Ranking of PMU

Ranking of phasor measurement units based on control strategy forsmall-signal stability

Charu Sharma*,† and Barjeev Tyagi

Electrical Engineering Department, Indian Institute of Technology, Roorkee, India

SUMMARY

This paper presents a methodology to rank phasor measurement unit (PMU) locations based on small-signalstability. In the proposed scheme, integer linear programming is utilized to identify the optimal locations ofPMUs. These locations are ranked using analytical hierarchy process. Modal analysis is conducted toidentify inter-area modes leading to instability. A control scheme is proposed, to nullify this instability.Based on the control scheme, few critical buses are determined, which are given the highest priorities whileranking. Because a critical bus can be a generator, or tie line or load bus, therefore, three different rankingcriteria are utilized. Based on ranking, PMUs are placed in multiple stages such that in the initial stage itself,all critical buses are observed. To check the effectiveness of the proposed scheme, fuzzy and proportional-integral-derivative controllers are employed. Proposed methodology is successfully tested on 16-machine,68-bus system. Copyright © 2014 John Wiley & Sons, Ltd.

key words: phasor measurement units; wide-area network; small-signal stability; Eigen value analysis;observability; analytical hierarchy process

1. INTRODUCTION

Small perturbations in load or small oscillations within a given power system can have significanteffects on damping characteristics of the system. These disturbances result in synchronization issuessuch as rotor angle displacement or oscillation problem due to insufficient damping. Monitoring ofthese oscillations is of immense importance for secure operation of power systems [1]. Recent devel-opments in wide-area monitoring provide real-time and accurate information, which was not possiblewith earlier energy management systems [1]. However, this wide-area monitoring starts with allocationof phasor measurement units in given system [1,2].Significant work has been carried out in the past to deploy phasor measurement units in power

systems. Authors in [3] determine phasor measurement unit (PMU) locations based on observabilityconcept. In References [4,5], integer linear programming (ILP) has been used to formulate the topolog-ical observability. Concept of pseudo-observability and its importance is nicely summarized in [6,7].Considerable work has been carried out in [8,9] to show the effect of conventional measurements onobservability. In [10], an integer quadratic approach has been introduced to minimize the PMUlocations, which ensures observability during normal and during loss of single line or PMU. Theaforementioned literature shows that PMU allocations are generally carried out according to topolog-ical observability. However, method for complete topological and numerical observability of powersystem has been considered in Reference [11]. It is reported that economic constraints associated withthis technology compels utilities to place the limited number of PMUs in the system. As a solution, fewresearchers have considered PMU placement in stages/phases [6,12,13]. Authors in [6] have used theconcept of depth of observability to place PMUs in stages. However, in [12], PMUs are placed in sucha manner that placement results after final stage are identical to single-stage PMU placement using ILP

*Correspondence to: Charu Sharma, Electrical Engineering Department, Indian Institute of Technology, Roorkee, India.†E-mail: [email protected]

Copyright © 2014 John Wiley & Sons, Ltd.

INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMSInt. Trans. Electr. Energ. Syst. (2014)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.1966

approach. Author in [13] has used multi-criteria decision-making approach to place PMUs consideringvarious criteria such as bus, tie line, and voltage observability.Recently, few researchers have utilized probabilistic approaches to locate significant PMU locations

in a given system. In [14,15], authors have utilized analytical reliability methods to improve pro-bability of observability for given system under random power outages. However, for placement ofPMU, authors have considered topological observability. In another reference [16], Gaussian Markovrandom field model of power system is proposed. Authors utilized greedy algorithm to find optimalPMU sites, which provides maximum information gain.Real-time control of small-signal oscillations is also as important as real-time monitoring of

small-signal oscillations. In literature, deterministic and probabilistic approaches for small-signalanalysis were reported [17–24]. Robust damping controller using h-infinity, linear matrixinequality techniques have been widely used [17,18] for damping out inter-area oscillations.Various intelligent controllers are also reported [19,20]. Apart from controller design, selectionof controller location and feedback signals is a recent topic of concern [21,22]. In Reference[21], the author described wide-area fuzzy controller (WAFC) for various operating points. Inthe aforementioned literature [17–22], the authors have assumed that PMUs are placed on allgenerator terminals, which is practically not possible. Few researchers have also applied proba-bilistic approach for small-signal stability studies [23,24]. In these references, authors haveexplored Monte Carlo-based probabilistic Eigen analysis technique for various operating pointsand uncertainties of the power system. However, authors have not considered topologicalobservability of the system. Therefore, the major contribution of this paper is to select, rank,and place PMUs on those buses, which are essential for monitoring and control of small-signalstability analysis of a large network.For secure operation of power system, monitoring and control of small-signal stability (SSS) is

