# Simulation and Optimisation of Utility-Scale PV-Wind Systems with Pumped Hydro Storage
## 1 Introduction
Variable penstock losses were considered (assuming laminar flow); however, the pump and turbine efficiencies were considered constant. In addition, fixed electricity prices were used to sell or purchase electricity from the grid. [PERSON] et al. [17] optimised the daily operation of a PV-wind-PHS (PHS mine in China), thereby reducing the volatility of the power injection to the grid and increasing the benefits; however, they did not consider variable losses in the pump, turbine, or penstock. Recently, [PERSON] et al. [29] presented the optimisation (minimisation of grid-usage factor) of the different combinations of PV, wind, and PHS grid-connected systems with load consumption, which includes the variability of the friction losses and variable height, water reservoir evaporation, and seepage in the simulations; however, the pump and turbine efficiencies are considered fixed values, and the energy management strategy is simple (injected into the grid only when there is surplus energy that cannot be stored in the reservoir), and the electricity grid price is a fixed value. [PERSON] et al. [30] presented a method for the multi-objective minimisation of power mismatch and the maximisation of revenues in offshore wind-PHSs, using accurate models for wind generation (including the wake effect) and considering hourly periods for the electricity price. However, simple models for the PHS were used (fixed efficiency for the pump-turbine performance including friction losses and no variable head). Recently, [PERSON] et al. [31] showed the optimisation of the operation of a grid-connected PV-wind-PHS system that must supply a specific load consumption for one year. The optimisation of the monthly strategy maximises the benefits using PHS to meet the demand not covered by renewable sources and injecting surplus energy into the grid (not considering arbitrage). They used hourly prices of the Spanish wholesale electricity market in 2019, while considering fixed values for pump turbine performance, including friction losses and no variable head. To the best of our knowledge, none of the previous studies considered the use of PHS for arbitrage in grid-connected systems with load consumption under a real-time pricing (RTP) scheme for the electricity price. In this study, we consider the use of PHS for arbitrage under electricity RTP, optimising the component size (PV, wind, pump turbine, and reser-voir) and set points for arbitrage and management. Further, we used advanced models that have not been used in previous studies related to the optimisation of renewable---PHS systems. The main features of this work are provided below:  
Both LSS, where the objective is minimising the electricity cost of the load supplied, and PGS, where there is no load and the objective is maximising income from selling electricity to the grid, were optimised. Two different energy arbitrage systems were used: allowing or not buying energy from the grid during low RTP price periods to store energy in the pumped water. Further, the case without PHS was optimised to compare the optimal results with and without PHS. Each combination was simulated in time steps of 15 min during the lifetime of the system (typically 25 years). Unlike most previous studies, we considered uncertainties in electricity prices, solar irradiation, and wind speed over the entire lifetime of a system. Further, an increase in load consumption during the system lifetime was considered. The RTP electricity price is updated every year considering the effect of the increase in renewable power in the national electrical mix ('duck curve' of the electricity price profile). The performance decay of equipment during the years of the system lifetime was considered.