# A Hybrid MILP and IPM for Dynamic Economic Dispatch with Valve Point Effect

## TL;DR

This paper introduces a hybrid MILP and IPM approach to efficiently solve the complex, non-convex dynamic economic dispatch problem with valve-point effects, including transmission loss, improving solution quality.

## Contribution

A novel hybrid MILP-IPM method is proposed, combining MILP for initial solution and IPM for refinement, effectively handling non-differentiability and non-convexity in DED-VPE.

## Key findings

- The method effectively solves DED-VPE with valve-point effects.
- Simulation results validate the approach's accuracy and efficiency.
- The hybrid approach outperforms traditional methods in solution quality.

## Abstract

Dynamic economic dispatch with valve-point effect (DED-VPE) is a non-convex and non-differentiable optimization problem which is difficult to solve efficiently. In this paper, a hybrid mixed integer linear programming (MILP) and interior point method (IPM), denoted by MILP-IPM, is proposed to solve such a DED-VPE problem, where the complicated transmission loss is also included. Due to the non-differentiable characteristic of DED-VPE, the classical derivative-based optimization methods can not be used any more. With the help of model reformulation, a differentiable non-linear programming (NLP) formulation which can be directly solved by IPM is derived. However, if the DED-VPE is solved by IPM in a single step, the optimization will easily trap in a poor local optima due to its non-convex and multiple local minima characteristics. To exploit a better solution, an MILP method is required to solve the DED-VPE without transmission loss, yielding a good initial point for IPM to improve the quality of the solution. Simulation results demonstrate the validity and effectiveness of the proposed MILP-IPM in solving DED-VPE.