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International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 http://iraj.in Volume-5, Issue-9, Sep.-2017 OPTIMUM CAPACITOR ALLOCATION IN THREE PHASE UNBALANCED RADIAL DISTRIBUTION SYSTEM WITH HARMONICS AND RESONANCE CONSIDERATION USING PSO ALGORITHMS 1 AYUSTA LUKITA WARDANI, 2ONTOSENO PENANGSANG, 3RONY SETO WIBOWO 1,2,3 Electrical Engineering Department, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia Email: [email protected], [email protected],[email protected] Abstract - Distribution system connects between generation system and transmission system to the load. Power quality in distribution system can affect the flow of electric distribution. Decrease in power quality can be caused of low power factor, voltage drop, line loses and harmonic. Installation of capacitors can overcome the power quality problems when placement is appropriate. In a distorted system the presence of a capacitor may aggravate the harmonic level and cause either parallel or series resonance. In this research, capacitor placement and capacities are limited by minimum voltage, maximum reactive power load, THD and resonance index. Resonance index based on limit of capacitor loading according to IEEE standard. This scheme is tested on a distorted three-phase unbalanced distribution system which is have under voltage characteristics. The simulation result shows the installation of capacitor using PSO algorithm by considering harmonics and resonance index is capable to fulfill standard of THD that is 4.6929 % and decrease of active power loss equal to 19.74% and minimum voltage 0.95 pu. Keywords - line loses, resonance index, THD, PSO. minimum voltage, maximum reactive power load, THD and resonance index. Resonance index based on limit of capacitor loading as in [2] and THD limit as in [3]. PSO Algorithm is used to solve multi objective problem. I. INTRODUCTION Distribution system is a vital component in the power system. Radial distribution system (RDS) is the most widely used system for power distribution because it has a simple form and also low investment costs. RDS system has many challenges about line loss, unbalanced issues, and harmonic spread due to increased use of power electronic devices. Power losses and voltage drop are main problem in the longest feeder in RDS. Line loss can be overcame with the installation of capacitors but the allocation must be appropriate to avoid aggravate the harmonic level and cause either parallel or series resonance. Harmonic effect can be divided into two term. Effect in Immediate and medium/long term. In immediate term can lead to overheating of conductor, transformer, capacitors, and malfunction of regulator devices. And in medium/long term can be reason for reduction of live time for motor and transformer. Harmonic in RDS cannot be avoid but it can be control by modify the frequency response of filters, inductors or capacitor. Move a capacitor to a point on the system with different short –circuit impedance or higher losses as in [1] or change the capacitor size. Not only reduce line losses but also can control IHD and THD to fulfill IEEE standard. The capacitor has standard loading to avoid heating, dielectric stress and decrease of lime time and to avoid system from resonance In this research used 25 bus unbalance RDS data which has low voltage characteristic. The system have six harmonic sources from ASD. The size of capacitor using standard capacitor available in industry. The allocation of capacitor limited by II. RESEARCH METHODS A. Radial Power Flow Analysis This research using network topology approach of RDPF. To clarify RDPF algorithm, flowchart of RDPF can be seen form figure 1 as follow: Figure 1: Radial Distribution Power Flow flowchart. Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 6 International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 http://iraj.in Network topology approach can determine the model of network by using K-matrix. K-matrix is one part of the graph theory which is also called branch-path incidence matrix as in [4]. Values of the K-matrix elements expressed as 1 if the branch is in the path of the bus to the reference in the same direction and vice versa, if the K-matrix elements will be -1 if the branch is in the bus heading in the opposite direction reference [5]. After distribution power flow is complete, the result will be used to analyze the influence of harmonics. Is Ih Volume-5, Issue-9, Sep.-2017 Capacitor Current Harmonic Current From this equation the number of capacitor must be the same number with capacitor. The capacitor number decided to six. C. Algorithm PSO PSO as an optimization method has several steps to run the algorithm. The algorithm can be divided into several points as follows: 1. Initialization of uniform distributed agent populations (particles) in a search field 2. Evaluate each position of the particle against objective function 3. If the current particle position is better than the previous best position then update the best position 4. Determine the best particles according to the best position of the particle 5. Update the velocity of each particle according to the equation: B. Harmonic Power Flow Analysis This research using backward/forward sweep based harmonic analysis method for distribution system [6]. To clarify HPF algorithm, flowchart of HPF can be seen form figure 2 as follow: Vi k 1 Vi k c1rand1 x Pbestik X ik c2rand2 x Gbest k X ik (2) Where Vi k individual velocity i on iteration k w parameter weight c1, c2 acceleration coefficient rand1, rand2random number between 0 and 1 Xi k individual position i on iteration k Pbesti kPbest individual i to iteration k Gbesti k Gbestgroup until iteration k 6. 7. Move the particle to its new position according to the equation (2) Repeat the algorithm in the second step until the desired criteria are met. III. PROBLEM FORMULATION The allocation capacitor is a nonlinear integer optimization which limited by power constraint and quality constraints. Objective Function: minimize fundamental real power loss and harmonic real power loss. Figure 2: Harmonic Power Flow flowchart =∑ HA matrix is used to find the presence of harmonic sources. Harmonic source in this research are six ASD. It will inject harmonic source to the system. The harmonic components of capacitor current can be calculate by Is = (HLF^-1)*(-HAsh)* (Ih) ( ) +∑ ∑ ( ) (3) Where P_loss Nb ho hmax (1) total power loss (kw) the branch number harmonic order to 1 maximum harmonic order And the limits used are the boundaries of equality and inequality. The equality boundary is the limitation used by non- linear power flow calculations whereas Where Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 7 International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 http://iraj.in inequality limits are used to limit bus voltages, magnitude of THD and amount of reactive power being compensated. Here are the constrainthat must be met. Volume-5, Issue-9, Sep.