Cost Allocation of Voltage Unbalance in Distribution Networks

The proliferation of distributed generation has increased the complexity of voltage regulation in distribution networks. Asymmetrical line impedance, the presence of single phase generation and unbalanced loading can produce voltage unbalance. The performance of high efficiency three-phase induction machines drops significantly with voltage unbalance. Currently, there is no mechanism to ensure that a customer in ownership of a voltage unbalance sensitive load is compensated for excessive voltage unbalance. In response, the authors propose a market framework where compensation is to be paid between offending and affected customers where voltage unbalance limits are exceeded. The ideal compensation payments are calculated using Shapley values, but this technique is found to be prohibitively computationally expensive for large numbers of loads. An approximate method using voltage unbalance sensitivities is proposed as a remedy. The approximate method is compared with the Shapley value method using a nine load bus case study with a voltage unbalance violation compensation cost of $10. The results show a $2.11 root mean squared error for individual voltage unbalance compensation calculations over 1000 randomly generated cases with an unacceptable voltage unbalance. The diversif cation of compensation payments over many violations substantially reduced the error.