Optimal PMU Placement in Power System Considering the Measurement Redundancy

Advance in Electronic and Electric Engineering ISSN 2231-1297 Volume 4 Number 6 (2014) pp 593-598 copy Research India Publications httpwwwripublicationcomaeeehtm

Optimal PMU Placement in Power System Considering the Measurement Redundancy

Satyendra Pratap Singh and SP 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 realreactive 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

Satyendra Pratap Singh amp SP Singh

594

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 wk 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

The constraints for this case can be formed as (Equ 7)

The operator ldquo+rdquo serves as the logical ldquoORrdquo 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 f1 ge 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 f2 ge 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 Fig1 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 Kirchhoffrsquos 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 lsquorsquo serves as the logical ldquoANDrdquo in the above equations The

expressions for fi 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 AB=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


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 amp 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

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 ApplicationsVol 38 pp 7263ndash7269

[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 1525ndash1526

[5] B Xu A Abur (2004) Observability analysis and measurement placement for systems with PMUs Proceedings of IEEE PES Conference and Exposition vol2 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


594

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 wk 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










Fig 1 7-bus system




596
























IEEE 14-bus 3 2 6 9 15 3 6 9 13

IEEE 24-bus 6 1 2 8 16 22 23 24


598

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




References


















Fig 1 7-bus system




596
























IEEE 14-bus 3 2 6 9 15 3 6 9 13

IEEE 24-bus 6 1 2 8 16 22 23 24


598

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




References










596
























IEEE 14-bus 3 2 6 9 15 3 6 9 13

IEEE 24-bus 6 1 2 8 16 22 23 24


598

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




References























IEEE 14-bus 3 2 6 9 15 3 6 9 13

IEEE 24-bus 6 1 2 8 16 22 23 24


598

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




References










598

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




References







