International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
Optimum Allocation of Active Filters In A 4-Bus System Using Genetic Algorithm Surasmi N.L.1, M.R.Sindhu. 2 1
Final Year M.Tech Power Electronics, Electrical & Electronics Engineering Department, Amrita Vishwa Vidyapeetham, Coimbatore, India 2 Assistant Professor, Electrical & Electronics Engineering Department, Amrita Vishwa Vidyapeetham, Coimbatore, India 1
2
[email protected] [email protected]
Abstract— Active power filters (APF) are employed for harmonic compensation in power systems. In this work genetic algorithms (GA) are used for the selection of optimum location of Active filters in power system. The purpose of the genetic algorithm is to minimize the cost of harmonic filters and, at the same time, to reach the harmonic limitations defined by standard IEEE-519. This algorithm is applied to 4-bus interconnected network for fixed harmonic load conditions. The control strategies selected to develop objective function are total harmonic distortion of voltage and current, telephone interference factor of voltage and current, harmonic transmission line loss and active filter current.
Conventionally, passive L-C filters are used to reduce harmonics but they have demerits of fixed compensation, large size, and resonance. In order to overcome these problems, active power filters (APFs) [3], which are also called active power line conditioners (APLC), have been developed. APLCs provide injected equal-but-opposite currents to the point of common coupling (PCC) that completely eliminate the nonsinusoidal requirements of the nonlinear load.These filters are connected in parallel with harmonic generator loads. A typical APLC includes a power electronic converter with either a capacitor or inductor acting as an energy storage element and also a controller for determining the desired reference signal and generation the converter gating pulse patterns. An example of this filter is shown in Fig.1.However, in practice, a more reasonable requirement is to reduce harmonic distortion to a minimum acceptable level for a given condition. But active power filters are still limited by their rating and cost.
Index Terms— Harmonics, Active power filters, 4-Bus system, Optimization, Genetic algorithm.
I.
INTRODUCTION
Power systems have evolved from isolated generators to interconnected power system. Interconnected power systems are more reliable than isolated systems. In case of disruption in one part of the system, power can be fed from alternate paths, thus maintaining the continuity of the system.Disturbances such as harmonic distortions quickly propogate throughout the system.This adversely affects every component or equipment connected to the power system. The introduction of power semiconductor based converters in electric utility sector has resulted in better performance of the industries in terms of energy saving, reduced maintenance, low running costs and increased production. However, semiconductor based converters introduce harmonic injection, poor power factor, nonsinusoidal supply, reactive power burden and low system efficiency. With growing awareness about these problems, the power system utilities, industries and commercial establishments started protecting themselves by investing in sophisticated protection equipment for harmonic mitigation. The various harmonic standard such as IEEE-519 [1, 2] etc. specify strict harmonic limits on currents and voltages.
Fig. 1: An APLC configuration
The installation of an APF in an appropriate place is one of the recent research topics [4, 5, 6]. The important factors to be considered for APF applications are: existing harmonic pollution levels, harmonic standard constraints, locations and sizes of APFs and finally network topology. The size of an APF is normally defined as its maximum effective injection current. Regardless of any solution procedure, allocation and sizing of APFs are normally found based on optimization process in which various objective functions may be employed. 251
International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012) In this paper a Genetic Algorithm based optimization method is adopted to determine the optimum allocation of active filters in a 4-bus test system. II.
Where OFthdv is objective function of voltage total harmonic distortion (THDv), OFtifv is objective function of voltage telephone interference factor (TIFv), OFthdi is objective function of current total harmonic distortion (THDi), OFtifi is objective function of current telephone interference factor (TIFi), OFhtll is objective function of harmonic transmission line loss (HTLL) and OFfi is objective function of active filter current (IF)
GENETIC ALGORITHM
A Genetic algorithm (GA) is an optimization based on the mechanics of natural selection and natural genetic. GA is inspired by natural genetics and a Darwinian theory of evolution. A genetic algorithm involves simulating competition between a numbers of individuals who represent solution to problem. A set of genes which corresponds to a "chromosome" in natural genetic is referred to as "string" in a GA. GAs start with a population of string and thereafter, generate successive population using the following three basic operator generation, crossover, mutation. Given a specific problem to solve, the input to the GA is a set of potential solutions to that problem, encoded in some fashion, and a metric called a fitness function that allows each candidate to be quantitatively evaluated. These candidates may be solutions already known to work, with the aim of the GA being to improve them, but more often they are generated at random. The GA then evaluates each candidate according to the fitness function However, purely by chance, a few may hold promise they may show activity, even if only weak and imperfect activity, toward solving the problem. These promising candidates are kept and allowed to reproduce and multiple copies are made of them, but the copies are not perfect; random changes are introduced during the copying process. These digital offspring then go on to the next generation, forming a new pool of candidate solutions, and are subjected to a second round of fitness evaluation. Genetic algorithms have been used in a wide variety of fields to evolve solutions to problems as difficult as or more difficult than those faced by human designers. Moreover, the solutions they come up with are often more efficient, more elegant, or more complex than anything comparable a human engineer would produce. III.
