Development of wide area monitoring system for smart grid application

Abstract

PMU can directly measure positive sequence voltage, phase and system frequency. In this paper, the design and implementation for optimum placement of PMU in power system network (PSN) has been performed using 5 different intelligent approaches at an emulation platform. Different case studies based on IEEE 7, 14 and 30 bus system have been performed and analyzed. In the studies, PMU device is used for the measurement of voltage and current magnitude as well as its phase and its performance has been compared with measured real signals of PSN. PMU measurement gives the accurate results and reliability to PSN. But PMUs are not economical, so PSN operator needs to install a minimum number of PMU in PSN so that system should be fully observable in a real-time scenario. In this paper for optimal placement of PMU, five different intelligent methods have been analyzed for three different bus systems and obtained results are compared. For the further validation of selected PMUs for the PSN, a state estimation using WLS algorithm has been performed using conventional data and PMU data on IEEE14 and IEEE30 bus systems. The obtained results for voltage estimation error and phase estimation error with and without PMU data are compared.

Keywords

Condition monitoring PMU placement wide area monitoring smart grid

1 Introduction

Currently, the power system network (PSN) requirement is increasing day-by-day due to increase in population and modern industry demand to fulfil the regulated supply. But uninterrupted supply is not an easy task due to unpredictable nature conditions such as heavy storms, heavy rain and/or highly snow fall, complex nature of power system and different difficulties occurring in the PSN. In present scenario increasing blackouts and reoccurring load shedding are big challenging problems faced by PSN professionals in the world. So it requires advanced device to monitoring and controlling of PSN to overcome problems in large PSN. So advance device such as PMU can do proper controlling and monitoring of power system and can provide PSN’s protection from various faults.

PMU is a synchronizing measurement instrument that gives angle, frequency and rate of change of frequency (ROCOF) obtained from sources. It is time stamped device with a clocking signal connected to GPS to obtain continuously voltage and current synchronized signal [1]. PMU is a microprocessor based device to obtain positive sequence estimation of voltage and current source. It is installing with the GPS receiver in the substation to obtain the synchronized measurement in real time. If phase difference between PMUs are detect, then fault can easily be traced. Since PMU is a costly device so it is uneconomical to installing PMU at every bus of PSN. So for complete observability, PSN’s engineers have required optimal number of PMUs in bus system [2].

Basics of a PMU came in the early 80 s [3]. At Virginia tech research lab, most of simulation and construction work of PMU was done by Professor Phadke and his team. Synchronized data sample used by early for protection system as data were used by different substation. So symmetrical distant relay were invented at Virginia tech. These works motivate the concept of phasor measurement. First industrial PMU was introduced by Macrodyne Company.

IEEE also started for PMU with large and complex global specifications. IEEE-1344 was the first version of standard for synchrophasor release in 1995 [4]. The IEEE versions were updated and further revised as required. Next version came in 2005 name as IEEE-C37.118 [5]. Current version of PMU standard release in 2014. These standards are base of the design solution as per as demand of PSN to manufacturer in steady and dynamic test conditions. The IEEE standard specified the accuracy of PMU assessment and differentiation. IEEE std. C37.118.1 has two versions of PMU forms: a P-class for protection, basically for steady state measurement and apply in fast response applications and an M-class- for measurement, used in higher accuracy demand applications [6]. An important standard release in 2013 as IEEE-C37.242 is guideline for installation of PMU and it’s testing [7].

In the development of PMU based technologies and methods for condition monitoring, protection, and control of PSN, three main domains have been analyzed by the researchers. These domains are: 1) Synchrophasor and Phasor Measurement Unit [8 –13], 2) Optimal PMU placement [14 –26] and 3) State Estimation of the system [27 –30]. In this regard, numerous research papers have been published in the digital domain.

