Optimal Capacitor Placement and Sizing on Radial Distribution System by using Fuzzy Expert System

Transcription

1 274 Optimal Placement and Sizing on Radial Distribution System by using Fuzzy Expert System T. Ananthapadmanabha, K. Parthasarathy, K.Nagaraju, G.V. Venkatachalam Abstract:--This paper presents a mathematical formulation for placement of capacitor in a radial system by approximate reasoning using fuzzy set theory. The objectives are to minimize the real power losses and to improve the voltage profile. Voltage and power loss indices at each node of distribution system are modeled by fuzzy membership functions. Then, suitable candidate node for capacitor placement is determined by using approximate reasoning. Further, the capacitor is sized for its optimum capacity. Simulation results shows the advantages of this system and are encouraging. INTRODUCTION Due to limited generation and Trans mission capacities for accommodating growing loads, reactive power allocation has received an ever-increasing attention from the electric utility industry in recent years. Reactive currents will produce losses and results in increased ratings for distribution system components. Shunt capacitors are largely used in primary feeders to reduce energy losses and peak demand, which releases the KVA capacities of distribution apparatus and also to improve the system voltage profile. Thus the problem of optimal capacitor placement consist of determining the location for placement and sizing of capacitor for its maximum capacity so that by further increasing size additional savings are not achieved, while operating constraints at different loading levels are satisfied. METHODOLOGY The proposed methodology can be divided in to two sections. In the first section, the location for placement of capacitor is determined by approximate reasoning by using fuzzy set theory. For determining the location of capacitor the voltage and power loss at each node will be calculated and are represented in fuzzy membership function. The fuzzy expert system (FES) contains a set of rules which are developed from qualitative descriptions. In a conventional ES system a rule is either fired or not fired, where as in FES rules may be fired with some degree using fuzzy inferencing. For the capacitor placement, rules are fired to determine the suitability of a node. Such rules are expressed in the following form. IF promise, THEN conclusion For determining the suitability of the node a set of fuzzy rules have been established. The inputs to the rules are the voltage drop and power loss indices and the output consequent is the suitability of capacitor placement. The rules are summerised in the fuzzy decision matrix in Table 1. Fuzzy variables power loss, voltage drop and capacitor placement suitability are described by the fuzzy terms high, high medium/normal, medium/normal, low medium/normal and low. The fuzzy variables described by linguistic terms are represented by membership functions. The membership functions are as shown below. Description of Low Low Medium Medium High Medium High Power loss < >0.75 Description of Low Low Normal Normal High Normal High Voltage < > 0.8 Description of placement suitability Low Low Medium Medium High Medium High < > 0.75 Dr. T. Ananthapadmanabha * Dr. K. Parthasarathy** K.Nagaraju*** G.V. Venkatachalam **** * The National Institute of Engineering, Mysore. ** Power Research and Development Consultants Private Limited, Bangalore. ***The Bapuji Institute of Engineering and Technology. Davangere. **** Karnataka Power Transmission Corporation Limited, Davanagere

2 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR , DECEMBER 27-29, TABLE-1 AND Voltage Drop High High Normal Normal Low Normal Low Low Low Med. Low Med. Low Low Low Low Med. Med. Low Med. Low Med. Low Low Power Loss Med. High Med. Med. Low Med. Low Low High Med. High Med. High Med. Med. Low Med. Low High High High Med. Med. Low Med. Low Med. The membership functions for the power and suitability indices are created for ranking. Therefore portions of the membership function for the power and suitability indices are equally spaced. The use of FES determines the nodes by finding a compromise between the possible loss reduction from capacitor installation and voltage levels. The following example will demonstrate the max_prod inferencing membership of FES. Ex: A given node has a power loss index 0.7 and voltage drop of 0.3 from the FES inferencing it can be seen that, this node has a medium and high medium power loss index and low normal voltage. Following rules are fired from the decision matrix. (1) If power loss index is Medium AND voltage is High Normal then suitability is medium. (2) If power loss index is High Medium AND voltage is High Normal then suitability is High Medium. To aggregate the output of the two rules, the Mamadani max_prod inferencing technique is applied so that the resulting membership function is de fuzzyified and suitability value is The above procedure is applied to each node of the distribution system and suitability of each node is calculated. The node with highest suitability value is the best node for capacitor installation. In the Second Part optimum capacitor sizing is carried in the following steps 1. After determining the suitable node for the capacitor installation, a small capacitor unit (Commercially available) is installed at that node. 2. The peak power loss voltage drops at each node are calculated by installing the capacitor. 3. The benefits due to reduction in the power demand (KP), released in feeder capacity (KF), reduced annual energy losses (KE) and cost of installation of capacitor (KC) are calculated. 4. The nets savings due to installation of capacitor is given by NS=KP+KF+KE-KC 5. Another capacitor unit installed at the same location and net savings are calculated as described above. 6. This procedure is repeated for maximum net savings. Also voltage constraint is checked for each iteration (During no load conduction). If the voltage exceeds the prescribed level then the installation of that capacitor unit is rejected The flow chart for maximum savings is as indicated in Fig.1 Solutions Algorithm Mainly consist of two steps Step1 Determine power loss and voltage drop at each node and to Determine the suitable node for capacitor placement using fuzzy expert system Step2 Size the capacitor for achieving maximum financial benefits Step1 Peak power loss at each node is calculated as below PPL = 3 x I 2 x r x l /1000 Kw I= Segment current r= resistance of the line = for rabbit conductor l= Segment length in kms. Segment current can be calculated by adding the nodal current from tail end. The node current = KW 3 x Er x D.F x P.F KW = Node Active power Er = Receiving end voltage of the segment D.F = Diversity Factor. P.F. Power factor of the segment. The receiving end voltage of the each segment can be calculated as below 2 Er= Es + Es - _ (Segment KW x Segment KM )x (r Cos θ + X Sin θ) 2 2 D.F x 1000 x P.F (For lagging P.F ) Es = Supply end voltage of the segment

