Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability

+Model JESIT 180 1–18

ARTICLE IN PRESS Available online at www.sciencedirect.com

ScienceDirect Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability

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Pushpendra Singh a,∗ , L.S. Titare b , S.C. Choube c , L.D. Arya d

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Department of Electrical Engg., Rajkiya Engineering College, Banda, UP 210201, India Department of Electrical Engg., Govt. Engineering College, Jabalpur, MP 482 011, India c Department of Electrical & Elex., UIT-RGPV, Bhopal, MP 462036, India d Department of Electrical Engg., SGSITS, 23-Park Road, Indore, MP 453331, India

Received 24 March 2016; received in revised form 22 October 2017; accepted 27 October 2017

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Abstract

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This paper presents a new algorithm for voltage stability security assessment accounting uncertainties in the line parameters and control variables. Security index has been evaluated using Monte-Carlo simulation with & without consideration of unavailability of transmission lines, which is used to perform contingency selection. Further, probabilistic insecurity index at various loading conditions considering voltage stability limit has been obtained using cut-set method for single & double line outages. Static voltage stability limit for various sampled values of system parameters and control variables have been obtained using continuation power flow methodology. Few cases have been used to train back propagation algorithm (BPA). Obtained results for contingency selection based on security index have been compared with well-established methods. © 2018 Electronics Research Institute (ERI). Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Keywords: Contingency ranking; Probabilistic insecurity index; Artificial neural network; Back propagation algorithm

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1. Introduction

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The monitoring and analysis of power system security has become an integral part of modern energy management systems (EMS), but its real time implementation is still a challenging task to power system engineers. For secure

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∗

Corresponding author. E-mail addresses: [email protected] (P. Singh), [email protected] (L.S. Titare), [email protected] (S.C. Choube), [email protected] (L.D. Arya). Peer review under the responsibility of Electronics Research Institute (ERI).

https://doi.org/10.1016/j.jesit.2017.10.002 2314-7172/© 2018 Electronics Research Institute (ERI). Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Nomenclature pf Probability of failure C1 , C2 , . . ., Cn Minimal cut-sets P, Q Real & reactive power flow P gk , Qgk Lower bound on active & reactive power generation at kth bus ¯ gk Upper bound on active & reactive power generation at kth bus P¯ gk , Q o Pgk , Qogk Active & reactive power generation at kth bus under current operating condition p p P gk , Qgk Active & reactive power generation at kth bus under predicted load condition V oi Load bus voltage at ith load bus under current operating condition p Load bus voltage at ith load bus under predicted load condition Vi ¯ V i , Vi Lower and upper bound on ith load bus voltage Number of generator buses NG Number of buses NB NL Number of transmission lines pˆ Security index without consideration of unavailability of transmission line SI Security index with consideration of unavailability of transmission line Load flow Jacobian J Y Output of the network R Line resistance Line reactance X Bc Line charging susceptance RT Total line resistance Total line reactance XT BcT Total line charging susceptance Sd Total system load (real & reactive power)

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operation of power system, the operating personnel must know which system disturbances or contingencies may cause limit violations and force the system to enter into the emergency state. Security assessment provides information to the system operators about the secure and insecure nature of the operating states in the event of an unforeseen contingency, so that proper control/corrective action can be initiated within the safe time limit. Due to time limitation in real time situations, it is not feasible to carryout detailed analysis of all the possible contingencies. Hence, contingency selection is performed to pick out those contingencies that are potentially harmful to the system and the probability of their occurrence, in order to reduce the number of contingencies. Two popularly used methods for contingency selection are ranking methods and screening methods. Ranking methods involve ranking of contingencies in approximate order of severity which is based on the value of performance index. Performance indices are explicitly expressed in terms of network variables and are directly evaluated. Screening methods use approximate network solutions such as distribution factors, DC load flow, linearised load flow, AC load flow, local solution methods etc. to identify cases causing limit violations (Ejbe et al., 1996; Naik et al., 2015). Contingency evaluation is one of the most important tasks encountered by planning and operation engineers of power systems. In planning, contingency analysis is used to examine the performance of a power system and the need for new transmission expansion due to load growth or generation expansion. The operation contingency analysis assists engineers to operate the power system at a secure operating point where equipments are loaded within safe limits and power is delivered to customers with acceptable quality standard. The purpose of contingency screening and ranking is to determine which contingencies may cause power system limit violations and/or system instability according to voltage stability criteria. The margin between the voltage collapse point and the current operating point is used as the voltage stability criterion. Several PI-based methods have been suggested and tested for voltage security analysis (Ejbe et al., 1996; Naik et al., 2015; EL-Abiad and Stagg, 1962; Bavghman and Schweppe, 1970; Ejebe and Wollenberg, 1979; Stott et al., 1987; Suzuki et al., 1992; Jasman and Lee, 1993; Moghavvemi and Omar, 1998; Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Schlueter, 1998; Greene et al., 1999; Vaahedi et al., 1999). Salama et al. (2001) developed a methodology for estimating the voltage collapse proximity indicator using artificial neural network. Choube et al. (2001) presented an algorithm for contingency selection based on singular value decomposition (SVD). Pandit et al. (2001) described contingency ranking for voltage collapse using parallel self-organizing hierarchical neural network. Arya et al. (2002) developed an algorithm for contingency selection based on vanishing eigenvalue concept. Amjady and Esmaili (2003) described a technique to evaluate voltage stability status efficiently in present as well as post contingency state. Ni et al. (2003) presented a technique for on-line security assessment using indices based on probabilistic risk for use by operators in the control room. Dey et al. (2004) developed a global voltage security indicator of an interconnected power system which voltage can ascertain stability for any variation of load for longitudinal power supply system (LPS). Kim and Singh (2005) developed technique for power system security assessment based on Bayes classifier. Verma and Shrivastava (2005) described an efficient algorithm for formulation of voltage control area considering impact of contingencies. The developed algorithm accounts the effect of P-V and Q-␦ coupling and network topology changes. Li Zarate et al. (2006) and Li Zarate and Castro (2006) developed fast computation of voltage stability security margins to voltage collapse based on sensitivity analysis and using non-linear programming techniques. Arya et al. (2006, 2007) presented techniques to assess probabilistic risk of voltage collapse and preventive control of voltage security margin using ANN. Srivani and Swarup (2008) presented a technique for static security assessment using ward network. Berizzi et al. (2009) presented a technique for on-line assessment of the voltage security at current operating point using Fuzzy logic. Bahmanyar and Karami (2014) presented a technique for on-line monitoring of a voltage stability margin (VSM) based on artificial neural network (ANN). Lee et al. (2010) developed a new index ‘area of the voltage stability region’ which provides useful information about contingency screening and ranking and load shedding. An artificial neural network (ANN) is being used in voltage stability analysis due to its ability to do parallel data processing with high accuracy and fast response. Kamalasadan et al. (2009) proposed a feed forward neural network under various training functions for on-line voltage stability assessment and monitoring. In recent years, research endeavors in the area of security assessment have been directed towards artificial neural network (Javan et al., 2013). Most utilities use deterministic criteria in the planning and design of power systems. The main disadvantage of deterministic criteria is that they do not recognize and reflect the inherent random nature of the site resources, the system behavior and the customer demands etc. Probabilistic techniques can be used to overcome this drawback and incorporate the inherent uncertainty in these factors. Power system planners and designers sometimes experience difficulties in interpreting and using probabilistic reliability indices. This difficulty can be alleviated by incorporating deterministic considerations into a probabilistic evaluation using the well-being concept. In this paper, a new algorithm has been developed for security assessment accounting uncertainties in the line parameters and control variables of the system. The proposed algorithm consists of two parts; one of it calculates the security index with & without consideration of unavailability of transmission line using Monte-Carlo simulation then ranked lines with the highest value of security index. Second part, evaluates probabilistic insecurity index (PISI) using cut-set method, considering single and double line outages. Voltage stability limits have been calculated using continuation power flows in each single and double line outage condition. The PISI have been obtained for various single and double line outages at various loading conditions, using these results a multi-layer ANN has been trained to obtain PISI for any operating conditions. Application of ANN makes it suitable for on-line applications.

