CHAPTER 2 LOAD FLOW ANALYSIS FOR RADIAL DISTRIBUTION SYSTEM

Transcription

1 16 CHAPTER 2 LOAD FLOW ANALYSIS FOR RADIAL DISTRIBUTION SYSTEM 2.1 INTRODUCTION Load flow analysis of power system network is used to determine the steady state solution for a given set of bus loading condition. The solution of a load flow study provides the information on voltage magnitude and phase angles, active and reactive power flow in the individual transmission lines and total real and reactive power losses. Load flow study is much important in the planning stages of new power system or additional to existing one. Load flow is essential for the analysis of the distribution system, to investigate the issues related to planning, design and the operation and control. Some applications like placement of distributed generation or capacitor need repeated power flow solution. The development of digital computers and their wide use in power system, made to develop many algorithms in 1950 s. The most popular algorithms such as indirect Gauss- Seidel (bus admittance matrix), direct Gauss-Seidel (bus impedance matrix), Newton-Raphson and its decoupled versions have been designed for transmission systems and these are unsuitable for distribution systems due to its own inherit characterizes like radial in structure, an unbalanced distributed load and unbalanced operation, Large number of nodes and branches, Wide range of resistance and reactance values. Methods like the Newton-Raphson and Gauss- Seidel do not exploit the radial structure of the distribution systems and require the solution of a set of equations whose size is of the order of the number of buses. This then results in long computational time. In addition, Y-bus matrix constructed is very sparse and this implies a waste of computer memory storage. Hence it can be

2 17 seen that the use of conventional power flow methods is not efficient for distribution systems. The high R/X ratio of distribution systems causes the distribution systems to be ill conditioned for conventional power flow methods, especially the fast-decoupled newton method, which diverges in most cases. Due to the characteristics of Radial Distribution System (RDS) the conventional load flow analysis is not suited to solve the RDS. Hence, a network topology based analysis has been used in this work for finding voltage, total power loss of the RDS under balanced operating condition employing a constant power model. 2.2 NETWORK TOPOLOGY BASED LOAD FLOW ANALYSIS This method carries out the load flow analysis for Radial Distribution System under balanced operating condition employing constant power load model. This method has three important steps, listed below: Equivalent current injection Formulation of BIBC matrix Formulation of BCBV matrix Equivalent current injection This method based on the current injection. At bus i, the complex power S i is specified and the corresponding equivalent current injection at the k-th iteration of the solution is computed as i i i S P jq i=1, N (2.1)

3 18 k r k i k Pi jq i Ii Ii ( Vi ) j( Ii)( Vi ) k Vi (2.2) Where, S i is the complex power at i-th bus P i is the real power at i-th bus Q i is the reactive power at i-th bus k Vi is the bus voltage at the k-th iteration for i-th bus k Ii is equivalent current injection at the k-th iteration for i-th bus r I i and i I i are the real and imaginary parts of the equivalent current injection at the k-th iteration for i-th bus Formulation of BIBC matrix BUS 4 BUS 5 B4 BUS 1 BUS 2 BUS 3 B3 SUB-STATION B1 B2 B5 I 4 I 5 BUS 6 I 2 I 3 I 6 Figure 2.1 A sample Radial Distribution System The sample Radial Distribution System (RDS) shown in Figure 2.1 will be used as an example. The power injections can be converted into the equivalent current injections using Equation (2.2). And a set of equations can be written by applying Kirchhoff s Current Law (KCL) to the distribution network. Then, the branch currents can be formulated as a function of the equivalent current injections. For example, the branch currents B5, B3 and B1 can be expressed as,

4 19 B 5 = I 6 B 3 = I 4 +I 5 B 1 = I 2 +I 3 +I 4 +I 5 + I 6 (2.3) Furthermore, the Bus-Injection to Branch-Current (BIBC) can be obtained as, B I 2 B I 3 B 3 = I 4 B I 5 B I 6 B = BIBC I 2.3 ALGORITHM FOR FORMATION OF BIBC MATRIX The power injections can be converted to the equivalent current injection and the relationship between the bus-current injection and branch-current injections are obtained by Kirchhoff s Current Law (KCL) to the distribution network. The branch currents are formulated as equivalent of current injection. Step[1] - Create a null matrix of dimension m * (n-1) Where, m = number of branches. n = number of buses. Step[2]- If a line section (B k ) is located between Bus i and Bus j, copy the column of the i-th bus of the BIBC matrix to the column of the j-th bus and fill a + 1 in the position of the k-th row and the j-th bus column.