The presented study has been organized in this paper as follow: section-1 presents the introduction and advantages of PMU for PSN, section-2 represents the methods for PMU model development and validation. The section-3 represents the intelligent methods for optimum placement of PMU in the PSN. The results and discussion of the research have been presented in section-4. Finally, section-5 represents the conclusion of the study.

2 PMU model development and validation

PMU is an essential device in power system for WAMS of power system network. PMU data is used in state estimation calculation in power system to enhance the measurement accuracy and reduce estimation error. PMU has been modelled with different technique for different uses. But a generic PMU is emulated so that it gives output results as positive sequence voltage, phase and with frequency. In this paper, MATLAB software is utilized for PMU emulation and other bus systems.

2.1 Emulation of PMU

PMU is designed to compute Positive sequence phasor (PSP) from voltage and current source as shown in Fig. 1. For working of PMU, a low pass filter is required, which restricts anti-aliasing signal to sampling theorem. Here, clock synchronization is given by GPS. Phased locked oscillator keeps frequency of measure and reference signal equal. The PSP from voltage source mathematically modelled by equation as: ${V = 1 / 3 (V}_{a} + α V_{b} + α^{2} V_{c})$ (1)

Fig. 1

Flow chart of PMU model.

Where, α = 1 ∠120° and V_a, V_b and V_c are the DFT phasor coefficient forms of 3-phase supply.

PLL-Driven block gives the positive sequence phase from voltage and current source. Frequency can be measured by normal three phase PLL block. Emulated Fig. 2 shows that voltage is feed into PLL block via MUX block and then voltage insert into sequence analyzer block also named PLL-driven. The PSP and frequency measure by PMU via their phase voltage and current measurement block output insert in PMU block.

Fig. 2

MATLAB/SIMULINK block of PMU.

2.2 Validation examples of PMU emulation

In this section, two examples for PMU emulation have been presented which shows the utilization of PMU in Figs. 3 and 4 for 2-bus and 3-bus system (3BS) respectively. The network parameters for 2BS and 3BS are shown in Tables 1 and 2 respectively. The systems are tested under heathy and faulty conditions to verify the PMU measurement capability. The emulated results for 2BS and 3BS are represented in Figs. 5 –7 and Figs. 8-9 respectively, which shows the correct measurement of frequency, positive sequence voltage and positive sequence angle and Voltage output measurement before/after entering PMU.

Fig. 3

Emulated Example of 2-Bus system.

Table 1

Network parameter for 2-bus system

Voltage Rating: 220 Kv
System frequency: 60 Hz
Distributed Line constant:
R₀ = 0.01273 (Ohms/Km); R₁ = 1 0.3864 (Ohms/Km)
L₀ = 0.9337 mH (H/Km); L₁ = 4.1264 mH (H/Km)
C₀ = 12.74 nF (F/Km); C₁ = 7.751 nF (F/Km)
Transmission Line Length: 100 km
Transformer rating – 13.8/220 kV
Primary: 13.8 kV, R₁ = 0.002 p.u, L₁ = 0.08 p.u
Secondary: 220 kV, R₂ = 0.002 p.u, L₂ = 0.08 p.u

Table 2

Network parameter for 3-bus system

Voltage Rating: 120 Kv
Bus System frequency: 60 Hz
Line constant:
R₁ = 0.1153 (ohms/Km), R₀ = 0.413 (ohm/km)
L₁ = 1.05e-3 (H/km), L₀ = 3.32e-3 (H/km)
C₁ = 11.33e-009 (F/Km), C₀ = 5.01e-009 (F/km)
Transmission Line Length: 25 km

Fig. 4

Emulated Example of 3-bus system.

Fig. 5

Frequency, positive sequence voltage and positive sequence angle for PMU-1.

Fig. 6

Frequency, positive sequence voltage and positive sequence angle for PMU-2.

Fig. 7

Voltage output before entering PMU for 2-Bus system.

Fig. 8

Frequency, positive sequence voltage and positive sequence angle for 3-Bus system.

