Advance in Electronic and Electric Engineering. ISSN 2231-1297, Volume 4, Number 6 (2014), pp. 593-598 Research India Publications http://www.ripublication.com/aeee.htm Optimal PMU Placement in Power System Considering the Measurement Redundancy Satyendra Pratap Singh and S.P. Singh Electrical Engineering Department, IIT (BHU) Varanasi, Varanasi, India. Abstract In this paper, Integer Programming based methodology is presented for the optimal placement of Phasor Measurement Unit (PMU) that minimizes the cost of installation and provide the entire power system observability. The concepts of zero injection buses are used in this paper for further reduction in number of PMUs. Integer Programming may produce multiple results if neighboring buses to zero injection buses are not handled properly. Though all the results are correct but create confusion in selecting one of them. In order to mitigate this problem a criterion has been proposed in this paper to select the appropriate location of PMU in such circumstances. The proposed algorithm is tested on IEEE 14-bus, IEEE 24-bus and IEEE 30-bus systems. Keywords: Phasor Measurement Unit; Integer Programming method; Redundancy Measurement; Observability analysis. 1. Introduction In recent years, series of blackouts have been encountered in power systems. For secure operation of power systems, close monitoring of the system operating conditions is required. Today with the presence of Global Positioning System (GPS) it is quite possible to monitor the operation of power systems. This is traditionally accomplished by the state estimator which innate in the control centre computer and has access to the measurements received from different substations in the monitored system. These measurements are commonly provided by the remote terminal units (RTU) at the substations and include real/reactive power flows, power injections, and magnitudes of bus voltages and branch currents. More recently, synchronized phasor measurements have started to become available at selected substations in the system
594 Satyendra Pratap Singh & S.P. Singh under observation. Phasor measurement unit (PMU) becomes more and more attractive to power engineers because it can provide time synchronized measurements of voltage and currents phasors (EPRI Report, 1997). Synchronization is achieved by same-time sampling of voltage and current waveforms using timing signals from the GPS. Voltage and current phasors, obtained from PMU buses, can be used to get full system data in control center computer using simple KVL and KCL equations. So the standards of power system monitoring, control and protection elevates to a new level because of Synchronized phasor measurement. Initiating work in PMU development and utilization is done by Phadke, 1986 and 1993. An algorithm which finds the minimal set of PMU placement needed for power system has been developed in (Baldwin, 1993 and Xu, 2004) where the graph theory and simulated annealing method have been used to achieve the goal. In (Chen, 2004) a strategic PMU placement algorithm is developed to improve the bad data processing capability of state estimation by taking advantage of PMU technology. Providing selected buses with PMUs can make the entire system observable. This will only be possible by proper placement of PMUs among the system buses. The authors in (Gou, 2008) developed an optimal placement algorithm for PMUs by using integer programming. However, the proposed integer programming becomes a nonlinear integer programming under the existence of zero injection buses. In (Ahmadi, 2011), authors presented a binary particle swarm optimization (PSO) methodology and considering measurement redundancy for optimal placement of PMUs when using a mixed measurement set. The paper is organized as follows: Section 2 states the Integer Programming method to minimize the optimal placement of PMUs. In section 3, mathematical formulations for optimal PMU placement are described. Finally test results are given in Section 4, and Section 5 concludes the paper. 2. Integer Programming Method for PMU Placement The Optimal PMU Placement (OPP) formulation based topological observability method finds a minimal set of PMUs such that a bus must be reached at least once by the PMUs. The optimal placement of PMUs for an N bus system is formulated as follows (Gou, 2008): Where, N is total number of system buses w k is weight factor accounting to the cost of installed PMU at bus k, X is a binary variable vector whose entries are defined as Eq. 4 and AX is a vector function that its entries are non-zero if the corresponding bus voltage is observable using the given measurement set and according to observability
Optimal PMU Placement in Power System Considering the Measurement 595 rules mentioned above, it ensure full observability while minimizing the total installation cost of the PMUs, otherwise its entries are zero. The entries in A are defined as follows: And b is a vector whose entries are all ones as shown in Eq. (5). The procedure for building the constraint equations will be described for two possible cases where there are (1) no conventional measurement, (2) zero injection buses. After getting the optimal number of PMUs, expression for redundancy measurement is given as: where, P is the total optimal number of PMUs, A is the connectivity matrix, and L is the location of PMUs at the power system buses. Equ.(6) gives the redundancy measurement for all the possible results of optimal location of PMUs. 3. Solution Method Case1: A system with no conventional measurements In this case, zero injection buses are ignored from the test system. In order to form the constraint set, the binary connectivity matrix A, will be formed first. Matrix A can be directly obtained from the bus admittance matrix by transforming its entries into binary form. Fig. 1: 7-bus system. Consider the 7-bus system and its measurement configuration shown above. Building the A matrix for the 7-bus system of Fig (1) yields:
596 Satyendra Pratap Singh & S.P. Singh The constraints for this case can be formed as (Equ. 7): The operator + serves as the logical OR and the use of 1 in the right hand side of the inequality ensures that at least one of the variables appearing in the sum will be non-zero. The constraint f 1 1 implies that at least one PMU must be placed at either one of buses 1 or 2 (or both) in order to make bus 1 observable. Similarly, the second constraint f 2 1 indicates that at least one PMU should be installed at any one of the buses 1, 2, 3, 6, or 7 in order to make bus 2 observable. Case 2: A system with zero injection measurements This case considers the most general situation where zero injection buses are presented in the power system. Consider again the 7-bus system shown in Fig.1, where bus 3 is assumed to be a zero injection bus. In this case, it is easy to see that if the phasor voltages at any three out of the four buses 2, 3, 4 and 6 are known, then the fourth one can be calculated using the Kirchhoff s Current Law applied at bus 3 where the net injected current is known. Hence, the constraints associated with these buses will have to be modified accordingly as shown below: The operator. serves as the logical AND in the above equations. The expressions for f i can be further simplified by using the following properties of the logical AND (.) and OR (+) operators. Given two sets A and B, where set A is a subset of set B, Then A+B=B and A B=A. Applying this simplification logic to all expressions will yield: Note that the constraints corresponding to all other buses will remain the same as given in equation (7). One exception is the constraint for bus 3 where the injection is measured (or known). This constraint will be eliminated from the constraint set. The reason for removing the constraints associated with injection buses is that their effects are indirectly taken into account by the product terms augmented to the constraints associated with the neighboring buses.
