# Optimal power flow of hybrid wind/solar/thermal energy integrated power systems considering renewable energy uncertainty via an enhanced weighted mean of vectors algorithm

## TL;DR

This paper introduces a new optimization algorithm to manage energy systems with wind, solar, and thermal power, improving efficiency and reducing costs despite renewable energy uncertainty.

## Contribution

A novel ARINFO algorithm is proposed, combining artificial rabbits optimization with a weighted mean of vectors approach to solve optimal power flow under uncertainty.

## Key findings

- ARINFO achieved 1st rank on CEC-2017 and CEC-2022 test suites.
- ARINFO reduced generation cost to 781.1538 $/h and emissions to 0.0922140 t/h in the IEEE 30-bus system.
- ARINFO attained a total cost of 20193.270 $/h in the IEEE 57-bus system, demonstrating scalability.

## Abstract

The rising global energy demand, along with the growth of electric power transmission and distribution systems, has intensified the need to incorporate renewable energy sources to foster sustainable development. However, achieving optimal operation within such systems poses significant challenges due to the stochastic nature of renewable energy generation. As a result, the optimal power flow (OPF) problem becomes increasingly complex when addressing the inherent uncertainty of renewable inputs. This study presents a new approach to addressing the OPF problem through the implementation of a hybrid Weighted Mean of Vectors Optimization Algorithm (INFO) based on artificial rabbits optimization (ARO) called ARINFO technique. The proposed ARINFO algorithm aims to reach an exploration-exploitation balance to improve search efficiency. To effectively manage the uncertainty associated with renewable energy output, modifications are implemented on standard test systems: in the IEEE 30-bus system (consisting of 30 buses, 6 thermal generators, and 41 branches), three thermal units are substituted with two wind turbines and one solar photovoltaic (PV) generator; a similar modification is made to the IEEE 57-bus system (which includes 57 buses, 7 thermal generators, and 80 branches) and large scale test system (IEEE 118-bus system). The stochastic characteristics of wind and solar power are modeled using Weibull and lognormal distributions, respectively. Their impact on the OPF problem is examined by incorporating reserve and penalty costs for overestimating and underestimating power output. Load demand variability is also assessed through standard probability density functions (PDF) to capture its uncertainty. Furthermore, operational constraints of thermal generators, such as ramp rate limits, are considered. The performance of the ARINFO algorithm is rigorously evaluated through 23 benchmark functions and the CEC-2022 test suite, with its effectiveness compared against nine established optimization methods. The results demonstrate that ARINFO achieved 1st rank overall on both the CEC-2017 and CEC-2022 test suites. When applied to the modified IEEE 30-bus system, ARINFO achieved a minimum generation cost of 781.1538 $/h, reduced emissions to 0.0922140 t/h, and minimized power losses to 1.734974 MW. For the larger IEEE 57-bus system, it attained a total cost of 20193.270 $/h, confirming its scalability and superior performance in managing the OPF problem under uncertainty in both generation and demand scenarios.