Fig. 9

Voltage output after fault clearing using frequency feedback from PMU for 3-Bus system.

3 Methods for optimum placement of PMU

PMUs are very accurate for phasor measurement and it helps enhance the efficiency of state estimation and reduce state estimation error greatly. PMUs are time stamped with GPS so it can measure phasor at common time reference of power system. Because of various applications of PMU it has great advantages over conventional measurement system. But PMU is costly device so it is uneconomical to install it into each bus. So it requires optimal placement (OPP) of PMU for a minimum number of PMU and its location. In this study, five OPP techniques are discussed and implemented in different IEEE buses to find the OPP solution of PMU.

3.1 Integer linear programming (ILP) method

An ILP refers to a model that involves an integer value that one or more of the decision variables have to take in the final solution. It is quite a task to solve an integer programming problem as compared to solving a linear programming model. Even the fastest computers are incapable of solving big integer programming problems, as they take excessively long time in coping with them. The mathematical model for integer linear programming is the LP model which has one additional restriction of having the variables as integer values. $Objective function : minimum \sum_{i = 1}^{n} x_{i}$ (2) where n = bus number, x_i= binary variables, Constraints: f (x) = Ax ⩾ b, x = [x₁x₂ . . . . . . x_n] ^T, x_i∈ { 0, 1 } and b = [1 1 1 1 . . . . .] ^T, binary incidence matrix A is filled as: A_ij = 1 if i = j or connected A_ij = 0 if i≠j.

3.2 Depth first search (DFS) method

The DFS method of a graph is same as Depth First Traversal (DFT) for a tree as shown in Fig. 10. The thing that varies here is that graphs may consist of cycles which are not there in case of trees and because of this fact user can reach the same node again and again. To discourage processing of a same node more than one time, Boolean visited array is utilized in DFS Algorithm as shown in Fig. 11. This algorithm is basically a recursive algorithm which makes the use of the idea of back tracking. By going-ahead it makes exhaustive searches for all the available nodes if there is a possibility of doing it. Otherwise it does so by backtracking method. Stacks is used to achieve the recursive nature of Depth First Search Algorithm.

Fig. 10

DFS- Flow chart.

Fig. 11

Order in which nodes are visited in DFS.

The basic logic behind DFS algorithm is as follows:

Select a first node and shove all neighbouring nodes into the stack.

Visit a certain node into the stack so as to choose the next node which is to be visited and force all of its neighbouring nodes into a stack.

Do work again as steps 1 and 2 till the time the stack becomes empty.

However, it is required to ensure that the visited nodes have been marked, which prevent to visit a node multiple time. And if marking for visit is not done and by chance user reach the same node in 2nd time, then there is no chance to escape and user might end up in an infinite loop.

PMU is placed with maximum number of connected bus branch. If connected bus branch have same largest number then PMU location is randomly chosen. Then other PMUs are located with same rule until full network observability obtained.

3.3 Simulated annealing (SA) method

SA is an effective search method and proves to be very useful to avoid getting stuck into the trap of local minima (Fig. 12). It is one of the best methods of finding global optima where there is a presence of large numbers of local optima. Annealing refers to an analogy which is used in thermodynamics, specifically the way in which the metals cool & anneal.

Fig. 12

Global minima and local minima.

This method aims at solving optimization problems that are either bound-constrained or unconstrained. Basically, this method creates a model of physical process wherein a material is being heated and then its temperature is lowered to minimize the flaw, so reducing the overall model energies.

At every iteration of this method, there is a generation of a new point and that too, randomly. Now the question arises, how do we find the gap in new and current point? This distance between the new point and current one is dependent in probable distribution which has directly proportional to that of temp. All the points that lower the objective are accepted by this algorithm but in certain cases, points which raise the objective are also accepted. And by doing so, i.e., accepting those points which increase the motive which algorithm avoids getting into the trap of local minima and is very much able to go through universally more expected results. There is a systematic selection of annealing schedule to reduce the temperature as the algorithm moves forward. And as temperature gets reduced this method minimizes the search and converges to a minimum value.

