Optimal substation-based joint allocation of PMUs and measuring channels considering network expansion planning

Electrical Power and Energy Systems 106 (2019) 274–287

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Optimal substation-based joint allocation of PMUs and measuring channels considering network expansion planning

T

⁎

Mohammad Ghamsari-Yazdela, Masoud Esmailia, , Nima Amjadyb a b

Department of Electrical Engineering, West Tehran Branch, Islamic Azad University, Tehran, Iran Electrical and Computer Engineering Department, Semnan University, Semnan, Iran

A R T I C LE I N FO

A B S T R A C T

Keywords: Expansion planning Measuring channel Multiple voltage levels Phasor measurement unit (PMU) Substation disruption Transformer tap setting

This paper proposes an integrated framework to design wide area measurement system (WAMS) addressing the challenges of expansion planning and unknown transformer taps. The proposed framework is formulated as a mixed-integer linear programming (MILP) problem. It minimizes the number of substations disrupted for phasor measurement unit (PMU) placement, PMU buses, and PMU measuring channels. Concepts of substations and buses are separately treated. Power system expansion planning is also considered in order to achieve an optimal solution with the least cost of disrupting existing and future substations. Observability constraints are defined to make both present and expanded grids observable since the time span of WAMS planning is usually shorter than network expansion planning. Moreover, special attention is paid to multiple voltage levels inside a substation; transformers with unknown tap settings are exempt from being treated as observability paths and locating vicious measurement channels. Furthermore, novel ideas are proposed to model branch outages using the concept of backup observability and to model PMU failure using a hybrid method which is a modified version of previous ones. Numerical results from testing the proposed framework on standard test systems verify its performance from perspectives of solution optimality and computational burden.

1. Introduction In today's power networks, which are interconnected across countries and loaded heavily to get more profit in electricity markets, it is almost inevitable to use phasor measurement units (PMUs) for monitoring and control purposes. Installation of PMUs in substations is completed by other auxiliary devices such as current transformers, potential transformers, data communication links, and phasor data concentrator (PDC). A PMU with a sampling rate of 30–120 samples per second is faster than updating interval (about 2 s) of Supervisory Control and Data Acquisition (SCADA) system. A PDC gathers timestamped phasor measurements from its subscribed PMUs. After adjusting the data and doing some calculations, PDC down-samples the data to be fed into SCADA systems. The data provided by PDCs can be used to enhance accuracy of existing SCADA systems and state estimation tools. Considering the cost of PMUs for developing countries and a lot of required PMUs for full observability of practical large-scale networks even with minimum security criteria (N −1), the problem of optimal PMU placement (OPP) is recommended as an economic optimization and has been economically fascinating for power system researchers. OPP deals with determining the optimal number of PMUs

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and their locations so that the whole system becomes observable with the least cost. In the design of wide area measurement system (WAMS), cost is usually the main objective function along with other objective functions such as reliability and data traffic [1]. There are some vital aspects that should be incorporated into OPP/WAMS to have a comprehensive model, as discussed below. One issue in OPP/WAMS is the effect of unknown tap setting of transformers on system observability as called also substation-based observability [2]. Traditionally, OPP is worked on a bus-based observability, where each node represents a bus or substation (comprised of multiple buses with different voltage levels) and the network is solved for observability of nodes. Different buses inside a substation are connected through transformers; therefore, results of bus-based OPP is valid only in a case where taps of all transformers are known in order to calculate voltage of buses. Although tap setting and voltage of both sides of transformers are measured in substations, they may not be sent to the SCADA control center [2,3]. Therefore, bus-based OPP loses its validity and substation-based OPP should be used to obtain a more practical solution. Although this issue is addressed in literature such as [2] and [3], they place a PMU at every bus of a substation to cover the unknown tap settings of transformers; however, this solution is too

Corresponding author. E-mail addresses: [email protected], [email protected] (M. Esmaili).

https://doi.org/10.1016/j.ijepes.2018.10.010 Received 24 January 2018; Received in revised form 27 August 2018; Accepted 7 October 2018 0142-0615/ © 2018 Elsevier Ltd. All rights reserved.

Electrical Power and Energy Systems 106 (2019) 274–287

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Nomenclature

zi ϕk

Sets

ΩE Ωout E ΩP Ωout P ΩS

Variables

set of buses in the expanded grid set of branches considered for outage in the expanded grid set of buses in the present grid set of branches considered for outage in the present grid set of substations in the expanded grid

fiEG fiPG qiEG

Parameters/constants

qiPG

bki CiPMU Cijch CkSub aijEG aijPG piEG piPG

tijEG

tijPG

between buses i and j in the present grid; otherwise 0 1 if bus i is a zero-injection bus; otherwise 0 the number of buses in substation k

1 if bus i belongs to substation k; otherwise 0 installation cost of PMU at bus i including PMU device and its accessories installation cost of PMU channel between buses i and j disruption cost of substation k i–j element of the connectivity matrix of the expanded grid i–j element of the connectivity matrix of the present grid 1 if bus i is connected to more than one ZIB in the expanded grid; otherwise 0 1 if bus i is connected to more than one ZIB in the present grid; otherwise 0 1 if there is a transformer with unknown tap setting between buses i and j in the expanded grid; otherwise 0 1 if there is a transformer with unknown tap setting

sk uij

xi yi μij ψij

F

observability function of bus i in the extended grid observability function of bus i in the present grid 1 if bus i remains observable in branch contingencies due to being connected to multiple ZIBs in the extended grid; otherwise 0 (binary variable) 1 if bus i remains observable in branch contingencies due to being connected to multiple ZIBs in the present grid; otherwise 0 (binary variable) 1 if substation k is disrupted for PMU installation; otherwise 0 (binary variable) auxiliary binary variable which is 1 if bus i becomes observable through ZIB property of bus j and 0 otherwise 1 if a PMU is installed at bus i; otherwise 0 (binary variable) number of PMUs allocated to bus i to cover PMU failure number of PMU channels allocated to line i–j by all PMUs at bus i to cover PMU failure 1 if a PMU channel is allocated to line i–j by a PMU at bus i; otherwise 0 (binary variable) objective function

the maximum number of PMU measuring channels is limited to a certain value for all buses in the OPP problem. In [11], authors imposed the same limitation on the measuring channels of all PMUs and proposed a technique to identify the best combination of channel assignment. To this end, the connectivity matrix is modified for each limitation and all possible combinations are examined when the number of channels is less than the number of branches connected to a bus. In [12] and [13], PMU measuring channel capacities are taken into account in numerical observability analysis using a semidefinite programming approach where a combination of channel assignments is formulated when the number of channels of a PMU is less than the number of branches connected to the bus. In [14], installation cost of PMUs is formulated based on their voltage and current measuring channels. On the other hand, some other works considered PMU channels as decision variables. Authors in [15] formulated PMU measuring channels as decision variables and they limited the number of channels of PMUs in OPP. Although the channel limitation is used to determine the optimal channel assignment of PMUs, the drawback is that the channels are not formulated in the cost objective function. Authors in [16] determined the optimal number of channels for each bus by formulating channels as decision variables in the cost objective function. As shown in [16], joint placement of PMUs and their channels as decision variables with considering their cost in the objective function leads to a more cost-effective solution. As a result, in order to have a more efficient solution, measuring channels should be optimized in the cost objective function. The next feature in OPP is the incorporation of contingencies (usually PMU losses and branch outages) as N −1 [17] or N −2 security constraints [18]. The network should remain observable in both base case and post-contingent states. In this regard, the base case OPP is traditionally extended to include post-contingent network configurations [17]. This technique needs new PMUs and a higher cost. However, the concept of backup observability is recently adopted in some works, such as [10] and [16], to incorporate contingencies in OPP with a lower cost. Although this technique is more economically fascinating than the traditional one, its drawback is that it offers low reliability due to using the same communication infrastructures shared between the primary and backup PMUs.

conservative and may unnecessarily allocate extra PMUs and communication facilities. Another aspect of OPP is substation disruption costs. PMUs are installed at buses of substations [4]. During the installation and setting up the communication and cyber-security infrastructures, the substation has to go under disruption, which means that it is out of service [2]. Although utilities usually try to do the upgrading during scheduled overhauls or off-peak periods, it may not be possible in electricity markets [5]. According to the U.S. Department of Energy [6], the cost of a new PMU installation project can be almost 20 times of the PMU device cost. Thus, the upgrading cost of substations is an important issue and should be considered in the OPP to minimize the costs realistically. Another issue with existing OPP methods is that OPP is a planning problem that is solved for next years. On the other hand, power network expansion planning, as another planning problem, is performed to expand the network in order to meet future electricity demands with the minimum cost and highest reliability. There are few previous works, such as [7] and [8], that addressed OPP considering network expansion planning. However, they plan full observability for the expanded grid while they neglect the present-day network configuration. That is, they use the expanded grid as their final test system. However, the time span of WAMS planning (e.g., installing 850 PMUs during about 3 years [9]) is usually shorter than network expansion planning (about 10 years). As a result, it is necessary to consider the present-day network along with the future expanded grid to have a more practical and cost-effective solution in OPP. Another aspect of OPP is the limitation of PMU measuring channels. Measuring channels may not be expensive compared with whole PMU device. However, their execution needs interruptions in existing substations and overhead lines (for installation of fiber optic cables to transmit PMU data) resulting in huge costs for system operators due to energy not supplied (ENS). In addition, using a large number of PMU measuring channels slowdowns the SCADA processor and PDC by increasing their computational burden. In the literature, most research works have imposed the same limit on the number of measuring channels of all PMUs. For instance, in [10] it has been suggested that 275

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observable buses j and k . As a result, in order to employ observability resources more effectively, it is necessary to consider the effect of unknown transformer tap settings on the OPP. It is noted that tap ratios of such transformers are not usually known to the control center. Thus, the unknown taps are input data to the proposed method to determine optimal PMU locations. It is worthwhile to note that there are two basic differences between our method and previous works ([2;3]) which try to model effects of different voltage levels on observability. The first is that the methods in both [2] and [3] place a PMU at every bus of a selected substation to cover the unknown tap settings of transformers. However, although these methods make observable all buses of the substation, they may use extra PMUs since the optimal solution may be achieved without extra PMUs. Thus, their methods may not lead to the optimal OPP solution. However, our proposed OPP approach determines optimal PMU placement for buses with unknown transformer tap settings. The second difference between the proposed OPP approach and previous methods lies in the modeling the effect of ZIBs on the unknown transformer tap settings. The previous work [3] does not model ZIBs in the unknown tap settings and [2] considers the ZIB property only for a case where all ZIB buses have the same voltage level. Hence, the model in [2] might be non-optimal and might eliminate combinations of better solutions. However, the proposed OPP approach can cope with different combinations of unknown transformer tap settings and ZIB properties presented in Fig. 1.

