In competitive electric power markets, electric utilities have to operate closer to their limits, causing unpredictable line loading, voltage variations, and stability problems. Flexible AC transmission system (FACTS) devices are used to provide direct control of power flows over designated transmission routes and increase power transfer capability of the transmission networks, resulting in a lower system loss, stability enhancement, operating cost reduction, and fulfilled contractual requirements (Hingorani & Gyugyi, 1999). The extent of these benefits depends upon where these devices are placed and how they are controlled in the systems, which in turn requires efficient methodologies to solve the optimal FACTS placement problems. This is an important aspect in the context of growing energy demand and the emergence of energy trading markets.
Available transfer capability is a measure of the transfer capability remaining in a physical transmission network for further commercial activity over and above already committed uses (Maliszewski, Rozier, & Cummings, 1996). Electrical power transfer capability calculation is required for each control area and posted on a public communication system for open-access of a transmission network to deliver electric energy (Withnell, Leahy, & Coleman, 1996). Mathematically, available transfer capability is defined as the total transfer capability (TTC) less the transmission reliability margin, less the sum of existing transmission commitments and the capacity benefit margin. TTC is defined as the amount of electric power that can be transferred over the transmission network in a reliable manner while meeting all of a specific set of defined pre- and post-contingency system conditions (Maliszewski, Rozier, & Cummings, 1996). Transmission reliability margin and capacity benefit margin are two transmission margins considering the inherent reliability and uncertainty in the transmission system.
Accurate determination of TTC is essential to maximize utilization of the existing transmission network while maintaining system security. Underestimated TTC may lead to under-utilization of transmission system, while overestimated TTC could lower system reliability. Wide varieties of mathematical methods such as: 1) linear method based on linear incremental DC load flow approximation considering only thermal limits (Ejebe, Waight, Nieto, & Tinney, 2000), 2) continuation power flow based on the continuation method to trace load flow solution curve through the maximum loading point (Ejebe et al., 1998), 3) repetitive power flow based on repeated load flow calculations to establish the maximum transfer capability (Gravener & Nwankpa, 1999), and 4) a bifurcation approach for assessing dynamic TTC considering transient stability limits (Kumar, Srivastava, & Singh, 2004) have been developed for TTC computations. In addition, optimal power flow (OPF) based methods, which can be implemented by traditional optimization techniques have been proposed to calculate TTC with various degrees of success (Ou & Singh, 2002; Shaaban, Li, Yan, Ni, & Wu, 2003).
These methods require convexity of objective function to obtain the optimal solution. However, the OPF problem is generally nonlinear and nonconvex optimization problem and, as a result, many local solutions may exist especially in power systems with embedded FACTS devices (Wong, Yuryevich, & Li, 2003). FACTS parameters are additional control variables that cannot be effectively solved by conventional optimization methods because these parameters will change the admittance matrix. Therefore, conventional techniques may converge to local optimal solutions or diverge altogether (Lai, 1998).
In recent years, power transfer capability enhancement (Ou & Singh, 2001; Xiao, Song, Liu & Sun, 2003) and power losses reduction (Chung & Shaoyun, 1998) using multi-type FACTS devices are significant because of competition enhancement and efficient existing transmission system utilization. Sensitivity index approaches have been commonly used to determine suitable locations of FACTS devices for maximizing TTC (Verma, Singh & Gupta, 2001) or minimizing power losses (Preedavichit & Srivastava, 1998). However, these methods may not lead to the optimal solution because of dependency to system topology and loading conditions.