3.4 Minimum N-1 spanning tree (MST) method

A spanning tree (as shown in Fig. 13) is one of the algorithms of graph theory. Basically, it is a part of graph theory G that has contained vertices under with minimum number of edges possible. Therefore, a spanning tree can’t be disconnected and it doesn’t include cycles.

Fig. 13

Spanning trees derived from Graph G.

By looking at this definition we can very much conclude that each and every undirected and connected graph has got one spanning tree at minimum. A graph that is disconnected can’t contains any spanning tree as it would not be possible to span to all of its vertices.

General characteristics of spanning tree connected to graph G are as given below –

More than one spanning tree can be made out from a connected graph G.

The entire feasible spanning tree is made out of graph G will be the equal quantity of edges and vertices.

A spanning tree doesn’t include any cycle or loop.

If 1 edge of the spanning tree is removed then it is called minimally connected.

If 1 edge is added to the tree, a circuit will be created and hence the spanning tree will become maximally acyclic.

A tree has n-1 edges, where n is equal to the number of nodes.

Maximum of n^n - 2 number of spanning trees will be there in a complete graph.

3.5 Graph theory procedure (GTP) method

Graph theory method describes about studies of graph, as they are actually mathematic structure apply to develop pair-wise combinations between different objects. There are various terms in a graph as; vertices, arcs and nodes (as shown in Fig. 14).

Fig. 14

Edges and Vertices of a graph.

In particular, Graph theory method is all about the study of point and line, involving the different ways in which the vertices i.e., the sets of point, as they could be connected by lines or edges. Graphs can be classified in accordance with the complexity involved, if there is any direction that has been assigned to the edges or the number of edges that are allowed between any two given vertices. Characteristics of graph are:

Adjacent node –If there is only a single edge that exists between two given nodes, then the two nodes are said to be adjacent to each other.

Node degree –Incident nodes in one single node gives its degree in an undirected graph. But in the case of directed graphs, the term in degree is used which the number of edges is arriving on a node. Another term out degree is used in case of directed graphs for representing the number of edges that are departing from a node.

Path –A path of length m is defined as a sequence of m + 1 nodes from one particular node to another.

Isolated node –An isolated node is one which has zero degree.

3.6 Performance validation using state estimation method

State estimator is one of the most powerful tools in dealing with the online analysis, monitor and control of electrical power system network. To identify the instant operating state of the power system network it is employed in Energy Management Systems. The Weighted least square (WLS) method is the majorly apply technique for SE for power system.

The mathematically realization of WLS is given below:

A set of data z₁ which is conventional data of a real and reactive power flow in network elements, bus injections and voltage magnitude at buses. Assumptions of bad data have been eliminated from usual method. Measure are nonlinear functions of the state vector x (a set of positive sequence voltages at all the buses of the network). $z_{1} = h (x) + e_{1}$ (3) where, h₁ are the nonlinear functions of the state vector x expressed in polar coordinates, and e₁ is the measurement error vector with a covariance matrix R₁.

The Jacobian Matrix, H₁ given by $H_{1} = \frac{{dh}_{i} (x)}{dx}$ (4)

The Gain matrix, G₁ (x^k) is given by $G_{1} (x^{k}) = [H_{1}^{T} (x^{k}) R_{1}^{- 1} H_{1} (x_{k})]^{- 1}$ (5)

The error matrix (Covariance) of the estimate x is as; $Cov ([x]) = [H_{1}^{T} R_{1}^{- 1} H_{1}]$ (6)

And the state vector is obtained from $[x^{K + 1}] = [x^{K}] + [G_{1} (x^{K})]^{- 1} [H_{1}^{T} R_{1}^{- 1}] [z_{1} - h_{1} (x^{k})]$ (7)

This is an iterative method and the repetition will stop when minimum two conditions continuously are same. Maximum allowance number if exceeded then called first iteration while if state variables are within acceptance range then it iteration is under second condition. $max | Δ x^{K} | ⩽ ɛ$ (8)

4 Results and discussion

The OPP has been analyzed by using five different methods (ILP, DFS, SA, MST and GTP). These methods have been implemented for IEEE 7, 14 and 30 bus system models. For the better understanding, IEEE 7BS, 14BS and 30BS have been represented below in Figs. 15 –17 respectively.