5 20 the BIBC matrix. Step [3] - Repeat Procedure (2) until all the line sections are included in The building Procedure for BIBC matrix shown in Figure 2.2, the algorithm can be easily expanded to a multi-phase line section or bus. i th bus j th bus Fill +1 at k th row and j th column Figure 2.2 BIBC matrix 2.4 ALGORITHM FOR FORMATION OF BCBV MATRIX The BCBV matrix is responsible for the relations between the branch currents and bus voltages. The corresponding variation of the bus voltages, which is generated by the variation of the branch currents, can be found directly by using the BCBV V 2 = V 1 B 1 Z 12 (2.4) V 3 = V 2 B 2 Z 23 (2.5) V 4 = V 3 B 3 Z 34 (2.6) rewritten as, By using Equation (2.4) and Equation (2.5), the voltage of Bus 4 can be V 4 = V 1 B 1 Z 12 B 2 Z 23 B 3 Z 34 (2.7)

6 21 From Equation (2.7), it can be seen that the bus voltage can be expressed as a function of the branch currents, line parameters and substation voltage. Similar procedures can be utilized for other buses, and the Branch-Current to Bus Voltage (BCBV) matrix can be derived as, V 1 V 1 V 1 - V 2 V 3 V 4 = Z Z 12 Z Z 12 Z 23 Z B 1 B 2 B 3 V 1 V 5 Z 12 Z 23 Z 34 Z 45 0 B 4 V 1 V 6 Z 12 Z Z 36 B 5 V = BCBV B Step [1] - Create a null matrix of dimension (n-1) * m m =number of branches n = number of buses Step [2] If a line section (B k ) is located between Bus i and Bus j, copy the row of the i-th bus of the BCBV matrix to the row of the j-th bus and fill the line impedance (Z ij ) in the position of the j-th bus row and the k-th column. Step [3] Repeat Procedure (2) until all the line sections are included in the BCBV matrix shown in figure 2.3. Rewriting Equation (2.7) in the general form, we have V BCBV B (2.8) The building Procedure for BCBV matrix shown in Figure 2.3, the algorithm can be easily expanded to a multi-phase line section or bus.

7 22 Fill Z ij at j th row and k th column Figure 2.3 BCBV matrix 2.5 ALGORITHM FOR DISTRIBUTION SYSTEM LOAD FLOW given below, A brief idea of how bus voltages can be obtained for a radial system is 1. Input data. 2. Form the BIBC matrix. 3. Form the BCBV matrix. 4. Form the DLF matrix. 5. Iteration k = Iteration k = k + 1. k * 7. Solve the equations iteratively and update voltages I i =(P i +Q i ) /V i [ V k+1 ] = [DLF] [I k ] k+1 k If I i I i >tolerance, go to step(6) else print result. The detailed control flow for the network based topolgy load flow analysis for 33 bus and 69 bus radial distribution system shown in Figure 2.4. From the figure, it is clear that for every iteration the bus voltages has been updated and

8 23 the power losses have been calculated. The iteration has been continued until the tolerance value has been reached. START Read Input Data Form the BIBC matrix Form the BCBV matrix Calculate DLF matrix and set iteration k = 0 Iteration k = k+1 Update voltages Yes k 1 k ( i i ) I I tolerance No Calculate line flows & losses using final voltages STOP Figure 2.4 Flowchart of network based topology load flow analysis for Radial Distribution System

9 RESULTS AND DISCUSSION Two test systems have been taken to test and validate the proposed algorithm, the 33 bus Radial Distribution System (RDS) [90] and 69 bus Radial Distribution System (RDS) [10]. The line data, load data and the one line diagram of the test systems are given in Appendix-2. The base MVA and base kv have been taken as 100 MVA and kv. The summary of load flow analysis is given in table 2.1. The 33 bus radial distribution system has the real power loss of kw, reactive power loss of kvar and the minimum voltage at the node 18 of p.u. The 69 bus radial distribution system has the real power loss of kw, reactive power loss of kvar and the minimum voltage at the node 65 of p.u. By proper allocation and sizing of Distributed Generation this real power loss is reduced further. The detailed base case load flow solution for 33 bus RDS and 69 bus RDS is given in Appendix-I. Table 2.1 Base case load flow solution for 33 bus RDS and 69 bus RDS Test System 33 bus RDS 69 bus RDS Real Power Loss (kw) Reactive Power Loss (kvar) Minimum Bus Voltage V (p.u) p.u at bus p.u at bus 65 Two matrices, which are developed from the topological characteristics of distribution systems are used to solve power flow problem. The BIBC matrix represents the relationship between bus current injections and branch currents and the BCBV matrix represents the relationship between branch currents and bus voltages. These two matrices are combined to form a direct approach for solving power flow problems. The time-consuming procedures, such as forward/backward substitution of the Jacobian matrix or admittance matrix are not necessary in this

10 25 load flow. The ill-conditioned problem that usually occurs during the other traditional methods will not occur in the network based topology load flow analysis. 2.7 SUMMARY In this chapter the network based topology load flow analysis for 33 bus and 69 bus radial distribution system has been analyzed. The load flow analysis of RDS gives the solution for bus voltages, line flows, total real power and reactive power losses. The real power loss of the distribution system is much higher due to the large value of resistance, low operating voltage and higher current values. Hence, it posses the keen interest to reduce the real power losses further by the placement of DG. The load flow analysis gives the solution for losses with and without DG and it makes to analysis the system with and without placement of DG and also it gives an analysis to find the optimal size and location of DG which reduces the losses at the maximum extend. By the proper allocation of DG, the real power loss is reduced further and the same time improper location of DG may increase the loss. Hence, the optimal location of DG is much important for loss reduction which is discussed in the next chapter.