Optimal Voltage Sag Mitigation Solution Provision using Customers Approximate Marginal Willingness-to-Pay Function

The requisite cost-benefit analysis for the deployment of voltage sag mitigation solutions often requires an explicit mathematical expression of the customers’ willingness-to-pay estimates. The willingness-to-pay function, which is also equal to the benefit received by customers through the prevention of process failures, is a function of the probability density function of sag occurrence, customer’s conditional process failure probability, and the process interruption cost. In this paper, through a detailed mathematical analysis, it has been shown that the customer’s marginal willingness to pay function is linearly decreasing. The conditional probability theory is used for calculating the total probability, which is primarily utilized for calculating benefits received from the prevention of process failures. The derived linear willingness to pay function of the customer has been utilized to obtain optimal voltage sag mitigation solution provision for a typical customer. The symbiotic behavior resulting from common mitigation solution provision for multiple customers is also presented.