Elsevier

Applied Energy

Volume 247, 1 August 2019, Pages 228-236
Applied Energy

An improved mathematical model for a pumped hydro storage system considering electrical, mechanical, and hydraulic losses

https://doi.org/10.1016/j.apenergy.2019.03.015Get rights and content

Highlights

  • A realistic PHS model is proposed for energy management applications.

  • Flow rate, water level, evaporation and precipitation affect model performance.

  • The proposed PHS model is validated with experiments in different operating points.

  • The error of the estimated stored water is reduced from 13.17% to 0.74%.

Abstract

This paper proposes a comprehensive pumped hydro storage model with applications in microgrids and smart grids. Existing models within current literature produce high error in calculating stored energy since some critical parameters are ignored. Thus, they are not suitable choices for energy management applications. Accordingly, the main objective of this study is to provide a more realistic model by estimating all the essential parameters in the system. First, all the losses due to the pump, pipes, and fittings are modelled. Next, a water balance approach is used to calculate the volume of water in the upper reservoir considering inflow, outflow, precipitation, and evaporation. Finally, the turbine power is calculated as a function of the water level in the reservoirs, considering the hydraulic losses of the turbine, pipes and fittings. The proposed model is validated using the experimental results of a physical system. The accuracy of the model is compared with other established models. The results demonstrate that the proposed model decreases the error of the estimated stored energy from 13.17% to 0.74%. Moreover, this study shows the capability of the model to simulate different configurations. The model provided in this paper assists researchers in the field and is of benefit to engineers in designing, sizing, and managing pumped hydro storage systems.

Introduction

Currently, power generation from renewable energy sources (RESs) is rapidly growing as a means of reducing greenhouse gas (GHG) emissions and providing a sustainable solution to increasing energy demands. However, unlike conventional power generation, renewable electricity depends on environmental factors such as solar irradiance and wind speed [1], [2]. Most importantly, power generation from RESs is not consistent, due to their intermittent nature which raises the issue of system reliability [3], [4]. The most practical solution to this is to integrate energy storage systems (ESSs) within RESs. In this case, when power generation is higher than demand, ESSs are charged, and when energy generation is lower than demand, ESSs meet the energy deficit. Thus, using ESSs can facilitate the mitigation of energy deficit and play a key role in future power systems [5], [6].

Conventional ESSs (e.g., Lead-acid and Li-ion batteries) have limitations relating to limited capacity, short lifespan, limited number of cycles, and high carbon footprint [7], [8]. However, as an alternative, pumped-hydro storage (PHS) is an eco-friendly energy storage system which can provide a more sustainable solution [9], [10], [11].

A PHS is comprised of two reservoirs, a pump, and a hydro turbine, storing electrical energy in the form of gravitational potential energy. When power generation is higher than demand, the water of the lower reservoir is pumped to the upper reservoir. When power generation is lower than demand, the stored water is released back into the lower reservoir through a hydro turbine in order to generate energy [12]. The capacity of a PHS depends on the volume of the upper reservoir and the height difference between the two reservoirs [13]. Therefore, a large reservoir at a height can form a PHS with lower cost and higher capacity compared to other ESSs. This method of energy storage has attracted much attention in recent years due to the fast growth of RESs in power systems [11], [14]. Ninety-four percent of energy storage projects in the world are PHS systems in terms of rated power [15], where they can be used for a variety of applications such as capacity firming, load levelling, peak shaving, power quality improvement, and spinning reserve.

Most research on PHS installation requires a model to accurately demonstrate the performance of a real PHS system [16], [17]. When sizing the pump, turbine, and reservoir, designers need a PHS model to optimally size the units [18], [19], [20], where a more accurate model produces a more realistic solution. Most energy management systems (EMSs) in this area require a PHS model with high accuracy in order to schedule the pump and turbine [21], [22], [23], [24]. The efficiency of these EMSs depends highly on the accuracy of estimated stored energy in the PHS. A model with low accuracy reduces the efficiency of EMSs by making wrong decisions. Accordingly, a model with high accuracy is necessary for both studying and managing PHS systems.