Where K1,K2,K3,K4,K5 &K6 are weight coefficients or penalty factors of THDv, TIFv, THDi, TIFi, HTLL and filter current IF respectively. IV.
TEST SYSTEM DETAILS
To evaluate the proposed method the test system selected is a four bus system with two non linear, one linear and one motor load. Single line diagram of four bus system is shown in Fig. 2.
Fig. 2: Single line diagram of four bus test system
A. Test system details Base voltage=400V, Base kVA=5kVA Base Impedance of the line = 484 Ω Bus 1-Slack bus Bus4-Voltage controlled bus Load1 - 3Ф, 415V, 2.2kW, 1430rpm Induction Generator and a 5kVA linear load. Load2-5kVA Six pulse converter with 100Ω Resistive load. Load3-5kVA Six pulse converter with 100Ω Resistive load. Load4-5kVA linear load.
OBJECTIVE FUNCTION
The most important objectives of placement and sizing of active filters in a power system are to reduce total harmonic distortion (THD) in voltage and current, harmonic transmission line losses (HTLL), telephone interference factor (TIF) in voltage and current and active filter rating. The constraints also maintain individual and total harmonic distortions within a standard level. The mentioned parts will be lumped into the objective function which is expressed as follows:
B. Design of transmission line A specific long line with its parameters as was chosen for this paper .The specifications of the line are as follows Power rating of the line: 100 MVA Voltage rating of the line: 220 kV. Resistance : 0.073 Ω per km.
OF=K1*OFthdv+K2*OFtifv+K3*OFthdi+K4*OFtifi+ K5*OFhtll+K6*OFfi (1) 252
International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012) Inductive reactance: 0.4794 Ω per km. Shunt admittance: 3.35 m mho per km. The scale down model of the transmission line is obtained by maintaining the per unit values of the resistance and reactance the same as that of the actual long line. For scaled down model base of 5KVA and 400V is chosen and length of transmission line as 50km [6]. Actual values of the resistance and reactance in the scaled down model work out to be: Actual value of Resistance R s.d = Per unit value of resistance*Base impedance = 0.0048 Ω per km. Actual value of Reactance XL s.d = Per unit value of reactance*Base impedance = 0.0316 Ω per km . Inductance L s.d = 0.10089 mH per km. The value of the shunt capacitance is obtained by keeping the ratios of XL / R and γ constant. Actual value of shunt capacitance C s.d = γ² / L s.d = 0.1625 x 10-6 F per km.
Fig. 3: ETAP model of test system Table 1: Harmonic load flow analysis results without filter THDi (%)
Fundam ental I (A)
RMS I (A)
THDv (%)
BUS1
BUS3
13.05
10.63
10.72
25.09
BUS2
13.05
10.63
10.72
BUS1
13.05
10.63
10.72
BUS4
41.38
2.94
3.18
BUS1
13.05
10.63
10.72
BUS4
41.38
2.94
3.18
BUS3
41.38
2.94
3.18
BUS2
41.38
2.94
3.18
BUS3
BUS4
HARMONIC LOAD FLOW ANALYSIS
To determine the content of distortion or harmonics in the test system, harmonic load flow analysis of the test system was conducted without filter in ETAP software. Fig.3 shows the ETAP model of the test system. A.
TO BUS ID
BUS2
Line Parameters for 50 km line: Resistance R s.d50 = R s.d * 50 = 0.241 Ω. Inductance L s.d50 = L s.d * 50 = 5.044 mH. Capacitance C s.d50 = R s.d * 50 = 8.056 mF. [7] . V.
