# Simulation and Optimisation of Utility-Scale PV-Wind Systems with Pumped Hydro Storage
## 2 Modelling Approach  
Figure 1 shows the PV-wind-PHS system. In this study, we expanded the megawatt hybrid optimisation by genetic algorithm (MHOGA v 3.4) [33; 34] software to perform simulations and optimisations. We considered two systems:  
LSS (Figure 1): In this system, electrical load \(P_{L}(t)\) must be supplied during every time step \(t\) of the entire system lifetime. The system can be applied to a small town or residential, commercial, or industrial area. Electricity is supplied by means of the grid and renewable-PHS system, and the objective is minimising the electricity cost (minimise net present cost, NPC) of the load supplied. PGS: In such systems, there is no load demand (or the load demand is very low only for the auxiliary consumption of the power system). The objective of the owner of the renewable-PHS power-generating system is maximizing the benefits obtained by selling electricity to the grid (maximising the net present value, NPV). It would be a specific case of LSS considering no load (\(P_{L}(t)=0\)\(\
abla\)\(t>0\)) or low load (for the auxiliary consumption of the PGS). Two different types of systems were considered for energy arbitrage (Table 1): Type A (allowed to purchase energy from the grid for energy arbitrage) and Type B (not allowed to purchase energy from the grid for energy arbitrage; purchase is allowed only for the load supply when it is required). Once the system type was defined, different combinations of components (PV generator, wind turbines, pump turbine, and reservoirs) and control strategies were simulated during the system lifetime in time steps of 15 min and evaluated. For each time step, the energy balance was determined based on the type of system and different variables. Input variables for each time step \(t\) were (Figure 1) maximum grid power \(P_{\text{max\_grid}}(t)\), load consumption \(P_{L}(t)\), PV output power \(P_{PV}(t)\), wind turbines' output power \(P_{WT}(t)\) (W), water volume of the upper and lower reservoirs, \(V_{UR}(t)\) and \(V_{LR}(t)\) (m\({}^{3}\)), electricity price (purchase to the AC grid price and sell to the AC grid price), and \(Pr_{Epurch}(t)\) and \(Pr_{Eell}(t)\) (EUR/kWh). Figure 1: PV–wind–PHS system. The set points are listed below:  
High limit of electricity price for energy arbitrage (\(\Pr_{E\textit{purch}/\textit{sell\_High\_stp}}\)). If the electricity price (purchase or sale price, depending on project type A or B, respectively) is higher than this limit, the priority is injecting electricity into the grid, including hydropower generation, at its maximum allowed power. Low limit of electricity price for energy arbitrage (\(\Pr_{E\textit{purch}/\textit{sell\_Low\_stp}}\)). If the electricity price is lower than this limit, a pump is used to store water in the upper reservoir. Depending on the type of project (A or B), the pump runs at its rated power (consuming electricity from the grid, if needed) or with the power supplied by the net renewable power. Limit of the purchase price for the electricity to supply the net load using the grid (if the electricity price is lower than this setpoint) or hydro turbine (if the price is higher): \(\Pr_{E\textit{purch\_load\_stp}}\). This setpoint has no meaning in the PGS if there is no load. In addition,