Fig. 15

IEEE 7 bus system.

Fig. 16

IEEE 14 bus system.

Fig. 17

IEEE 30 bus system.

4.1 Optimal placement of PMU using ILP method

Consider 14 bus system as shown in Fig. 16 for the analysis first: $Objective function : min \sum_{i = 1}^{14} x_{i}$ (9) $x_{1} + x_{2} + x_{5} ⩾ 1$ $x_{1} + x_{2} + x_{3} + x_{4} + x_{5} ⩾ 1$ $x_{2} + x_{3} + x_{4} ⩾ 1$ $x_{2} + x_{3} + x_{4} + x_{5} + x_{7} + x_{9} ⩾ 1$ $x_{1} + x_{2} + x_{4} + x_{5} ⩾ 1$ $x_{6} + x_{11} + x_{12} + x_{13} ⩾ 1$ $x_{4} + x_{7} + x_{8} + x_{9} ⩾ 1$ $A . X = x_{7} + x_{8} ⩾ 1$ $x_{4} + x_{7} + x_{9} + x_{10} + x_{14} ⩾ 1$ $x_{9} + x_{10} + x_{11} ⩾ 1$ $x_{6} + x_{10} + x_{11} ⩾ 1$ $x_{6} + x_{12} + x_{13} ⩾ 1$ $x_{9} + x_{12} + x_{13} ⩾ 1$ $x_{9} + x_{14} + x_{13} ⩾ 1$

Then after running optimization we get optimal results in binary as: $X = [0 1 0 0 0 1 1 0 1 0 0 0 0 0]$

Where 1 indicates PMU at that particular bus and 0 indicates absent of PMU.

Similarly, ILP is implemented for IEEE 7BS, 30BS as well and obtained results are shown in Table 3.

Table 3

OPP using ILP

IEEE Buses System	Optimal Number(with zero injection)	Optimal number(without zero-injection)
IEEE 7	2 (1,3)	2 (1,3)
IEEE 14	3 (2,6,9)	4 (2,6,7,9)
IEEE 30	9 (2,4,6,9,10, 12,15,18,27)	10 (2,4,6,9,10,12,15,18,25,27)

4.2 Optimal placement of PMU using DFS method

DFS method is implemented using PSAT package [31] in Matlab. The obtained results for IEEE 14BS is shown in Fig. 18 in green coloured.

Fig. 18

IEEE 14 bus system after DFS algorithm.

Similarly, DFS is implemented for IEEE 7BS and 30BS as well and obtained results are shown in Table 4.

Table 4

OPP using DFS

IEEE Buses System	Number of PMU for full observable	PMU Location	Time Elapsed (sec)
IEEE 7	2	2,4	0.058619
IEEE 14	6	1,4,6,8,10,14	0.10173
IEEE 30	12	3,5,6,11,12,17,18,20,21,24,26,27	0.13367

4.3 Optimal placement of PMU using SA method

SA method is implemented for IEEE 7BS, 14BS and 30BS and obtained results are shown in Table 5.

Table 5
OPP using SA

IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 1 2 0.13958

IEEE 14 4 1,4,10,13 0.60591

IEEE 30 7 2,4,10,12,19,24,27 224.032

IEEE Buses System	Number of PMU for full observable	PMU Location	Time Elapsed (sec)
IEEE 7	1	2	0.13958
IEEE 14	4	1,4,10,13	0.60591
IEEE 30	7	2,4,10,12,19,24,27	224.032

4.4 Optimal placement of PMU using MST method

MST method is implemented for IEEE 7BS, 14BS and 30BS and obtained results are shown in Table 6.