3 276 X= Inductance of the circuit Cos θ = P.F. of the segment The annual energy losses can be calculated as below Annual energy losses = PPL x LLR x 8760 units P.P.L = Peak Power losses in KW L.L.F = Loss load Factor = 0.2 (LF) x 0.8 (LF) 2 L.F = Load Factor = Average load Peak load or = Annual energy sent out peak load x 8760 Finally the voltage regulation of the feeder is given by % VR = ES Er x Es = Supply end voltage of the segment in KV. Er = Receiving end voltage of the segment in KV. After calculating the above, peak power loss and voltage drop at each node are represented by fuzzy membership function. The node at which max peak power loss occurs will have the value 1 and the max voltage drop node will have the value 1.The peak power losses and voltage drop at each node were calculated and are linearly normalized in to a [0,1] range. It is advisable to install the capacitor at the node with high peak power loss [so as to reduce max power loss] and the high voltage drop [so as to improve the voltage profile to the maximum extent]. The voltage drop and power loss indices are the inputs and the out put consequent is the suitability capacitor placement by applying the rules as indicated in the table 1.The consequent obtained for each node is recorded and nodes are ranked according to the suitability value. The node having the high suitable value will be best location for the capacitor installation. Step 2 The best suitable node was determined in the previous step. The optimal capacitor size to be placed at the chosen node to be determined for most economic savings in this step. In this step a 200KVAR capacitor unit (least rated commercially available unit) is placed at the chosen node and varies parameters are calculated due to addition of the capacitor. The net savings function NS, maximized by this capacitor sizing algorithm is given by NS = KP + KF+ KE KC KP = Benefits due to released demand (KW) KF = Benefits due to released feeder capacity (KVA) KE = Benefits due to saving in energy (KWH) KC = Cost of installation of the capacitor. Commercially available 200KVAR capacitor unit is installed at the chosen node by adding this unit, reactive power of the line will be altered. Let the system reactive power (up to the chosen node from sending end) be Q, and capacitor added be Qc then, new reactive power of the line up to the chosen node is Q2. That is Q2 = Q-QC The new P.F = P P 2 + Q 2 2 Released KVA = KF = S P 2 + Q 2 2 S = apartment power (original) By knowing the releasing feeder capacity the benefits due released feeder capacity can be calculated. Improvement in P.F. results in improvement in voltage profile causing reduction in current, which in turn reduces the peak power loss, and reduction in annual energy losses. The savings of energy (units) due to additions of this capacitor can be calculated by deducing the annual energy losses due to installation of capacitor from the Annual energy losses of the original system. Thus by knowing the savings of energy due to capacitor placement, benefits due to energy savings can be calculated. Benefits due to Reduced demand Benefits due to Reduced demand KP = KP x CKP x ikp KP = Reduced demand (KW) CKP = Cost of generation / KW (Taken as Rs 10,000/KW) IKP = Annual rate for generation cost. (Taken as 0.2) Benefits due to released feeder capacity Benefits due to released feeder capacity KF = KF x CKF x ikf KF = released feeder capacity CKF = Cost of the feeder / KVA (Taken as Rs 1,41,090/KM) IKF = Annual rate of cost of feeder (Taken as 0.2) Benefits due to savings in energy Benefits due to savings in energy KE = KE x r KE = savings in energy KE= (Annual energy losses before installing the capacitor) (Annual energy losses after installing the capacitor.) r = Rate of energy in Rs / Unit. (Taken as Rs 3/unit) Cost of installation of capacitor KC= KC x ICKC x ikc KC = No. of 200 KVAR capacitor units ICKC = Cost of each 200 KVAR capacitor (Taken as Rs 40,000/200kvar) ikc = Annual rate of cost of capacitor (Taken as 0.2)