of immense importance. This paper focuses on ranking of PMU locations in a given network forSSS studies. Based on these rankings, PMUs are placed in stages to completely observe the sys-tem. The proposed ranking scheme is divided into three steps. The optimal PMU number andlocations are determined in the first step using ILP, such that each bus is observable at least bytwo PMUs. In the second step, Eigen value analysis is carried out to compute inter-area modesresponsible for small-signal instability, and control scheme is proposed for small-signal instability.For each inter-area mode, location of controllers and feedback signals are determined throughparticipation factors and controllability indices. Buses associated with controller locations or feed-back input signals are identified as critical buses. All optimal PMU locations obtained through firststep are ranked in the third step. Three criteria’s, namely, generator bus observability index(GBOI), tie-line bus observability index (TLBOI), and bus observability index (BOI) are utilizedin the analytical hierarchy process (AHP) to compute priority-based final performance indices(FPIs). Based on these FPIs, PMUs are ranked. All critical buses identified in Step 2 are giventhe highest priorities in ranking the PMU locations. Further, important tie lines of the system arealso determined and given the next higher priority. To test the effectiveness of the proposedapproach, fuzzy logic and proportional-integral-derivative (PID) controller has been considered atthe selected locations to control the perturbations.

2. FORMULATION FOR PMU PLACEMENT

The PMU can make installed bus and its neighboring buses observable [1]. The objective of placingPMUs in power systems is to decide a minimal set of PMUs such that the whole system is observable.The problem to determine optimal PMU location for complete observability can be formulated infollowing manner [4].

MinimizeXNk¼1

Ckyk; yk ¼1; if PMU is placed over bus

0; otherwise

�(1)

C. SHARMA AND B. TYAGI

Copyright © 2014 John Wiley & Sons, Ltd. Int. Trans. Electr. Energ. Syst. (2014)DOI: 10.1002/etep

Subject to GY ≥ 2; gij ¼1; if i ¼ j or if i and j are connected

0; otherwise

�(2)

Where N is the total number of PMUs, Ck is the cost of a kth PMU, yk is the kth binary placementvariable, G is the connectivity matrix, and Y is a vector of binary variable y. In proposed work, cost ofeach PMU is taken equal. To make formulation simple, Ck is generally taken as 1 per unit. Con-nectivity matrix G is formed using topological connectivity of buses as given in Equation 2. Detailsfor formation of G are nicely summarized in [11]. The aforementioned formulation is an ILP problem.Equation 1 computes the minimal subset of PMUs and 2 is the basic constraint equation. In 2, right-hand side of inequality ensures that each bus in the system is observed by two PMUs, such that anyloss of the line or a line outage will not affect complete observability of the system [13]. Presenceof conventional measurements reduces the number of PMUs required for complete observability[12,25]; therefore, zero injection measurements are also incorporated in the aforementioned formula-tion. The aforementioned ILP problem is solved using the algorithm described in [12] to obtain optimalallocations for PMUs.

3. CONTROL AND IDENTIFICATION OF CRITICAL BUSES

In multi-machine power system, small-signal oscillations are the result of group of the generators inone area swinging against a group of generators in another area. To prevent system from theseoscillations, wide-area damping controllers are generally provided [17]. In this paper, a control schemeis proposed, which comprises of selection of controller location and selection of controller inputsignals. However, design of wide-area damping and PID controllers is described in [26,27]. Thefollowing sections give a detailed description of proposed schemes for control, selection of inputsignals, and controller locations.

3.1. Selection of input signals

In the control scheme of a wide-area network, proper selection of feedback signals is of utmost impor-tance. In this work, generator speed signals are considered as input signals for damping controllers.Therefore, selection of the input signal is the selection of generator speed signal. Signals that areselected as input signals for wide-area controllers should affect the inter-area modes that are responsi-ble for small-signal oscillations. Therefore, Eigen value analysis [28] is carried out to determine inter-area modes. According to Reference [29], to modify a mode of oscillation by the feedback, the choseninput must excite the mode, and it must also be visible in chosen output. The measures of these twoproperties are controllability and observability [30,31]. Consider the state space model of a systemas follows:

x ¼ Axþ Bu (3)

y ¼ CTx (4)

Where x is the state vector, y is the output vector, u is the control vector, A is the state matrix, B is theinput matrix, and C is the output matrix. The controllability [30] of ith mode of 3 from the jth input isproportional to the cosine of the angle between bj and qi. This relationship is called as modal control-lability index (CI) and is given as

CI ¼ cos θ qi; bj� �� ¼ qTi bj

�� qik k bj�� (5)

Where the symbol | | means that the absolute value of a scalar and || || means the standard two-normof a vector. qi is the left Eigen vector of A (state matrix) satisfying equation ATqi= λiqi, and bj is the jthcolumn of B (input matrix). The selections of appropriate wide-area feedback signals for proposedcontrollers are carried out through the modal CI given by Equation 5. Thus, a higher value of CI fora particular mode indicates that the chosen input signal will be effective in controlling the mode.

RANKING OF PHASOR MEASUREMENT UNITS


3.2. Selection of controller locations

In wide-area network, controllers are needed with machines that have the largest effect over oscillatingmodes of interest. Reference [21] utilized joint controllability and observability modal indices forselecting the location of wide-area controller. Reference [31] relates participation factors of selectivemodal analysis with modal controllability and observability index. Therefore, participation factorsare utilized in the proposed work to determine suitable controller location.

