In a distribution system, load and distributed generation connected to a feeder are subject to uncertainty. Conventional capacitor placement and sizing methods do not consider uncertainty in power injections, due to which the results may be erroneous. In literature, affine arithmetic (AA) is one of the tools used for incorporating uncertainty in power system analysis. However, conventional division operation in AA gives rise to extra noise terms in the resulting affine form, which are not due to the actual uncertainty sources but are due to the nonaffine operations. The present work incorporates modified AA division which does not generate any additional noises, thereby improving the accuracy. Buses in the distribution network are ranked in decreasing order of rate of change of active power loss in line with respect to the change in the effective reactive power flow in that line. The top three ranked buses are chosen as candidate buses for capacitor connection. The required affine reactive current injection at the candidate buses is calculated, and the corresponding affine capacitive kVAR required is obtained through modified AA-based backward/forward sweep (BFS) power flow analysis. The intervals for the cost incurred in losses, voltage profiles with and without capacitor are calculated, and savings for capacitor connected system is calculated. Switchable capacitors are used for reactive power injection. The proposed method is tested on 15, 33 and 118 bus radial distribution systems. The results show that the proposed modified AA method is accurate than existing interval arithmetic-based method.

在配电系统中，连接到馈线的负荷和分布式发电存在不确定性。传统的电容器放置和尺寸确定方法没有考虑功率注入的不确定性，因此结果可能是错误的。在文献中，仿射算法（AA）是用于将不确定性纳入电力系统分析的工具之一。但是，AA中的常规除法运算会在最终的仿射形式中产生额外的噪声项，这不是由于实际的不确定性来源，而是由于非仿射运算。本工作结合了改进的AA划分，该划分不会产生任何其他噪声，从而提高了准确性。相对于该线路中有效无功功率流的变化，按网络中有功功率损耗变化率的降序排列配电网络中的总线。选择排名前三的母线作为电容器连接的候选母线。计算了在候选总线上所需的仿射无功电流注入，并通过基于AA的改进的后向/前向扫描（BFS）潮流分析获得了所需的仿射电容kVAR。计算损耗成本，带和不带电容器的电压分布的间隔时间，并计算电容器连接系统的节省量。可开关电容器用于无功功率注入。该方法在15、33和118母线径向分配系统上进行了测试。