Dynamic available transfer capability determination in power system restructuring environment using support vector regression

Electrical Power and Energy Systems 69 (2015) 123–130

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

Dynamic available transfer capability determination in power system restructuring environment using support vector regression A. Srinivasan a,⇑, P. Venkatesh b, B. Dineshkumar b, N. Ramkumar b a b

Department of Electrical and Electronics Engineering, Sethu Institute of Technology, Kariapatti, Tamil Nadu, India Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai, Tamil Nadu, India

a r t i c l e

i n f o

Article history: Received 31 March 2014 Received in revised form 31 December 2014 Accepted 3 January 2015 Available online 30 January 2015 Keywords: Dynamic available transfer capability Multilayer perceptron Power system restructuring Support vector regression Transient energy function

a b s t r a c t This paper presents dynamic available transfer capability (DATC) determination in power system restructuring environment using support vector regression (SVR). Dynamic available transfer capability is first determined based on the conventional method of potential energy boundary surface transient energy function. Simulations were carried out on a WSCC 3-machine 9-bus system and a Practical South Indian Grid test system by considering load increases as the contingency. The data collected from the conventional method is then used as an input training sample to the SVR in determining DATC. To reduce training time and improve accuracy of the SVR, the kernel function type and kernel parameter are considered. The proposed SVR based method, its performance is validated by comparing with the multilayer perceptron neural network (MLPNN). Studies show that the SVR gives faster and more accurate results for DATC determination compared with MLPNN. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction Electric power systems have become more and more complicated due to the rapid development of restructuring in electricity sector. Under power system restructuring environment, besides the system operator, certain real-time information of the transmission grid to be known by its market participant for their future power contract under secure operation. Real-time available transfer capability (ATC) is one of the important information to be published on the open-access sametime information system for the market participants to arrange possible secure power transactions. Therefore, a fast and accurate evaluation of the available transfer capability has been more important to assure the secure, economic, stable and reliable operation of power systems. Available transfer capability of a transmission network quantifies the measure of unutilized transfer capability remaining in the transmission network for the further commercial activity over and above already committed usage [1]. In [2] available transfer capability is classified as static ATC (SATC) and dynamic ATC (DATC) based on the consideration of different power system constraints. SATC involves the line thermal limit, bus voltage limit and saddle node bifurcation limit. DATC involves the small signal stability limit and transient stability limit. In real

⇑ Corresponding author. Mobile: +91 9486608059. E-mail address: [email protected] (A. Srinivasan). http://dx.doi.org/10.1016/j.ijepes.2015.01.001 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

time approach of ATC calculation, the effect of all the abnormal conditions has to be considered, hence transient stability constraints based DATC is more appropriate rather than SATC. A number of methods have been reported to date in literature for DATC determination. An iterative algorithm based on the Gauss–Newton solution of a nonlinear least square problem for determining transient stability based DATC has been proposed in [3]. Optimization approach of incorporating transient stability constraint optimal power flow to determine DATC has been used by few researchers [4–6]. New optimization techniques proposed in [7] deals with available transfer capability calculation incorporating system dynamics to avoid exhaustive numerical simulations directed by energy margin (EM) and energy margin sensitivity. Hybrid approach of combining transient energy margin and eigenvalue analysis to screen critical contingencies for fast ATC assessment with stability constraints has been proposed in [8]. A fast and accurate dynamic method considering transient stability analysis and voltage stability analysis for computing ATC using potential energy boundary surface (PEBS) and point of maximum potential has been proposed in [9]. The structure preserving energy function method has been proposed in [10,11] for the determination of DATC and to enhance the DATC through optimal placement of FACTS controllers respectively. In recent years, the application of artificial neural network for the determination of DATC has gained a lot of interest among researchers due to its ability to do parallel data processing with

