Voltage stability primarily depends on the voltage magnitude, phase angle, real and reactive power constraint of the electric power system. Even during emergencies like contingency (outages), the stability of the electric power structure will be enhanced by improving the Loadability Limit (LL) of the transmission sector. Flexibility in the real and reactive power flow in the transmission system is achieved by the Flexible AC Transmission System (FACTS) devices. These devices can be placed anywhere in the transmission sector. To get effective control over the power flow through the transmission lines and to achieve the maximum loadability with the minimal installation cost, optimal choice and placement of FACTS devices are essential. In this manuscript, efforts had been taken to analyze the LL with outages for hybrid electric power structures. The proposed method is simulated and tested with the hybrid version of standard IEEE 30 bus system. Three types of FACTS devices like Thyristor Controlled Series Capacitor (TCSC), Static VAr Compensator (SVC) and Unified Power Flow Controller (UPFC) are efficiently selected and placed in the transmission lines. For the optimal positioning and placement of these devices, the Contingency Severity Index (CSI) and Fast Voltage Stability Index (FVSI) have been used. Differential Evolution (DE) and Modified Differential Evolution (MDE) algorithms are applied to optimize the obtained results. DE is an evolutionary search based soft computing algorithm popularly handed to resolve multifarious problems. MDE is the enhanced version of DE that embraces a prior knowledge about the solution space at every stage of the search. The main focus of this work is (i) to identify the weak branches and buses in the system using CSI and FVSI. (ii) to optimize the number, location and settings of FACTS devices using various soft computing techniques like DE and MDE. (iii) to evaluate ML of a transmission system with FACTS devices under normal and contingency conditions using DE and MDE. (iv) to calculate the cost required for the installation of FACTS devices. (v) to enhance ML of pool and hybrid model of deregulated electric power market with contingency using the optimal number, rating and positioning of FACTS devices.

电压稳定性主要取决于电源系统的电压幅度，相角，有功和无功功率约束。即使在诸如突发事件（停电）之类的紧急情况下，通过改善输电部门的负荷极限（LL）也会提高电力结构的稳定性。灵活的交流传输系统（FACTS）设备可实现传输系统中有功和无功潮流的灵活性。这些设备可以放置在传输扇区中的任何位置。为了有效控制通过传输线的功率流并以最小的安装成本获得最大的负载能力，FACTS设备的最佳选择和放置至关重要。在此手稿中，已进行了努力以分析混合电力结构停电时的LL。所提出的方法在标准IEEE 30总线系统的混合版本中进行了仿真和测试。可以有效地选择三种类型的FACTS设备，例如晶闸管控制串联电容器（TCSC），静态VAr补偿器（SVC）和统一潮流控制器（UPFC），并将其放置在传输线中。对于这些设备的最佳定位和放置，已使用了偶然性严重程度指数（CSI）和快速电压稳定性指数（FVSI）。应用差分进化（DE）和改进的差分进化（MDE）算法来优化获得的结果。DE是一种基于进化搜索的软计算算法，通常用于解决各种问题。MDE是DE的增强版本，在搜索的每个阶段都包含有关解决方案空间的先验知识。这项工作的主要重点是（i）使用CSI和FVSI识别系统中的弱分支和总线。（ii）使用各种软计算技术（例如DE和MDE）优化FACTS设备的数量，位置和设置。（iii）使用DE和MDE评估带有FACTS设备的传动系统在正常和偶发情况下的ML。（iv）计算安装FACTS设备所需的成本。（v）通过使用FACTS设备的最佳数量，额定值和位置来偶然性地增强去监管化电力市场的池和混合模型的ML。（iii）使用DE和MDE评估带有FACTS设备的传动系统在正常和偶发情况下的ML。（iv）计算安装FACTS设备所需的成本。（v）通过使用FACTS设备的最佳数量，额定值和位置来偶然性地增强去监管化电力市场的池和混合模型的ML。（iii）使用DE和MDE评估带有FACTS设备的传动系统在正常和偶发情况下的ML。（iv）计算安装FACTS设备所需的成本。（v）通过使用FACTS设备的最佳数量，额定值和位置来偶然性地增强去监管化电力市场的池和混合模型的ML。