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2. Problem formulation

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System parameters & control variables exhibit uncertainties in real time operation and in fact, these are random variables. Computed values of transmission line parameters usually contain various inaccuracies. Mainly errors arise owing to (i) mathematical approximations used in calculation namely truncation of Taylor series expansion (ii) simplified modeling assumptions namely; flat earth, completely transposed lines and roundness of conductor etc. (iii) occasional gross human errors due to manual data handling at the initial input phase (iv) weather effects that modify conductors’ temperature, causing different level of sagging (v) frequency variation. Studies have concluded these errors may vary in the range 5–10%. Further, in case of human data input errors, the resulting parameter errors can be much larger. Few percentage errors may be quite tolerable in the area of system planning where there are inaccuracies in all the data used. Moreover, the system can always be designed to have sufficiently low probability of voltage collapse and large stability margin so that worst effect of parameter uncertainty can be accounted for. Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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The probability of failure accounting uncertainties in the line parameters & control variable is mentioned as follows: ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ n ⎥ n,m ⎢ pf = ⎢ P(Ci ) − P((Ci ) ∗ (Pj ))⎥ ⎥ i = 1 ⎢ i=1 ⎥ ⎣ ⎦ j=2 i= / j

(1)

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Above objective function is calculated subject to following constraints under base case condition as well as next predicted loading condition accounting uncertainties in the line parameters and control variables:

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(i) Power flow constraints:

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P = f (V , δ) Q = g(V , δ)

(2)

(ii) Reactive power generation constraint: Qg k ≤ Qg ok ≤ Qg k

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p

Qgk ≤ Qg k ≤ Qg k

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p

P gk ≤ Pg k ≤ Pg k

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k = 1, 2, . . ., NG

(4)

(iv) Load bus voltages constraint: V i ≤ Vio ≤ V i

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(3)

(iii) Active power generation constraint: P g k ≤ Pg ok ≤ Pg k

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k = 1, 2, . . ., NG

p

V i ≤ Vi ≤ V i

i = (NG + 1), . . .. . .. . ., NB

(5)

3. Evaluation of security index with & without consideration of unavailability of transmission line using Monte-Carlo simulation Line resistances, reactances, line charging susceptances, and voltages of PV-buses are random variables. Static voltage stability limit for sampled values of parameters/variables is calculated using continuation power flow technique. This in turn is a random variable. Monte-Carlo simulation is implemented in the following steps: Step-1: Obtain sample vector z ∈ Z from respective probability density functions. ‘Z’ vector contains line resistances, reactances, line charging susceptances and PV-bus voltages at constant power factor of loads. Step-2: Repeat step-1 for large number of times say ‘N’. Step-3: Select transmission line outage i = 1, where, i = 1, 2, 3, . . ., NL. Step-4: Obtain static voltage stability limit for each sampled state ‘Z’ using continuation power flow technique (Ajjarapu and Christy, 1992). Step-5: In Step-4 one has in all ‘N’ static voltage stability limits. For various load levels, obtain value of X(Zj ) for j = 1, 2, 3, . . ., N indicating voltage collapse or otherwise i.e. X(Zj ) = 1, if for this sampled state nominal load level (Sd ) exceeds static voltage stability limit. = 0, Otherwise. Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Down state

Fig. 1. Two state model for each transmission line.

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Step-6: Estimate security index without consideration of unavailability of transmission line pˆ as follows: pˆ j = [

N 

X(Zj )]/N

(6)

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Step-7: Estimate security index with consideration of unavailability of transmission line SI as follows: ¯j SIj = pˆ j ∗ A

Step-8: Obtain estimates pˆ j and SIj for various line outage conditions repeating from step-5 onwards. Step-9: Step-1 to Step-8 is repeated for ‘N’ times. It is clear that using Step-1–Step-9 large number of sample can be generated, which are used to rank the transmission line. A two-state model (up state and down state) is used to model the operation of each transmission line. The up state indicates that the transmission line is in operating state and down state implies that the element is inoperable due to a failure or scheduled off. Fig. 1 shows the two-state model. Fig. 1 shows the, λj and μj are failure and repair rates of transmission line respectively. This model is used to provide availability and unavailability of transmission line in long run. Expressions for these are given as follows (Rubinstein, 1981): Aj = μj /(λj + μj )

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Aj = λj /(λj + μj )

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Aj and Aj denote respectively availability and unavailability of transmission line.