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high accuracy and fast response in real time. In [12], the application of back propagation algorithm and radial basis function neural network is used for the computation of DATC. In [13], proposed an adaptive wavelet neural network to determine DATC having bilateral as well as multilateral transactions. The results of the proposed adaptive wavelet neural network model outperforms has been compared to the radial basis function neural network in determining DATC, in terms of accuracy. In [14,15] the drawback of the neural network is overcome by the pattern recognition approach such as support vector machine (SVM) and relevance vector machine (RVM). This paper focuses the attention on the support vector regression (SVR) approach to determine the transient stability based dynamic available transfer capability. The PEBS transient energy function based on the computation of energy margin is used as the conventional method for determining DATC. The pre-screening of line outages using energy margin values is also carried out to reduce the computational burden in determining DATC. The conventional method consumes longer computational time since it repeats the transient stability analysis many times. To overcome the computational difficulty of conventional method, SVR technique for determining more reasonable accuracy of DATC with less computational time is proposed in this paper. The proposed SVR based DATC assessment is tested on a WSCC 3-machine 9-bus system and a practical South Indian Grid test system and its performance is validated by comparing with the multilayer perceptron neural network. It was developed using the MATLAB Neural Network Toolbox, whereas SVR was developed using the Spider, adopted from [16].

where di, xi are rotor angle and speed of the machine i with respect to synchronous reference frame respectively; Mi is inertia constant of the machine i; Pmi is the mechanical power input to machine i; Pei is the electrical power output of i; Ei is the voltage magnitude behind transient reactance of machine i; Gij is transfer conductance between nodes i and j of the reduced bus admittance matrix; Gii is self conductance at ith node of the reduced bus admittance matrix; and Bij is transfer susceptance between nodes i and j of the reduced bus admittance matrix. The transformation of above equations into the Center of Inertia (COI) coordinates not only offers physical insight to the transient stability problem formulation in general, but also provides a concise framework for the analysis with transfer conductance [18]. The COI frame of reference is defined as:

Transient energy function

where

Power system transient stability [17] is the ability of the power system to remain in synchronism when the system is subjected to large disturbances such as sudden change in load and three phase fault. When the system undergoes large disturbances, the system will go to unstable state after sometime if the fault is not cleared within its critical clearing time. Hence the objective of transient stability analysis is to find the critical clearing time of circuit breakers to clear the fault. Conventionally, transient stability assessment has been performed using time-domain simulation process. It is an off-line and more time consuming process so it does not match with the real time operating conditions. To overcome this, the more reliable transient energy function method is considered for the fast and accurate evaluation of transient stability assessment. In this paper, potential energy boundary surface method is used for calculating energy margin of the system.

PCOI ¼

Mathematical formulation of transient energy function

d0 ¼

n 1 X M i di ; MT i¼1

MT ¼

ð6Þ

i¼1

By defining new rotor angles and speeds relative to this reference,

~ i ¼ xi  x0 x

h0 ¼ di  d0 ;

i ¼ 1; 2; . . . ; n

Pi ¼ Pmi  E2i Gii n X ½C ij sinðdi  dj Þ þ Dij cosðdi  dj Þ

The equation of motion becomes

)

~i h_ i ¼ x

ð8Þ

~_ ¼ P  P  Mi P ffi f ðhÞ i ¼ 1; 2; . . . ; n Mi x i i ei i M T COI

n nþ1 X n X X Pi  2 Dij cos dij i¼1

ð9Þ

i¼1 j¼iþ1

We note that the centre of inertia variable satisfy the constraints n n X X ~i ¼ 0 M i hi ¼ Mi x i¼1

ð10Þ

i¼1

~ Þ is defined for the post Therefore, the transient energy Vðh; x fault system at any instant can be illustrated by

~ Þ ¼ V KE ðx ~ Þ þ V PE ðhÞ Vðh; x ~Þ ¼ V KE ðx

n X 1 i¼1

2



ð11Þ

~ 2i Mi x

ð12Þ

n X Pi ðhi  hsi Þ n1 X n X i¼1 j¼iþ1

" C ij ðcos hij  cos hsij Þ  Dij

hi þ hj  hsi  hsj ðsin hij  sin hsij Þ hij  hsij

#

ð13Þ

ð1Þ

~ Þ and V PE ðhÞ are the total changes in kinetic and potenwhere V KE ðx tial energy of the system relative to the COI. hij ¼ hi  hj , hsij ¼ hsi  hsj and hs is stable equilibrium point of the post fault system.