3.3. Control scheme for small-signal stability

In the proposed control scheme, speed signals of the machines that are having the highest CI are treatedas wide-area signals. These remote signals are communicated via PMUs to other areas, if the generatorbus is observed by PMUs directly or in directly [32]. The controller is placed with the machine that hashighest participation factor, and the speed feedback is taken from the machine having highest CI.Differences between speed signals of generators that are having highest CI and participation factorfor a given mode are calculated. These speed deviations and derivative of speed deviations are givenas inputs to WAFCs. Output signals of controllers are fed back to the generator, through the exciter.From the aforementioned control scheme, it is observed that there are certain buses that are critically

important, such as generator buses to which controller is attached or generator buses from which feed-back signals are taken or tie-line buses to monitor inter-tie performance. Therefore, all such buses aretermed as critical buses of the given network. In such cases, PMUs are placed at these preferred busesin initial stages. Rests of buses are made observable in later stages.

4. RANKING OF OPTIMAL PMU LOCATION

The main focus of this paper is to provide a methodology to rank the optimal PMU locations based onthe control scheme described in the previous section. Based on this ranking, PMUs are placed inmultiple stages to observe the given system. In this work, three criteria, namely, generator bus, tie line,and bus observability criteria, are proposed to monitor and control SSS. For SSS monitoring, tie-lineobservability criterion is considered, and for control, GBOI criterion is considered. However, busobservability criterion depends on topological connectivity of the bus. These criteria are utilized inanalytic hierarchy process [33] to rank PMU locations.Few important considerations:

• It is observed that every optimal location (obtained in Step 1) is either a generator or tie line orsimple load bus and may be or may not be a significant bus.

• It is also noted that all generator, tie line, and load buses present in optimal locations are notcritical buses. Therefore, to distinguish between critical and noncritical buses, each criterion(i.e., generator, tie line, and bus observability) is further divided into two criteria, one forcritical buses and another for noncritical buses.

• It may happen that a critical bus does not belong to the optimal locations. In such case, nearestoptimal bus is considered as critical bus, and highest priority is assigned to that bus.

4.1. Generator bus observability index

In a power system, the angular separation between generators indicates that whether system will beleading to angular instability or not. Also, to improve inter-tie performance, wide-area damping con-trollers are generally provided with generators [17,21]. According to Reference [21], generator speeds,terminal bus frequency, and active power are the most commonly used control input signals, which canbe used in designing damping controllers. Therefore, it is important to monitor the generator busesdirectly or indirectly using the PMUs. It is to be noted here that there may be few buses that are stra-tegically important and are not present in optimal locations obtained in Step 1. In such a case, nearestor second nearest optimal location to that critical bus is given priority.



According to the control scheme described in the previous section, there may be situations when a gen-erator bus is having controller or providing speed feedback signals. In such situation, these generator busesare of prime importance and termed as critical buses. Therefore, all generator buses present in optimallocations are divided into two groups, that is, critical generator buses and noncritical generator buses.For critical generator bus, the generator observability index is represented as GBOIS and is given as

GBOISk ¼ wc1�X∀gen

Uk

gen

0@

1Aþ wc2�

X∀Ngen

UkNgen

!þ wc3�

X∀NNgen

UkNNgen

!(6)

Where GBOISk is the GBOI for kth bus, which has more significance for SSS analysis. Ukgen repre-

sents number of generator buses connected to kth bus. Similarly, UkNgen and Uk

NNgen represent thenumber of neighboring and neighbor to neighboring buses, respectively, connected to bus k. wc1,wc2, and wc3 are constant weights related to GBOIS and assigned higher values.In case of noncritical generator bus, the generator bus observability index is indicated as GBOI and

is given by the following expression:

GBOIk ¼ w1�X∀gen

Ukgen

!þ w2�

X∀Ngen

UkNgen

!þ w3�

X∀NNgen

UkNNgen

!(7)

Where GBOIk is the GBOI for any kth bus. w1, w2, and w3 are constant weights, which are havinglower values as compared with wc1, wc2, and wc3.

4.2. Tie-line bus observability index

In large power systems, performances of damping controllers are observed through dynamic changesin inter-ties. Therefore, to monitor tie-line response, PMUs should be placed on these tie lines. To ob-serve tie lines, seven different cases are considered throughout this paper. Six cases are directly takenfrom Reference [13]. Details of these six cases are not included in this paper because of space limita-tions. However, first and second cases are described here for understanding. For example, P and Q areend buses of a tie line. R and S are the neighboring buses of P and Q, respectively. In the first case,both end buses of the tie line (P and Q) belong to optimal PMU locations, obtained in the first stage.Because PMUs are to be placed on both the end buses, both buses will have equal importance; there-fore, TLBOI will be TLBOIP= TLBOIQ= 1. Likewise, in the second case, the first end of the tie lineand the neighbor of the second end are present in PMU locations. To monitor tie-line performanceat least from one end, TLBOIP has been given higher priority than TLBOIS [13].In a similar manner, PMU locations are prioritized in seventh case, which is additionally introduced

in this work. In this particular case, one end bus of tie line (P) and its adjacent bus (R) at same end bothare candidate of optimal PMU sites.As stated before, tie-line bus is of great importance. Therefore, TLBOI of tie-line bus (P) is

