Frequency-constrained expansion planning for wind and photovoltaic power in wind-photovoltaic-hydro-thermal multi-power system

Frequency security is one of the most critical factors for ensuring the safe and stable operation of power systems. In wind-photovoltaic-hydro-thermal multi-power systems (WPHTMPS), the increase in new energy share and the water hammer effect weaken the frequency modulation (FM) capability, threatening the frequency security of the power system. To address this issue and ensure the frequency security of WPHTMPS under the trend of large-scale development of wind and photovoltaic (PV) power, this paper proposes a novel expansion planning method for wind and PV power in WPHTMPS that considers FM capability in the planning stage. The method realizes the coordinated optimization of long-term planning and short-term operation while adhering to the frequency se-curity constraints. The constraints are derived from the multi-power system frequency response model (MPSFR) which integrates virtual inertia, synchronous inertia, and the water hammer effect. However, due to the high -order characteristic of the MPSFR model, the frequency security constraints cannot be expressed explicitly to be embedded in the planning model by current study. Therefore, the boundary equivalence method is proposed to deal with this problem, which is effective to convert the frequency security constraints into inertia constraints and embed them in the planning model according to their relationship with installed capacity and unit commitment. Finally, simulation for a power system in Southwest China validates the proposed method, with results indicating that around 13% more capacity of new energy is needed to provide adequate FM reserve and power supply. Furthermore, it is demonstrated that the FM capability of new energy can improve the installed share of new energy from 46.5% to 70% while effectively ensuring frequency security.