ð2Þ

Computation of transient energy margin using PEBS method

ð3Þ

The procedure for computing the energy margin consists of the following steps:

j¼1

C ij ¼ Ei Ej Bij ;

ð7Þ

)

where

Pei ¼

ð5Þ

n X Mi

i¼1

d_ i ¼ xi _ i ¼ Pi  Pei Mi x

n 1 X M i xi MT i¼1

where

V PE ðhÞ ¼ 

For a classical model of n-generator system, the equation of the motion with respect to an arbitrary synchronous reference frame and neglecting the damping effect are given by

x0 ¼

Dij ¼ Ei Ej Gij

ð4Þ

1. Read the power system dynamic data. 2. Run the base case power flow for the pre fault system.

A. Srinivasan et al. / Electrical Power and Energy Systems 69 (2015) 123–130

3. Form bus admittance matrix for faulted and post fault system. 4. Find the post fault stable equilibrium point (hs) by solving non linear algebraic equation f i ðhÞ ¼ 0. 5. The differential Eq. (8) of the faulted system are solved by Runge–Kutta method up to fault clearing time tcl. ~ i are calcu6. At each time step of 0.001, the values of hi and x lated and theses values are used in the calculation of total ~ Þ for the post fault system. energy Vðh; x 7. The critical energy Vcr is obtained at the maximum value of VPE(h) occurring when faulted trajectory crosses the PEBS T function f i ðhÞ  ðh  hsi Þ where f i ðhÞ refers to the post fault system. ~ Þ ¼ V cr : 8. The critical clearing time tcr is calculated when Vðh; x 9. The critical clearing time tcr is also verified by the time at which the zero crossing of energy margin curve. 10. Determine total system energy at the fault clearing time tcl is Vcl. 11. The transient energy margin is calculated using Eq. (14) and check for transient stability. If EM is positive, the system is stable; otherwise the system is unstable.

EM ¼ V cr  V cl

ð14Þ

Conventional DATC assessment The Dynamic natures of power system lean toward the measure of DATC with the possible (n  1) line contingencies. The computational time for the determination of DATC considering all possible (n  1) line contingencies varies with the system size hence the computational time increases with the large system. Therefore, it is important to look after the sensitive analysis method first for determining the most severe line contingencies from the possible (n  1) line contingencies and then the DATC is calculated for the most severe line contingencies of the system. Contingency screening index In real time electricity market, fast assessment of ATC considering the effect of line contingencies is more important. The contingencies screening method provides the solution for the above issue by identifying severe line contingencies based on the contingency screening index values. This is explained through the following procedure.  Choose all the possible (n  1) line contingencies.  Compute the energy margin for base case condition (EMbk).  Compute the energy margin for additional amount of transaction tk (EMtk).  Then compute the contingency screening index Sk using the Eq. (15).

Sk ¼

EMbk  EMtk EMbk

ð15Þ

The calculated contingency screening index values for all possible (n  1) line contingencies are assembled in descending order. The screening index Sk becomes high, if the energy margin decreases considerably by the introduction of transaction. Contingency with high screening index value are considered for the determination of DATC. Determination of DATC using PEBS method DATC with respect to a bilateral/multilateral contract can be calculated by increasing the generation at the seller bus/buses

125

and simultaneously, the loads by the same amount at the buyer bus/buses until the energy margin of the system reaches the threshold value (EM 6 0.0001). The new load and generation as follows: 0 Pnew Di ¼ P Di ð1 þ k  T SDi Þ

Pnew Gi ¼

" # NDT X 0 ðPnew  P Þ  T SGi þ P0Gi Di Di

ð16Þ ð17Þ

i¼1

where P 0Di , P0Gi are the base case load and generation at bus-i, T SDi , T SGi are the transaction share ratio of load and generation at bus-i, NDT is the total number of load bus consider in the transaction tk, k is the loading factor. Total transfer capability (TTC) and ATC in each contingency case are calculated as follows:

