Development of a Multi-Objective Optimisation Model for Mitigating Frequency Instability in a Renewable Energy-Sourced Power System

Abstract

The power grid is changing in order to reduce the negative effect of greenhouse gas emissions from thermal generators while meeting the global net zero emission goal by 2050. Conversely, as the drive towards a renewable energy-dominant grid is propelled, the overall system inertia of the power grid declines, which causes frequency instability in the modern power grid. This study aimed to develop a multi-objective optimisation model for mitigating frequency instability in a renewable energy-sourced power system. This was achieved by firstly reviewing the various types of virtual inertia control strategies and topology in the power system while highlighting the inertia requirement of the modern power system. The review revealed that adequate system inertia is required for the modern renewable energy-dominant grid to ensure stability; it should therefore be considered in power system operational and planning optimisation models. A new mathematical model was formulated to maximise the overall system inertia of the grid, while minimising system cost and carbon dioxide (CO2) emissions. The model was developed as a mixed-integer quadratic constrained programming (MIQCP) problem and solved using CPLEX solver in the General Algebraic Modeling System (GAMS). The model was validated using a modified Institute of Electrical and Electronics Engineers (IEEE) 9-bus test system. The results revealed that the developed model achieved higher system inertia than the conventional model, which does not consider the inertia requirement of the grid in planning. Furthermore, the model was extended to consider possible expansion in the transmission network as more renewable energy generators (REGs) are integrated into the grid, while considering the inertia requirement of the grid. A new mathematical model was formulated as an MIQCP problem and solved using CPLEX solver in GAMS. To combat declining inertia and mitigate frequency instability in the modern grid, appropriate inertia constraint was introduced into the planning model. Also, an emission reduction initiative (ERI) was introduced in the joint generation and transmission expansion planning (GTEP) model in which power operators were incentivised if they are able to maintain a preset emission limit. The results revealed that the developed model achieved a 24% increase in system inertia and a 9.62% reduction in CO2 emissions. This shows the effectiveness of ERI constraints in meeting the goal of emission reduction in the power system. Furthermore, sensitivity analysis of feed-in tariff (FiT) (economic incentive) was considered in the model. A novel FiT and inertia-integrated GTEP optimisation model was developed, which considered the influence of an economic incentive (FiT) in promoting the integration of REGs into the grid while meeting the inertia requirement of the grid. The model was developed as an MIQCP model to minimise the total system cost and CO2 emissions, while maximising the overall system inertia and FiT incentives. The developed model was implemented on an IEEE 6-bus test system and solved using CPLEX solver in GAMS. Sensitivity analysis of the model revealed that the higher the penetration of renewable energy sources (RESs), the higher the total system cost and total FiT received; however, the fraction of FiT payments received relative to the total investment cost decreased after 50% RES penetration for the same FiT rate. Finally, the model was extended to consider the uncertainties of renewable energy resources (RERs) and system inertia. The intermittencies of wind speed and solar irradiance were addressed using a scenario-based approach. The variability of RER (solar irradiance and wind speed) in the Mangaung Metropolitan Municipality in the Free State province of South Africa was considered for the year 2019. The model was further developed as an MIQCP model to minimise system cost of energy (CoE) while maximising system inertia. The model was solved using CPLEX solver in GAMS and implemented on an IEEE 6-bus system. The model analysis results revealed that considering both system inertia and renewable energy uncertainties provides appropriate planning results with a notable 9% reduction in the total system cost and a 7.9% reduction in the CoE, while the overall system inertia is enhanced by 7.3%. In addition, January was revealed as the best-performing month for wind resources, while October was revealed as the best-performing month for solar resources at the study location (Mangaung Metropolitan Municipality in the Free State). These results show the importance of considering system inertia in power system optimisation modelling to ensure the frequency stability of the modern grid with high penetration of renewable generators is not compromised.