Taking into account the above-mentioned features, the aim of this paper is to present an integrated framework with main contributions as follows: (1) We introduce an OPP model in which power network expansion planning is considered. This means that our OPP solution is valid not only for the present network but also for the future expanded grid. (2) The proposed substation-based OPP approach can determine optimal PMU placement at transformer buses, which is different from previous methods that place a PMU at every transformer bus and give a too conservative and non-optimal solution. Zero-injection bus (ZIB) properties are also used to achieve a more efficient solution. (3) The proposed OPP approach determines the optimal joint allocation of PMUs and their channels. That is, the optimal location of PMUs and the optimal number of channels for each node are determined. This is done by modeling PMU channels as decision variables in the cost objective function. At the same time, the cost of substation disruption to place PMUs is minimized to enhance reliability. (4) A modified hybrid approach is introduced to model PMU failure and branch outage using the concept of backup observability in which the drawback of low reliability due to secondary PMUs is improved. The rest of this paper is organized as follows. In Section 2, the proposed substation-based joint placement of PMUs and measuring channels considering network expansion planning (OJP-NEP) is introduced. In Section 3, an illustrative example is brought to clarify the paper concepts. In Section 4, security constraints of OJP-NEP are detailed. Numerical results are presented in Section 5 and Section 6 concludes the paper.

2.2. The proposed substation-based model considering network expansion planning Power system observability can be studied using either numerical or topological observability models. The topological observability approach may be more preferred due to its lower computational burden and convex model [18]. Our model in this paper is based on topological observability. The main objective function in the proposed OJP-NEP model is to minimize total cost of substations’ disruptions, PMU base units, and their measuring channels expressed as:

2. Proposed problem formulation The proposed framework has two observability resources to make the network observable: PMU measuring channels and zero-injection bus (ZIB) properties. A PMU voltage channel observes its host bus by measuring its voltage through a potential transformer. PMU current channels make observable PMU adjacent buses by measuring branch currents/powers through current transformers and calculating the voltages of the PMU adjacent buses. In case of a single ZIB, one of buses in a ZIB set (including ZIB and its adjacent buses) can be left unmonitored by PMUs to be observed through the current summation equation at ZIB. In case of n ZIBs connected to each other, out of the ZIB set buses (including the ZIBs and their adjacent buses), n buses can be left unmonitored by PMUs to be observed through n current summation equations of ZIBs.

MinF =

∑ k ∈ ΩS

Cksub sk +

∑ i ∈ ΩE

CiPMU xi +

∑ i, j ∈ ΩE

Cijch ψij .

(1)

The first term in (1) represents the cost of substations which are disrupted due to PMU installation. This term includes substation upgrading costs and expected energy not served (EENS) due to disruption; the second term in (1) indicates PMU installation cost; and the last term is the installation cost of PMU voltage and current measuring channels. Disruption cost of substations, installation cost of PMUs, and channel cost differs for each substation, PMU, and channel, respectively, depending on diverse parameters such as geographical location and voltage level. For substations that have a degree of PMU infrastructure, values of Cksub and CiPMU can be assumed lower than other substations that have no existing PMU infrastructure. It is noted that although the network expansion planning has no direct cost term in (1), it affects

2.1. The concept of different voltage levels in OPP There are usually different voltage levels inside a substation, where buses with different voltages are connected through power transformers. In view of the fact that the tap setting of transformers is not usually known to the control center [2], different voltage levels are decoupled from each other from the viewpoint of observability as shown in Fig. 1. As seen from this figure, in general, there are four situations of unknown transformer tap settings in PMU measurements. Fig. 1(a) represents a substation with two voltage levels. Even if a PMU at bus i has assigned a current channel to observe bus j , it does not help since the transformer impedance is unknown and therefore it is impossible to calculate bus j voltage using the measured current. In Fig. 1(b), this happens with the ZIB property of bus i . In Fig. 1(c), voltage of bus j cannot be calculated due to unknown transformer tap setting and so the ZIB property of bus j cannot be used to observe bus k . Similarly, in Fig. 1(d), ZIB properties of buses i and j cannot make

Fig. 1. Vicious measuring kinds due to unknown transformer tap ratio (a) single vicious observation by a branch PMU, (b) single vicious observation by ZIB property, (c) multiple vicious observations by branch PMU and ZIB property, (d) multiple vicious observations by ZIB properties. 276

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ψij ≤ aijEG (1−tijEG ) x i , ∀ i, j ∈ ΩE .

total cost due to additional PMUs/channels for the expanded grid. Inasmuch as we pay special attention to power network expansion planning in the proposed OJP-NEP model, we define two observability functions, unlike previous works, to ensure complete observability of the present and expanded power grids using following equations. It is noted that the expansion planning problem is not modeled in this paper; only the outcome of expansion planning is assumed as the future grid. The expanded grid includes the present network and new lines and substations as a whole.

fiPG =

∑

ajiPG (1−t jiPG ) ψji +

j ∈ ΩP

fiEG =

∑

∑

ajiEG (1−t jiEG ) ψji +

j ∈ ΩE

∑

If a PMU is placed at bus i (i.e., x i = 1), a branch exists between buses i and j (i.e., aijEG = 1), and there is not a transformer with unknown tap between buses i and j (i.e., tijEG = 0 ), the right-hand side of (9) becomes 1. Since ψij is a binary variable, it can be zero (i.e., a measuring channel is not assigned to PMU at bus i to observe bus j ) or it can be one (i.e., a measuring channel is assigned to PMU at bus i to observe bus j ). However, if the transformer on branch ij has unknown tap (i.e., tijEG = 1), the right-hand side of (9) becomes zero: it forces ψij = 0 implying that the PMU at bus i does not allocate a current channel to measure branch ij current because voltage phasor of bus j cannot be calculated due to indeterminacy of transformer impedance. The optimal assignment of PMU channels is determined through minimizing the objective function. This type of allocating channels to branches makes possible exploiting current measuring channels more efficiently and does not waste measuring channels. In this case, unwanted and vicious measurements are kept low; we can easily provide observability redundancy at required locations (e.g., critical buses). Furthermore, unlike channel-based OPP method in [16], the proposed substation-based method is capable of being used as optimal joint allocation of traditional and modern PMUs. Unlike traditional PMUs which are standalone and whose single function is to measure phasors, modern PMUs are designed to observe a branch by measuring the voltage and current phasors at one end of the branch and to report synchro-phasor data while performing their relaying functions. The proposed substation-based OJP-NEP does not impose locating PMU on every bus of a selected substation as done in [2] or [3]. Regardless of the cost of PMUs/measuring channels, the optimal observation of transformers helps SCADA retain its computational efficiency by not transmitting unnecessary measurements to SCADA. To this end, the proposed approach makes a decision in order to obtain the best solution by:

aijPG (1−tijPG ) uij zj , ∀ i ∈ ΩP . (2)

j ∈ ΩP

aijEG (1−tijEG ) uij zj , ∀ i ∈ ΩE .

(3)

j ∈ ΩE

Expressions (2) and (3) account for observability functions of buses in the present and expanded networks, respectively. The first and second terms in (2) give the observability provided by PMU measuring channels and ZIB properties, respectively. In both terms, (1−t jiPG ) excludes observations of transformers with unknown taps from the observability function of the present grid. Also, (1−t jiEG ) does the same action in (3) for the expanded grid. Note that both observability functions of the present and expanded grids share the same variable uij and parameter zj to handle ZIB properties. Connectivity matrix elements of the present and extended grids as used in (2) and (3) are defined as:

⎧1, if i = j aijPG = 1, if i and j are connected ⎨ ⎩ 0, otherwise.

aijEG

(4)

PG PG ⎧ aij , if aij = 1 ⎪ 1, if bus i is added after expansion and i = j = ⎨ 1, if i and j are connected after expansion ⎪ ⎩ 0, otherwise.

(5)

sk ≤

It should be noted that the mentioned observability functions are unknown tap setting-based versions of the ones used in [16]. In the base case, the following constraints should be satisfied for all buses to make the present and extended networks observable. PG

≥ 1, ∀ i ∈ ΩP .

(6)

fiEG ≥ 1, ∀ i ∈ ΩE .

(7)

fi

∑

sk ≥

bki x i , ∀ k ∈ ΩS . (10)

∑i ∈ ΩE bki x i ϕk

, ∀ k ∈ ΩS .

(11)

Eqs. (10) and (11) establish a relationship between x i and sk encountering the two following situations:

• No PMU is installed at buses of substation k : The right-hand side of

aijEG (1−tijEG ) uij , ∀ j ∈ ΩE .

