An approach for contingency ranking analysis of electrical power system

This paper presents an algorithm for ranking the critical contingencies in a high voltage power system. The presented approach based on a hybrid weighted performance index. The hybrid performance index measures the overloaded transmission lines and bus voltage deviation out the permissible limits. A linear technique is used in computing the hybrid performance index. The proposed algorithm is applied to the IEEE24 bus reliability test system. There is a good match between the results obtained with the proposed algorithm with those obtained by applying a full AC load flow iterative method.


INTRODUCTION
With the increased growth of electric power demand, the transmission systems are operated in a much-stressed conditions. The environmental constraints and economic crisis pose difficulties in building a new transmission line. The secure operation is becoming a vital issue in power system utilities. One of the major functions of a security analysis is to study the severity of all possible contingencies (line outage, generation unit outage) on the performance of the power system elements. A detailed contingency assessment requires examining the effect of all contingencies of power system by a full AC load flow method. Such a detailed analysis on a large-scale power system would be infeasible for the substantial computer time requirements and the few real contingencies that threat the security of the power system. Contingency ranking is the process of selecting the critical contingency severely violate the operational limits of the system components. Contingency ranking techniques are the subject of extensive research since the pioneering work of El-Abiad [1]. Ranking critical contingencies in terms of transmission line overload had become the focus of many researchers [2][3][4][5][6][7][8][9][10][11][12][13][14]. Most of the algorithms are based on the concepts of adjoint networks and Tellegen's theorem or using the first iteration of fast decoupled load flow. Other attempts tackled contingency ranking in terms of on its severity on bus voltage out of limit conditions [15][16][17][18][19]. An attempt to assess the branch outage contingencies using continuation method was presented in Reference [20]. A compact algorithm using reduced matrix has been implemented in steady state security assessment [21]. Artificial intelligence techniques have been proposed for contingency ranking [22][23][24][25][26][27][28][29]. The contingency ranking was addressed from a probabilistic point of view [30][31]. The real time contingency was based on a probabilistic index which considered the stochastic nature of the electric power system equipment outages.
A new algorithm, which ranks the critical contingencies, is proposed. Two linear non iterative power flow model are presented. Two performance indices which quantify the severity of the contingency are evaluated. The proposed algorithm was tested on IEEE 24 bus reliability test system. The ranking list obtained was compared with those obtained by applying full AC iterative load flow. This paper is organized as follows: Section II presents the proposed performance indices. The proposed linear active and reactive power flow model are presented in section III. Section IV discusses the results obtained by applying the proposed algorithms on the IEEE 24 bus reliability system. Finally, section V presents the conclusion.

II. HYBRID PERFORMANCE INDEX
The most important features of a reliable contingency selection algorithm are its simplicity and the speed of filtering the most severs contingencies. For this end, a hybrid contingency performance index (CPI h ) have to be defined for quantifying the severity of the contingency. Since some contingencies may cause only violation of the bus voltage limit. Others may lead to overload the MVA rating of transmission lines. The proposed algorithm in this paper considered both effects simultaneously by defining a hybrid contingency performance index as follow: Where CPI S is the contingency performance index which provides a measure of the transmission line rating overload CPI |E| is the contingency performance index which provides a measure of the deviation of nus voltage beyond their tolerable values The components of the contingency performance index is. given by Equations (2 and 3): Where W S is line MVA rating weighting factor S l flow is MVA flow in line l S l max is the maximum MVA rating of the line l α is the set of overloaded Where W |E| is the bus voltage magnitude weighting factor |E| i limit is the bus voltage magnitude limit at bus i |E| i is bus voltage magnitude at bus i μ is the set of buses whose voltage magnitude is out of the limits The values of apparent power flow in the lines and bus voltages in Equations 2 and 3 are computed by a linear power flow model as presented in the next section III.
PROPOSED LINEAR POWER FLOW MODEl The steady state performance at each bus of n bus electrical power system may be described by the following current balance equation: Where Y ik is the i,k th element of bus admittance matrix E k is the bus voltage at bus k The complex bus power S i may be specified by the following equation: Where P Gi is the active power generation at bus i P Di is the active power demand at bus i Q Gi is the reactive power generation at bus i Q Di is the reactive power demand at bus i Using (5), the left-hand side of (4) can be rearranged as: The right-hand side of (4) may be arranged as: =1 ≠ By substituting Equations (6) and (7) into Equation (4), and separating the real part and imaginary part of the resulting equation yield the following two real nonlinear algebraic equations at each bus: Using the decoupling behavior of the high voltage power system, equation (8) is simplified and used to solve for the voltage angle θ while equation (9) is simplified and used to solve for voltage magnitude |E| as follow:

A. LINEAR ACTIVE POWER FLOW MODEL
To determine the bus voltage angle θ, equation (8) may be simplified by assuming all the voltage magnitude to be 1 p.u. Also, the trigonometric functions may be expressed by using Taylor series with only first linear term. This is justified in practice by the small value of. the operating power angle: One feature of the high transmission networks is their line conductances are much less than line susceptances.

( ) ≪ ( )
Also, the reactive power flow from a particular bus is much higher than the injected reactive power at that bus

(( 2 ) ≫ ( ))
By considering the above approximations, Equation (8) can be described by the following linear form: Equation (12)  Where S P a vector is whose elements are the left-hand side of (12). The matrix H P is a real and square matrix whose elements are the negative of the bus susceptance matrix.

B. REACTIVE POWER FLOW MODEL
A linear reactive power flow model can be obtained by simplifying equation (9) as follow: The variable |E| appears in Equation (9) can be expanded around the nominal value 1 p.u. by using Taylor series expension and retaining only the first order term: Again, the trigonometric functions may be expressed by using Taylor series with only linear term is considered. Substituting the above simplification into (9) yields the following linear form: Equation (16) can be written in matrix form as: Each element of the vector S Q is evaluated by the left hand side of (16). The matrix H Q is a real and square matrix whose elements are as follow:

IV. PROPOSED ALGORITHM
The following algorithm may be adopted to rank the critical contingencies: i. Read the transmission system parameters, bus data ii.
Build the bus admittance matrix iii.
Solve the linear active power model by using equation to get the bus voltage angles iv.
Solve the linear reactive power model by using equation to get the bus voltage magnitudes v.
Evaluate the performance indices using equation vi.
Short list the critical contingencies according to their corresponding performance indices It is worth to be noted that the ranking is carried out simultaneously for both line overloads and voltage violation. Fig. (1) shows the flow chart of the proposed algorithm.  V.

RESULTS AND DISCUSSION
The proposed algorithm was applied to the 24 IEEE reliability test system. The bus data and the line data is given in Appendix A (Table A1 and A2). The system has twelve generating stations and 39 transmission lines. The performance index is evaluated for each contingency and the contingencies are ranked in descending order as given in Table 1 for the first top ten contingencies. It is shown that outage of the line connecting bus 15 to bus 21 has a pronounced effect on system security. The ranking of the critical contingencies obtained by the proposed algorithm is like those obtained by using full AC iterative load flow. Fig.2 shows the discrepancy in the value of performance index of the critical contingencies which is due to simplification of the proposed algorithm.  ACKNOWLEDGMENT The author would like to thank the Department of Electrical Engineering, Faculty of Engineering, Mustansiriyah University (www.uomustansiriyah.edu.iq)Baghdad-Iraq for its support in the present work.