-2017 Harmonic source will be placed in six location to equalize the amount of capacitor. In that way capacitor harmonic current can be calculate. Harmonic source will be placed in according to table 4. 1. Voltage Bus IV. SIMULATION AND DATA ANALYSIS ≤| |≤ (4) This research used 25 bus unbalanced three phase radial distribution system. As figure 3. Where the lower limit of the voltage is 0.95 pu and the upper limit of the voltage is 1.05 pu so it is still within the range of 5% of the nominal voltage. 2. THD level ≤ 5% (5) THD limit for bus voltage below 69kV is 5%. 3. Reactive Power ∗ ≤ (6) The maximum reactive power that is compensated by using capacitors is limited by the total reactive power demand of the load. 4. Capacitor Loading limits Capacitor limit as resonance index will be used in case number 3 and 4. The result will be compare with case number 1 and 2 to get the best result which fulfill the constraint. Index Description Limit S Apparent power of the capacitor RMS voltage of the capacitor Peak voltage of the capacitor RMS current of the capacitor 135% Vrms Vpeak Irms Figure3: Single Line Diagram 25 Bus Unbalance System From radial distribution power flow the voltage profile are 110% 120% 180% Table 1 : Standard Capacitor Loading Indices and Limits Branch Bus Voltage (kV) I J Current(A) Losses (kW) 1 4.16 1 2 588.24 24.15 1 4.16 1 2 594.16 25.13 1 2 4.16 1 2 594.24 24.89 4.02 2 3 315.93 3.48 2 4.02 2 3 320.85 3.66 Table 4: The result from RDPF The data of harmonic source are from ASD which only used orde 5, 7, 11, and 13 because as in [7] it was observed that in their vicinity, resonances close to the fifth or the seventh harmonic order occurred. Bus Voltage (kV) 2 Branch I J Current (A) Losses (kW) 4.02 2 3 320.32 3.62 Order Magnitude (%) Angle 3 3.99 3 4 128.28 0.57 5 23.520 111 3 3.99 3 4 139.48 0.69 7 6.080 109 3 3.99 3 4 122.14 0.53 11 4.570 -158 4 3.97 4 5 27.96 0.07 13 4.200 -178 4 3.97 4 5 32.78 0.10 4 3.97 4 5 26.66 0.07 Table 3: Harmonic Injection Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 8 International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 http://iraj.in Volume-5, Issue-9, Sep.-2017 5 3.97 2 6 272.31 6.87 19 3.93 18 20 52.58 0.41 5 3.96 2 6 273.34 6.96 20 3.94 18 21 18.93 0.05 5 3.97 2 6 273.92 6.97 20 3.94 18 21 22.00 0.07 6 3.97 6 7 217.60 4.38 20 3.94 18 21 24.33 0.09 6 3.96 6 7 223.44 4.65 21 3.93 21 22 33.11 0.16 6 3.96 6 7 225.34 4.72 21 3.94 21 22 26.91 0.11 7 3.92 6 8 32.88 0.20 21 3.93 21 22 28.27 0.12 7 3.92 6 8 28.06 0.15 22 3.92 4 23 78.53 0.46 7 3.92 6 8 26.75 0.13 22 3.93 4 23 82.63 0.51 8 3.95 7 9 105.81 1.04 22 3.92 4 23 76.74 0.44 8 3.95 7 9 102.27 0.97 23 3.96 23 24 51.83 0.20 8 3.95 7 9 105.92 1.04 23 3.96 23 24 49.83 0.19 9 3.90 9 10 105.81 1.04 23 3.96 23 24 48.74 0.18 9 3.89 9 10 102.27 0.97 24 3.95 24 25 32.98 0.16 9 3.89 9 10 105.92 1.04 24 3.95 24 25 25.64 0.10 10 3.87 10 11 83.46 0.39 24 3.95 24 25 26.82 0.11 10 3.87 10 11 79.91 0.36 25 3.94 10 3.87 10 11 83.54 0.39 25 3.94 11 3.86 11 12 27.40 0.05 25 3.94 11 3.86 11 12 28.75 0.06 11 3.86 11 12 33.70 0.08 12 3.86 11 13 22.44 0.04 12 3.86 11 13 22.45 0.04 3.85 11 13 22.46 3.86 7 14 62.68 0.36 13 3.86 7 14 65.84 0.40 13 3.86 7 14 68.96 0.44 14 3.91 14 15 24.51 0.03 14 3.90 14 15 19.10 After getting the results from the RDPF then proceed HPF to get the Ploss harmonics and the amount of THD early. 