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4. Cut-set method and evaluation of probabilistic insecurity index (PISI)

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(7)

(8)

The cut-set method is a powerful technique for determining the reliability of a power network. The method can be easily programmed on a digital computer for fast and efficient solution of any general network. Moreover, cut-sets are directly related to the modes of system failure and therefore identify the distinct and discrete ways in which a system may fail. In identifying cut-set, one identifies the most important line or combination of lines, which are of greatest importance. A minimal cut-set is a set of transmission line which when failed, causes failure of the system but when any one element of the set has not failed, does not cause system failure. All components of a minimal cut-set must be in the failure state to cause system failure. Failure probability of a power network can be written as follows: pf = [P(C1 + C2 + . . ., +Cn ) − P(C1 C2 + C1 C3 + . . .. . .. . .., +Cn Cm )]

(9)

where, C1 , C2 , . . ., Cn , Cm are minimal cut-sets. This precise evaluation is always theoretically possible, but it is exhaustive and time-consuming exercise, which becomes prohibitive with power network. To overcome this problem, approximations are usually made in the evaluation of failure probability which although reduce precision but permits much faster evaluation. The degree of inaccuracy introduced is usually negligible and within the tolerance associated with the data of the transmission line availability for power system, which have large Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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values of repair rates and low value of failure rates for each transmission line. Hence, failure probability is approximated by retaining first order terms in the expansion of Eq. (9) as follows: pf = [

n 

P(Ci ) −

i=1 157

n,m 

P((Ci ) ∗ P(Cj ))]

i=1

(10)

j=2 / j i=

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In this chapter cut-sets up to second order have been considered. This is due to the fact that probability of outage of more than two transmission lines is negligible. Further higher order cut-set under usual loading conditions may not be minimal cut-sets, which are required in Eq. (9). Hence, Eq. (10) is utilized for evaluating probability of failure (pf ) under above-mentioned approximation. Minimal cut-set (first and second order) for a specified load, is obtained by comparing the load with static voltage stability limit in base case as well as various line outage conditions. Static voltage stability limit under single or double line outage condition is obtained using continuation power flow methodology (Arya and Verma, 1996). For adequate system operation, an adequate stability margin must be maintained. Using the results of continuation power flow, one can prepare a capacity available table, which gives permissible loading and corresponding state of the network. Now, for various load levels one identifies cut-set from the capacity availability table. Eq. (10) is utilized to get probability of failure. This probability of failure is termed as probabilistic insecurity index (PISI) of transmission system. It is further stressed that loadability limit depends on the system parameters and control variables. Hence, failure probability or PISI is obtained accounting uncertainties. The proposed algorithm for computation of PISI is as follows: Step-1: Perform base case load flow solution and obtain static voltage stability limit. Step-2: Perform continuation power flow for single and double line outage conditions and obtain stability limit for each contingent condition. Step-3: Prepare capacity-outage probability Table indicating stability limit and contingencies. Step-4: Identify cut-sets C1 (i), C2 (i), C3 (i), . . .. . .., Cr (i) for various peak load considerations for ith loading condition. where, (i = 1, 2, 3, . . ., NL) Step-5: Calculatepf failure probability using Eq. (10). Step-6: Stop.

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5. Evaluation of probabilistic insecurity index (PISI) using Artificial Neural Network (ANN)

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Instances obtained in Section-4 are used to train a multi-layer feed forward network. This network contains one input layer, two hidden layers and one output layer. The network is trained using back propagation artificial neural network (BPANN) algorithm (Fu, 1994). Number of units in input layer equals to number of line parameters (resistances, reactances & line charging susceptances), voltage of generator buses and total system load. Number of unit in output layer is one, which gives output as PISI. Further, the neurons in the hidden layer are assumed to be sigmoidal. Neuron in the output layer is assumed to be non-sigmoidal (linear). Network equations of Fig. 2 are written as follows: Y=

m 

Wjo Oj

(11)

j=1

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where, Wjo are the weights connected between jth hidden neuron and output neuron. Output of jth neuron in the hidden layer is as follows: Oj = 1/(1 + e−Netj ), j = 1, 2, ..., n

(12)

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Fig. 2. Generalized diagram of back propagation network for voltage security assessment and PISI calculations. 192

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where, Netj is Netj = [

n 

(Wij ∗ Xi )] j = 1, 2, ..., n

(13)

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where, Wij are the weight connected between ith input node and jth hidden neuron. Xi is input variable at ith node. Weight change hidden neuron and output neuron ΔWjo are given by the following formulae (Haykin, 2003):

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ΔWjo = [η ∗ δ ∗ Oj ]

(14)

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δ = (T − Y )

(15)

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where, T and Y are target value and output of the network respectively. η is learning rate lies between (0, 1). Weight change ΔWij (for hidden layer) is given as follows using back propagation algorithm: ΔWij = [η ∗ δj ∗ Xi ]

(16)

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Table 1 Q7 Contingency ranking for the 14-bus, 20-line system accounting uncertainty based on security index with & without consideration of unavailability

of transmission line, voltage performance index and line flow performance index (Sd = 3.10 pu). Sr. no.

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Security index without consideration of unavailability of transmission line

Security index with consideration of unavailability of transmission line

Voltage performance index (PIV )

Line flow performance index (PIMW )

pˆ

Line No.

SI

Line No.

PIV

Line No.

PIMW

Line No.

1.0000000 0.9814815 0.9807692 0.8800000 0.8600000 0.8148148 0.8076923 0.8000000 0.6607143 0.6545455 0.6400000 0.5844156 0.5156250 0.4761905 0.4423077 0.4406780 0.3064516 0.3000000 0.2962963

10 15 8 3 13 1 16 2 4 12 9 6 17 5 11 20 18 19 7

0.0042791 0.0041149 0.0039088 0.0037656 0.0037034 0.0035961 0.0029782 0.0028852 0.0027721 0.0027566 0.0025008 0.0023449 0.0018892 0.0018556 0.0016252 0.0015040 0.0013467 0.0012856 0.0010992

10 8 13 3 1 15 2 4 16 6 12 9 11 17 5 20 7 18 19

0.0528 0.2067 0.2431 0.3247 0.3895 0.4087 0.4111 0.4209 0.4223 0.4365 0.4511 0.4538 0.4570 0.4821 0.4878 0.4917 0.5004 0.5023 0.5027

15 10 8 13 3 1 2 16 4 12 6 9 17 5 11 20 18 19 7

0.9671 0.6890 0.6875 0.6190 0.5828 0.4320 0.3991 0.3667 0.3612 0.2548 0.2457 0.1998 0.1986 0.1957 0.1505 0.1407 0.1344 0.1156 0.1107

8 10 15 3 13 1 16 2 4 12 9 6 17 11 5 20 7 18 19

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where, δj is error gradient and is given as follows:

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δj = [δ ∗ .Wjo ∗ Oj ∗ (1 − Oj ) ∗ Xi ]

(17)

Xi is the element of input vector [X], 204 205

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where, [X]T = [R1 , R2 , . . ., RNL , X1 , X2 , . . ., XNL , Bc1 , Bc2 , . . ., BcNL , V1 , V2 , . . .VNG &Sd ]T

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Xi is the element of input vector [X].

