Group 4 Topic 8 Presentation

8/13/2019 Group 4 Topic 8 Presentation

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Optimal Placement of Phasor Measurement Unitsfor State Estimation using Integer Linear

Programming

Presentation

byAjinkya Sinkar & Vikas Kurariya(M.Tech, Power Electronics & Power Systems)

November 5, 2013

CAPSA Course Project Presentation 1
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Block Diagram of a Generic PMU

A PMU consists of the following:

Filter

A/D ConverterGPS ReceiverMicroprocessor

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Block Diagram of a Generic PMU

A PMU consists of the following:

Filter

A/D ConverterGPS ReceiverMicroprocessor

Basic Assumption made in the project is that a PMU installed at aparticular bus can measure the voltage at that bus as well as thecurrent along all the lines connected to that bus.

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PMUs for State Estimation

Conventional State EstimatorsNon-linear ( Measurements available are power ow overlines and voltage magnitude at buses)

Time consuming as they use iterative methods.

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PMUs for State Estimation

Conventional State EstimatorsNon-linear ( Measurements available are power ow overlines and voltage magnitude at buses)

Time consuming as they use iterative methods.State Estimators using PMU measurements

Linear ( Voltage and current phasors are measured)Time is saved as no iterations required for calculating the stateestimates.

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Need for Optimal Placement of PMUs

Placing PMU at every bus for direct monitoring is possible butnot a feasible solution.

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Cost of PMU is very high

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Cost of PMU is very highCommunication lines may not be available from a particularbus.

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Cost of PMU is very highCommunication lines may not be available from a particularbus.

It is not necessary to place PMUs at every bus in the system.( We can use Ohms Law and KCL to nd voltage at otherbuses and current ows over other lines)


l d l b b l
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Complete and Incomplete Observability


C l d I l Ob bili
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Complete ObservabilityIn this placement strategy, there are no buses in the systemwhich are unobservable.


C l d I l Ob bili
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Complete ObservabilityIn this placement strategy, there are no buses in the systemwhich are unobservable.

Incomplete Observability

In this strategy, there is atleast one bus which remainsunobservable.The topographical distance of this bus is very less from itsobserved neighbours.Voltage at this bus is calculated by interpolation techniques.

In our project, we have done the optimal placement forcomplete observability.


Obj ti f O ti l Pl t P bl
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Objective of Optimal Placement Problem

The objective is to make the system completely observablewith minimum number of PMUs.


Objecti e of Optimal Placement Problem
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The objective is to make the system completely observablewith minimum number of PMUs.For achieving the above objective, we have made use of abinary integer variable x i , such that:


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x i = 1 if PMU is installed at i th bus

0 if PMU is not installed at i th bus


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x i = 1 if PMU is installed at i th bus

0 if PMU is not installed at i th bus

We have made use of the IEEE 14 bus system shown in thefollowing slide for simulation.


Single Line Diagram of IEEE 14 Bus System
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Problem Formulation in ILP Framework without Zero


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Problem Formulation in ILP Framework without ZeroInjection Bus

Objective: min x 1 + x 2 + x 3 + ...... + x 14

subject to:



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subject to:Bus 1 : x 1 + x 2 + x 5 1Bus 2 : x 1 + x 2 + x 3 + x 4 + x 5 1Bus 3 : x 2 + x 3 + x 4 1


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subject to:Bus 1 : x 1 + x 2 + x 5 1Bus 2 : x 1 + x 2 + x 3 + x 4 + x 5 1Bus 3 : x 2 + x 3 + x 4 1Bus 4 : x 2 + x 3 + x 4 + x 5 + x 7 + x 9 1Bus 5 : x 1 + x 2 + x 4 + x 5 + x 6 1Bus 6 : x 5 + x 6 + x 11 + x 12 + x 13 1Bus 7 : x 4 + x 7 + x 8 + x 9 1Bus 8 : x 7 + x 8 1Bus 9 : x 4 + x 7 + x 9 + x 10 + x 14 1

Bus 10: x 9 + x 10 + x 11 1Bus 11: x 6 + x 10 + x 11 1Bus 12: x 6 + x 12 + x 13 1Bus 13: x 6 + x 12 + x 13 + x 14 1Bus 14: x 9 + x 13 + x 14 1


