Supply‐demand optimizer for economic emission dispatch incorporating price penalty factor and variable load demand levels

Abstract

The Economic and Emission Dispatch (EED) method is widely used to optimize generator output in a power system. The goal is to reduce fuel costs and emissions, including carbon dioxide, sulphur dioxide, and nitrogen oxides, while maintaining power balance and adhering to limit constraints. EED aims to minimize emissions and operating costs while meeting power demands. To solve the multi‐objective EED problem, the supply‐demand optimization (SDO) algorithm is proposed, which employs a price penalty factor approach to convert it into a single‐objective function. The SDO algorithm uses a swarm‐based optimization strategy inspired by supply‐demand mechanisms in economics. The algorithm's performance is evaluated on seven benchmark functions before being used to simulate the EED problem on power systems with varying numbers of units and load demands. Established algorithms like the Grey Wolf Optimizer (GWO), Moth‐Flame Optimization (MFO), Transient Search Optimization (TSO), and Whale Optimization Algorithm (WOA) are compared to the SDO algorithm. The simulations are conducted on power systems with different numbers of units and load demands to optimize power generation output. The numerical analyses demonstrate that the SDO technique is more efficient and produces higher quality solutions than other recent optimization methods.

Optimizing Economic Dispatch with Renewable Energy and Natural Gas Using Fractional-Order Fish Migration Algorithm

“…2024, 8, 350 9 of 30 power (P PV sch , the system uses reserve units to satisfy demand [60]. The reserve capacity (C r PV ) cost is expressed in Equation (13).…”

“…When the actual power (𝑃 ) drops below the scheduled power (𝑃 ), the system uses reserve units to satisfy demand [60]. The reserve capacity 𝐶 cost is expressed in Equation (13).…”

“…Iterative or conventional techniques are commonly used as conventional approaches in addressing the EED problem. These techniques include the linear programming approach [10], gradient iterative approach [11], quadratic programming approach [12], Lagrange's method (LM) [13,14], hybrid mixed-integer linear programming and the interior point technique [15], and Newton-Raphson approach [16]. In a study [17], the EED issue has been reformulated into a quadratic programming problem, which can be further expressed as a semidefinite programming formulation.…”