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6. Results & discussions

(18)

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The developed algorithm has been implemented on 14-bus 20-line, and 25-bus 35-line IEEE standard test system (Appendix A). Vector of random variables ‘Z’ to be sampled consists of resistances, reactances, line charging susceptances, voltage of generator buses and power factor of load buses. The desired range of load bus voltages and generator bus voltages are 0.80 pu − 1.05 pu and 0.95 pu − 1.10 pu respectively.

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6.1. 14-Bus system

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This system consists of three generator buses and eleven load buses. Availabilities of lines from line no. 1 to line no. 20 are assumed as 0.99545486, 0.99627723, 0.996336033, 0.99580437, 0.99658704, 0.99572088, 0.99545486, 0.99580437, 0.996336033, 0.99572088, 0.99580473, 0.99559204, 0.99545486, 0.99580473, 0.996336033, 0.99658704, 0.99572088, 0.99580473, 0.996336033, and 0.99658704 (Billinton and Allan, 1984). Evaluate the security index with & without consideration of unavailability of transmission line by using the Eqs. (6) & (7) and arrange the order of transmission lines according severity. Severity of line has been decided by the value of security index. Table 1 shows the comparison of contingency ranking of transmission line based on security index with & without consideration of unavailability of transmission line accounting uncertainty, voltage performance index Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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0.082

Probability of Failure

0.072 0.062 0.052 0.042

Double Line Outage

0.032

Single Line Outage

0.022 0.012 0.002 2.0000

2.5000 3.0000 3.5000 Total System Load (pu)

4.0000

Fig. 3. Plot of probability of failure v/s various load levels for V˜ 1 = 1.0916pu, V˜ 2 = 1.0267pu, V˜ 3 = 1.0444pu RT = 1.5675pu, XT = 4.5046pu and BcT = 0.2780pu for 14-bus system.

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and line flow performance index (Verma and Niazi, 2012). Line no. 14 is radial (connects buses 7 and 8 not shown in Table 1) and its outage results in islanding of bus (Dester and Castro, 2009). Probability of failure or PISI has been calculated accounting uncertainties in the line parameters, control variables at various loading conditions using the Eq. (10). Static voltage stability limits have been used for calculating PISI, which were obtained using predictor–corrector technique (Arya and Verma, 1996). Table 2 shows the inputs of input layer in ANN, values of PISI as calculated using cut-set method considering the single & double line outage, and as obtained using trained network and the percentage error. Number of neurons in the hidden layer were adjusted to sixty four. Variables of the input layer are line resistances (R1 − R20 ), line reactance (X1 − X20 ), line charging susceptances (Bc1 − Bc20 ), PV-bus voltages (V1 − V3 ) and total system load (Sd ). Trained ANN has been validated with few testing instances other than used in training. The PISI as obtained using the trained network and cut-set method considering the single and double line outage have been shown in Table 3 along with percentage errors for the test cases. There is no rule for proportion between training and testing instances. In the present study 1000 training instances have been selected so as to encompass wide range of operating conditions for the power system. Further, testing instances have been selected in this range, other than training instances. The trained network has been tested for other 1500 test instances. Only few are given in Table 3 having highest magnitudes of percentage errors. Fig. 3 shows a plot of estimated probability of failure versus various load levels, setting as V˜ 1 = 1.0916 pu, V˜ 2 = 1.0267 pu, V˜ 3 = 1.0444 pu, RT = 1.5675 pu, XT = 4.5046 pu and BcT = 0.2780 pu considering the single and double line outage. The probability of failure as obtained with trained ANN has percentage error less than ±3%.

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6.2. 25-Bus system

222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238

241 242 243 244 245 246 247 248 249 250 251 252 253

This system consists of five generator buses and twenty load buses. Availabilities of lines from line no.1 to line no. 35 are assumed as 0.99559204, 0.99658704, 0.99545486, 0.99580473, 0.996336033, 0.99559204, 0.99572088, 0.99658704, 0.99545486, 0.99627723, 0.99559204, 0.99658704, 0.99545486, 0.99572088, 0.99580473, 0.996336033, 0.99559204, 0.99627723, 0.99545486, 0.99580473, 0.99658704, 0.996336033, 0.99559204, 0.99658704, 0.99627723, 0.99572088, 0.99545486, 0.99545486, 0.99580473, 0.99580473, 0.99627723, 0.99627723, 0.99559204, 0.996336033, and 0.99572088 (Billinton and Allan, 1984). Table 4 shows the comparison of contingency ranking of transmission line; based on security index with & without consideration of unavailability of transmission line accounting uncertainty, voltage performance index and line flow performance index (Verma and Niazi, 2012). Line no. 2, 6, 12 and 28 are radial (connects bus 1 & 16, 1 & 25, 4 &19 and 15 & 16 not shown in Table 4) and their outage results in islanding of bus (Dester and Castro, 2009). Table 5 shows the inputs of input layer in ANN, values of PISI as calculated using cut-set method considering the single & double line outage, and as obtained using trained network and the percentage error. Number of neurons in the hidden layer were adjusted to 111. Variables of the input layer are line resistances (R1 − R35 ), line reactances (X1 − X35 ), line charging susceptances (Bc1 − Bc35 ), PV-bus voltages (V1 − V5 ) and total Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

Total susceptance (pu)

PV-bus voltage (pu)

Total system load (pu)

Single line outage

Double line outage

RT

XT

BcT

V1

V2

V3

Sd

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

1.5675 1.6457 1.6638 1.5875 1.5937 1.6727 1.5556 1.5698 1.6611 1.6011 1.6611 1.6788 1.6821 1.5690 1.5184

4.5046 4.5515 4.4576 4.3757 4.6211 4.5344 4.6318 4.4476 4.5932 4.5417 4.5932 4.5001 4.4633 4.4927 4.4947

0.2780 0.2835 0.3019 0.2929 0.3576 0.3537 0.3287 0.3385 0.3765 0.2988 0.3765 0.2606 0.2753 0.3306 0.3570

1.0916 0.9716 1.0064 1.0713 1.0889 1.0930 1.0768 1.0744 1.0868 1.0712 1.0868 1.0199 1.0131 1.0648 1.0073