•

(8)

i ∈ ΩE

∑ i ∈ ΩE

The technique used here to model ZIBs is based on the formulation introduced in [19] and used in subsequent works like [9]. The auxiliary variable uij in (2) and (3) are constrained by [19]:

zj =

(9)

(aijEG )

Since the connectivity matrix entries of the expanded grid are introduced in (5) by adding expansion transformers to the connectivity matrix of the present network (aijPG ), (8) is capable to support the both observability functions. In order to properly model ZIBs by (8), a ZIB is defined as a bus with the following conditions: (1) it should have no generation (2) it should have no load, and (3) it should be involved in power transmission in order to make it sensible to apply the KCL at that bus. In addition, the observability function in (6) and (7) should only be satisfied for buses that are involved in power transfer. In the proposed substation-based OJP-NEP, a PMU located at a bus, which belongs to a substation, can assign current measuring channels to observe its adjacent buses if it is not a vicious measurement and is economically acceptable; this is a decision made by optimizing the objective function. This decision-making process is substantially different from previous works, where a PMU placed at a bus has to assign channels to all of its connected buses even if it is neither necessary nor economical. The constraint to assign measuring channels is formulated as

(10) becomes zero and this constraint turns into sk ≤ 0 implying that sk = 0 . Eq. (11) turns into sk ≥ 0 that has no effect on the optimization problem. Consequently, substation k is not disrupted and it does not have disruption cost in the objective function (1). At least one PMU is installed at buses of substation k : Eq. (10) turns into sk ≤ ϑ where ϑ is a positive integer value: this equation will not have any effect on the optimization problem. Eq. (11) turns into sk ≥ ν where ν is a nonzero real value smaller than unity. Since sk is a binary variable, (11) forces sk to be 1. Consequently, substation k is selected for disruption and its disruption cost is accounted in the objective function (1).

As seen, Eqs. (10) and (11) derive sk from x i using two soft/relaxed inequality constraints, which are more preferred than hard equality constraints. This procedure improves the convergence of the proposed MILP model. 2.3. Numerical explanation of the proposed model In order to better clarify the proposed OJP-NEP, the model is elicited on the IEEE 9-bus test system having both expansion plan and transformers with unknown taps as shown in Fig. 2. Observability constraints (2) and (6), related to the observability of present grid, are 277

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written as follows (dashed lines in Fig. 2 are considered):

G 1

45

f1EG = ψ1,1 + ψ4,1 + ψ10,1 + u1,4 ≥ 1 f2EG = ψ2,2 + ψ8,2 + ψ10,2 + u2,8 ≥ 1 f3EG = ψ3,3 + ψ6,3 + u3,6 ≥ 1 f4EG = ψ1,4 + ψ4,4 + ψ9,4 + u4,4 ≥ 1

9

10

6

3

f5EG = ψ5,5 + ψ6,5 + u5,6 ≥ 1

G f6EG

= ψ3,6 + ψ5,6 + ψ6,6 + ψ7,6 + u6,6 ≥ 1 f7EG = ψ6,7 + ψ7,7 + u7,6 ≥ 1 f8EG

f9EG

G 2

8

= ψ2,8 + ψ8,8 + ψ9,8 + u8,8 ≥ 1

= ψ4,9 + ψ8,9 + ψ9,9 + ψ10,9 + u9,4 + u9,8 ≥ 1 f10EG = ψ1,10 + ψ2,10 + ψ9,10 + ψ10,10 ≥ 1

7

(13)

ZIB constraint (8) is written for the expanded grid as:

Legend:

existing bus, added bus, existing line, added line.

1 = u1,4 + u4,4 + u9,4 1 = u2,8 + u8,8 + u9,8 1 = u3,6 + u5,6 + u6,6 + u7,6

Fig. 2. IEEE 9-bus test system with expansion planning and transformers with unknown tap.

The value of 1 in (14) implies that the ZIB property of a bus can be assigned to observe only one bus. For instance, in 1 = u1,4 + u4,4 + u9,4 , if u1,4 = 1, bus 1 is observed through ZIB property of bus 4. The assignment of PMU channels is constrained by (9) as:

written as follows (dashed lines in Fig. 2 are not considered in the present grid):

f1PG = ψ1,1 + ψ4,1 + u1,4 ≥ 1

f4PG

f2PG = ψ2,2 + ψ8,2 + u2,8 ≥ 1

ψ1,1 ≤ x1, ψ1,4 ≤ x1, ψ1,10 ≤ x1

f3PG

ψ2,1 ≤ x2 , ψ2,2 ≤ x2 , ψ2,10 ≤ x2

= ψ3,3 + ψ6,3 + u3,6 ≥ 1

ψ3,3 ≤ x3 , ψ3,6 ≤ x3

= ψ1,4 + ψ4,4 + ψ9,4 + u4,4 ≥ 1 f5PG

ψ4,1 ≤ x 4 , ψ4,4 ≤ x 4 , ψ4,9 ≤ x 4

= ψ5,5 + ψ6,5 + u5,6 ≥ 1

ψ5,5 ≤ x5 , ψ5,6 ≤ x5

f6PG = ψ3,6 + ψ5,6 + ψ6,6 + ψ7,6 + u6,6 ≥ 1

ψ6,3 ≤ x 6 , ψ6,5 ≤ x 6 , ψ6,6 ≤ x 6 , ψ6,7 ≤ x 6

f7PG = ψ6,7 + ψ7,7 + u7,6 ≥ 1

ψ7,6 ≤ x 7 , ψ7,7 ≤ x 7

f8PG = ψ2,8 + ψ8,8 + ψ9,8 + u8,8 ≥ 1 f9PG = ψ4,9 + ψ8,9 + ψ9,9 + u9,4 + u9,8 ≥ 1

(14)

ψ8,2 ≤ x 8 , ψ8,8 ≤ x 8 , ψ8,9 ≤ x 8 ψ9,4 ≤ x 9 , ψ9,8 ≤ x 9 , ψ9,9 ≤ x 9 , ψ9,10 ≤ x 9

(12)

ψ10,1 ≤ x10 , ψ10,2 ≤ x10 , ψ10,9 ≤ x10 , ψ10,10 ≤ x10

The fiPG ≥ 1 in (12) ensures that each bus be observable in the present grid by PMU channels or ZIB properties. For instance, in f1PG = ψ1,1 + ψ4,1 + u1,4 ≥ 1, at least one of variables ψ1,1, ψ4,1, or u1,4 should be 1 to satisfy the constraint. If ψ1,1 = 1, bus 1 is observed by its own PMU; if ψ4,1 = 1, bus 1 is observed by the PMU at bus 4; if u1,4 = 1, bus 1 is observed by ZIB property of bus 4. Similarly, observability constraints related to the expanded grid are

(15)

Eq. (15) indicate that if a PMU is installed at a bus, it can assign measuring channels to observe its host bus and/or connected buses. For instance, if a PMU is installed at bus 1 ( x1 = 1), each of relevant decision variables ψ1,1, ψ1,4 , and ψ1,10 can be unity; for example, if ψ1,4 = 1, the PMU at bus 1 assigns a channel to observe bus 4. In contrast, if no PMU

Fig. 3. Illustrative example on the IEEE 9-bus test system (a) without considering expansion planning, (b) with considering expansion planning. 278

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For example, if no PMU is installed at buses of substation 4 (that encompasses bus 4 and 5), in the 4th equation we have x 4 = x5 = 0 that makes s4 = 0 . This means that substation 4 is not disrupted. In contrast, if at least one PMU is installed at one of buses of substation 4, we have s4 ≥ 1/2 that forces s4 = 1; this implies that the substation is disrupted.

to calculate voltage of bus 1 (as shown by a dashed arrow on line 4–1 in the figure). Similarly, the ZIB property can be applied to other ZIB sets of SZ6 and SZ8 . Both cases in Fig. 3(a) and (b) result in the same number of 2 PMUs and 9 measuring channels (including 2 voltage channels at PMU buses, 4 current channels, and 3 ZIB properties). However, there is a vital difference between the two solutions. In Fig. 3(a), after adding bus 10 in the future, we should equip one of buses 1, 2, 9, or 10 by a PMU and should disrupt the substation in order to make bus 10 observable. On the other hand, in case of the configuration of Fig. 3(b), after adding bus 10 in the future, no substation disruption is needed because the new bus 10 can be observable by assigning a current measuring channel of the existing PMU at bus 9. Consequently, the proposed OJP-NEP framework is capable to make observable both present and expanded grids with minimum number of substation disruptions, PMU installations, and PMU channel installations as formulated in the objective function (1).

3. Illustrative examples

3.2. Illustrative example for multiple voltage levels

3.1. Illustrative example for network expansion planning

In the one-line diagram of the IEEE 9-bus test system shown in Fig. 4, we consider two transformers with unknown taps between buses 4–5 and 7–8. In Fig. 4(a), the network is solved without paying attention to transformer unknown taps; the result is that 2 PMUs are placed at buses 4 and 7. In contrast, in Fig. 4(b), the problem is solved with considering unknown transformer taps and the result is to install two PMUs at buses 6 and 9. Although the number of PMUs is the same, the network is unobservable in Fig. 4(a). The reason is that buses 5 and 8 cannot be observed in Fig. 4(a) since the transformer taps are unknown and it is not possible to calculate voltage phasors of buses 5 and 8 using the measured currents. As a result, buses 2 and 3 also remain unobservable since the ZIB properties of buses 6 and 8 are not useful anymore. Totally, four buses (2, 3, 5, and 8) are left unobservable in Fig. 4(a) when the unknown transformer taps are not considered. On the other hand, in Fig. 4(b) where the unknown transformer taps are considered, the whole network is made observable using 2 PMUs. Consequently, it is vital in OPP to consider and model transformers with unknown taps in order to achieve a practical and correct solution.

is installed at bus 1 ( x1 = 0 ), no channel is made available by ψ1,1 = ψ1,4 = ψ1,10 = 0 . Finally, the status of substation disruption in (10) and (11) is written as:

s1 ≤ x1, s1 ≥ x1 s2 ≤ x2 , s2 ≥ x2 s3 ≤ x3 , s3 ≥ x3 s4 ≤ x 4 + x5 , s4 ≥ (x 4 + x5)/2 s5 ≤ x 6 , s5 ≥ x 6 s6 ≤ x 7 + x 8 , s6 ≥ (x 7 + x 8)/2 s7 ≤ x 9 , s7 ≥ x 9 s8 ≤ x10 , s8 ≥ x10

(16)

