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Direct approach for optimal allocation of multiple capacitors in distribution systems using novel analytical closed-form expressions
Electrical Engineering ( IF 1.6 ) Pub Date : 2020-08-01 , DOI: 10.1007/s00202-020-01073-9
Karar Mahmoud , Matti Lehtonen

In this paper, novel and efficient analytical closed-form expressions are proposed for the optimal allocation of multiple capacitors in distribution systems to maximize the total cost reduction (CR) while considering power losses. The proposed expressions are novel since they can directly solve the allocation problem without requiring iterative processes or optimization algorithms. Specifically, two analytical closed-form expressions are introduced to determine the optimal number, locations, and sizes of multiple capacitors. The first analytical expression computes directly the optimal sizes of multiple capacitors where it is employed for the optimal sizing of capacitors for all possible combinations of locations. In turn, the best combination is then assigned by using a second analytical expression which directly evaluates all the combinations in terms of their contribution in CR. Unlike the existing methods/expressions that utilize sensitivity factors or optimize each capacitor individually, the proposed analytical closed-form expressions involve a unified mathematical model for multiple capacitors. The proposed direct approach is tested using a 69-bus distribution system. The accuracy and efficacy of the proposed analytical closed-form expressions are verified by comparisons with existing methods and intensive simulations of various allocation scenarios.

中文翻译:

使用新颖的分析闭式表达式优化分配系统中多个电容器的直接方法

在本文中,针对配电系统中多个电容器的优化分配,提出了新颖且有效的分析闭式表达式,以在考虑功率损耗的同时最大限度地降低总成本 (CR)。所提出的表达式是新颖的,因为它们可以直接解决分配问题,而无需迭代过程或优化算法。具体来说,引入了两个解析式闭合表达式来确定多个电容器的最佳数量、位置和大小。第一个分析表达式直接计算多个电容器的最佳尺寸,其中它用于为所有可能的位置组合优化电容器尺寸。反过来,然后通过使用第二个分析表达式分配最佳组合,该表达式直接评估所有组合在 CR 中的贡献。与利用灵敏度因子或单独优化每个电容器的现有方法/表达式不同,所提出的分析封闭式表达式涉及多个电容器的统一数学模型。建议的直接方法使用 69 总线分配系统进行测试。通过与现有方法的比较和各种分配场景的密集模拟,验证了所提出的分析封闭形式表达式的准确性和有效性。建议的分析封闭式表达式涉及多个电容器的统一数学模型。建议的直接方法使用 69 总线分配系统进行测试。通过与现有方法的比较和各种分配场景的密集模拟,验证了所提出的分析封闭形式表达式的准确性和有效性。建议的分析封闭式表达式涉及多个电容器的统一数学模型。建议的直接方法使用 69 总线分配系统进行测试。通过与现有方法的比较和各种分配场景的密集模拟,验证了所提出的分析封闭形式表达式的准确性和有效性。
更新日期:2020-08-01
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