1.0267 0.9614 0.9995 1.0543 0.9650 1.0749 1.0768 0.9599 1.0778 1.0082 1.0778 1.0099 0.9692 1.0244 0.9651

1.0444 0.9523 0.9629 0.9603 0.9885 1.0366 1.0079 0.9906 1.0360 1.0452 1.0360 1.0020 0.9545 1.0763 1.0395

4.00 2.00 3.50 3.70 3.70 3.20 3.90 3.10 2.60 2.50 2.40 3.60 3.40 3.10 3.70

0.076280058 0.015861487 0.020300828 0.068080071 0.028615374 0.020096817 0.027705047 0.027833064 0.032133434 0.017511340 0.024154547 0.041719937 0.068285549 0.052519274 0.072000938

0.076401098 0.016126520 0.020096817 0.068012148 0.028946965 0.020325555 0.027958272 0.028181085 0.031846627 0.017868839 0.024370649 0.042094457 0.068278168 0.052480071 0.072114593

−0.1586786 −1.6709184 1.0151386 0.0998694 −1.1587860 −1.1381796 −0.9140049 −1.2503852 0.9005875 −2.0415291 −0.8946659 −0.8977012 0.0108097 0.0746445 −0.1578521

0.073425500 0.014590139 0.019719942 0.067324552 0.028057678 0.018478687 0.027366816 0.026864372 0.031434510 0.017186911 0.023940190 0.040981794 0.067513687 0.052420094 0.071869847

0.074547461 0.014856001 0.019924149 0.067393339 0.028389550 0.018708290 0.027620209 0.027212927 0.031721551 0.017544604 0.024156418 0.041356693 0.066521994 0.051381488 0.070484322

−1.5050291 −1.8222041 −1.0355333 1.4025699 −1.1828215 −1.2425274 −0.9259138 −1.297460 −0.9131385 −2.0811943 −0.9032020 −0.9147946 1.4907746 2.0213622 1.9657208

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Total reactance (pu)

P. Singh et al. / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Sr. no. Total resistance (pu)

+Model JESIT 180 1–18

10

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

Table 2 Training instances for training ANN, PISI as obtained using cut-set method and ANN for 14-bus test system.

+Model JESIT 180 1–18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Total reactance (pu)

Total susceptance (pu)

PV-bus voltage (pu)

Total system load (pu)

Single line outage

RT

XT

BcT

V1

V2

V3

Sd

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

1.6249 1.6724 1.6457 1.6804 1.6611 1.6457 1.6141 1.5030 1.6042 1.6073 1.7125 1.7125 1.6724 1.5937 1.5608

4.5410 4.4602 4.5515 4.5245 4.5932 4.5515 4.4124 4.5796 4.5329 4.4569 4.4361 4.4361 4.4602 4.5097 4.4150

0.2873 0.2976 0.2835 0.3550 0.3765 0.2835 0.2955 0.3891 0.2849 0.3579 0.2608 0.2608 0.2976 0.3045 0.3487

1.0278 1.0405 0.9716 1.0559 1.0868 0.9716 1.0350 1.0018 1.0985 1.0922 1.0155 1.0155 1.0405 1.0927 1.0275

0.9727 1.0284 0.9614 1.0102 1.0778 0.9614 0.9995 0.9613 1.0867 0.9876 0.9730 0.9730 1.0284 1.0355 0.9885

1.0073 1.0385 0.9523 0.9667 1.0360 0.9523 0.9909 0.9704 1.0357 1.0148 0.9768 0.9768 1.0385 1.0911 0.9937

4.00 3.50 3.00 3.70 3.70 2.20 3.10 2.60 3.60 3.30 2.50 3.20 2.80 3.30 2.60

0.051594311 0.039967942 0.072000938 0.076280058 0.059803041 0.031679184 0.072589808 0.048324364 0.033257763 0.067805668 0.014936524 0.047049531 0.023372597 0.023819587 0.020962977

0.051634881 0.039805447 0.072049453 0.076343224 0.059796348 0.031801492 0.072557288 0.048454482 0.033116707 0.067809402 0.014951159 0.047202319 0.023412139 0.023891840 0.020948390

−0.0786337 0.4082240 −0.0673815 −0.0828085 0.0111917 −0.3860833 −0.0448195 −0.2692587 0.4259365 −0.0055068 −0.0979787 −0.3247383 −0.1691831 0.3033333 .0695823

0.050936664 0.038712495 0.071073542 0.073982852 0.056337708 0.027905095 0.071000007 0.046695428 0.032807500 0.065946763 0.013989503 0.046895090 0.024436052 0.023815697 0.019445258

0.051711545 0.039166784 0.071388590 0.074920697 0.055425256 0.027754221 0.070332142 0.047139957 0.032374219 0.066912068 .013914679 0.046586100 0.024258678 0.023937537 0.019225662

−1.5212643 −1.1734951 −0.4432702 −1.2676515 1.61961217 0.54066678 0.94065479 −0.9519760 1.32067687 −1.4637633 0.53485759 0.65889576 0.72587201 −0.5115967 1.1293045

Double line outage

ARTICLE IN PRESS

Sr. no. Total resistance (pu)

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Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

Table 3 Validation of trained network using test cases as generated using cut-set method for 14-bus system.

+Model JESIT 180 1–18 12

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Table 4 Contingency ranking for the 25-bus, 35-line system accounting uncertainty based on security index with & without consideration of unavailability of transmission line, voltage performance index and line flow performance index (Sd = 13.20 pu). Sr. no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Security index without consideration of unavailability of transmission line

Security index with consideration of unavailability of transmission line

Voltage performance index (PIV )

Line flow performance index (PIMW )

pˆ

Line No.

SI

Line No.

PIV

Line No.

PIMW

Line No.