TLBOIP = 1.5, and observability index of its adjacent bus (R) is TLBOIR = 0.25. All cases are summa-rized in Table I and Figure 1. For a given system, each tie line will satisfy any one condition, fromstated seven conditions. TLBOI for kth tie line or its neighboring bus is given by expression 8.

TLBOIk ¼ TL; if kth bus is tie line or its neighboring bus; TL value is taken from Table 1

0; otherwise

�(8)

As mentioned before, not all tie lines have significance in SSS analysis. Therefore, tie lines are alsodivided into critical and noncritical tie lines. Tie-line observability index for critical and noncritical tie-line buses are represented as TLBOIS and TLBOI, respectively.Table I and Figure 1 give tie-line observability indices for noncritical tie lines. However, in

case of critical tie line, TLBOI of the higher priority end is assigned with value greater thanor equal to 2. For example, if an important tie line belongs to Case “b”, then its higher priorityend, TLBOI (i.e., TLBOIP) is modified as TLBOIS, and a value greater than or equal to 2 is



assigned to it. Likewise, TLBOI of every significant tie line or its neighbor is modified andrenamed as TLBOIS and is represented as

TLBOISk ¼ TLS; if kth bus is significant tie line or its neighboring bus; TLS > TL and TLS≥2

0; otherwise

�(9)

4.3. Bus observability index

The BOI depends upon the topological connectivity of the bus. Like other two indices, this index isalso divided into two indices. Bus observability index for noncritical bus is represented as BOI. How-ever, for critical bus, the BOI is abbreviated as BOIS. BOI for a PMU bus k is defined as the number ofbuses directly connected to kth bus and mathematically expressed as

BOIk ¼XNj¼1j≠k

Gkj ¼ 1; if j and k are connected

0; otherwise

�(10)

This criterion prioritizes those buses that have maximum connectivity in the given system. BOI forcritical buses are given as

BOISk ¼ 1�BOIk; if k-th bus itself is significant generator bus (11)

However, if a significant generator does not belong to optimal placement locations (obtained inStage 1), then its immediate neighbor bus BOI (BOInk) is modified as BOIS.

BOISnk ¼ 1�BOInk (12)

Table I. Various cases for tie-line bus observability index (TLBOI).

Case a When both tie-line buses (P,Q) have PMUs TLBOIP= TLBOIQ= 1

Case b When one tie-line bus (P) and neighboring busof other end (S) have PMUs

TLBOIP= 1.5 TLBOIS = 0.5

Case c When two different tie lines are neighbor ({P-Q}and {P′-Q′})

TLBOIQ=TLBOIP′ =1.5 TLBOIP= 1

Case d When two different tie lines are having sameneighbor ({P-Q} and {P′-Q′})

TLBOIP= TLBOIQ= 1.5 TLBOIS = 1

Case e None of tie-line buses (P,Q) have PMUs TLBOIR= TLBOIS = 2Case f When one tie-line bus (P) and adjacent bus of

the same end (R) have PMUsTLBOIP= 1.5 TLBOIR= 0.25

Case g When a tie line is not present in optimal PMUlocations (obtained through Step 1).

TLBOIP= TLBOIQ= 0

Figure 1. Various cases to determine TLBOI.



Where nk is the neighbor bus of the significant generator bus. From the aforementioned expression,it is clear that BOI of significant buses are separated from the rest of BOIs, athough they have the sameformulation. This is carried out to distinguish between critical and noncritical buses. This distinction isuseful for analysis, particularly, while assigning priority in AHP. After computing, in all six criteriaand optimal PMU locations, AHP is applied, which is described in the following section.

4.4. Analytical hierarchical process

The AHP is a structured technique for analyzing complex decision problems. In AHP, the problem isbroken into various criteria and alternatives [33]. In PMU placement problem, optimal placementlocations obtained through first step are treated as alternatives and various observability indices arecriteria. In AHP, first pairwise matrix (PM) is constructed, which selects relative importance ofdifferent criteria. According to SSS problem, GBOIS is given highest priority, TLBOIS is givensecond highest, and BOIS is assigned third highest priority, whereas GBOI, TLBOI, and BOI are givenlower priorities, as shown in Figure 2.All six criteria are prioritized using 15 priority rules given in Table II, and PM is constructed based

on these rules.The PM considered in this paper is given in Table III. In this table, the second element of the first row

depicts that GBOIS is six times more important than GBOI (as per first priority rule). Likewise, all en-tries of the Table III are derived from Table II. PM is then utilized to compute weights for each criterion.To calculate weights, Eigen values of PM are determined. Eigenvector associated with the largest

Eigen value of PM, gives W, that is, the weight vector W = [w1,w2,w3,w4,w5,w6]. Weights for allcriteria are normalized by utilizing expression 13.

nwj ¼ wj

∑6wjj ¼ 1; 2; 3; 4; 5; 6 (13)

After computing weights for each criterion, all six criteria (i.e., GBOIS, TLBOIS, BOIS, GBOI,TLBOI, and BOI) are further normalized using 14 for each PMU location.