FROM BUS ID
35.58
35.58
28.54
B. Telephone Interference Factor (TIF) Telephone Interference Factor of voltage and current waveform in electric supply circuit is the ratio of square root of the sum of the squares of the weighted root mean square values of all sine wave components (including alternating current waves both fundamental and harmonics) to the root mean square value (unweighted) of the entire wave.TIF of both voltage and current waveforms are directly obtained from the harmonic load flow analysis in ETAP. Table 2 shows the voltage and current TIF in each of the four buses and lines.
Total Harmonic Distortion
Table 1 show the voltage and current THD in each bus and line. Also fundamental and rms current in each line is shown. Harmonic content is found to be more near to the non-linear load, i.e. near bus no 2 and 3.
Table 2: Voltage and current TIF values
253
BUS ID
TIFv
LINE ID
TIFi
BUS 1
1311.24
LINE 1 (1-3)
413.18
BUS 2
1851.19
LINE 2 (1-2)
413.18
BUS 3
1851.19
LINE 3 (2-4)
1191.89
BUS 4
1476.20
LINE 4 (3-4)
1191.89
International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012) VI.
Table 4: THDi values for 15 combinations
HARMONIC LOAD FLOW ANALYSIS WITH COMPENSATION
Shunt active filter with ICOSФ control algorithm [8, 9, 10] is used for compensate harmonics in the given test system. Since test system is 4 bus system, 15 different combinations of Active filter allocations are tried. Table 3 and Table 4 shows the voltage THD values and current THD values in four buses for 15 combinations, where 1 indicates active filter installed and 0 indicates no active filter at corresponding location(bus).
SL NO
Table 3: THDv values for 15 combinations S L N O
AF LOCATION
B4 B3 B2 B1
THD v (%) LINE 1(1-3)
THD v (%) LINE 2(1-2)
THD v (%) LINE3 (2-4)
THD v (%) LINE 4(3-4)
1
0
0
0
1
13.72
13.72
49.99
49.99
2
0
0
1
0
14.38
3.79
8.74
144.9 7
3
0
0
1
1
14.59
3.23
8.56
81.85
4
0
1
0
0
1.59
13.79
57.81
10.26
AF LOCATION
THDv (%)
THDv (%)
THDv (%)
THDv (%)
5
0
1
0
1
3.35
14.56
181.15
9.27
B4 B3 B2 B1
BUS1
BUS2
BUS3
BUS4
6
0
1
1
0
0
0
0
0
1
0
0
0
1
21.21
30.35
30.35
24.18
7
0
1
1
1
0
0
0
0
2
0
0
1
0
9.06
8.92
18.13
9.88
8
1
0
0
0
12.94
12.94
56.90
56.90
9
1
0
0
1
13.42
13.42
54.91
54.91
3
0
0
1
1
8.89
8.84
18.07
9.92
1
0
1
0
14.30
4.29
8.44
184.4 7
0
1 0.16
19.20
10.66
11.43 11
1
0
1
1
14.56
3.35
9.27
181.1 5
12
1
1
0
0
4.29
14.30
184.47
8.44
13
1
1
0
1
3.35
14.56
181.15
9.27
14
1
1
1
0
0
0
0
0
15
1
1
1
1
0
0
0
0
4
5
0
0
1
1
0
0
1
8.65
17.59
8.57
10
9.50
6
0
1
1
0
0
0
0
0
7
0
1
1
1
0
0
0
0
8
1
0
0
0
24.09
33.91
33.91
26.84
9
1
0
0
1
21.91
31.14
31.14
24.72
10
1
0
1
0
9.24
9.07
18.48
10.06
11
1
0
1
1
8.65
8.57
17.59
9.50
12
1
1
0
0
9.24
18.48
9.07
10.06
13
1
1
0
1
8.65
17.59
8.57
9.50
14
1
1
1
0
0
0
0
0
15
1
1
1
1
0
0
0
0
A. ACTIVE FILTER CURRENT Active filter rating or current for 15 different active filter combinations is determined using simulation of MATLAB model of the four bus system. IcosФ algorithm is the control algorithm used for the shunt active filter. Table 5 shows the active filter current for the 15 different active filter locations.
