Dynamic optimization technique with differential equations

Abstract

One of the primary objectives of the problem is to reduce the cost of fuel consumed by generator units, and in recent years, we have developed new models to accomplish this goal. The first model problem represents a load following scenario, which is a common occurrence in power grids. The optimizer's objective is to balance demand and supply in response to fluctuating demand dynamics. At two different stages of the production process, a single producer tries to satisfy two constrained objectives in this model problem 2. By replacing a cogeneration system with n = 2 generators that generate (1) electricity and (2) heat in response to variations in demand, Model II improves on Model I. Using a n = 3 system with two products, three products, and three distinct order profiles, the third model issue builds on the prior two. The primary product remains unchanged from the preceding standard, and the slope rate is limited to the production of the two primary products (for example, electricity and heat). To create a third product (for example, a solid oxide electrolysis cell), the first two products are combined (for example, hydrogen).