Multi-objective multiperiod stable environmental economic power dispatch considering probabilistic wind and solar PV generation

The economic-environmental power dispatch (EEPD) problem, a widely studied bi-objective non-linear optimization challenge in power systems, traditionally focuses on the economic dispatch of thermal generators without considering network security constraints. However, environmental sustainability necessitates reducing emissions and increasing the penetration of renewable energy sources (RES) into the electrical grid. The integration of high levels of RES, such as wind and solar PV, introduces stability issues due to their uncertain and intermittent nature. This article addresses these concerns by formulating and solving the economic environmental and stable power dispatch (EESPD) problem, which includes fixed zonal reserve capacity from conventional thermal generators and uncertain reserves from RES. Uncertainties in RES and load demand are modelled using random variable generation techniques, applying Gaussian, Weibull, and log-normal probability density functions (PDFs) for load demand, wind velocity, and solar irradiance, respectively. The stochastic EESPD problem extends to multiple periods by replicating the single-period problem for each interval in the planning horizon, linking periods through intertemporal ramping costs, physical ramp rate, and fixed zonal reserve constraints on dispatch variables. Multi-objective evolutionary algorithms (MOEAs) have gained prominence for solving complex non-linear problems involving multi-objective functions. This article applies the latest MOEAs to tackle the proposed EESPD problem, incorporating stochastic wind and solar PV power sources. Network security constraints, such as transmission line capacities and bus voltage limits, are considered along with constraints on generator capabilities and intertemporal spinning reserves, ramp-up and ramp-down constraints for thermal generators. A bidirectional coevolutionary-based multi-objective evolutionary algorithm is employed, integrating an advanced constraint-handling technique to ensure compliance with system constraints. The simulation results show that the proposed formulation achieves a better trade-off between various conflicting objective functions compared to other state-of-the-art MOEAs. The modified IEEE 30-bus network, as shown in Figure, has three thermal generators located at buses 1, 2, and 8 and two wind farms, each with a rated capacity of 75 MW. The output of wind farms is connected to buses 5 and 11, while solarunits with a rated capacity of 50 MW supply power to bus 13. As an obvious fact, outputs from wind and solar PV are uncertain, and any deficit in total output from these units must be mitigated by spinning reserve. image