3.6. The 20
43、kV distribution network example is shown in Figure 2. 023451 PCC0PCC1PCC2PCC3PCC4PCC5 5km5km5km5km5km Si=500kVA 1 2 3 4 5 6 6 feeders 5x 2500MVA 1x40MVA XT=15% 20kV132kV Figure 2: Homogeneous MV distribution network with six feeders and six loads per feeder. The system consists of six 20kV overhead
44、feeders of 25km length fed by one HV/MV 40MVA transformer. We will assume that all loads are directly supplied at MV and the system is at full capacity. The example calculations are performed only for the 5th harmonic. The planning levels for the 5th harmonic are LhMV=5% and LhHV=2%. Using these val
45、ues and the recommended value of =1.4 for the 5th harmonic the resulting value for the global harmonic voltage emission GhMV from Equation (2) is 3.97%. All feeders in the example are identical, thus any feeder can be chosen as the weakest feeder for the calculation of k. Table 1 shows the results f
46、rom an exact calculation of k, and the three approximation methods described previously. As all feeders are identical in this example the approximation using the assumption of similar feeders produces the same value as the exact value of k. Table 1: Allocation constant k using different calculation
47、methods Calculation methodAllocation constant k I.Exact value9.20% II.Pessimistic value6.88% III.Similar feeders value9.20% IV.Adjusted pessimistic value9.09% From Table 1 we can see that the adjusted pessimistic value gives good results as compared to the exact value of k. The adjusted pessimistic
48、approximation should be used when feeders are not all similar and only limited data is available. The resulting harmonic current allocations of each load along the feeder are shown in Figure 3 for the different methods of calculating k. 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 012345 Node Harmonic current (% of fundamental) Exact value Pessimistic value Similar feeders value Adjusted pessimistic value Figure 3: Harmonic current allocations using methods I-IV from Table 1 to calculate k As can be seen in Figure 3 each approximation method provides a suitable value for k. The voltages arising f