TTC ¼

NDT X P0Di ð1 þ kEM  T SDi Þ

ð18Þ

i¼1

ATC ¼ TTC 

NDT X

P0Di

ð19Þ

i¼1

where kEM is the loading factor at which the energy margin reaches the threshold value. The procedure for calculating DATC is given as follows i. Select the sources bus/buses and sink bus/buses for the transaction tk. ii. Select a line contingency. iii. Initialize the loading factor k = 0 and incremental loading factor 4k = 1. iv. Increment the loading factor k = k + 4k. v. Run the PEBS transient energy function approach by changing the corresponding the load and generation bus value for the transaction tk given in Eqs. (16) and (17) to obtain the energy margin of the system. vi. Check the obtained EM P 0, if yes goes to step (vii) otherwise go to step (viii). vii. Check the EM 6 0.0001, if yes goes to step (x) otherwise go to step (iv). viii. Decrement the loading factor k = k  4k and change the incremental load loading factor 4k = 4k/10. ix. Check the 4k 6 0.0001, if yes goes to step (x) otherwise go to step (iv). x. Calculation of TTC using k as given in Eq. (18) where k = kEM. xi. Calculation of DATC using Eq. (19). Modeling of support vector regression Generally in support vector regression, our aim is to find a function f(x) for the given training data ðx1 ; y1 Þ; . . . ; ðxn ; yn Þ  W R. Where W denotes the space of input patterns xi and yi is the associated output values of xi. The function f(x) should be at most e deviation from the original targets yi for all the training data. In other words, do not cares about the errors if they are less than e but any deviation larger than e will not be accepted. The main idea of SVR is to map the data  x of the low dimensional input space into high dimensional feature space F through a nonlinear mapping and to do a linear regression in this space. We consider the function in form as [20,21]

f ðxÞ ¼ hw; /ðxÞi þ b with / : Rn ! F; w 2 F

ð20Þ

xÞ is an output function, w is weight vector, x is an input where f ð space, b is bias threshold and h., .i is dot product in the feature space. The small value of weights w gives flatness for the function. The weights are determined from the finite samples by minimizing

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the function which includes the sum of Empirical risk Remp[f] the average value of the Loss function Le and Euclidean norm kwk2. This function can be minimized by solving quadratic programming problem that can be normalized as

/ðw; nÞ ¼

n X 1 kwk2 þ C ðni þ nþi Þ 2 i

ð21Þ

Subject to

9 yi  hw; /ðxi Þi  b 6 e þ ni > = hw; /ðxi Þi þ b  yi 6 e þ nþi > ; ni ; nþi P 0

ð22Þ Determination of DATC using SVR

where n represents the number of samples, C is the positive nonzero constant which determines the tradeoff between the flatness of f and the amount up to which the deviations larger than e can þ be tolerated. n i ; ni are the upper and lower training error subject to e-insensitive tube jyi  hw; /ðxi Þi  bj 6 e. This e-insensitive loss function jnje can be described by the following equation

 jnje ¼

0 ; if jn < ej jnj  e ; otherwise

ð23Þ

Then construct a Lagrange function from the objective function of Eq. (21) and the corresponding constraints Eq. (22) by introducing a dual set of variables ai ; ai . These variables are called Lagrange multipliers. The maximal dual function in Eq. (21) has the following form

max Wða; a Þ ¼ max    a;a

a ;a

þ

n X n 1X ðai  ai Þðaj  aj Þh/ðxi Þ; /ðxj Þi 2 i¼1 j¼1

n X

ai ðyi  eÞ  ai ðyi þ eÞ

ð24Þ

i¼1

With constraints

9 0 6 ai ; ai 6 C i ¼ 1; 2; . . . ; n > = n X  > ðai  ai Þ ¼ 0 ;

ð25Þ

i¼1

The Lagrange multipliers ai ; ai are determined by maximizing the dual function of Eq. (24) and the weights as in the regression function of Eq. (16) is given by

w¼

n X ðai  ai Þxi

The parameter r2 associated with RBF function has to be tuned to get the desired output. SVR can solve high dimensional problems independent of the input space and it depends only on the number of support vectors. The number of support vectors which represents the sparse level of the solution is determined by e value. The conventional neural network minimizes the training error using empirical risk minimization principle, whereas SVR uses the structure risk minimization principle to minimize the generalþ ization error bound by minimizing n i ; ni and flatness is achieved by minimizing 12 kwk2 to achieve generalized performance.