NIkj ¼Ikj � I min;j� �I max;j � I min;j� � j ¼ 1; 2; 3; 4; 5; 6 (14)

Where NIkj represents normalized value of jth criterion for kth optimal location. Imin,j and Imax,j arethe minimum and maximum value of jth criterion, respectively. However, Ikj is the actual value of jthcriterion for kth optimal location. Normalized values of weights and criteria are used to compute theFPI for each optimal PMU location, which is given as

FPIk ¼ ∑6j¼1nwj

NIkj k ¼ 1; 2; 3…K (15)

Figure 2. Priority Scale.

Table II. Priority matrix rules.

GBOIS is 6 times more important than GBOI GBOI is 3 times more important than BOIGBOIS is 2 times more important than TLBOIS TLBOIS is 6 times more important as TLBOIGBOIS is 4 times more important than BOIS TLBOIS is 2 times more important than BOISGBOIS is 7 times more important than TLBOI TLBOIS is 7 times more important than BOIGBOIS is 9 times more important than BOI BOIS is 5 times more important than TLBOITLBOIS is 4 times more important than GBOI TLBOI is 2 times more important than BOIGBOI is 2 times more important than TLBOI BOIS is 5 times more important as BOIBOIS is 5 times more important than GBOI



Where NIkj are normalized value of all six indices; nwj is the normalized weight for each criterion;FPI1, FPI2…FPIk correspond to FPIs for each PMU location; and K represents the total number ofoptimal locations. These FPIs prioritize the PMU locations. Now, for a fixed number of phases,priority placement is carried out to make all generators, tie line, and load buses observable.

5. SIMULATION RESULTS AND DISCUSSION

The five-area 16-machine, 68-bus power system shown in Figure 3 represent New England and NewYork Interconnection. Reference [29] shows that a given power system based on coherency can bedivided into five groups. Generators 14, 15, and 16, each forms a single-generator group. However, group4 consists of New England system (generator 1–9), and group 5 (generators 10–13) consists of New Yorksystem. Each generator is assumed to be provided with governors; IEEE ST1A type static exciter.In present work, all simulation studies are carried out on Intel Core i7-2600 central processing

unit, with 3.40GHz processing speed and 16GB RAM. SSS analysis is conducted on the systemaccording to Reference [29]. Calculation of state matrices, Eigen value analysis and inter-areamode identification are performed as described in [29] and implemented with Power System Tool-box [34] and MATLAB [35]. However, for designing fuzzy controllers, Fuzzy Logic Toolbox is uti-lized along with Power System Toolbox.

Table III. Pairwise matrix for the 16-bus system.

GBOIS GBOI TLBOIS TLBOI BOIS BOI

GBOIS 1 6/1 2/1 7/1 4/1 9/1GBOI 1/6 1 1/4 2/1 1/5 3/1TLBOIS 1/2 4/1 1 6/1 2/1 7/1TLBOI 1/7 1/2 1/6 1 1/5 2/1BOIS 1/4 5/1 1/2 5/1 1 5/1BOI 1/9 1/3 1/7 1/2 1/5 1

Figure 3. Five-area 16 bus system.



5.1. Optimal PMU placements

As described in Section 2, the optimal placement locations of PMUs are found according to Equations1 and 2. To achieve the complete observability of the given system, total 42 PMUs are required. Theoptimal locations for these PMUs are 6, 8, 11, 12, 14, 16, 17, 19, 20, 22, 23, 25, 26, 29, 31, 32, 34, 36,37, 41, 42, 44, 45, 46, 47, 48, 49, 51, 52, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, and 68. PlacingPMUs on these locations will make the system completely observable at least by two PMUs, evenwhen single-transmission line or PMU is lost.

5.2. Eigen value analysis and identification of critical buses

To prevent the system from small-signal instability, first inter-area modes are determined from Eigenvalue analysis, which are given in Table IV.Table IV shows that three inter-area modes and one unstable mode are present. To implement the

control scheme for the aforementioned inter-area modes, speed participation factors and controllabilityindices are computed. Participation factors determine the suitable location for placing the damping

Table IV. Eigen value analysis of 16-machine system.