4 INDIAN INSTITUTE OF TECHNOLOGY, KHARAGPUR , DECEMBER 27-29, Thus the net savings due to the addition of the capacitor is calculated. Further another 200KVAR capacitor is installed at the same node and net savings due to this is calculated. This procedure is repeated up to the size that there is no additional net savings. Checking the constraint for voltage Limit volition The voltage of all sections shall be below the statutory upper limit at light load condition. The voltage at the section of installation of capacitor may go beyond the prescribed limit at light loads. This constraint has to be checked before proceeding to the installation of capacitor unit. The approximate voltage due to installation of the capacitor at no load is given by Er= Es + Es + Qc x L QC= Installed capacitor in KVAR L = Length of the line from sending end Es = Supply end voltage in KV. This constraint is checked before proceeding to the next steps. If the % VR is > 6% then the installation of the capacitor is rejected. System Studied The described method is applied to 11 KV, 21 bus radial distribution system as shown below. MUSS 11KV Gopanahally Feeder The input data of the existing system is as below From node To Node Node KVA Node KW At 0.8 pf Segment Length Conductor Type Resistance In ohms Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit Rabbit After calculation of the node voltage and power loss indices, the FES determines that node 11 has a high power loss and normal voltage level. The defuzzifide suitability index indicated at node 11 is the most suitability location for capacitor installation. The optimum size of capacitor is found to be 1200 KVAR. The comparison of savings and voltage due to various size of capacitor are as followings.

5 278 Particulars Abstract of Results by placing different sizes of capacitors at node KVA R Capacito r 400KVAR 600KVAR 800KVAR 1000KVAR 1200 KVAR 1400 KVAR Power Factor (leading) (leading) Released Demand ( KP) in KW KP in Rs. 10,606 19,205 25, ,979 52,855 51,889 Released KVA KF in Rs. 3,876 7,169 9,845 11,766 12,829 13,035 12,349 Energy Saved in units / annum 12,876 23,317 31,362 36,955 40,041 64,173 63,000 KE in Rs. 38,62 69,951 94,086 1,10,865 1,20,123 1,92,519 1,89,000 8 Cost of capacitor 8,000 16,000 24,000 32,000 40,000 48,000 56,000 installation (KC) Net savings 45,110 80,325 1,05,761 1,21,068 1,25,931 2,10,409 1,97,238 (NS) in Rs. V.R. at Tail End No load voltage at capacitor bank CONCLUSIONS The proposed technique presents a mathematical formulation for capacitor placement in a radial system by approximate reasoning using fuzzy expert system it offers following advantages. (1) Simple mathematical formulas are used for the calculation and power loss, voltage at each node instead of load flow. (2) In many analytical approaches, the locations and sizes of capacitors calculated will not match the physical locations of nodes and the discrete sizes of availability capacitors. There solution will need to the rounded up or down to the nearest node position and capacitor size. This method finds most suitable placement for capacitor installations, which are actual physical node locations in the system and desecrate sizes and capacitors are also considered. (3) In this method the loss reductions and the voltage profile are considered simultaneously when deciding the node for capacitor placement. Hence a good compromise of loss reduction and voltage profile improvement is achieved. (4) This method does not require training of data and will never have convergence problems. (5) Most simple and flexible. This can be easily be adapted for expansion and operation plans of distribution system. REFERENCE: (1) MMA Salama, AY Chikhani, R. Hakman Control of reactive power in distribution system with an end load and fixed load condition IEEE Transactions on PAS-104, No. 10, October (2) MMA Salama and AY Chikhani An expert system for reactive power control of distribution system IEEE transactions on power deliver, Vol. 7, No. 2, 1992 (3) MMA Salama and AY Chikhani A simplified network approved to the VAR control problem for radial distribution system Part I & II IEEE Transactions on power delivery vol.8, No. 3, IEEE transaction on power Vol. 10, No. 3, August (4) MMA Salama and AY Chikhani Allocation by approximate reasoning fuzzy capacitor placement. IEEE transactions on power delivery Vol. 115, No.1, January 2000.