In Fig. 3, the expanded grid of the IEEE 9-bus test system is depicted. It is supposed that bus 10 and three lines 1–10, 2–10, and 9–10 are added to the system in the expansion scenario. The present grid is solved in Fig. 3(a) using ordinary OJP (ignoring network expansion scenario), whereas the future grid is solved in Fig. 3(b) using OJP-NEP (considering the expansion scenario). Some voltages in Fig. 3 are calculated by ZIB properties. In Fig. 3, there are three ZIBs (buses 4, 6, and 8) since they have neither load nor generation. Each ZIB constitute its own ZIB set that includes the ZIB and its adjacent buses. Thus, there are three ZIB sets in Fig. 3 as SZ4 = {1, 4, 5, 9} , SZ6 = {3, 5, 6, 7} , SZ8 = {2, 7, 8, 9} . It is possible to observe one of buses in each ZIB set by a KCL at the ZIB. For instance, applying KCL (in terms of bus voltages) to ZIB 4 in Fig. 3(a) results in (V4−V1) y1,4 + (V4−V5) y4,5 + (V4−V9) y4,9 = 0 , where Vi is the voltage phasor of bus i and yi, j is the complex admittance of branch ij . In this KCL, branch admittances are known before solving the problem. Consequently, there are four unknown voltages in the KCL as: V1, V4 , V5, and V9 . Out of these four voltages, if three of them are known by other means (for instance, they are measured by PMU channels), the remaining voltage can be calculated from the KCL; we call this feature as the ZIB property in this paper. In other words, the ZIB property of bus 4 in Fig. 3(a) can be used to calculate the voltage of one of buses (1, 4, 5, or 9) and this is decided by the optimization problem. For instance, in Fig. 3(a), the ZIB property of bus 4 is assigned

4. N −1 Security constraints of the proposed OJP-NEP A power grid should remain completely observable not only in its normal operating point but also in post-contingency states. Contingencies that are considered in OPP in the literature mainly include branch outages and PMU failures as N −1 security constraints

Fig. 4. Illustrative example on the IEEE 9-bus test system (a) without modeling transformer taps, (b) with modeling transformer tap. 279

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observed only through current channels from PMUs on buses 9 and 1, respectively. However, both of them remain observable in case of any single branch outage because their own ZIB property is able to provide observability for them. For example, if branch 4–9 goes out of service, ZIB bus 4 remains observable. Since bus 7 is observed by a current measuring channel of PMU on bus 9, the backup observability of bus 7 (the ZIB property of bus 5) is no longer needed and then, it can be used for observability of bus 6. Consequently, the ZIB property of bus 4 becomes free and can be used for observing this bus. As another instance, with outage of branch 1–5, observability of bus 5 is not lost. The reason is that similar to the prior example, bus 7 is observable and so the ZIB property of bus 5 is free and can be used for observing itself. In this sample grid, the fourth group bus 6 can be observed by two ZIB properties of buses 4 and 5, which their ZIB properties are not used for themselves. If branch 4–6 (or 5–6) is not in service, the ZIB property of bus 5 (or bus 4) can be used to make bus 6 observable. Ultimately, there are both primary and backup observations for other buses (2 and 7) to maintain their observability against any single branch outage. Considering the above aspects, the following constraints should be satisfied for all buses to make the present and extended networks observable in both base case and post-contingency states:

which have direct effects on observability. 4.1. OJP-NEP formulation for incorporating branch outages using backup observability The prevalent technique in the literature to incorporate branch outage in OPP problem is to consider different outage scenarios, in each of which one branch is removed [20,21]. In this way, OPP problem is extended to include branch outage scenarios and OPP is solved with extended constraints. Although this technique makes the grid observable in post-contingency states, it needs not only a higher number of PMUs but also a higher computational burden confining its application in large-scale WAMS design problems. Accordingly, we employ a different and more efficient approach that is based on backup observability concept which is established as: to keep the system observable after contingencies such as outage of branches, a redundant observability in addition to the main (primary) observability for buses is required since buses that are observed in the base case through PMU measuring channels (ψij ) or ZIB properties (uij ) may lose their observability in post-contingency due to topological changes. The backup observation can be provided through unallocated PMU measuring channels or even new PMUs. However, even if this method requires new PMUs, the number of its new PMUs is less than the number of new PMUs required in the previous scenario-based method [10]. The main point is that the primary and backup observations should not be provided through the same branch; otherwise, both observations are lost after the outage of that branch. For more clarification, consider Fig. 5 where bus i is being observed by a measuring channel of a PMU located at bus j (i.e., ψji = 1) and the backup observability of bus i is provided by ZIB property of bus j (i.e., uij = 1). Although bus i in Fig. 5 has an observability redundancy, both of its observations depend on branch i−j and they are lost in case of branch i−j outage. Therefore, the primary and backup observability (from PMU measuring channels and ZIB properties) should not be provided through the same branch. In order to fulfill this aim, the following constraint is imposed:

ψji + uij ≤ 1, ∀ i, j ∈ ΩE .

fiPG + x i + qiPG ≥ 2, ∀ i ∈ Ωout P .

(18)

fiEG + x i + qiEG ≥ 2, ∀ i ∈ Ωout E .

(19)

Constraint (18) indicates that all buses in the present grid should have backup observation except the mentioned groups. At first, assume that bus i is not equipped by a PMU ( x i = 0) and is not connected to more than one ZIB (qiPG = 0). Accordingly, (18) leads to fiPG ≥ 2 which indicates that bus i needs both primary and backup observabilities. However, if x i = 1 or qiPG = 1, (18) can be satisfied with fiPG ≥ 1. It means that bus i does not require a redundant observability since it belongs to bus group 1 or 4. This is due to the fact that such buses remain observable during any branch outage. Additionally, if we focus on bus groups 2 and 3, they are exempt from satisfying (18) as they are not included in the set (∀ i ∈ Ωout P ). This type of buses always needs only one observation and satisfying (6) is adequate for them. Similar explanations can be said for buses in the expanded grid using (19). Variables qiPG and qiPG as discussed above are constrained by:

(17)

It is noted that some buses do not need a backup observation in considering branch outages. The first group includes buses on which a PMU is located. Such buses remain observable in case of any branch outage since they are observed by the voltage measuring channel of their own PMUs independent of branches. The second group is radial buses. According to the logical reasons of [9] that we will mention later in the next illustrative example in Fig. 6, considering radial buses in branch outage is unessential. Hence, only one observability is sufficient for radial buses. The third group is ZIBs which are not connected to radial buses. Such a ZIB bus can remain observable in case of any single branch outage because of its ZIB property that is able to support it in any circumstance. The fourth group includes buses connected to more than one ZIB which their ZIB properties are not used for their own observation. Such a bus with single observability can remain observable in the case of single branch outage since one of the ZIB properties is sufficient to make it observable. To further clarify the mentioned groups, consider Fig. 6 where branch outage circumstances are shown on a 9-bus sample network. As shown, the first group buses that are equipped with a PMU (1, 3, and 9) remain observable through a voltage measuring channel in case of any branch outage. Radial bus 8 (the second group) is observed only by one current measuring channel from PMU on bus 3 because a radial bus is isolated from the network if its single connecting branch goes out of service. Hence, if it is a load bus, it becomes without any energy and if it is a generation bus, it usually trips due to frequency protection [9]. As a result, the outage of radial branches is not incorporated into the security constraints of PMU placement [22]. As seen in Fig. 6, the third group buses 4 and 5 as ZIBs which are not connected to radial buses are

qiPG ≤ piPG

qiEG ≤ piEG

∑j ∈ ΩP aijPG (1−tijPG ) zj (1−ujj ) 2

∑j ∈ ΩE aijEG (1−tijEG ) zj (1−ujj ) 2

, ∀ i ∈ ΩP .

(20)

, ∀ i ∈ ΩE .

(21) PG

PG

In (20), if bus i is not connected to multiple ZIBs ( pi = 0), qi is forced to be zero. Moreover, if all ZIBs connected to bus i use their ZIB properties to observe themselves (ujj=1) , qiPG is forced to be zero again. This also happens when only one ZIB with ujj = 0 (i.e., it does not use its ZIB property for itself) is connected to bus i since the right hand-side of (20) becomes 1/2. However, if two or more ZIBs with ujj = 0 are connected to bus i , the right hand-side in (20) becomes unity or greater and so the binary variable qiPG can be 0 or 1. Since the optimization problem intends to minimize the number of required PMU measurements, it uses the least values for fiPG as much as possible and so sets qiPG = 1. Similarly, (21) is optimized for the expanded network.

Fig. 5. Improper main and backup observability on the same branch. 280

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μij ≤ aijEG (1−tijEG ) yi ∀ i, j ∈ ΩE .

sk ≤

∑

(27)

bki yi , ∀ k ∈ ΩS .

(28)

i ∈ ΩE

sk ≥

∑i ∈ ΩE bki yi 2ϕk

, ∀ k ∈ ΩS .

(29)

At a glance, the objective function and constraints of the proposed OJP-NEP optimization problem in different cases can be summarized as:

• “Base case”: objective function (1) is optimized subject to (2)–(11). • “Base case + branch outages”: objective function (1) is optimized subject to (2)–(11) and (17)–(21). • “Base case + PMU failures”: objective function (22) is optimized subject to (4), (5), (8), and (23)-(29). • “Base case + branch outages + PMU failures” (as N −2 security

Fig. 6. Illustration of the proposed branch outage concept on a 9-bus sample test system.

constraints): At first, “Base case + branch outages” is solved, then, its results are imposed as constraints to “Base case + PMU failures”.

4.2. OJP-NEP formulation for incorporating PMU failures using a hybrid concept

All of these OJP-NEP models are mixed-integer linear programming (MILP) optimization problems which can be easily solved using commercial mathematical-based software packages or evolutionary algorithms [23–25]. Each case as defined above is solved at one stage by an individual solution algorithm.