The step by step procedure for DATC calculation by implementation of SVR is described below: i. Read the test system data. ii. Select M number of critical line contingency for the transaction tk using the contingency screen method mentioned in Section ‘Contingency screening index’. iii. Generate N number of load scenario by randomly changing the real power values of all generators and loads of the test system. iv. Compute the DATC for each selected line contingency using the proposed conventional DATC assessment mention in Section ‘Determination of DATC using PEBS method’ by considering N number of load scenario as the base case condition. v. Create N M input patterns in the form of N load scenario for each line contingency as an input features and their corresponding dynamic ATC as the output vectors. vi. Normalize the input patterns between 0.1 and 0.9. vii. To differentiate the load scenario for each selected line contingency topology number is added with the normalized input patterns. viii. Select the Kernel function type and Kernel parameter values to train the SVR. ix. Train the SVR for all the training data sets selected from the input patterns and calculates the normalized mean square error (NMSE). x. Repeat step (ix) until the specified iteration or the specified error acceptance (e) is reached. xi. Test the SVR, so trained, for the testing data selected from the input pattern.

ð26Þ

i¼1

Simulation results and discussion

Finally, the function in terms of Lagrange multipliers and kernel functions as.

Fðx; ai ; ai Þ ¼

n X

ðai  ai ÞKðx; xi Þ þ b

ð27Þ

i¼1

The Karush–Kuhn Tucker condition that are satisfied by the solution are

ai ; ai ¼ 0; i ¼ 1; 2; . . . ; n

ð28Þ

Therefore, the support vectors are points where exactly one of Lagrange multipliers is greater than zero which means that they fulfill the Karush–Kuhn–Tucker condition. Training points with nonzero Lagrange multipliers are called support vectors. For nonlinear case, the dot product becomes a kernel function. Several kernel functions are available such as Gaussian radial basis function kernel, linear kernel and multilayer perceptron kernel. But the most common kernel function used is Gaussian RBF kernel, which is given by kxyk2 2r 2

Kðx; yÞ ¼ e

ð29Þ

To illustrate the effectiveness of the proposed SVR based DATC assessment is tested on system network and its performance is validated by comparing with the MLPNN. All the simulations have been done in MATLAB 7.3 environment. Proposed conventional DATC assessment The proposed conventional DATC formulation has been tested on WSSC 3-machine 9-bus test system [19] and a Practical 6machine 21-bus South Indian Grid test system [22] by considering two different types of electricity power transactions in both the test systems. The two different transactions of WSSC 3-machine 9-bus test system includes a bilateral transaction (T1) between a seller at bus 2 and a buyer at bus 5, a multilateral transaction (T2) between the two seller at buses 2,3 with transaction ratio of 0.5 each and a buyer at bus 5. Similarly the two different transactions of Practical 6-machine 21-bus South Indian Grid test system includes a bilateral transaction (T1) between a seller at bus 4 and a buyer at bus 12, a multilateral transaction(T2) between the two

A. Srinivasan et al. / Electrical Power and Energy Systems 69 (2015) 123–130

seller at buses 2,5 with transaction ratio of 0.5 each and a buyer at bus 14. The pre screening of all possible (n  1) line contingencies [8] have been carried out by calculating severity index using base case energy margin value and with an additional amount of 50 MW transaction case energy margin value as mentioned in Section ‘Contingency screening index’ for the two transaction cases considered in the two test systems. The energy margin calculated using the procedure as mentioned in Section ‘Computation of transient energy margin using

127

PEBS method’ is illustrated in Fig. 1 for the WSCC 3-machine 9bus system with fault occurred at bus 7 and cleared by tripping line 5–7 after 3 cycles (0.05 s). Critical clearing time shown in Fig. 1 is verified by the time at which energy margin curve crossing zero is shown in Fig. 2. It is inferred that the time at which the PEBS function crossing [19] the zero shown in Fig. 2 is same as the time at which maximum potential energy occurs shown in Fig. 1. Similarly, the energy margin computation procedure is illustrated in Fig. 3 for the South Indian Grid test system with fault occurred at bus 4 and cleared by tripping line 15–4 after 5 cycles

Fig. 1. Transient energy curve and computation of EM in base case condition of WSCC 3-machine 9-bus system when fault on bus 7 tripped by line 5–7.

Fig. 2. The monitoring of the PEBS crossing and critical clearing time of WSCC 3-machine 9-bus system when fault on bus 7 tripped by line 5–7.

Fig. 3. Transient energy curve and computation of EM in base case condition of South Indian Grid test system when fault on bus 4 tripped by line 15–4.

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A. Srinivasan et al. / Electrical Power and Energy Systems 69 (2015) 123–130

Fig. 4. The monitoring of the PEBS crossing and critical clearing time of South Indian Grid test system when fault on bus 4 tripped by line 15–4.