Current PHS models within the literature have high errors in calculating stored water. The simple PHS simulation model (model one) has two equations [16], [17], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], including the pump equation and the turbine equation. Both equations consider the efficiency of the pump and the turbine, but hydraulic and mechanical losses of the system are not considered.

Some other studies [32], [33] have improved the accuracy of the PHS simulation model by considering hydraulic losses involved in pumping water (model two). Accordingly, the authors added a head loss to the static head of the pump to account for the hydraulic losses of the penstock due to friction. The authors calculated pipes and fittings losses, but some parameters such as friction factor, relative roughness, and Reynolds number were considered as fixed values. However, these parameters depend on water velocity, pipe diameter, and pipe material. In addition, this model does not calculate the hydraulic losses of the turbine mode. This model improved the accuracy of the PHS model compared to model one, but the error of model two is still high.

The next limitation of model two is that the weather effect on the water level of the reservoir has not been considered. Usually, upper reservoirs are open top, and they are exposed to the sun and wind, where water surface evaporates every day. This reduces the volume of water in the reservoir, which leads to a reduction in stored energy. Contrastingly during precipitation, rain water is added naturally to the reservoir. Therefore, to obtain a complete PHS model the effect of weather on the volume of water in the reservoir should be considered.

Another problem with both established PHS models is that they ignore changes in water levels of the reservoirs. While a PHS is in pump mode or turbine mode water levels go up and down. These variations in water levels change the heads of the pump and the turbine.

This study proposes three major modifications to previous PHS models: (1) to reduce errors in flow rate calculation in the pump mode, the proposed model calculates the head loss of the penstock by calculating the friction factor, the relative roughness, and the Reynolds number according to the water velocity, pipe diameter, and pipe material; (2) to increase the accuracy of the water volume calculation, this model estimates the evaporation from the water surface of the upper reservoir; (3) to reduce errors in turbine power calculation, the turbine model calculates the head loss and the flow rate as a function of the water levels in both reservoirs. All these modifications help the model to calculate generated and stored energy with greater accuracy.

The paper is organized as follows: Section 2 presents the proposed pump, reservoir, and turbine models. Section 3 validates the mathematical model by comparing the simulated model and experimental results. In Section 4.1, the proposed model is compared with others PHS models in different scenarios and weather conditions to show how much the modifications have increased the accuracy of the model. Section 4.2 shows the capabilities of the model in different configurations, and finally, Section 5 provides conclusions.

Section snippets

Pumped hydro storage model

This section presents mathematical models for different components of the proposed PHS model. The main focus here is to take account of all the losses of the three PHS components including the pump, the reservoir and the hydro turbine. The proposed model is designed in a way that all the required parameters can be found in the technical manuals of the components, so researchers are able to use this model without any further experiments.

Simulation and experimental validation

This section compares the results of the proposed mathematical PHS model with the experimental results to verify the accuracy of the model. The proposed model is simulated in MATLAB Simulink (Fig. 2). All the equations in Section 2 are written in the MATLAB function blocks and connected together to simulate a PHS model. The experiments were conducted on an experimental setup, a physical PHS system installed at Edith Cowan University (Fig. 3). Fig. 4 depicts the PHS configuration, and Table. 1

Comparison of the PHS models

This section compares the results of the proposed model with model one [16], [17], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31] and model two [32], [33]. The operation of the physical PHS model was measured for 10 different days between August and December. In this experiment, 10 random scenarios were used for the operating mode of the PHS, and a weather station was installed near the experimental setup to measure temperature, humidity, wind speed, irradiance,

Conclusion

This study has improved the mathematical models of pumped hydro storage systems to calculate stored water volume and power generation with higher accuracy. The results of the proposed model are compared with the results of established models presented in other papers. The results of this study indicate that both model one and two significantly overestimate the volume of water. However, the proposed model has reduced this error from 13.17% to 0.74%. The error of the proposed model in the pump

Acknowledgment

This research was supported by an Australian Government Research Training Program Scholarship and Edith Cowan University, Australia.

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