Generally, there are two available approaches to consider single PMU failure in OPP. The first one, as proposed in previous works, such as [19] and [21], locates PMUs at new buses in order to observe each bus at least two times. As shown numerically in previous works, such as [9] and [19], the number of PMUs is at least doubled using this approach. Although this approach keeps the whole system observable in case of single PMU failure, its solution is costly. The second approach, as explained in previous works, such as [16] and [20], installs a secondary PMU besides each primary PMU of the base case sharing the same infrastructure (GPS antenna, panel, power supply, communication networks, fiber optics, and etc.) of the primary PMUs. Although the second approach offers a more cost-effective solution than the first one, the WAMS reliability may be low due to employing the shared communication since any failure in the communication components leads to loss of both primary and secondary PMUs. Accordingly, a hybrid approach is proposed here in which the drawbacks of existing approaches are fixed. Our approach combines previous methodologies with some modifications as follows. Our proposed hybrid approach is formulated by substituting already explained Eqs. (1)–(3), (6), (7), and (9)–(11) with the following Eqs. (22)–(29). Constraints (25) and (26) ensure that observability of buses observed by PMUs is at least 2 and observability of buses observed by ZIBs is at least 1 since ZIB properties are not affected by a single PMU failure if (25) and (26) are satisfied. The secondary PMUs are installed with independent communication infrastructures to improve WAMS reliability. This is justified since the cost of PMU communication infrastructures is much less than the cost of interrupting substations [6]. In (22), yi is the total number of PMUs (primary and secondary) at bus i and CiPMU is the cost of installing PMU at bus i . That is, both primary and secondary PMUs are accounted with full PMU cost (CiPMU ) in order for independent infrastructures.

MinF =

∑ k ∈ ΩS

fiPG =

∑

Cksub sk +

∑

CiPMU yi +

i ∈ ΩE

ajiPG (1−t jiPG ) μji +

j ∈ ΩP

fiEG =

∑ j ∈ ΩE

fiPG +

∑

∑

∑

∑

∑ j ∈ ΩE

(22)

(23)

j ∈ ΩP

ajiEG (1−t jiEG ) μji +

Different features of the proposed OJP-NEP model are investigated by testing it on the IEEE 39-bus, 57-bus, 118-bus, and RTS 96 test systems. This method is evaluated against ordinary OJP (without the expansion planning scenario included). The overall specifications of these test systems are shown in Table 1. Since this research work focuses on OJP-NEP and an inclusive expansion plan is not available for these test systems, this paper does not study expansion planning methods and we only assume a suitable expansion plan scenario for these test systems as given in Table 2. In constructing expansion plans in Table 2, existing networks are expanded by adding new load areas as new buses, new branches to connect new loads to the rest of the network, and/or new power plants. This creates another snapshot of examined test systems along with their base case. However, the proposed OJP-NEP method can be run with any other expansion planning scenarios. In simulations, unit costs for substation upgrading, PMU device, and PMU measuring channels are assumed as $40000, $3400, and $2000, respectively [2]. In addition, PMU installation and communication infrastructure costs for extra PMUs with independent PMU accessories in each selected substation are assumed as $20,000 [10]. The independent infrastructure gives higher reliability but at higher cost. In simulations, we considered all transformers with unknown tap setting (tijPG = 1 and tijEG = 1) and with no existing PMU infrastructure for sake of simplicity. All optimizations are implemented and solved using the CPLEX solver of GAMS software package [26], which can be used to solve MILP problems consisting of binary and integer variables. It is noted that binary variables are inherently bounded to {0,1} and integer variables are bounded to integer values in GAMS. CPLEX uses a branch and cut

aijPG (1−tijPG ) uij zj , ∀ i ∈ ΩP .

aijEG (1−tijEG ) uij zj , ∀ i ∈ ΩE .

j ∈ ΩE

Table 1 Number of branches, ZIBs, voltage levels, radial buses, and substations for the considered test systems.

(24)

aijPG (1−tijPG ) uij zj ≥ 2, ∀ i ∈ ΩP . (25)

j ∈ ΩP

fiEG +

Cijch μij .

i, j ∈ ΩE

5. Case studies and numerical experiments

aijEG (1−tijEG ) uij zj ≥ 2, ∀ i ∈ ΩE .

(26) 281

Test system

Branch

ZIB

Voltage level

Radial bus

Substation

IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus

46 78 108 179

12 15 13 10

2 3 3 4

9 1 2 7

36 47 61 107

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Table 2 Assumed expansion planning scenario for the considered test systems. Test system

New substations

New buses

New branches

IEEE 39-bus IEEE 57-bus RTS 96

37, 38, 39 48 49, 50, 51, 52, 53 –

IEEE 118-bus

108, 109, 110, 111, 112, 113, 114, 115

40, 41, 42 58, 59, 60, 61, 62, 63 125, 126, 225, 226, 326, 327 119, 120, 121, 122, 123, 124, 125, 126

20–41, 20–42, 25–40, 26–40, 28–42, 39–41 2–58, 3–61, 6–58, 6–63, 7–61, 10–60, 10–62, 14–58, 16–59, 17–60, 19–59, 21–61, 53–62, 62–63 104–125, 107–126, 116–125, 123–126, 125–126, 205–225, 207–226, 214–225, 220–226, 225–226, 304–326, 307–327, 316–326, 323–327, 326–327 1–123, 8–124, 10–124, 21–125, 22–126, 28–126, 33–123, 44–121, 50–120, 50–121, 53–122, 64–120, 86–119, 102–119, 115–125, 120–122, 123–124, 125–126

Table 3 Comparison the channel-based feature of OJP with a previous work. Method

Parameter

IEEE 14-bus

IEEE 39-bus

IEEE 57-bus

IEEE 118-bus

[14]

# PMUs # Channels EOI # PMUs # Channels EOI

3 13 1.077 3 13 1.077

8 28 1.429 8 27 1.444

11 46 1.326 11 42 1.357

28 115 1.087 28 108 1.093

OJP

Table 6 Comparison of ordinary OJP with the proposed OJP-NEP (unknown transformer taps are modeled).

OJP

Table 4 Comparison of ordinary OJP with the proposed OJP-NEP (unknown transformer taps are not modeled).

OJP

OJP-NEP

Test System

# Subs.

# PMUs

# Ch.

Cost (k$)

IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus

9

9

30

450.6

2

14

14

48

703.6

6

19 31

21 33

66 116

1003.4 1624.2

7 10

8

8

30

407.2

2

11

12

48

596.8

4

18 27

18 29

66 116

913.2 1450.6

4 10

OJP-NEP

# Vicious

Incomplete observability

Test System

# Subs.

# PMUs

# Ch.

Cost (k$)

# Vicious

IEEE 39bus IEEE 57bus RTS 96 IEEE 118-bus IEEE 39bus IEEE 57bus RTS 96 IEEE 118-bus

10

11

30

517.4

0

14

16

48

750.4

0

18 33

20 36

66 116

960.0 1734.4

0 0

8

9

30

430.6

0

11

13

48

620.2

0

18 28

18 31

66 116

913.2 1517.4

0 0

Completely observable

without and with modeling unknown transformer taps. Next, N −1 security constraints including single branch outages and PMU failures are imposed and their effects on the OJP-NEP solution are studied. Then, results of N −2 constraints are presented. 5.1. OJP-NEP in the base case In order to evaluate the channel-based feature of the proposed approach, it is compared with one of channel-based literature works [14] in Table 3. To have a fair criterion for comparison, we define efficiency of observability (EO) as EO = TTO/ ∑i, j ∈ ΩP ψij , where TTO = ∑i ∈ ΩP fiPG is the total times of observability and ∑i, j ∈ ΩP ψij represents total number of measuring channels. The EO is in fact the ability of methods in using PMU measuring channels to achieve a higher observability. As seen in Table 3, while the two methods result in the same number of PMUs, the proposed OJP method has a less number of channels and higher EO index. In Table 4, the results of the proposed OJP-NEP method are compared with the results of ordinary OJP. In this comparison, unknown transformer tap ratios have not been considered for both OJP and OJP-

algorithm to solve MILP problems. The main problem is split into two subproblems that are repeatedly solved using the simplex method. During iterations, non-integer solutions to the LP relaxations serve as upper bounds and integer solutions serve as lower bounds. Upon approaching the difference of upper and lower bounds to the optimality gap, the MILP solution converges. The technical specifications of the computer used for the simulations are 2.6 GHz Intel(R) Core(TM) i53230 CPU with 4 GB of RAM. The case studies will be given in two subsections. First, the OJP-NEP problem is solved in the base case

Table 5 Location of PMUs in the base case (unknown transformer taps are not modeled). Test System OJP

OJP-NEP

Disrupted substations

PMU buses

IEEE 39-bus IEEE 57-bus RTS 96

3, 7, 9, 14, 18, 21, 27, 35, 37. 1, 4, 6, 10, 13, 20, 23, 26, 29, 34, 37, 43, 46, 49. 2, 4, 9, 16, 18, 22, 23, 25, 28, 29, 33, 37, 38, 42, 44, 48, 49, 56, 58.

IEEE 118bus IEEE 39-bus IEEE 57-bus RTS 96

2, 9, 11, 12, 17, 20, 22, 23, 27, 33, 36, 41, 43, 48, 52, 58, 64, 68, 70, 74, 75, 76, 79, 83, 90, 94, 99, 103, 110, 111, 112. 3, 7, 14, 18, 21, 23, 27, 30. 1, 6, 10, 13, 19, 23, 26, 29,34, 36, 46. 1, 4, 7, 9, 16, 18, 22, 25, 27, 33, 38, 40, 42, 48, 49, 52, 53, 60.

IEEE 118bus

1, 10, 11, 12, 17, 20, 23, 27, 33, 36, 41, 43, 46, 49, 52, 58, 64, 68, 70, 74, 75, 79, 83, 90, 94, 99, 104.