Optimal PMU Placement in Power System Considering the Measurement 597 4. Test Results In this paper integer programming of MATLAB is used to optimize the PMU placement. The proposed integer linear programming algorithm has been tested on IEEE 14-bus, IEEE 24-bus and IEEE 30-bus systems. The Information of the test systems for the numbers and locations of zero injections are given in table 1. Table 1: System information of All the IEEE test bus systems. Test System No. of zero injection buses Location of zero injection buses IEEE 14-bus 1 7 IEEE 24-bus 4 11, 12, 17, 24 IEEE 30-bus 6 6, 9, 22, 25, 27, 28 The results of proposed method without and with zero injection measurement are displayed in Tables 2 and 3 respectively. In case of zero injection buses, higher values of measurement redundancy maximize the observability of power system buses. Table 2 shows the results of proposed method without considering zero injection buses. In case 1 single result is obtained so there is no need for redundancy measurement to obtained the best result in Table 2. Table 2: Simulation results for all the test systems without considering zero injections. Test System Optimal No. of PMUs Optimal location of PMUs IEEE 14-bus 4 2, 6, 7, 9 IEEE 24-bus 7 2, 3, 8, 10, 16, 21, 23 IEEE 30-bus 10 1, 7, 9, 10, 12, 18, 24, 25, 27, 28 Now Table 3 shows the test results of proposed method having more than one optimal placement of PMUs set considering zero injection buses. In case 2, IEEE 14- bus test system has three optimal number of PMUs and their location are {2, 6, 9} & {3, 6, 9}. Redundancy value of first set (2, 6, 9) is 15 and for second set (3, 6, 9) is 13. According to the proposed method best result has the maximum redundancy value so the final optimal PMU set is {2, 6, 9}. Table 4 shows the best solution of optimal placement of PMUs in power system considering zero injection buses on the basis of measurement redundancy value from Table 3. Table 3: Simulation results for all the test system with considering zero injections. Test System Optimal No. of PMUs Optimal location of PMUs Measurement Redundancy IEEE 14-bus 3 2, 6, 9 15 3, 6, 9 13 IEEE 24-bus 6 1, 2, 8, 16, 22, 23 24
598 Satyendra Pratap Singh & S.P. Singh 1, 2, 8, 16, 21, 23 25 2, 8, 10, 15, 18, 20 24 IEEE 30-bus 7 1, 2, 10, 12, 15, 19, 27 34 2, 4, 10, 12, 15, 18, 27 36 3, 5, 10, 12, 15, 18, 27 32 Table 4: Final results for all the test system with considering zero injections. Test System Optimal location of PMUs Measurement Redundancy IEEE 14-bus 2, 6, 9 15 IEEE 24-bus 1, 2, 8, 16, 21, 23 25 IEEE 30-bus 2, 4, 10, 12, 15, 18, 27 36 5. Conclusion An Integer Programming method is presented in this paper, which minimize the cost of installation of PMUs in power system by minimizing the number of PMUs for full observability of power system. Besides the placement of mere PMUs, this study also considers the placement of PMUs when zero injection buses are present in the power system. In addition, multiple choices of locations are eliminated by selecting the combination of buses having maximum redundancy. Simulation results on IEEE 14- bus, IEEE 24-bus and IEEE-30 bus test systems indicate that the proposed placement method satisfactorily provides full observable system measurements with minimum number of PMUs. References [1] A. Ahmadi, Y. A. Beromi, M. Moradi (2011), Optimal PMU placement for power system observability using Binary PSO and considering measurement redundancy, Expert Systems with Applications,Vol. 38, pp. 7263 7269. [2] A. G. Phadke, J. S. Thorp, and K. J. Karimi (1986), State Estimation with Phasor Measurements, IEEE Transactions on Power Systems, Vol. 1, No. 1, pp. 233-241. [3] A. G. Phadke (1993), Synchronized phasor measurements in power systems, IEEE Computer Applications in Power, Vol. 6, Issue 2, pp. 10-15. [4] B. Gou (2008), Optimal placement of PMUs by integer linear programming, IEEE Trans. Power Syst., vol. 23, no. 3, pp. 1525 1526. [5] B. Xu, A. Abur (2004), Observability analysis and measurement placement for systems with PMUs, Proceedings of IEEE PES Conference and Exposition, vol.2, pp. 943-946. [6] EPRI Final Report (1997), Assessment of Applications and Benefits of Phasor Measurement Technology in Power Systems, GE Power Syst. Engineering. [7] J. Chen and A. Abur (2006), Placement of PMUs to Enable Bad Data Detection in State Estimation, IEEE Trans. on Power Systems, Vol. 21, No. 4, pp. 1608-1615. [8] T. L. Baldwin, L. Mili, M. B. Boisen, and R. Adapa (1993), Power System Observability With Minimal Phasor Measurement Placement, IEEE Transactions on Power Systems, Vol. 8, No. 2, pp. 707-715.