Table 1 Conventional DATC values in MW for the selected critical line contingencies . Transaction number

Faulted bus

Test system 1: WSCC 3-machine 9-bus system T1 5 7 7 6 9 T2

5 7 6 9 4

Test system 2: South Indian test system T1 4 4 14 8 15 T2

2 2 15 15 15

Line tripped

EMbk

EMtk

Sk

DATC (MW)

Comp. time (s)

5–7 5–7 7–8 6–9 6–9

0.8307 0.9660 1.7406 1.2543 1.9306

0.0289 0.1820 0.8083 0.6839 1.0590

0.9652 0.8115 0.5356 0.4547 0.4514

52.137 66.750 117.075 135.425 129.100

43.797 42.649 41.396 35.433 39.595

5–7 5–7 6–9 6–9 4–6

0.8307 0.9660 1.2543 1.9306 2.4694

0.1534 0.2084 0.6845 1.2088 1.7645

0.8152 0.7842 0.4543 0.3738 0.2854

64.462 65.742 130.300 173.675 245.621

61.750 52.955 40.742 64.361 63.609

14–4 15–4 14–4 1–8 15–4

6.2469 10.037 5.0550 1.0787 8.0153

4.5948 8.3637 5.5387 0.9860 7.7925

0.2644 0.1667 0.0956 0.0858 0.0277

224.259 317.010 430.044 463.674 436.740

55.810 58.468 178.702 70.602 70.046

15–2 2–20 15–16 15–17 15–19

41.843 89.360 10.073 10.056 9.7616

3.7340 59.469 6.7576 6.7629 6.6507

0.9107 0.3345 0.3291 0.3275 0.3186

279.560 593.700 945.260 945.592 940.788

215.89 71.977 64.725 80.062 67.285

(0.1 s). Critical clearing time shown in Fig. 3 is verified by the time at which energy margin curve crossing zero is shown in Fig. 4. It is inferred that the time at which the PEBS function crossing the zero shown in Fig. 4 is same as the time at which maximum potential energy occurs shown in Fig. 3. From the pre screening contingency method, the top five severe lines tripped due to the fault at the corresponding buses are shown in the second column and the tripped lines are shown in the third column of Table 1 for the two test systems. These selected top five severe lines based on the severity index value are calculated using the energy margin value for the base case condition and the additional amount of transaction cases are shown in the fourth and fifth column of Table 1. The screening index values are shown in the sixth column of Table 1. The DATC for the corresponding severe contingencies are calculated when the energy margin of the system is less than or equal to threshold value (EM 6 0.0001) are shown in the seventh column of Table 1. From Table 1 it is inferred that the values of DATC for the most severe contingencies are very much lower compared with other contingencies and take more computational time in both two transaction cases of the test systems.

Determination of DATC using SVR In the real time restructured power market, ATC values available on the open access same time information system (OASIS) should be updated at a specific interval of time for further commercial activities of system to avoid the inefficient utilization of transmission network. The proposed conventional approach for the DATC assessment applied for the WSCC 3-machine 9-bus test system and a Practical 6-machine 21-bus South Indian Grid test system consumes more computational time. To reduce the computational time, SVR based pattern recognition approach is employed to determine the DATC for the two transaction cases of the test systems considered in the proposed conventional approach. For the two transaction cases of the test systems, 150 input patterns are generated for the DATC assessment using SVR based on the 50 load scenario for each of the top three severe contingencies by changing the loads and generations randomly between ±40% and ±10% of their base case values respectively. The input feature set for the WSCC 3-machine 9 bus test system composed of three real power output of generation (PG1, PG2 and PG3) and three real

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A. Srinivasan et al. / Electrical Power and Energy Systems 69 (2015) 123–130

Normalized DATC value in p.u

0.9

Actual

SVR

Normalized DATC value in p.u

1

Actual

0.9

SVR

MLPNN

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

Testing Data Fig. 7. Comparison of testing patterns results of SVR and MLPNN based DATC for transaction T2 in South Indian test system.