3, 8, 10, 16, 20, 23, 29, 37, 40. 1, 4, 6, 10, 13, 20, 25, 29, 32, 38, 41, 51, 54, 59. 102, 109, 110, 119, 121, 125, 202, 203, 205, 208, 210, 216, 220, 221, 302, 308, 309, 310, 319, 321, 326. 2, 9, 11, 12, 17, 20, 22, 23, 28, 34, 37, 42, 45, 49, 52, 56, 62, 71, 75, 77, 80, 85, 86, 87, 90, 94, 101, 105, 110, 114, 121, 122, 123. 3, 8, 16, 20, 23, 25, 29, 32. 1, 6, 10, 13, 19, 25, 29, 32, 38, 49, 54, 56. 101, 104, 107, 110, 119, 121, 202, 205, 207, 216, 221, 223, 302, 308, 310, 315, 316, 323. 1, 10, 11, 12, 17, 20, 23, 28, 34, 37, 42, 45, 49, 50, 53, 56, 62, 71, 75, 77, 80, 85, 86, 90, 94, 101, 105, 110, 115.

282

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Table 7 Location of PMUs in the base case (unknown transformer taps are modeled). Test System OJP

OJP-NEP

IEEE 39bus IEEE 57bus RTS 96

Disrupted substations

PMU buses

1, 3, 5, 14, 18, 21, 27, 32, 35, 37.

1, 3, 4, 6, 16, 20, 23, 29, 34, 37, 40.

1, 4, 6, 10, 13, 20, 23, 26, 29, 34, 36, 43, 46, 49.

1, 4, 6, 10, 13, 20, 25, 26, 29, 32, 38, 49, 51, 54, 56, 59.

2, 7, 9, 13, 18, 20, 22, 27, 28, 29, 36, 38, 41, 42, 48, 53, 55, 60.

IEEE 118bus IEEE 39bus IEEE 57bus RTS 96

2, 9, 11, 12, 17, 20, 22, 23, 27, 33, 35, 39, 41, 42, 48, 52, 58, 59, 65, 68, 70, 72, 75, 76, 78, 81, 85, 89, 94, 99, 103, 111, 112. 3, 5, 8, 14, 18, 21, 23, 27

102, 107, 109, 110, 116, 121, 123, 202, 208, 210, 211, 219, 221, 226, 301, 302, 308, 316, 318, 323. 2, 9, 11, 12, 17, 20, 22, 23, 28, 36, 40, 43, 44, 47, 49, 52, 56, 62, 63, 69, 72, 75, 77, 78, 83, 86, 87, 89, 92, 96, 100, 105, 110, 114, 122, 123. 3, 4, 6, 16, 20, 23, 25, 29, 39.

1, 6, 10, 13, 19, 23, 26, 29, 34, 36, 46.

1, 6, 10, 13, 19, 25, 26, 29, 32, 38, 49, 54, 56.

1, 2, 8, 13, 14, 20, 21, 22, 28, 31, 37, 38, 41, 42, 48, 53, 58, 60.

IEEE 118bus

1, 10, 11, 12, 17, 20, 23, 27, 35, 39, 41, 42, 49, 52, 58, 60, 63, 69, 70, 72, 75, 78, 81, 85, 89, 94, 99, 104.

101, 102, 108, 116, 117, 123, 201, 202, 208, 214, 220, 221, 301, 302, 308, 316, 321, 323. 1, 10, 11, 12, 17, 20, 23, 24, 28, 36, 40, 44, 47, 49, 53, 56, 62, 64, 69, 70, 76, 78, 83, 86, 89, 92, 96, 100, 105, 110, 115.

PMU

13

12

PMU

14

11

10

PMU

11

PMU

9

PMU

PMU

9

PMU

PMU

6

6 PMU PMU

14

13

12

10

5

4

4

7

PMU

1

7

5 1

8

8 3

3 PMU

2

PMU

2 (b)

(a) Legend: PMU Primary PMU, PMU Secondary PMU,

Current measurement of Primary PMU,

Current measurement of Secondary PMU. Fig. 7. Illustration of the proposed approach on the IEEE 14-bus test system. (a): branch outage, (b): PMU failure.

Table 8 OJP-NEP results considering single branch contingencies/single PMU failures (unknown transformer taps are not modeled).

Branch outage

PMU failure

Test System

# Subs.

# PMUs

# Ch.

Cost (k$)

# Vicious

IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus

13 21 27 49 8 16 18 33

13 21 3 51 8+8 16 + 11 18 + 18 33 + 30

39 69 97 174 30 + 30 56 + 40 69 + 63 123 + 109

642.2 1049.4 1436.0 2521.4 654.4 1143.8 1466.4 2598.2

4 8 6 5 1 6 2 1

Incomplete observability

buses are left unobservable as listed in the last column of Table 4. For example, it shows that the IEEE 39-bus test system by the ordinary OJP requires 9 substations to be upgraded as well as 9 PMUs and 30 measuring channels to be installed with total cost of $450.6 k (k stands for 1000). However, there are 2 vicious measurements because of ignoring indeterminacy of transformer tap ratios. In Table 6, the OJP/OJP-NEP performances are reported by taking into account transformer unknown

NEP. The location of PMUs is also reported in Table 5. In columns 2–6 of Table 4, the number of disrupted substations, PMUs, measuring channels, total cost, and vicious measurements are reported, respectively. The number of measuring channels is computed by summing up assigned channels by individual PMUs across the network. As seen, all cases of Table 4 are unobservable since transformer unknown taps do not let calculate voltage phasor of some buses and consequently, some 283

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Table 9 OJP-NEP results considering single branch contingencies/single PMU failures (unknown transformer taps are modeled).

Branch outage

PMU failure

Test System

# Subs.

# PMUs

# Ch.

Cost (k$)

# Vicious

IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus

14 24 29 49 9 17 18 33

15 26 35 53 9+9 17 + 10 18 + 18 33 + 30

38 67 97 173 30 + 30 60 + 36 66 + 66 124 + 108

707.0 1222.4 1593.0 2566.2 721.2 1163.8 1466.4 2598.2

0 0 0 0 0 0 0 0

Completely observable

Table 10 Disrupted substations and PMU locations for OJP-NEP considering N −1 security (unknown transformer taps are not modeled). Test System Branch outage

IEEE 39bus IEEE 57bus RTS 96

IEEE 118bus PMU failure

IEEE 39bus IEEE 57bus RTS 96

IEEE 118bus

Disrupted substations

PMU buses

3, 6, 8, 11, 14, 16, 18, 20, 21, 23, 24, 27, 39.

4, 7, 12, 16, 18, 20, 22, 23, 25, 26, 29, 39, 42.

2, 5, 8, 10, 14, 15, 16, 17, 19, 23, 24, 26, 28, 29, 34, 36, 37, 43, 45, 47, 53.

2, 5, 8, 10, 14, 15, 16, 17, 19, 25, 27, 29, 31, 32, 38, 41, 50, 53, 55, 56, 63. 101, 102, 107, 109, 110, 116, 118, 120, 121, 125, 202, 205, 207, 209, 210, 214, 216, 220, 221, 222, 223, 301, 302, 307, 309, 310, 316, 320, 321, 326. 1, 6, 10, 11, 12, 15, 17, 19, 21, 22, 25, 28, 29, 32, 34, 35, 39, 41, 44, 46, 49, 50, 51, 53, 56, 59, 62, 66, 70, 72, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 100, 102, 105, 107, 108, 110, 115, 120, 124. 8, 8, 10, 10, 16, 16, 18, 18, 20, 20, 23, 23, 25, 25, 29, 29.

1, 2, 4, 7, 9, 13, 15, 17, 18, 22, 25, 27, 29, 31, 33, 37, 38, 39, 40, 41, 42, 44, 47, 49, 53, 57, 58. 1, 6, 10, 11, 12, 15, 17, 19, 21, 22, 24, 27, 28, 31, 33, 34, 38, 40, 41, 42, 44, 46, 47, 49, 52, 55, 58, 61, 63, 65, 68, 69, 70, 73, 75, 77, 79, 81, 83, 85, 89, 91, 94, 96, 97, 99, 104, 109, 113. 7, 9, 14, 16, 18, 21, 23, 27. 1, 6, 9, 10, 13, 19, 24, 27, 29, 30, 31, 34, 37, 41, 43, 45. 1, 2, 8, 13, 14, 20, 21, 22, 28, 31, 37, 38, 41, 42, 48, 53, 55, 60.

1, 8, 11, 12, 17, 20, 22, 23, 26, 27, 35, 39, 42, 44, 46, 49, 51, 54, 58, 63, 64, 69, 71, 73, 75, 78, 81, 85, 89, 94, 99, 104, 105.

1, 1, 6, 6, 9, 9, 10, 10, 19, 19, 27, 27, 30, 30, 32, 33, 35, 38, 38, 41, 41, 47, 47, 49, 50, 53, 53. 101, 101, 102, 102, 108, 108, 116, 116, 117, 117, 123, 123, 201, 201, 202, 202, 208, 208, 214, 214, 220, 220, 221, 221, 301, 301, 302, 302, 308, 308, 316, 316, 318, 318, 323, 323. 1, 1, 8, 8, 11, 11, 12, 12, 17, 17, 20, 20, 22, 23, 27, 28, 28, 36, 36, 40, 40, 44, 44, 46, 46, 50, 50, 53, 53, 55, 55, 58, 58, 62, 62, 70, 70, 71, 71, 76, 76, 79, 79, 83, 84, 84, 86, 89, 89, 92, 92, 96, 96, 100, 100, 105, 105, 110, 110, 115, 115, 116, 116.

Table 11 Disrupted substations and PMU locations for OJP-NEP considering N −1 security (unknown transformer taps are modeled). Test System Branch outage

PMU failure

IEEE 39bus IEEE 57bus RTS 96

Disrupted substations

PMU buses

3, 6, 8, 11, 13, 14, 18, 20, 21, 23, 24, 25, 27, 39.

3, 4, 7, 12, 15, 16, 20, 22, 23, 25, 26, 27, 29, 39, 42.