Table 6
OPP using MST

IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 3 2,3,4 0.213185

IEEE 14 8 2,5,6,7,9,10,13,14 0.29027

IEEE 30 12 3,5,6,11,12,17,18,20,21,24,26,27 17.846

IEEE Buses System	Number of PMU for full observable	PMU Location	Time Elapsed (sec)
IEEE 7	3	2,3,4	0.213185
IEEE 14	8	2,5,6,7,9,10,13,14	0.29027
IEEE 30	12	3,5,6,11,12,17,18,20,21,24,26,27	17.846

4.5 Optimal placement of PMU using GTP method

GTP method is implemented for IEEE 7BS, 14BS and 30BS and obtained results are shown in Table 7.

Table 7
OPP using GTP

IEEE Buses System No. of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 1 2 0.071812

IEEE 14 5 1,4,6,10,14 0.11255

IEEE 30 7 2,4,10,12,19,24,27 0.2362

IEEE Buses System	No. of PMU for full observable	PMU Location	Time Elapsed (sec)
IEEE 7	1	2	0.071812
IEEE 14	5	1,4,6,10,14	0.11255
IEEE 30	7	2,4,10,12,19,24,27	0.2362

4.6 Comparative result analysis for OPP

The comparative results for IEEE 7BS, 14BS and 30BS have been represented in Table 8, which have been evaluated by 5-OPP methods.

Table 8
Summary of evaluated number of OPP

Evaluating method No. of PMU required

IEEE 7BS IEEE 14BS IEEE 30BS

LIP 2 3 9

DFS 2 6 12

SA 1 4 7

MST 3 8 12

GTP 1 5 7

Evaluating method	No. of PMU required
LIP	2	3	9
DFS	2	6	12
SA	1	4	7
MST	3	8	12
GTP	1	5	7

After detailed analysis of Tables 3 to 8, it is concluded that SA and GTP gives better result and select the optimal number of PMUs for placement without changing the required information.

4.7 PMU Performance validation using state estimation method

The performance validation of power network using conventional type recorded dataset and PMU dataset has been performed by using WLS method. For the better understanding, IEEE-14BS and 30BS have been validated here using WLS method as results are given below in Figs. 19 –22 and Figs. 23 –26 respectively.

Fig. 19

Voltage phasor estimation error using traditional data for IEEE14BS.

Fig. 20

voltage phasor estimation error with PMU data for IEEE14BS.

Fig. 21

Voltage magnitude estimation error using traditional data with IEEE14BS.

Fig. 22

Voltage magnitude estimation error with PMU for IEEE14BS.

Fig. 23

Voltage phasor estimation error using traditional data for IEEE-30BS.

Fig. 24

voltage phasor estimation error with PMU data for IEEE-30BS.

Fig. 25

Voltage magnitude estimation error using traditional data with IEEE-30BS.

Fig. 26

Voltage magnitude estimation error with PMU for IEEE-30BS.

After analyzing Figs. 19 to 26, it is concluded that PMU data based estate estimation of the power network is outperforming and can be implemented for online monitoring of the power system in real-time domain.

5 Conclusion

The PMUs are main part of WAMS. It gives phasor based accurate positive sequence measurement of voltage, phase and frequency. The PMU helps the power system operators for condition monitoring, protection and control and enhance the accuracy of system’s state estimation. In this paper, OPP using five different methods have been performed and its performance is validated by using estate estimation method to estimate the state with both measured data and PMU based dataset. This analysis shows that PMU based dataset gives outperform results, which is very helpful in online condition monitoring, protection, and control of power network. The SA method required less number of PMUs for complete observability but converging speed is slow. The GTP has fast converging speed, and MST technique enhances the optimized rules using pseudo current measurement. Obtained results show that using PMU data converging time is lesser and as the size of power system increase estimation error decrease.