0.08

SVR

0.07

MLPNN

0.06

Absolute Error

power value of load (PD5, PD6 and PD8). Similarly, the input feature set for the South Indian Grid test system composed of six real power output of generation (PG1–PG6) and twenty real power value of load (PD2–PD21). To differentiate the load scenario for each contingency, bipolar digit (1, +1) based topology number [23] has been used as an additional input feature in the generated input pattern. Four bipolar digits and six bipolar digits are used as the topology number for 9 and 21 bus systems respectively, based on their number of transmission lines. For example the first severe contingency is represented by a bipolar string (–1, –1, –1, +1) for 9 bus system and (–1, –1, –1, –1, –1, +1) for South Indian Grid test system. From the generated 150 input patterns, 120 (40 3) patterns are chosen for training and remaining 30 (10 3) patterns are chosen for testing. In this paper, Gaussian radial basis kernel function is selected since both the normalized mean square error (NMSE) and computational time are less compared with the other Kernel function type. The optimum values of Kernel Parameter r are 1.0 and 4.0 for 9-bus and practical test system respectively is determined by trial and error method with the specified value of trade off parameter C as infinity and error acceptance (e) as 0.0001. Before training, the input patterns are normalized between the values of 0.1 and 0.9 to overcome the suppression of smaller input variable’s influence by higher variable ones. The performance of SVR in DATC assessment is compared with the MLPNN. The MLPNN is designed and trained using the Neural Network Toolbox in MATLAB 7.3. For both the test systems, the design consists of a hidden layer with 16 neurons of ‘tansig’ transfer function and an output layer with one neuron of ‘logsig’ transfer function. The designed Neural network is trained using Levenberg Marquardt algorithm with the learning rate value of 0.6, the

0.05 0.04 0.03 0.02 0.01 0

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

Testing Data Fig. 8. Comparison of absolute error for testing patterns results of SVR and MLPNN for transaction T2 in South Indian test system.

MLPNN

0.8 0.7

Table 2 Performance comparison of SVR and MLPNN in DATC assessment.

0.6

Transaction number

0.5 0.4

Method

Training phase NMSE

0.3 0.2 0.1 0

Test system 1: WSCC 3-machine 9-bus system T1 SVR 8.97 107 MLPNN 1.27 104

0.3621 0.4913

3.29 105 1.32 104

9.25 104 2.18 104

0.1694 0.6016

1.42 104 2.49 104

Test system 2: South Indian test system T1 SVR 1.00 108 MLPNN 2.80 103

0.2202 2.510

6.62 104 1.70 103

9.89 109 4.84 104

0.1563 2.9414

1.71 105 5.50 104

T2 1

3

5

7

9

11

13

15

17

19

21

23

25

27

Comp. time (s)

Testing phase NMSE

29

SVR MLPNN

Testing Data Fig. 5. Comparison of testing patterns results of SVR and MLPNN based DATC for transaction T1 in WSCC 3-machine 9-bus system.

T2 0.025

SVR

MLPNN

Absolute Error

0.02 0.015 0.01 0.005 0

1

3

5

7

9

11

13

15

SVR MLPNN

17

19

21

23

25

27

29

Testing Data Fig. 6. Comparison of absolute error for testing patterns results of SVR and MLPNN for transaction T1 in WSCC 3-machine 9-bus system.

momentum value of 0.8, performance goal value of 0.0001 and the epochs value of 1000. The comparison of normalized DATC obtained for the various testing patterns using SVR and MLPNN with actual results are shown in Figs. 5 and 7 for the transaction T1 taken in WSCC 3machine 9-busystem and transaction T2 taken in practical test system. From the figures it is inferred that the SVR results are very much closer to the actual results than MLPNN results. The absolute error of SVR and MLPNN testing patterns results is compared and shown in Figs. 6 and 8 for the transaction T1 carried out in WSCC 3-machine 9-busystem and transaction T2 carried out in practical test system. From the figures it is observed that the SVR is providing DATC with more reasonable accuracy for all the transactions.