1, 3, 6, 12, 14, 18, 20, 22, 23, 24, 26, 27, 29, 35, 38, 39, 40, 41, 43, 45, 47, 49, 50, 53. 1, 2, 4, 7, 9, 13, 15, 16, 18, 20, 21, 22, 25, 27, 29, 33, 35, 37, 38, 40, 41, 42, 44, 47, 49, 53, 56, 58, 60.

1, 3, 6, 12, 14, 18, 20, 23, 25, 27, 29, 30, 32, 34, 42, 43, 44, 47, 50, 51, 53, 55, 57, 59, 60, 63. 101, 102, 107, 109, 110, 111, 116, 118, 119, 121, 123, 125, 201, 202, 207, 209, 210, 211, 216, 218, 220, 221, 223, 225, 301, 302, 307, 309, 310, 311, 316, 319, 321, 323, 326. 1, 6, 10, 11, 12, 15, 17, 19, 21, 22, 25, 28, 29, 32, 36, 37, 40, 42, 43, 44, 46, 49, 50, 51, 53, 56, 59, 62, 66, 69, 70, 72, 75, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 100, 102, 104, 107, 108, 110, 115, 122, 123. 2, 2, 6, 6, 13, 13, 16, 16, 18, 18, 20, 20, 23, 23, 25, 25, 29, 29.

IEEE 118bus

1, 6, 10, 11, 12, 15, 17, 19, 21, 22, 24, 27, 28, 31, 33, 35, 36, 39, 41, 42, 44, 46, 47, 49, 52, 55, 58, 61, 63, 65, 68, 69, 70, 73, 75, 77, 79, 81, 83, 85, 89, 91, 93, 96, 97, 99, 104, 111, 112.

IEEE 39bus IEEE 57bus RTS 96

2, 5, 12, 14, 16, 18, 21, 23, 27.

IEEE 118bus

1, 8, 11, 12, 17, 20, 22, 23, 26, 27, 35, 39, 42, 44, 46, 49, 54, 55, 61, 63, 66, 69, 71, 72, 75, 78, 81, 85, 89, 94, 99, 104, 105.

1, 6, 9, 10, 13, 14, 15, 19, 25, 27, 30, 34, 35, 36, 37, 43, 45. 1, 2, 8, 13, 14, 20, 21, 22, 28, 31, 37, 38, 41, 42, 48, 53, 55, 60

1, 1, 6, 6, 9, 9, 10, 10, 14, 15, 19, 19, 28, 28, 30, 30, 33, 33, 38, 38, 41, 49, 50, 53, 53, 56, 57. 101, 101, 102, 102, 108, 108, 116, 116, 117, 117, 123, 123, 201, 201, 202, 202, 208, 208, 214, 214, 220, 220, 221, 221, 301, 301, 302, 302, 308, 308, 316, 316, 318, 318, 323, 323. 1, 1, 8, 8, 11, 11, 12, 12, 17, 17, 20, 20, 22, 23, 27, 28, 28, 36, 36, 40, 40, 44, 44, 46, 46, 50, 50, 53, 53, 58, 58, 59, 59, 66, 66, 70, 70, 73, 73, 76, 76, 79, 79, 83, 83, 86, 86, 89, 89, 92, 92, 96, 96, 100, 100, 105, 105, 110, 110, 115, 115, 116, 116.

In addition, both Tables 4 and 6 illustrate higher effectiveness of the proposed OJP-NEP than ordinary OJP. From Table 4, it is seen that with a lower number of upgraded substations and a lower number of installed PMUs, the proposed OJP-NEP leads to equal/fewer vicious measurements than ordinary OJP for all test systems. Table 6 shows that while both OJP-NEP and ordinary OJP provide full observability,

taps and the location of PMUs are shown in Table 7. There is no unobserved bus in this case (the last column in Table 6 is all zero). The comparison between Tables 4 and 6 shows that although modeling unknown transformer taps increases WAMS costs a bit, it provides complete observability which is required by the WAMS applications, such as state estimation. 284

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PMUs, the OJP-NEP offers a better solution because the OJP-NEP requires 33−28 = 5 less substation disruptions, 36−31 = 5 less PMUs, and 12.5% less total installation cost. The reason for higher effectiveness of the proposed OJP-NEP than ordinary OJP can be explained as follows. Ordinary OJP optimizes PMU placement for the present network and then adds further PMUs to make observable the extended network. However, the proposed OJP-NEP simultaneously optimizes PMU placement for both present and extended networks, and thus can obtain a more optimal solution.

Table 12 Number of PMUs obtained by the proposed method and previous methods in the cases of branch outage and PMU failure (without modeling network expansion planning and unknown transformer taps). Case

Method

IEEE 39-bus

IEEE 57-bus

RTS 96

IEEE 118-bus

Branch outage

[9,27] Proposed [9,19,27] [21,28] [15,29,30] [31] [32] [33] [34] Proposed

– 12 18 – 17 18 17 – – 16

18 18 26 22 22 26 25 25 29 22

– 27 – – – – – – – 32

50 49 63 61 61 64 61 61 64 56

PMU failure

5.2. OJP-NEP imposed by N −1 security constraints In this subsection, the proposed OJP-NEP is implemented on the test systems considering N −1 security constraints of branch outages and PMU failures. In order to examine the performance of the proposed approach in more details, its results are presented graphically on the simple IEEE 14 test system in Fig. 7. In case of branch outage in Fig. 7(a), the proposed approach makes observable the system with 7 PMUs such as previous works [9]. However, the proposed method needs 19 measuring channels compared with [9] that needs 26 measuring channels. Also, Fig. 7(b) presents the case of PMU failure, where the proposed method needs 6 PMUs which is more economical than 7 PMUs of [9]. In addition, it needs 31 measuring channels against [9] that needs 33 measuring channels. Consequently, the proposed method offers more economical solutions because of using more efficient concepts of backup and secondary PMUs. The obtained results without/with modeling unknown transformer tap ratios for the examined four systems are shown in Tables 8 and 9, respectively. The number of PMUs/measuring channels in these tables for the PMU failure case is reported as x + y , where x and y are the number of primary and secondary PMUs/channels, respectively. As expected, a robust WAMS against single branch outage or PMU failure requires more disrupted substations, PMUs, and measuring channels than the case ignoring security constraints. Moreover, in comparison with branch outage, PMU failure has more unfavorable effect on the system observability, which can be concluded from the obtained number of PMUs and measuring channels in the relevant cases. Similar to previous tables, it is seen that the OJP-NEP computation times reported in Tables 8 and 9 are very low. In order to present more detailed results for the case of Table 8, the disrupted substations and PMU buses are reported in Table 10 for this case. Similarly, the detailed results are also provided in Table 11 for the case of Table 9. The difference of Tables 10 and 11 is in the modeling of unknown transformer tap ratios. As seen, considering transformers with unknown taps alters disrupted substations and location of PMUs. In fact, results of Table 11 are more realistic compared with Table 10 due to modeling unknown transformer tap ratios.

Table 13 Comparison of execution times (in seconds) elapsed by the proposed and previous methods. Case

Method

IEEE 14-bus

IEEE 57-bus

IEEE 118-bus

Branch outage

[21] [28] [30] Proposed [21] [28] [30] Proposed

0.1 0.130 <1 0.095 0.072 0.093 <1 0.081

0.671 0.530 3.240 0.308 0.392 0.310 <1 0.280

0.913 0.810 1.48 0.587 0.622 0.590 <1 0.411

PMU failure

Table 14 OJP-NEP results with combined contingencies as N −2 security constraints. Test System

# Subs.

# PMUs

# Ch.

Cost (k$)

Observability

IEEE 39-bus IEEE 57-bus RTS 96 IEEE 118-bus

14 24 29 49

30 52 70 106

76 134 194 346

1134.0 1964.8 2606.0 4152.4

Complete Complete Complete Complete

the proposed OJP-NEP requires fewer substation disruptions and fewer PMU installations than ordinary OJP in all test systems. As seen in Table 6, referring to the IEEE 118-bus test system for example, OJP-NEP requires that 28 substations are disrupted for installation of 31 PMUs (some substations have more than one PMU installation) with total cost of $1517.4k. However, in case of OJP, 33 substations should be disrupted and 36 PMUs are needed at the cost of $1734.4k. Since the cost of substation disruption is considerable in addition to the number of

Table 15 Disrupted substations and PMU locations for OJP-NEP considering N −2 security constraints (unknown transformer taps are modeled). Test System

Disrupted substations

PMU buses

IEEE 39-bus

3, 6, 8, 11, 13, 14, 18, 20, 21, 23, 24, 25, 27, 39.

IEEE 57-bus

1, 3, 6, 12, 14, 18, 20, 22, 23, 24, 26, 27, 29, 35, 38, 39, 40, 41, 43, 45, 47, 49, 50, 53.

RTS 96

1, 2, 4, 7, 9, 13, 15, 16, 18, 20, 21, 22, 25, 27, 29, 33, 35, 37, 38, 40, 41, 42, 44, 47, 49, 53, 56, 58, 60.

IEEE 118bus

1, 6, 10, 11, 12, 15, 17, 19, 21, 22, 24, 27, 28, 31, 33, 35, 36, 39, 41, 42, 44, 46, 47, 49, 52, 55, 58, 61, 63, 65, 68, 69, 70, 73, 75, 77, 79, 81, 83, 85, 89, 91, 93, 96, 97, 99, 104, 111, 112.