Footnotes

Acknowledgments

“The authors extend their appreciation to the Researchers Supporting Project at King Saud University, Riyadh, Saudi Arabia, for funding this research work through the project number RSP-2020/278”.

References

Phadke

A.G.

, Synchronized phasor measurements and their applications, Synchronized Phasor Measurements and their Applications (2008).

Peng

, at al., An optimal PMU placement algorithm for full network observability, Automation of Electric Power Systems 27(4) (2003), 10–16.

Phadke

A.G.

and Thorp

J.S.

, Synchronized Phasor Measurements and Their Application, New York: Springer, (2008).

IEEE Std. 1344–1995, IEEE standards for synchrophasor for power systems, March 17 2001, (2001).

IEEE Std. C37. 118 -2005, IEEE Standards for Synchrophasor for Power Systems, October 21, (2005).

IEEE Std. C37. 118. 1-2011, IEEE Standard for Synchrophasor Measurements for Power Systems, (2011).

IEEE-C37.242-2013

Phadke

A.G.

, et al., A New Measurement Technique for Tracking Voltage Phasors, Local System Frequency, and Rate of Change of Frequency, Power Apparatus and Systems, IEEE Transactions on PAS-102(5) (1983), 1025–1038.

Phadke

A.G.

and Bogdan

, Synchronized phasor and frequency measurement under transient conditions, IEEE Trans Power Deliv 24(1) (2009), 89–95.

10.

Ree

D.L.

, et al., Synchronized Phasor Measurement Applications in Power Systems, IEEE Transactions on Smart Grid 1(1) (2010), 20.

11.

Phadke

A.G.

and Thorp

J.S.

, Synchronized phasor measurements and their applications, Springer, New York, (2008).

12.

America recovery and reinvestment act of 2009. Synchrophasor technologies and their deployment in the recovery act smart grid program, US department of energy (2013).

13.

Phadke

A.G.

, Synchronized Sampling and Phasor Measurements for Relaying And Control, IEEE Transactions on Power Delivery 9(1) (1994), 442–452.

14.

Aminifar

, Contingency constrained PMU placement in power networks, IEEE Transaction Power System 25(1) (2010), 516–523.

15.

Dua

, et al., Optimal multistage scheduling of PMU placement: An ILP approach, IEEE Trans Power Del 23(4) (2008), 1812–1820.

16.

Mousavian , et al., A two-phase investment model for optimal allocation of phasor measurement units considering transmission switching, Electric Power Systems Research 119 (2015), 492–498.

17.

Gou

, Generalized Integer Linear Programming Formulation for Optimal PMU Placement, in, IEEE Transactions on Power Systems 23(3) (2008), 1099–1104 10.1109/TPWRS.2008.926475.

18.

Abbasy

N.H.

and Ismail

H.M.

, A Unified Approach for the Optimal PMU Location for Power System State Estimation, in, IEEE Transactions on Power Systems 24(2) (2009), 806–813. doi: 10.1109/TPWRS.2009.2016596

19.

Aminifar

, et al., Optimal placement of phasor measurement units using immunity genetic algorithm, IEEE Trans Power Syst 24(3) (2009), 1014–1020.

20.

Milosevic

and Begovic

, Nondominated sorting genetic algorithms for optimal phasor measurement placement, IEEE Trans Power Syst 18(1) (2003), 69–75.

21.

Nuqui

R.F.

and Phadke

A.G.

, Phasor measurement unit placement techniques for complete and incomplete observability, IEEE Trans Power Syst 20(4) (2005), 2381–2388.

22.

Chakrabarti

and Kyriakides

, Optimal placement of phasor measurement units for power system observability, IEEE Trans Power Syst 23(3) (2008), 1433–1440.