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Table 2 gives the performance of SVR and MLPNN based DATC determination in terms of accuracy (NMSE) and computational time. It is found that testing phase computational time is for both the neural networks less compared to training phase. Hence, it is observed that the performance of SVR based DATC is better results in terms of speed and accuracy. Conclusions Dynamic available transfer capability determination in power system restructuring using convention potential energy boundary surface transient energy function method require long computation time and therefore to accelerate the calculation process, SVR approach is proposed. In this study, the SVR is tested for DATC determination on a WSCC 3-machine 9-bus system and practical South Indian Grid test system. The performance of the SVR method in calculating DATC based on EM values, is evaluated by comparing it with the MLPNN. In terms of accuracy, both the SVR and MLPNN provide reasonable DATC value for all the transaction taken in the test systems. In terms of computational speed, SVR takes less computational time for all the test system but MLPNN increase its computational time for larger interconnected system. Thus the SVR features of fast computational speed and reasonable accuracy of DATC clearly indicate that the SVR based DATC assessment is exactly suitable for the real time application of deregulated market. References [1] North American Electric Reliability Council (NERC). Available transfer capability definitions and determinations; June 1996. [2] Kumar A, Srivastava SC, Singh SN. Available transfer capability determination in a competitive market using AC distribution factors. Electr Power Compon Syst 2004;32(9):927–39. [3] Hiskens IA, Pai MA, Sauer PW. An iterative approach to calculating dynamic ATC. In: Proceeding of bulk power system dynamics and control IVrestructuring. Santorini, Greece; 1998. p. 585–90. [4] Tuglie ED, Dicorat M, Scala ML, Scarpellini P. A static optimization approach to assess dynamic ATC. IEEE Trans Power Syst 2000;15(3):1069–76.

[5] Yue Yuan, Junji Kubokawa, Takeshi Nagata, Hirishi Sasaki. A solution of dynamic available transfer capability by means of stability constraint optimal power flow. In: Proceeding of IEEE Bologna power tech conference. Bologna, Italy; June 2003. [6] Zhang X, Song YH, Lu Q, Mei S. Dynamic ATC evaluation by dynamic constrained optimization. IEEE Trans Power Syst 2004;19(2):1240–2. [7] Joo SK, Liu CC. Optimization techniques for available transfer capability (ATC) and market calculations. IMA J Manage Math 2004;15:321–37. [8] Masaki Nagata, Kazuyuki Tanaka. A hybrid approach of contingency screening for ATC assessment with stability constraints. In: Proceeding of quality and security of electric power delivery system. Montreal, Que, Canada; 2003. p. 137–42. [9] Eidiani M, Shanechi MHM. FAD-ATC: a new method for computing dynamic ATC. Int J Electr Power Energy Syst 2006;28(2):109–18. [10] Jain T, Singh SN, Srivastava SC. Dynamic available transfer capability computation using hybrid approach. IET Proc Gener Transm Distrib 2008;2(6):775–8. [11] Jain T, Singh SN, Srivastava SC. Dynamic ATC enhancement through optimal placement of FACTS controllers. Electr Power Syst Res 2009;79:1473–82. [12] Vinod kumar DM, Venkaiah.Ch. Available transfer capability determination using intelligent techniques. In: Proc IEEE power India conference; October 2008. [13] Jain T, Singh SN, Srivastava SC. Adaptive wavelet neural network based fast dynamic available transfer capability determination. IET Proc Gener Transm Distrib 2010;4(4):519–29. [14] Takahashi Hiroaki, Kumano Terushisa. Available transfer capability screening considering transient stability by support vector machine. In: Proc IEEE PES general meeting. Pittsburgh; July 2008. [15] Wada Akihiro, Kumano Terushisa. Fast estimation of transient stability constrained ATC by relevance vector machine. In: Proc IEEE power and energy conference. Johor Bahru; December 2008. [16] www.kyb.mpg.de/bs/people/spider. [17] Kundur P. Power system stability and control. New Delhi: Tata McGraw Hill; 2009. [18] Athay T, Podmore R, Virmani S. A practical method for direct analysis of transient stability. IEEE Trans Power Apparatus Syst 1979;98(2):573–84. [19] Sauer PW, Pai MA. Power system dynamics and stability. New Jersey: PrenticeHall Inc.; 1998. [20] Cortes PC, Vapnik V. Support-vector networks. Machine Learning 1995;20:273–97. [21] Smola AJ, Scholkopf B. A tutorial on support vector regression. NeuroCOLT technical report, NC-TR-98-030; 1998. [22] Dora Arul Selvi B, Kamaraj N. Evolutionary support vector machines for transient stability monitoring. J Inst Eng (India): Ser B 2012;93(1):43–9. March. [23] Srivastava L, Singh SN, Sharma J. Comparison of feature selection techniques for ANN based voltage estimation. Electr Power Syst Res 2000;53:187–95.