1.0000000 0.9000000 0.8000000 0.7500000 0.5614035 0.5512821 0.5068493 0.4821429 0.3281250 0.3090909 0.2235294 0.2168675 0.2125000 0.2105263 0.2077922 0.2023810 0.1940299 0.1923077 0.1917808 0.1891892 0.1891892 0.1818182 0.1739130 0.1714286 0.1688312 0.1666667 0.1500000 0.1428571 0.1369863 0.1219512 0.1206897

5 35 11 13 3 4 10 33 14 17 9 8 21 20 1 15 18 22 29 24 26 34 25 16 19 31 7 23 27 30 32

0.0038512 0.0036640 0.0035264 0.0034089 0.0025517 0.0023128 0.0021253 0.0018869 0.0014041 0.0013625 0.0010160 0.0009159 0.0008832 0.0008490 0.0008096 0.0008046 0.0007674 0.0007402 0.0007253 0.0007223 0.0007046 0.0006662 0.0006474 0.0006457 0.0006419 0.0006297 0.0006281 0.0006226 0.0006205 0.0005116 0.0004493

35 5 11 13 3 4 33 10 14 17 9 1 20 15 26 29 19 8 21 18 22 34 25 24 7 23 16 27 31 30 32

0.1428 0.1581 0.1801 0.1998 0.2298 0.2557 0.2698 0.2911 0.2966 0.3059 0.3186 0.3425 0.3430 0.3475 0.3498 0.3531 0.3532 0.3549 0.3551 0.3556 0.3557 0.3562 0.3564 0.3607 0.3613 0.3623 0.3626 0.3663 0.3665 0.3676 0.3677

11 35 5 3 13 4 33 10 17 14 9 1 21 15 20 29 18 8 22 24 34 26 25 16 19 23 7 31 27 32 30

0.9370 0.8840 0.8716 0.8684 0.8284 0.7931 0.7844 0.7672 0.7666 0.7553 0.7502 0.7491 0.7457 0.7419 0.7383 0.7375 0.7343 0.7328 0.7277 0.7262 0.6369 0.6289 0.6133 0.5998 0.4915 0.3195 0.1996 0.1879 0.1523 0.1407 0.1175

35 5 11 3 13 4 10 33 14 9 17 8 20 15 1 29 19 22 21 18 26 34 25 24 16 23 7 27 31 30 32

262

system load (Sd ). Trained ANN has been validated with few testing instances other than used in training. The PISI as obtained using the trained network and cut-set method considering the single and double line outage have been shown in Table 6 along with percentage errors for test cases. In the present study 1500 training instances have been selected so as to encompass wide range of operating conditions for the power system. Further, testing instances have been selected in this range, other than training instances. The trained network has been tested for 1500 test instances. Only few are given in Table 6 having highest magnitudes of percentage errors. Fig. 4 shows a plot of estimated probability of failure versus various load levels, setting as V˜ 1 = 0.9559 pu, V˜ 2 = 1.0564 pu, V˜ 3 = 1.0181 pu, V˜ 4 = 1.0275 pu, V˜ 5 = 0.9885 pu, RT = 3.2884 pu, XT = 8.4570 pu and BcT = 3.2884 pu considering the single and double line outage. The probability of failure as obtained with trained ANN has percentage error less than ±3%.

263

7. Conclusions

254 255 256 257 258 259 260 261

264 265 266 267

An algorithm with new viewpoints has been presented for voltage security assessment accounting uncertainties in the line parameters and control variables. Security index has been evaluated using Monte-Carlo simulation with & without consideration of unavailability of transmission lines, which is used to perform contingency selection. Further, probability of failure at various loading conditions considering voltage stability limit has been obtained using cut-set Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

+Model JESIT 180 1–18

Sr. no.

Total reactance (pu) XT

Total susceptance (pu) BcT

PV-bus voltage (pu) V1

V2

V3

V4

V5

Total system load (pu) Sd

3.0886 3.2642 3.1326 3.2845 3.2544 3.2454 3.2503 3.1989 3.2832 3.2336 3.2670 3.3596 3.2419 3.2503 3.3321 3.3071 3.2884 3.3251 3.3852 3.2012

8.3500 8.3465 8.2178 8.3421 8.2392 8.2349 8.3769 8.2810 8.3042 8.2406 8.2441 8.3251 8.3403 8.3769 8.3963 8.4263 8.4570 8.3824 8.3226 8.3095

1.7975 1.8327 1.7776 1.8646 1.8475 1.7222 1.8786 1.7617 1.8473 1.7656 1.8710 1.9022 1.8722 1.8786 1.7994 1.8431 1.9387 1.6558 1.8737 1.8615

1.0072 0.9793 1.0543 0.9508 0.9614 1.0568 0.9868 1.0370 1.0058 0.9569 1.0385 0.9530 1.0938 0.9868 1.0592 1.0684 0.9559 1.0502 0.9922 0.9937

0.9635 1.0199 0.9603 1.0312 0.9523 1.0825 1.0875 1.0499 1.0033 1.0507 1.0377 1.0818 0.9522 1.0875 1.0323 1.0465 1.0564 1.0890 0.9825 1.0703

1.0868 1.0099 0.9622 1.0426 1.0579 0.9785 1.0350 0.9743 1.0865 1.0365 1.0246 0.9538 1.0111 1.0350 0.9560 1.0657 1.0181 1.0178 1.0831 1.0684

1.0778 1.0020 1.0164 1.0239 1.0051 0.9524 0.9995 0.9793 1.0199 1.0614 0.9666 0.9954 1.0795 0.9995 1.0969 1.0529 1.0275 0.9752 1.0071 1.0514

1.0360 1.0712 0.9897 1.0369 1.0490 0.9777 0.9909 1.0517 1.0139 1.0149 1.0390 0.9747 0.9708 0.9909 1.0392 1.0169 0.9885 0.9593 0.9618 1.0633

16.000 15.750 14.250 12.000 14.500 15.250 16.250 16.000 14.250 12.500 14.750 13.000 15.500 14.250 14.500 15.000 14.000 15.000 13.500 15.500

Single line outage

Double line outage

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

PISI as obtained by cut-set method

PISI as obtained by ANN

% Error

0.060664032 0.11741382 0.056423854 0.049067637 0.084656514 0.099087899 0.088792981 0.118295001 0.113749861 0.073563401 0.122171658 0.076525784 0.084890814 0.088792981 0.100175460 0.105275471 0.109283098 0.094628034 0.093396924 0.067823691

0.059393091 0.119221774 0.057651539 0.050027458 0.086704238 0.097060891 0.090034667 0.119741593 0.115639941 0.072724637 0.123535993 0.078206764 0.086461646 0.090630629 0.098361234 0.107569186 0.111116276 0.092652931 0.093581200 0.069496389

2.1398795734 −1.5398065012 −2.1758269557 −1.9561183090 −2.4188618698 2.0883875114 −1.3984056654 −1.2228679441 −1.6616112503 1.1533417062 −1.1167362708 −2.1966189441 −1.8504147989 −2.0695870648 1.8444526949 −2.1787747512 −1.677458070 2.1317221585 −0.1973041262 −2.4662441780

0.057184539 0.112625830 0.053382004 0.045882739 0.081874794 0.096270567 0.084833891 0.113553473 0.109100725 0.069555746 0.116697451 0.073444567 0.082696324 0.084946759 0.094782693 0.100036740 0.104054267 0.089097445 0.088597466 0.065318686