Eigen values Frequency Damping

Unstable mode1 0.3264 ± 6.8364i 1.0880 -0.0477

Inter-area mode1 -0.2251 ± 2.393i 0.3809 0.09362 -0.2782 ± 3.280i 0.5221 0.08453 -0.1781 ± 4.219i 0.6715 0.0422

(a) (b)

(c) (d)

0 2 4 6 8 10 12 14 16-0.1

0

0.1

0.2

0.3

0.4

0 2 4 6 8 10 12 14 160

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 2 4 6 8 10 12 14 16-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0 2 4 6 8 10 12 14 16-0.05

0

0.05

0.1

0.15

0.2

Figure 4. (a) Participation factors for unstable mode, (b) participation factors for first inter-area mode, (c)participation factors for second inter-area mode, and (d) participation factors for third inter-area mode.



Table

V.Controllabilityindextable.

12

34

56

78

910

1112

1314

1516

UnstableM

ode

0.19

0.25

0.21

0.04

0.06

0.08

0.07

0.11

0.08

0.041

0.0118

0.02

0.0014

0.0012

0.0012

0.0021

Inter-areaMode1

0.04

0.06

0.12

0.92

0.06

0.03

0.05

0.01

0.004

0.002

0.008

.001

1.6e-4

2.8e-5

6.3e-5

2.8e-5

Inter-areaMode2

0.17

0.04

0.25

0.011

0.01

0.014

0.01

0.161

0.032

0.463

0.124

0.24

0.037

0.038

0.003

0.162

Inter-areaMode3

0.44

0.03

0.03

0.021

0.50

0.44

0.033

0.580

0.043

0.063

2.3e-4

0.02

4.5e-5

1.6e-4

7.5e-6

4.1e-4



controller, and CI determines the feedback signal selection. Figure 4(a–d) shows speed participationfactors corresponding to unstable and inter-area modes of Table IV.Figure 4(a) corresponds to unstable mode and shows that unstable mode is coupled to ninth gener-

ator (G9). Therefore, placing damping controller with G9 will make the system more stable. Figure 4(b) shows that for first inter-area mode, damping controller can be placed with any generator becauseeach generator has a positive speed participation factor. However, the 13th generator (G13) has thehighest participation, so it is the best candidate for placing damping controller. Similarly, Figure 4(c) and (d) shows that 16th and 13th generators have the highest participation for second and thirdmode respectively. Therefore, 9th, 13th, and 16th generators are three possible locations, which areselected for the wide-area damping controller.To select the appropriate feedback signal for three proposed damping controllers, controllability

indices are computed corresponding to each mode. Results so obtained are shown in Table V.For unstable mode, second generator (G2) has the highest CI. For first and third inter-area modes, a

single damping controller is placed with G13. The CI table shows that generator 4 signal has highestCI compared with generator 8 (G8). Therefore, generator 4 speed signals should be fed to dampingcontroller placed with 13th generator. Likewise, for the second mode, 10th generator (G10) speedsignal is selected as feedback signal, and damping controller is placed with 16th generator (G16).From the aforementioned Eigen value analysis, it is clear that six generators 2nd, 4th, 9th, 10th,

13th, and 16th are of immense importance for SSS. Hence, it becomes essential to place PMUs onthese generator buses in the initial phases.

5.3. Phased PMU placement

In this work, it is considered that the PMUs are placed in the network in four phases. In first threephases, 11 PMUs are placed in each phase, while in fourth phase, 9 PMUs are placed. There are 16generator buses and eight tie lines in the given system (as shown in Table VI). From the SSS viewpoint, only six generators from 16 generators and four tie lines from eight tie lines are of importance.Third column of Table VI shows placement scheme according to various cases of TLBOI.For each PMU location, values of GBOIS, TLBOIS, BOIS, GBOI, TLBOI, and BOI criteria are

computed and normalized according to normalization expressions given in Section 4.4.The PM is formed to compare the relative importance of each criterion. Further, PM is utilized to

calculate the weight vectorW, which is Eigenvector associated with largest Eigen values of PM. In thispaper, W, that is, weight vector is [0.7976, 0.1278, 0.4779, 0.0873, 0.3286, 0.0590], and FPIs arecomputed according to 15.Table VII shows normalized values of each criterion for every PMU location, and FPI are also given

in eighth column of Table VII. Ninth and tenth columns of the same table depict ranking and priori-tized FPI, respectively.Phased PMU placement for 16-bus system is given in Table VIII. For the given 16-machine bus

system, tie lines 1–27, 1–2, 8–9, and 50–51 are most important tie lines [29]. Eigen value analysisshows that generator buses 54, 56, 61, 62, 65, and 68 corresponding to generator G2, G4, G9, G10,G13, and G16 are critical buses for controlling small-signal instability.

Table VI. Tie-line buses in the 16-bus system.

Tie-line data

From bus To bus Placement scheme

1 2 No PMUs on tie line end buses1 27 No PMUs on tie line end buses1 47 Second end bus of tie line will have PMU8 9 First end bus of tie line will have PMU42 41 Both buses of tie line are with PMUs52 42 Both buses of tie line are with PMUs46 49 Both buses of tie line are with PMUs50 51 Second end bus of tie line will have PMU



Table

VII.Normalized

values

ofcriteriaandfinalplacem

entindexfor16-bus

system

.