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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012) Table 5: Active Filter current for 15 combinations
SL N O
AF LOCATION
Table 6: HTLL for 16 active filter combinations
AF4 rms(A)
AF3 rms(A)
AF2 rms(A)
AF1 rms(A)
B4 B3 B2 B1 1
0
0
0
1
0
0
0
0.2603
2
0
0
1
0
0
0
1.1314
0
3
0
0
1
1
0
0
1.1262
0.0758
4
0
1
0
0
0
1.2966
0
0
5
0
1
0
1
0
1.1112
0
0.0902
6
0
1
1
0
0
1.4355
1.4355
0
7
0
1
1
1
0
1.3565
1.3565
1.4355
8
1
0
0
0
0.1267
0
0
0
9
1
0
0
1
0.1484
0
0
0.0345
10
1
0
1
0
1.0349
0
1.0424
0
11
1
0
1
1
1.003
0
1.1112
0.0902
12
1
1
0
0
0.9429
1.0425
0
0
13
1
1
0
1
1.0863
1.0863
0
0.0915
14
1
1
1
0
1.3565
1.4355
1.4355
0
15
1
1
1
1
1.3565
1.4355
1.4355
1.3565
SL NO
AF LOCATION B4 B3 B2 B1
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1
0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1
VII.
HTLL(W)
0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1.24 0.01977 1.761 0.3724 1.387 0.643 1.092 0.1463 0.199 106.92 8.39 0.3703 310.68 0.3703 6.97 0.915
OPTIMIZATION
From the harmonic load flow analysis control strategies required to obtain the objective function are obtained. MATLAB code is written for the objective function, which is optimized using GATOOL. Truth table for genetic algorithm optimization is shown in Fig. 4.
B. HARMONIC TRANSMISSION LINE LOSS In order to determine harmonic transmission line loss with and without filter MATLAB code is written in embedded matlab function block. Table 6 shows harmonic transmission line loss for 16 active filter combination. Fig. 4: GA truth table
255
International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012) [5] Iman Ziari, and Alireza Jalilian, ―A New Approach for Allocation and Sizing of Multiple Active Power-Line Conditioners‖, IEEE Transactions on Power Delivery, vol. 25, no. 2, April 2010. [6] Reza Keypour, Hossein Seifi, Ali Yazdian-Varjani, ―Genetic based algorithm for active power filter allocation and sizing‖, Electric Power Systems Research 71 (2004) 41–49 [7] R. Jayabarathi, M .R Sindhu, N. Devarajan, and T. N. P. Nambiar, ―Development of a Laboratory Model of Hybrid Static Var Compensator‖, 2006 IEEE. [8] H. L. Jou, "Performance comparison of the three-phaseactive-power filter Algorithms", in Proc. IEE Conf On Generation, Transmission, Distribution, pp. 646-652, 1995. [9] G. Bhuvaneswari, Manjula G.Nair, ―Comparison Synchronous Detection and I.CosØ Shunt Active Filtering Algorithms‖, IEEE 2006. [10] Manjula G Nair and G. Bhuvaneswari, ―Design, Simulation and Analog Circuit Implementation of a Threephase Shunt Active Filter using the Icos Ǿ Algorithm‖ IEEE PEDS 2005.
GA optimization for a population size of 15 and generation size of 100 is done in GATOOL. Plot for best individual obtained from GATOOL is shown in Fig. 5. From the plot it is clear that best individual is corresponding to variable 6, i.e. 0110 combination. That is, placing two active filters near to nonlinear load at bus 2 and bus 4 is found to be the optimum location for active filter. Current Best Individual 1 0.9
Current best individual
0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5
6 7 8 9 10 11 Number of variables (15)
12
13
14
15
Fig. 5: Best individual plot
VIII. CONCLUSION Harmonic load flow analysis of the four bus test system is done in ETAP and in MATLAB. From the results of the harmonic load flow analysis objective function is developed. The control strategies used to develop the objective function are total harmonic distortion of voltage and current, telephone interference factor of voltage and current, harmonic transmission line loss and active filter current. The objective function is optimized using genetic algorithm in GATOOL box. From the optimization results the optimum location of active filter is found. The result shows that placing active filter near to non-linear load will provides good harmonic compensation.
REFERENCES [1] ―IEEE Recommended Practice for monitoring Electric Power Quality‖, IEEE STD 1159-1995. [2] ―IEEE Recommended Practice and Requirements for harmonic Control in Electric Power system‖, IEEE std.519, 1992. [3] Bhim Singh, Kamal Al-Haddad and Ambrish Chandra, ―A Review of Active Filters for Power Quality Improvement‖ ieee transactions on industrial Electronics, vol. 46, no. 5, October 1999. [4] W.M. Grady, M.J. Samotyj, A.H. Noyola, ―Minimizing network harmonic voltage distortion with an active power line conditioner‖, IEEE Trans. Power Delivery 6 (4) (1991) 1690–1697.
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