3, 3, 4, 4, 7, 7, 12, 12, 15, 15, 16, 16, 20, 20, 22, 22, 23, 23, 25, 25, 26, 26, 27, 27, 29, 29, 39, 39, 42, 42. 1, 1, 3, 3, 6, 6, 12, 12, 14, 14, 18, 18, 20, 20, 23, 23, 25, 25, 27, 27, 29, 29, 30, 30, 32, 32, 34, 34, 42, 42, 43, 43, 44, 44, 47, 47, 50, 50, 51, 51, 53, 53, 55, 55, 57, 57, 59, 59, 60, 60, 63, 63. 101, 101, 102, 102, 107, 107, 109, 109, 110, 110, 111, 111, 116, 116, 118, 118, 119, 119, 121, 121, 123, 123, 125, 125, 201, 201, 202, 202, 207, 207, 209, 209, 210, 210, 211, 211, 216, 216, 218, 218, 220, 220, 221, 221, 223, 223, 225, 225, 301, 301, 302, 302, 307, 307, 309, 309, 310, 310, 311, 311, 316, 316, 319, 319, 321, 321, 323, 323, 326, 326. 1, 1, 6, 6, 10, 10, 11, 11, 12, 12, 15, 15, 17, 17, 19, 19, 21, 21, 22, 22, 25, 25, 28, 28, 29, 29, 32, 32, 36, 36, 37, 37, 40, 40, 42, 42, 43, 43, 44, 44, 46, 46, 49, 49, 50, 50, 51, 51, 53, 53, 56, 56, 59, 59, 62, 62, 66, 66, 69, 69, 70, 70, 72, 72, 75, 75, 76, 76, 78, 78, 80, 80, 82, 82, 84, 84, 86, 86, 88, 88, 90, 90, 92, 92, 94, 94, 96, 96, 100, 100, 102, 102, 104, 104, 107, 107, 108, 108, 110, 110, 115, 115, 122, 122, 123, 123.

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contingent cases of PMU failure (e.g., 1 less PMU in the IEEE 118-bus test system) and branch outage (e.g., 5 less PMUs in the IEEE 118-bus test system) compared with existing methods, and d) the execution times of the proposed method are in orders of seconds making it tractable for large-scale real-world power systems. The current work can be extended to include uncertainty evaluation by stochastic programming/robust optimization, substation reliability enhancement, and optimization of renewable energy penetration level in a marketbased framework.

Since the hybrid and backup approaches are used in this paper to model PMU failure and branch outage, respectively, and these approaches are pretty different from other methods in the literature, in order to evaluate the performance of the hybrid and backup approaches, their results are compared with the results of several other methods as shown in Table 12. Since the previously published methods, as considered for comparison in Table 12, are based on simpler models without considering network expansion planning and transformer unknown taps, the same conditions of these methods have been also applied for the proposed method in the numerical test of Table 12 for the sake of a fair comparison. The comparison between the results in both branch outage and PMU failure cases reveals higher effectiveness of the proposed method than all comparative methods in Table 12. For instance, in the case of PMU failure in the IEEE 118-bus test system, full observability is attained by the best and worst previous methods with 61−56 = 5 and 64−56 = 8 more PMUs than the proposed method, respectively. Also, in the case of branch outage, the IEEE 118-bus test system becomes observable by 49 PMUs using the proposed method, while the previous ones require 50 PMUs. The reason why the proposed method outperforms previous ones in case of branch outage lies in the fact that it excludes some buses from duplicate observability as formulated by (18) and (19); such buses remain observable with one observability even in case of branch outages. In case of PMU failure, the reason why the proposed method outperforms previous methodologies is that it uses a novel secondary PMU concept to make observable all buses. For instance, in the IEEE 118-bus test system, it locates 28 primary PMUs in the base case and 28 secondary PMUs. However, other methods need higher number of PMUs because they place PMUs at new buses. In Table 13, the execution time elapsed by the proposed method is compared with some previous methods. As seen, the proposed method offers a faster solution due to its efficient linear modeling than previous methods.

Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijepes.2018.10.010. References [1] Yu JJQ, Lam AYS, Hill DJ, Li VOK. A unified framework for wide area measurement system planning. Int J Electr Power Energy Syst 2018;96:43–51. https://doi.org/10. 1016/J.IJEPES.2017.09.032. [2] Pal A, Vullikanti AKS, Ravi SS. A PMU placement scheme considering realistic costs and modern trends in relaying. IEEE Trans Power Syst 2017;32:552–61. https://doi. org/10.1109/TPWRS.2016.2551320. [3] Pal A, Jones KD, Mishra C, Centeno VA. Binary particle swarm optimisation-based optimal substation coverage algorithm for phasor measurement unit installations in practical systems. IET Gener Transm Distrib 2016;10:555–62. https://doi.org/10. 1049/iet-gtd.2015.1077. [4] Khorram E, Taleshian Jelodar M. PMU placement considering various arrangements of lines connections at complex buses. Int J Electr Power Energy Syst 2018;94:97–103. https://doi.org/10.1016/J.IJEPES.2017.06.028. [5] Rather ZH, Chen Z, Thogersen P, Lund P, Kirby B. Realistic approach for phasor measurement unit placement: consideration of practical hidden costs. IEEE Trans Power Deliv 2015;30:3–15. https://doi.org/10.1109/TPWRD.2014.2335059. [6] U.S. Department of Energy Office of Electricity Delivery and Energy Reliability (DOE-OE). Factors Affecting PMU Installation Costs; 2014. [7] Aminifar F, Fotuhi-Firuzabad M, Shahidehpour M, Khodaei A. Probabilistic multistage PMU placement in electric power systems. IEEE Trans Power Deliv 2011;26:841–9. https://doi.org/10.1109/TPWRD.2010.2090907. [8] Gomez O, Rios MA. ILP-based multistage placement of PMUs with dynamic monitoring constraints. Int J Electr Power Energy Syst 2013;53:95–105. https://doi.org/ 10.1016/j.ijepes.2013.03.038. [9] Esmaili M, Gharani K, Shayanfar HA. Redundant observability PMU placement in the presence of flow measurements considering contingencies. IEEE Trans Power Syst 2013;28:3765–73. https://doi.org/10.1109/TPWRS.2013.2257883. [10] Aminifar F, Fotuhi-Firuzabad M, Safdarian A, Shahidehpour M. Observability of hybrid AC/DC power systems with variable-cost PMUs. IEEE Trans Power Deliv 2014;29:345–52. https://doi.org/10.1109/TPWRD.2013.2264022. [11] Abiri E, Rashidi F, Niknam T. An optimal PMU placement method for power system observability under various contingencies. Int Trans Electr Energy Syst 2015;25:589–606. https://doi.org/10.1002/etep.1848. [12] Manousakis NM, Korres GN. Optimal PMU placement for numerical observability considering fixed channel capacity-a semidefinite programming approach. IEEE Trans Power Syst 2016;31:3328–9. https://doi.org/10.1109/TPWRS.2015. 2490599. [13] Manousakis N, Korres G. Optimal allocation of PMUs in the presence of conventional measurements considering contingencies. IEEE Trans Power Deliv 2017:1. https://doi.org/10.1109/TPWRD.2016.2524658. [14] Mouwafi MT, El-Sehiemy RA, Abou El-Ela AA, Kinawy AM. Optimal placement of phasor measurement units with minimum availability of measuring channels in smart power systems. Electr Power Syst Res 2016;141:421–31. https://doi.org/10. 1016/J.EPSR.2016.07.029. [15] Azizi S, Gharehpetian GB, Dobakhshari AS. Optimal integration of phasor measurement units in power systems considering conventional measurements. IEEE Trans Smart Grid 2013;4:1113–21. https://doi.org/10.1109/TSG.2012.2213279. [16] Esmaili M, Ghamsari-Yazdel M. Voltage stability-constrained optimal simultaneous placement of PMUs and channels enhancing measurement reliability and redundancy. IEEE Power Energy Technol Syst J 2017;4:32–9. https://doi.org/10. 1109/JPETS.2017.2688020. [17] Aghaei J, Baharvandi A, Rabiee A, Akbari MA. Probabilistic PMU placement in electric power networks: an MILP-based multiobjective model. IEEE Trans Ind Informatics 2015;11:332–41. https://doi.org/10.1109/TII.2015.2389613. [18] Zhu S, Wu L, Mousavian S, Roh JH. An optimal joint placement of PMUs and flow measurements for ensuring power system observability under N-2 transmission contingencies. Int J Electr Power Energy Syst 2018;95:254–65. https://doi.org/10. 1016/J.IJEPES.2017.08.025. [19] Aminifar F, Khodaei A, Fotuhi-Firuzabad M, Shahidehpour M. Contingency-constrained PMU placement in power networks. IEEE Trans Power Syst 2010;25:516–23. https://doi.org/10.1109/TPWRS.2009.2036470. [20] Ghamsari-Yazdel M, Esmaili M. Reliability-based probabilistic optimal joint placement of PMUs and flow measurements. Int J Electr Power Energy Syst

5.3. OJP-NEP in the case of contingency combinations as N −2 security constraints In order to assess robustness of the proposed method, it is also solved with the combined contingencies of branch outage and PMU failure (as N −2 security constraints) and results are presented in Tables 14 and 15. These results are obtained by considering unknown transformer taps. As shown in the tables, with due attention to the N −2 security criterion, the complete observability of the test systems is obtained but by a higher number of PMUs and channels (including primary and secondary) in comparison with previous security cases. For instance, the complete observability of the IEEE 39-bus test system is obtained by approximately 38% and 36% higher total costs in comparison with single branch outage and single PMU failure cases (N −1 security criterion), respectively. 6. Conclusions In this paper, an integrated framework called OJP-NEP is introduced to model power system expansion and transformer unknown tap settings in the optimal WAMS design. The proposed substation-based OJPNEP is formulated as an MILP optimization problem to minimize the cost of substation disruptions, PMUs, and measuring channels with ensuring the observability of the present and expanded grids. Key findings of this paper are (a) WAMS design with simultaneous consideration of base case and network expansion (OJP-NEP) offers a more cost-effective solution compared to individual design of the network in two stages (e.g., 5 less substation disruptions, 5 less PMUs, and 12.5% lower cost in the IEEE 118-bus test system), (b) modeling unknown taps of transformers increases cost of WAMS a bit (e.g., 1 more substation disruption and 2 more PMUs in the IEEE 118-bus test system), but it gives a more realistic solution avoiding unobservability, (c) the proposed concept of hybrid modified backup channels offers a lower cost in 286

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