OPP

vector

TLBOI

(normalized)

GBOI

(normalized)

BOI

(normalized)

TLBOIS

(normalized)

GBOIS

(normalized)

BOIS

(normalized)

FPI

Rank

Priority

FPI

Final

priority

placem

ent

60

0.375

00

01

0.205

100.468

568

00

0.60

10

00.271

70.468

6111

00.625

0.60

00

00.060

250.468

6212

00

0.40

00

00.012

420.468

6514

00

0.60

00

00.018

400.468

6816

00.312

10

00

0.052

330.343

5117

00

0.60

0.571

00

0.163

120.271

819

00.687

0.60

00

00.064

200.211

2620

00.687

0.40

00

00.058

320.209

2522

00.687

0.60

00

00.064

210.205

623

00.687

0.60

00

00.064

220.194

3125

00.687

0.60

0.571

00

0.209

90.163

1726

00.625

0.80

0.571

00

0.211

80.156

4729

00.375

0.60

00

00.043

340.130

4231

00.375

0.80

0.571

00

0.194

110.115

5232

00.375

0.60

00

00.043

350.109

4134

00.312

0.60

00

00.039

370.086

3636

0.333

0.687

0.80

00

00.086

170.073

6637

00.687

0.60

00

00.064

230.073

6741

10.687

0.60

00

00.109

160.064

1942

11

0.60

00

00.130

140.064

2244

00

0.60

00

00.018

410.064

2345

0.166

00.80

00

00.032

380.064

3746

0.666

00.40

00

00.042

360.063

4947

00

0.40

0.571

00

0.156

130.060

1148

0.166

00.40

00

00.019

390.058

5749

0.666

0.312

0.40

00

00.063

240.058

5851

00

01

00.50

0.343

60.058

5952

10.687

0.80

00

00.115

150.058

6056

00

00

10.25

0.468

10.058

6357

00.781

0.20

00

00.058

260.058

6458

00.781

0.20

00

00.058

270.058

2059

00.781

0.20

00

00.058

280.052

1660

00.781

0.20

00

00.058

290.043

29 (Contin

ues)



Table

VII.(Contin

ued)

OPP

vector

TLBOI

(normalized)

GBOI

(normalized)

BOI

(normalized)

TLBOIS

(normalized)

GBOIS

(normalized)

BOIS

(normalized)

FPI

Rank

Priority

FPI

Final

priority

placem

ent

610

00

01

0.25

0.468

20.043

3262

00

00

10.25

0.468

30.042

4663

00.781

0.20

00

00.058

300.039

3464

00.781

0.20

00

00.058

310.032

4565

00

00

10.25

0.468

40.019

4866

0.333

0.781

0.20

00

00.073

180.018

1467

0.333

0.781

0.20

00

00.073

190.018

4468

00

00

10.25

0.468

50.012

12



A close inspection of phase-1 of Table VIII reveals that in phase-1 itself, all important tie lines andgenerators are having PMUs, to aid wide-area monitoring and control. First, five locations correspondto generators, which are important for SSS. Bus 51 aids in monitoring tie line between areas 1 and 4.PMU placement at bus 8 will help in monitoring tie lines 8–9. Similarly, 25 and 26 PMU locationshelp in monitoring tie lines connecting buses 1–2 and 1–27 respectively, which are between areas 4and 5. Tenth location of phase-1 will provide measurements from generator-2 from depth first. Lastlocation in phase-1, provides measurements for tie lines 46–49. However, by the end of phase-1, allcritical tie-line buses and critical generator buses are observed, either by placing PMU directly onbus or neighboring buses connected to critical buses. After second-, third-, and fourth-stage placement,whole system is made observable. Proposed phased PMU placement approach makes all generatorsand tie-line buses observable, which assists in small-signal monitoring in the initial phases.Based on the previous text, it can be concluded that instead of placing PMUs on all generator buses

[17–22], it is good to place few PMUs on significant generator buses. From proposed method,significant PMU locations are easily identified based on control scheme designed for SSS.Presented method is also compared with probabilistic technique of Reference [23]. In [23], authors

have only taken account of fast and slow dynamic observability of the system utilizing probabilisticapproach. Complete topological observability is not considered, in the work. Authors of [23] haveidentified PMU locations for New England system, which only satisfy dynamic observability criteria.However, proposed ranking and placement approach deal simultaneously with complete topologicalobservability and small-signal dynamics.In addition to the previous text, both small-signal and transient stability analysis requires real-time

rotor measurements. Therefore, in proposed work, GBOI is introduced for small-signal analysis. ThisGBOI is given highest priority, which ensures PMU placement on generator buses. Consequently,proposed technique can be applied for transient stability studies also, without any significant changes.There may be situation, when a tie-line bus and its adjacent bus are suitable candidate for PMU