0.058335161 0.114267636 0.054496251 0.046756343 0.083726308 0.098097361 0.085963508 0.114869907 0.110816048 0.070320350 0.117942096 0.074966931 0.084116810 0.086612430 0.096426472 0.102117116 0.105720148 0.090885947 0.088777960 0.066831801

−2.012120745 −1.4577522709 −2.0873074120 −1.9039935519 −2.2613971584 −1.8975620035 −1.3315628248 −1.1593073499 −1.5722378416 −1.0992678537 −1.0665567695 −2.0728064130 −1.7177134965 −1.9608410400 −1.7342609373 −2.0796124228 −1.6009728158 −2.0073544967 −0.2037241671 −2.3165120554

ARTICLE IN PRESS

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Total resistance (pu) RT

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Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

Table 5 Training instances for training ANN. PISI as obtained using cut-set method and ANN for 25-bus test system.

Total reactance (pu) XT

Total susceptance (pu) BcT

PV-bus voltage (pu) V1

V2

V3

V4

V5

Total system load (pu) Sd

3.2454 3.2642 3.2845 3.2884 3.2544 3.2544 3.1327 3.2035 3.2832 3.3763 3.3596 3.2833 3.2845 3.2503 3.3335 3.2330 3.3067 3.2012 3.3852 3.3219

8.4066 8.3465 8.3421 8.4570 8.2392 8.2392 8.1714 8.2343 8.3042 8.4492 8.3251 8.2892 8.3421 8.3769 8.3239 8.3647 8.2536 8.3095 8.3226 8.5095

2.0789 1.8327 1.8646 1.9387 1.8475 1.8475 1.6052 1.7687 1.8473 1.9616 1.9022 1.8549 1.8646 1.8786 2.0016 1.7827 1.7473 1.8615 1.8737 1.9738

1.0073 0.9793 0.9508 0.9559 0.9614 0.9614 1.0362 1.0357 1.0058 0.9612 0.9530 1.0244 0.9508 0.9868 1.0693 1.0225 0.9841 0.9937 0.9922 0.9868

0.9651 1.0199 1.0312 1.0564 0.9523 0.9523 1.0559 0.9977 1.0033 0.9798 1.0818 1.0763 1.0312 1.0875 1.0860 0.9883 1.0582 1.0703 0.9825 0.9568

1.0395 1.0099 1.0426 1.0181 1.0579 1.0579 1.0102 1.0109 1.0865 0.9596 0.9538 0.9733 1.0426 1.0350 1.0957 1.0727 1.0851 1.0684 1.0831 0.9549

1.0849 1.0020 1.0239 1.0275 1.0051 1.0051 0.9667 0.9704 1.0199 1.0038 0.9954 1.0664 1.0239 0.9995 0.9643 1.0244 0.9613 1.0514 1.0071 0.9746

1.0827 1.0712 1.0369 0.9885 1.0490 1.0490 1.0846 1.0295 1.0139 1.0231 0.9747 1.0839 1.0369 0.9909 1.0599 1.0776 1.0751 1.0633 0.9618 0.9829

16.500 14.500 14.500 16.000 14.000 13.500 15.000 16.250 16.250 16.250 14.750 15.250 13.500 14.750 16.500 14.750 16.250 15.000 14.750 15.000

Single line outage

Double line outage

PISI as obtained by cut-set method

PISI as obtained by ANN

PISI as obtained by cut-set method

PISI as obtained by ANN

PISI as obtained by cut-set method

PISI as obtained by ANN

0.118099018 0.118600184 0.109204721 0.109283098 0.084656514 0.084656514 0.101202831 0.126366928 0.114990147 0.117679848 0.076525784 0.084921797 0.105481951 0.089998835 0.097273581 0.105275471 0.096794871 0.067823691 0.094691328 0.110027091

0.118556330 0.117413828 0.109571124 0.109492590 0.084546763 0.086000252 0.102523762 0.127298223 0.113749861 0.118585115 0.077628903 0.085952487 0.105078624 0.088792981 0.098466495 0.106780562 0.096725699 0.068087316 0.093396924 0.110453342

−0.3872278824 1.0104056626 −0.3355193017 −0.1916967231 0.1296423934 −1.5872821390 −1.3052309158 −0.7369769505 1.0903624090 −0.7692628996 −1.4414996838 −1.2136927178 0.3823657304 −1.3580513920 −1.2263490625 −1.4296687503 0.0714628492 −0.3886918173 1.3859176219 −0.3874054036

0.119993594 0.112625830 0.105076553 0.102981946 0.082874794 0.081174794 0.097270567 0.116033292 0.109100725 0.113118696 0.073386302 0.085170740 0.095385916 0.084946759 0.097277641 0.100685202 0.093677440 0.065318686 0.089597466 0.104829987

0.121485055 0.114285771 0.105960119 0.101675701 0.083699338 0.080162101 0.098099824 0.114898427 0.107497954 0.114699368 0.074147720 0.084099955 0.094573970 0.086030009 0.096258002 0.099558187 0.092299963 0.064499995 0.090738414 0.105799990

−1.24295039 −1.47385442 −0.84087880 1.26842098 −0.99492711 1.24754655 −0.85252633 0.978051180 1.46907464 −1.39735698 −1.03754743 1.25722144 0.85122191 −1.27521060 1.04817444 1.11934495 1.47044678 1.25337916 −1.27341508 −0.92531097

ARTICLE IN PRESS

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Total resistance (pu) RT

P. Singh et al. / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Sr. no.

+Model JESIT 180 1–18

14

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

Table 6 Validation of trained network using test cases as generated using cut-set method for 25-bus system.

+Model JESIT 180 1–18

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15

0.1400

Probability of Failure

0.1200 0.1000 0.0800 Double line outage

0.0600

Single line outage 0.0400 0.0200 0.0000 11.00

12.00

13.00

14.00

15.00

16.00

17.00

Total System Load in (pu)

Fig. 4. Plot of probability of failure v/s various load levels for V˜ 1 = 0.9559pu, V˜ 2 = 1.0564pu, V˜ 3 = 1.0181pu, V˜ 4 = 1.0275pu, V˜ 5 = 0.9885pu, RT = 3.2884pu, XT = 8.4570pu and BcT = 3.2884pu for 25-bus system.

