# Reactive Power Compensation Game under Prospect-Theoretic Framing Effects

## TL;DR

This paper models reactive power compensation as a game influenced by prospect theory, revealing how subjective customer evaluations impact grid performance and decision-making strategies.

## Contribution

It introduces a behavioral framework based on prospect theory into reactive power coordination, extending traditional models with subjective decision-making considerations.

## Key findings

- PT causes customers to adopt more conservative strategies.
- Customers under PT increase power factor by 29%.
- The game converges to a mixed-strategy Nash equilibrium.

## Abstract

Reactive power compensation is an important challenge in current and future smart power systems. However, in the context of reactive power compensation, most existing studies assume that customers can assess their compensation value, i.e., Var unit, objectively. In this paper, customers are assumed to make decisions that pertain to reactive power coordination. In consequence, the way in which those customers evaluate the compensation value resulting from their individual decisions will impact the overall grid performance. In particular, a behavioral framework, based on the framing effect of prospect theory (PT), is developed to study the effect of both objective value and subjective evaluation in a reactive power compensation game. For example, such effect allows customers to optimize a subjective value of their utility which essentially frames the objective utility with respect to a reference point. This game enables customers to coordinate the use of their electrical devices to compensate reactive power. For the proposed game, both the objective case using expected utility theory (EUT) and the PT consideration are solved via a learning algorithm that converges to a mixed-strategy Nash equilibrium. In addition, several key properties of this game are derived analytically. Simulation results show that, under PT, customers are likely to make decisions that differ from those predicted by classical models. For instance, using an illustrative two-customer case, we show that a PT customer will increase the conservative strategy (achieving a high power factor) by 29% compared to a conventional customer. Similar insights are also observed for a case with three customers.