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S g e e ag a o us Syste

Figure: IEEE 14 Bus Test System (Bus 7 is zero injection bus)


Problem Formulation in ILP Framework considering Zero
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gInjection Bus

If conventional method suggested by [2] is used, theconstraints become non-linear.For linearising the zero injection constraint, we make use of another index called the bus observability conrmation indexwhich is dened by [4] as:

u i = 1 if i th bus is observable

0 if i th bus is unobservable

The zero injection constraint for IEEE 14 bus is as shown:u 4 + u 7 + u 8 + u 9 3


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gInjection Bus contd ...

The constraint at bus no. 4, 7, 8 and 9 now become:x 2 + x 3 + x 4 + x 5 + x 7 + x 9 u 4x 4 + x 7 + x 8 + x 4 + x 9 u 7x 7 + x 8 u 8x 4 + x 7 + x 9 + x 10 + x 14 u 9


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Only these constraints change as bus no. 4, 8 and 9 areconnected to bus no. 7




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Only these constraints change as bus no. 4, 8 and 9 areconnected to bus no. 7

Objective function as well as other constraints formulatedearlier (without zero injection bus) remain the same.


Result & Observation
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The result of simulation on IEEE 14 Bus System usingbintprog function in Optimisation toolbox of MATLAB is asfollows:

Without Zero Injection With Zero Injection

No. of PMU Location No. of PMU Location4 2,6,7,9 3 2,6,9


Result & Observation
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The result of simulation on IEEE 14 Bus System usingbintprog function in Optimisation toolbox of MATLAB is asfollows:

Without Zero Injection With Zero Injection

No. of PMU Location No. of PMU Location4 2,6,7,9 3 2,6,9

It can be seen that the number of PMUs required for

complete observability decreases when zero injection bus ispresent in the system.


Conclusion
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Optimal placement of PMUs using binary integerprogramming has been done.


Conclusion
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Optimal placement of PMUs using binary integerprogramming has been done.Results of simulation on IEEE 14 bus system shows that the

number of PMUs required for complete observability areabout 1/ 3 of the total number of buses present in the system.


Conclusion
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Optimal placement of PMUs using binary integerprogramming has been done.Results of simulation on IEEE 14 bus system shows that the

number of PMUs required for complete observability areabout 1/ 3 of the total number of buses present in the system.Number of PMUs required decreases when zero injectionbuses are present in the system.


Future Scope of Work
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The present algorithm can be used for placement of PMUs onlarger systems to verify its effectiveness.

PMU placement problem for incomplete observability can beformulated and solved as an ILP problem.Phasing of PMU placements can be implemented.


References
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1 A.G. Phadke and J.S. Thorp Synchronized Phasor Measurements and their Applications, SpringerPublication, 2008.

2 B. Xu and A. Abur, Optimal placement of phasor measurement units for state estimation, Final ProjectReport, Power System Engineering Research Centre PSERC Publication 05-58 , Oct. 2005.

3 X. Dongjie, H. Remmu, W. Peng and X. Tao, Comparison of several PMU placement algorithms for stateestimation, Proc. Inst. Elect. Eng.E Int. Conf. Develop. Power Syst. Protection , pp. 32-35, April 2004.

4 D. Dua, S. Dambhare, R.K. Gajbhiye and S.A. Soman, Optimal multistage scheduling of PMU placement:An ILP approach, IEEE Transactions on Power Delivery , vol. 23, no. 4, pp. 1812-1820, Oct. 2008.

5 T.L. Baldwin, L. Mili, M.B. Boisen and R Adapa, Power system observability with minimal phasormeasurement placement, IEEE Transactions Power Systems , vol. 8, no. 2, pp. 707-715, May 1993.

6 R. Nuqui and A.G. Phadke, Phasor measurement unit placement techniques for complete and incompleteobservability, IEEE Transactions on Power Delivery , vol. 20, no. 4, pp. 2381-2388, Oct. 2005.

7 Hadi Saadat, Power system analysis, WCB McGraw-Hill Publication, 1999.

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THANK YOU !!!

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Group 4 Topic 8 Presentation