0.04 13 0.02 14 3.90 14 15 22.22 0.03 15 3.90 7 16 27.02 0.07 15 3.90 7 16 33.23 0.10 15 3.90 7 16 28.37 0.07 16 3.91 14 17 19.10 0.04 16 3.91 14 17 24.55 0.07 16 3.91 14 17 22.23 0.05 17 3.90 3 18 168.97 2.64 17 3.90 3 18 159.65 2.38 17 3.90 3 18 174.18 2.82 18 3.95 20 19 40.89 0.15 18 3.95 20 19 40.90 0.16 18 3.95 20 19 48.62 0.22 19 3.94 18 20 55.13 0.44 19 3.94 18 20 45.83 0.31 143.71 Bus THD R THD S THD T Bus THD R THD S THD T 2 2.27 2.26 2.46 14 3.02 2.90 3.13 3 2.29 2.28 2.48 15 3.07 2.90 3.13 4 2.30 2.29 2.49 16 3.06 2.98 3.23 5 2.30 2.29 2.50 17 3.07 2.99 3.24 6 2.47 2.46 2.68 18 2.31 2.30 2.51 7 2.67 2.66 2.90 19 2.32 2.31 2.52 8 2.65 2.64 2.87 20 2.32 2.30 2.51 9 2.79 2.77 3.00 21 2.32 2.31 2.52 10 2.92 2.87 3.10 22 2.33 2.31 2.52 11 2.99 2.93 3.16 23 2.31 2.30 2.50 12 2.99 2.93 3.17 24 2.31 2.30 2.51 13 2.99 2.93 3.17 25 2.32 2.31 2.51 Table 5: The result from HPF From table number 5 the biggest THD is 3.24 % and the lowest is 2.26%. The biggest THD is in the phase T and the lowest in the phase S. Ploss harmonic is 0.0658 kW. So the total loss of active power is 143.7716 kW. Profile THD 3.3 3 THD (%) 12 Total Losses 2.7 2.4 2.1 1.8 1 3 5 7 9 11 13 15 17 19 21 23 25 Bus Table 6 Profile THD Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 9 International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 http://iraj.in In this research have 4 study cases. 1. Case no 1 only limited Voltage and reactive power compensation. 2. Case no 2 limited Voltage, reactive power compensation and THD. 3. Case no 3 limited Voltage, reactive power compensation and RI. 4. Case no 4 limited voltage, reactive power compensation, THD and RI. no 3 doesn’t meet IEEE THD standard. So case number 3 cannot be used. Bus 2 3 4 5 6 7 8 9 10 11 12 13 From the simulation the results from study case no 1 the THD profile is describe by table number 6. Bus 2 3 4 5 6 7 8 9 10 11 12 13 THD R 5.94 5.99 6.01 6.02 6.45 6.95 6.91 7.29 7.63 7.84 7.89 7.89 THD S THD T 2.78 3.39 2.81 3.42 2.82 3.43 2.82 3.43 3.02 3.67 3.25 3.95 3.23 3.93 3.35 4.09 3.45 4.23 3.52 4.31 3.52 4.34 3.53 4.35 Bus 14 15 16 17 18 19 20 21 22 23 24 25 THD R THD S THD T 7.99 3.54 4.35 8.07 3.54 4.37 8.05 3.62 4.46 8.07 3.62 4.47 6.05 2.83 3.45 6.07 2.84 3.46 6.06 2.84 3.46 6.07 2.84 3.46 6.09 2.85 3.47 6.03 2.83 3.44 6.05 2.83 3.45 6.06 2.84 3.45 Bus 2 3 4 5 6 7 8 9 10 11 12 13 From case number 1 allocation kapasitor are in bus 11 R 450 kVAR, bus 12 R 150 kVAR, 12 S 450 kVAR , 12 T 450 kVAR, 14 S 450 kVAR and 15 T 350 kVAR. The biggest THD is 8.07 %and the lowest is 2.78 %. Case no 1 does not meet IEEE THD standard. So case number 1 cannot be used. THD T 2.23 2.25 2.26 2.26 2.42 2.61 2.59 2.68 2.76 2.80 2.81 2.80 Bus 14 15 16 17 18 19 20 21 22 23 24 25 THD R 4.19 4.23 4.25 4.25 4.54 4.88 4.87 5.07 5.25 5.37 5.42 5.42 THD S THD T 3.42 2.66 3.45 2.69 3.46 2.70 3.47 2.70 3.71 2.89 4.00 3.11 3.98 3.10 4.19 3.21 4.38 3.31 4.48 3.37 4.54 3.37 4.55 3.38 Bus 14 15 16 17 18 19 20 21 22 23 24 25 THD R THD S THD T 5.43 4.54 3.38 5.48 4.54 3.38 5.47 4.60 3.47 5.48 4.62 3.48 4.27 3.48 2.71 4.29 3.49 2.72 4.28 3.49 2.72 4.29 3.49 2.72 4.30 3.50 2.73 4.26 3.47 2.70 4.27 3.48 2.71 4.28 3.49 2.72 Table 8: THD Profile from Case Number 2 Table 6: THD Profile from Case Number 1 Bus THD R THD S 2 3.48 3.69 3 3.52 3.72 4 3.53 3.74 5 3.53 3.74 6 3.78 4.00 7 4.07 4.31 8 4.05 4.29 9 4.33 4.54 10 4.59 4.77 11 4.73 4.91 12 4.76 4.90 13 4.75 4.95 Volume-5, Issue-9, Sep.