276

method for single & double line outages. These cases have been used to train back propagation algorithm (BPA), which overcome the disadvantages of probabilistic approach namely; exhaustive and time consuming. Obtained contingency selection results based on security index have been compared with well estabilished methods. Results obtained using proposed BPA network are precise and fast compared to the conventional methods, which allows to take preventive action in time. The applicability of PISI has been made on-line using BPA. Since voltage security assessment is possible on-line using artificial neural network. Such type of risk assessment becomes significant for modern large interconnected power systems, which are operating very closed to collapse point due to shortage of reactive power reserves and limitations of power networks. Proposed algorithms have been implemented on IEEE 14-bus 20-line and 25-bus 35-line test systems.

277

Appendix A. System data

278

Data for IEEE 14-bus system (100 MVA base)

268 269 270 271 272 273 274 275

See Tables A1 and A2.

Q6

Table A1 Line data. Line no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Bus no. From

To

1 1 2 2 2 6 8 6 6 8 4 4 4 7 7

2 8 3 6 8 3 6 7 9 4 11 12 13 5 9

Resistance (pu)

Reactance (pu)

Susceptance (pu)

Tap

Flow limit (pu)

0.01938 0.05403 0.04699 0.05811 0.05695 0.06701 0.01335 0.00000 0.00000 0.00000 0.09498 0.12291 0.06613 0.00000 0.00000

0.05917 0.22304 0.19790 0.17632 0.17388 0.17103 0.04211 0.20912 0.55628 0.25202 0.19890 0.25581 0.13027 0.17615 0.08450

0.0264 0.0246 0.0219 0.0187 0.0170 0.0173 0.0064 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.92 0.55 0.41 0.70 0.50 0.04 0.42 0.42 0.20 0.52 0.09 0.10 0.20 0.01 0.42

279

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

+Model JESIT 180 1–18

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P. Singh et al. / Journal of Electrical Systems and Information Technology xxx (2017) xxx–xxx

Table A1 (Continued) Line no.

16 17 18 19 20

Bus no. From

To

9 9 11 12 13

10 14 10 13 14

Resistance (pu)

Reactance (pu)

Susceptance (pu)

Tap

Flow limit (pu)

0.03181 0.12711 0.08205 0.22092 0.17093

0.08450 0.27038 0.19207 0.19988 0.34802

0.0000 0.0000 0.0000 0.0000 0.0000

1.0 1.0 1.0 1.0 1.0

0.08 0.12 0.05 0.025 0.08

Table A2 Bus data. Bus no.

Generation

1 2 3 4 5 6 7 8 9 10 11 12 13 14

280

Load

Real (pu)

Reactive (pu)

Real (pu)

Reactive (pu)

1.6730 0.7000 0.5000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.2170 0.9420 0.1120 0.0000 0.4780 0.0000 0.0760 0.2950 0.0900 0.0350 0.0610 0.1350 0.0580

0.0000 0.1270 0.1900 0.0750 0.0000 0.0390 0.0000 0.0180 0.1660 0.0580 0.0180 0.0160 0.0580 0.0580

Data for IEEE 25-bus system (100 MVA base) See Tables B1 and B2. Table B1 Line data. Line no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Bus no. From

To

1 1 1 1 1 1 2 2 2 3 3 4 4 4 5 5 5 6

3 16 17 19 23 25 6 7 8 13 14 19 20 21 10 17 19 13

Resistance (pu)

Reactance (pu)

Susceptance (pu)

Tap

Flow limit (pu)

0.0720 0.0290 0.1012 0.1487 0.1085 0.0753 0.0617 0.0511 0.0597 0.0564 0.1183 0.0196 0.0382 0.0970 0.0479 0.0144 0.0929 0.0263

0.2876 0.1379 0.2794 0.3897 0.2245 0.3593 0.2935 0.2442 0.2763 0.1487 0.3573 0.0514 0.1007 0.2547 0.2372 0.1269 0.2442 0.0691

0.0179 0.0337 0.0148 0.0224 0.0573 0.0873 0.0186 0.0155 0.0175 0.0085 0.0185 0.0113 0.0220 0.0558 0.0577 0.1335 0.0140 0.0040

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.460 0.490 0.170 0.08 0.360 0.420 0.300 0.390 0.380 0.260 0.490 0.430 0.440 0.260 0.370 1.03 0.530 0.100

Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Table B1 (Continued) Line no.

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Bus no. From

To

7 7 8 8 9 10 11 12 14 15 17 18 20 21 22 22 24

8 12 9 17 10 11 17 17 15 16 18 19 21 22 23 24 25

Resistance (pu)

Reactance (pu)

Susceptance (pu)

Tap

Flow limit (pu)

0.0529 0.0364 0.0387 0.0497 0.0973 0.0898 0.1068 0.0460 0.0281 0.0256 0.0806 0.0872 0.0615 0.0141 0.2250 0.0970 0.0470

0.1465 0.1736 0.1847 0.2372 0.2691 0.2359 0.2807 0.2196 0.0764 0.0673 0.2119 0.2294 0.1613 0.1087 0.3559 0.2595 0.1458

0.0078 0.0110 0.0118 0.0572 0.0085 0.0135 0.0161 0.0135 0.0044 0.0148 0.0122 0.0132 0.0354 0.0238 0.0169 0.0567 0.0317

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.075 0.150 0.075 0.080 0.110 0.080 0.0250 0.026 0.230 0.130 0.200 0.050 0.150 0.200 0.160 0.095 0.105

Table B2 Bus Data. Bus no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Generation

Load

Real (pu)

Reactive (pu)

Real (pu)

Reactive (pu)

2.6730 0.9930 1.4719 0.3910 1.9300 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

3.0000 1.0000 1.0000 1.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

2.0000 0.1000 0.5000 0.3000 0.2500 0.1500 0.1500 0.2500 0.1500 0.1500 0.0500 0.1000 0.2500 0.2000 0.3000 0.3000 0.6000 0.1500 0.1500 0.2500 0.2000 0.2000 0.1500 0.1500 0.2500

0.6500 0.0300 0.1700 0.1000 0.0800 0.0500 0.0500 0.0000 0.0500 0.0500 0.0000 0.0000 0.0800 0.0700 0.1000 0.1000 0.2000 0.0500 0.0500 0.0800 0.0700 0.0700 0.0500 0.0500 0.0800

281

282

283 284

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Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002

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Please cite this article in press as: Singh, P., et al., Security assessment accounting uncertainties in line parameters and control variables with the considerations of transmission line unavailability. J. Electr. Syst. Inform. Technol. (2017), https://dx.doi.org/10.1016/j.jesit.2017.10.002