locations. TLBOI for this situation is not reported in [13]. In present work, TLBOI for this particularcase is also introduced. Proposed ranking technique is robust because it satisfies the robustness criteriafor different placement budget mentioned in [16]. Because PMUs are added sequentially in the systemand phase-1 is always subset of phase-2, -3, and -4.Further, in [24], authors have used Monte Carlo-based probabilistic Eigen value analysis for various

operating conditions and uncertainties. In terms of performance, the proposed ranking and placementwill also work well for different operating scenarios. Ranking methodology presented in this papertotally depends on control scheme employed. If there is any change in control algorithm, ranking ofPMUs will change. In such situation, problem of changing operating conditions can be solved byemploying a suitable adaptive control scheme, without affecting ranking. For example, variation inloading conditions results into multiple operating conditions. At different operating conditions, gener-ator speed signals will be different. According to proposed control scheme, this speed variation willvary speed error and error derivative. This speed error will be reflected as variation in universe ofdiscourse of fuzzy inputs. An adaptive controller such as fuzzy controller dealing with this variationwill work well for various operating scenarios, as described in Reference [21].

Table VIII. Phased PMU placement for 16-bus system.

No. of PMUS Phase-1 Phase-2 Phase-3 Phase-4

1. 56 17 37 292. 61 47 49 323. 62 42 11 464. 65 52 57 345. 68 41 58 456. 51 36 59 487. 8 66 60 148. 26 67 63 449. 25 19 64 1210. 6 22 20 -11. 31 23 16 -



Suggested PMU placement technique ensures complete observability with high redundancy.Therefore, once placement is accomplished, any changes in operating conditions will not affect systemperformance as system is completely observable.

5.4. Wide-area damping controller

After first-stage placement, control scheme proposed in Section 3 is implemented, to check the effec-tiveness of the proposed placement scheme. WAFC and PID controller described in the Reference[26,27] are utilized.

0 2 4 6 8 10 12 14 16 18 20-100

-80

-60

-40

-20

0

20

40

60

80

Time(s)

Cha

nge

in In

tera

rea

Pow

er (

p.u)

Figure 5. Inter-tie power response without control.

(a) Tie line between buses 1-2 (area4,5) (b) Tie line between buses 8-9 (area4,5)

(c) Tie line between buses 50-51 (area1,4) (d) Tie line between buses 1-27 (area4,5)

0 2 4 6 8 10 12 14 16 18 20-8

-6

-4

-2

0

2

4

6

8

Time(s)

Cha

nge

in In

ter

area

pow

er (

p.u)

Cha

nge

in In

ter

area

pow

er (

p.u)

Cha

nge

in In

ter

area

pow

er (

p.u)

Cha

nge

in In

ter

area

pow

er (

p.u)

WAFCPID

0 2 4 6 8 10 12 14 16 18 20-6

-4

-2

0

2

4

6

Time(s)

WAFCPID

0 2 4 6 8 10 12 14 16 18 20-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Time(s)

WAFCPID

0 2 4 6 8 10 12 14 16 18 20-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Time(s)

WAFCPID

Figure 6. Inter-tie response with control.



To simulate the system for SSS, a disturbance of 5% increase in magnitude of reference voltage ofgenerator-1 has been considered between t= 2.0 and 2.5 s. The system is initially unstable even forsmall disturbances as shown by Figure 5.Figure 6(a–d) shows the performance of fuzzy and PID controllers on four major tie lines of the

16-machine system. These tie lines are 1–2, 8–9, 50–51, and 1–27. Figure 6 shows that fuzzycontrollers perform well, and control inter-tie oscillations satisfactorily.

6. CONCLUSION

In this paper, multi-staged PMU placement scheme has been proposed to monitor and control small-signal instability in a large network. In the proposed approach, first optimal placement sites arecomputed, which make the system completely observable, even under loss of single PMU or transmis-sion line. For the given control scheme, critical buses are determined based on modal controllabilityand participation factors. Generator, tie line, and bus observability criteria are developed, and optimallocations are ranked according to these criteria. AHP algorithm is utilized, and PMU placements arecarried out to make all generators and tie lines observable. From placement results, it is observed thatall critical generator and tie-line buses are observed in first-stage itself. Therefore, control scheme canbe implemented after first-stage placement, which will benefit in wide-area SSS analysis. The proposedscheme is robust for different stage budget and can be extended for transient and voltage stabilityanalysis. To check the effectiveness of control scheme, PMU measurements are used to damp inter-area oscillations by wide-area fuzzy and PID controllers. Results show that the proposed placementscheme provides a maximum advantage in terms of observability and stability of a large system.

7. LIST OF SYMBOLS AND ABBREVIATIONS

7.1. Symbols

x state vectory output vectoru control vectorq left Eigen vectorλ Eigen value

7.2. Abbreviations

PMU phasor measurement unitAHP analytical hierarchy processEMS energy management systemsSSS small-signal stabilityILP integer linear programmingGBOI generator bus observability indexTLBOI tie-line bus observability indexBOI bus observability indexCI controllability indexPM pairwise matrixW weight vectorFPI final performance indexOPP optimal PMU placement

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