-2017 THD R 3.05 3.07 3.08 3.09 3.31 3.56 3.55 3.75 3.94 4.02 4.03 4.05 THD S 2.45 2.47 2.48 2.49 2.66 2.86 2.85 3.02 3.18 3.28 3.28 3.28 THD T 3.42 3.46 3.47 3.47 3.71 4.00 3.98 4.26 4.53 4.69 4.69 4.69 Bus 14 15 16 17 18 19 20 21 22 23 24 25 THD R THD S THD T 4.10 3.28 4.66 4.13 3.28 4.66 4.12 3.30 4.66 4.13 3.31 4.67 3.10 2.49 3.49 3.11 2.50 3.50 3.11 2.50 3.50 3.11 2.50 3.50 3.12 2.51 3.51 3.10 2.49 3.48 3.10 2.50 3.49 3.11 2.50 3.49 Table 9: THD Profile from Case Number 1 From case number 4 allocation kapasitor are in bus 11 R 350 kVAR, 10 R 150kVAR, 14 T 150 kVAR, 11 S 450 kVAR, 10 T 450 kVARdan 15 S150 kVAR. The biggest THD is 4.62 %and the lowest is 2.45 %. Case no 4 meet IEEE THD standard. So case number 4 can be used. THD R THD S THD T 4.76 4.94 2.80 4.76 4.94 2.81 4.75 4.99 2.89 4.77 5.00 2.90 3.55 3.75 2.27 3.56 3.77 2.28 3.56 3.76 2.28 3.56 3.77 2.28 3.57 3.77 2.29 3.54 3.75 2.27 3.55 3.76 2.27 3.56 3.76 2.28 Compare Before After Allocation Allocation Case 1 Case 2 Case 3 Case 4 Losses (kW) 143.67 113.53 115.88 115.38 115.30 Total Losses (kW) 143.77 113.63 115.98 115.44 115.40 Maximal THD 3.24 8.07 5.00 5.48 4.69 Reduction Total Ploss (%) - 20.98 19.34 19.69 19.75 Total Capasitor (kVAR) 2300.00 2150.00 2250.00 2250.00 Table 10: Comparison of Capacitor Optimization Results Before And After Capacitors. Table 7: THD Profile from Case Number 1 From the table the best case which fulfil the equality, inequality and the biggest reduction Ploss is case no 4. From case number 2 allocation kapasitor are in bus 10 R 150 kVAR, bus 11 R 600 kVAR, 11 S 150 kVAR , 12 T 600 kVAR, 13 S 600 kVAR and 16 R 150 kVAR The biggest THD is 5 % and the lowest is 3.69 %. Case no 2 meet IEEE THD standard. So case number 2 can be used. CONCLUSION From the simulation results on the distribution system of 25 unbalanced three-phase bus, the following conclusions are obtained: 1. The unbalanced three-phase bus distribution system has a significant under voltage characteristic of nearly 40%. And the maximum voltage is 0.97 pu. From case number 3 allocation kapasitor are in 7 R 600 kVAR, 10 R 150kVAR, 12 R 150 kVAR, 12 S 600 kVAR, 12 T 600 kVARdan 150 kVAR.. The biggest THD is 5.48 %and the lowest is 2.66 %. Case Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 10 International Journal Of Electrical, Electronics And Data Communication, ISSN: 2320-2084 Volume-5, Issue-9, Sep.-2017 http://iraj.in [7] IEEE Recommended Practices and Requirements for 2. Without considering the THD and the resonance Harmonic Control index proven to cause 8% THD which is exceed the in Electrical Power Systems, IEEE Standard 519, 1992 limit IEEE. Although it can reduce the loss of active [8] Cheng T-H., dan Yang N-C, “Three-Phase Power-Flow by power by 20.97% Direct Zbr Method for Unbalanced Radial Distribution Systems”, IET Gener.Transm.Distrib., Vol3, Iss.10, hal. 9033. Resonance index cannot stand alone because it will 910. 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Optimum Capacitor Allocation in Three Phase Unbalanced Radial Distribution System with Harmonics and Resonance Consideration using PSO Algorithms 11