23.

Rakpenthai

, et al., An optimal PMU placement method against measurement loss and branch outage, IEEE Trans Power Del 22(1) (2007), 101–107.

24.

Peng

, at al., Optimal PMU placement for full network observability using Tabu search algorithm, Elec Power Syst Res 28(4) (2006), 223–231.

25.

Baldwin

T.L.

, et al., Power system observability with minimal phasor measurement placement, IEEE Trans Power Syst 8(2) (1993), 707–715.

26.

Chakrabarti

and Kyriakides

, Optimal placement of phasor measurement units for power system observability, IEEE Trans Power Syst 23(3) (2008), 1433–1440.

27.

Phadke

A.G.

, et al., State Estimation with Phasor measuremet, in, IEEE Transactions on Power Systems 1(1) (1986), 233–241.

28.

Abbasy

N.S.

and Ismail

H.M.

, A Unified Approach for the Optimal PMU Location for Power System State Estimation, Power Systems, IEEE Transactions on 24(2) (2009), 806–813.

29.

Zivanovie

and Cairns

, Implementation of PMU Technology in State Estimation: An Overview, IEEE Transactions (1996), 0-7803-3019-6/96/$3100.

30.

Schweppe

F.C.

and Wildes

, Power System Static State Estimation, Part I, 11, and 111, IEEE Transactions on PAS PAS-89(1) (1970), 120–135.

31.

Milano

Evaluating method	No. of PMU required
	IEEE 7BS	IEEE 14BS	IEEE 30BS
LIP	2	3	9
DFS	2	6	12
SA	1	4	7
MST	3	8	12
GTP	1	5	7

Development of wide area monitoring system for smart grid application

Abstract

Keywords

1 Introduction

2 PMU model development and validation

2.1 Emulation of PMU

3.1 Integer linear programming (ILP) method

Table 5 OPP using SA IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec) IEEE 7 1 2 0.13958 IEEE 14 4 1,4,10,13 0.60591 IEEE 30 7 2,4,10,12,19,24,27 224.032

Table 6 OPP using MST IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec) IEEE 7 3 2,3,4 0.213185 IEEE 14 8 2,5,6,7,9,10,13,14 0.29027 IEEE 30 12 3,5,6,11,12,17,18,20,21,24,26,27 17.846

Table 7 OPP using GTP IEEE Buses System No. of PMU for full observable PMU Location Time Elapsed (sec) IEEE 7 1 2 0.071812 IEEE 14 5 1,4,6,10,14 0.11255 IEEE 30 7 2,4,10,12,19,24,27 0.2362

Table 8 Summary of evaluated number of OPP Evaluating method No. of PMU required IEEE 7BS IEEE 14BS IEEE 30BS LIP 2 3 9 DFS 2 6 12 SA 1 4 7 MST 3 8 12 GTP 1 5 7

Footnotes

Acknowledgments

References

Table 5
OPP using SA

IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 1 2 0.13958

IEEE 14 4 1,4,10,13 0.60591

IEEE 30 7 2,4,10,12,19,24,27 224.032

Table 6
OPP using MST

IEEE Buses System Number of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 3 2,3,4 0.213185

IEEE 14 8 2,5,6,7,9,10,13,14 0.29027

IEEE 30 12 3,5,6,11,12,17,18,20,21,24,26,27 17.846

Table 7
OPP using GTP

IEEE Buses System No. of PMU for full observable PMU Location Time Elapsed (sec)

IEEE 7 1 2 0.071812

IEEE 14 5 1,4,6,10,14 0.11255

IEEE 30 7 2,4,10,12,19,24,27 0.2362

Table 8
Summary of evaluated number of OPP

Evaluating method No. of PMU required

IEEE 7BS IEEE 14BS IEEE 30BS

LIP 2 3 9

DFS 2 6 12

SA 1 4 7

MST 3 8 12

GTP 1 5 7