An improved mathematical model for a pumped hydro storage system considering electrical, mechanical, and hydraulic losses
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.
References (41)
- et al.
Intermittent and stochastic character of renewable energy sources: consequences, cost of intermittence and benefit of forecasting
Renew Sustain Energy Rev
(2018) - et al.
A review on compressed air energy storage: basic principles, past milestones and recent developments
Appl Energy
(2016) - et al.
Overview of current development in electrical energy storage technologies and the application potential in power system operation
Appl Energy
(2015) - et al.
Overview of energy storage systems in distribution networks: placement, sizing, operation, and power quality
Renew Sustain Energy Rev
(2018) - et al.
Techno-economic role of PV tracking technology in a hybrid PV-hydroelectric standalone power system
Appl Energy
(2018) - et al.
Comparative study of hydrogen storage and battery storage in grid connected photovoltaic system: storage sizing and rule-based operation
Appl Energy
(2017) - et al.
Classification and assessment of energy storage systems
Renew Sustain Energy Rev
(2017) - et al.
Geographic information system algorithms to locate prospective sites for pumped hydro energy storage
Appl Energy
(2018) - et al.
Study on unit commitment problem considering pumped storage and renewable energy via a novel binary artificial sheep algorithm
Appl Energy
(2017) - et al.
Value of pumped hydro storage in a hybrid energy generation and allocation system
Appl Energy
(2017)
Feasibility study and economic analysis of pumped hydro storage and battery storage for a renewable energy powered island
Energy Convers Manage
Technical feasibility study on a standalone hybrid solar-wind system with pumped hydro storage for a remote island in Hong Kong
Renewable Energy
Pumped storage-based standalone photovoltaic power generation system: modeling and techno-economic optimization
Appl Energy
Optimal operation scheduling of grid-connected PV with ground pumped hydro storage system for cost reduction in small farming activities
J Storage Mater
Optimal power dispatch of a grid-interactive micro-hydrokinetic-pumped hydro storage system
J Storage Mater
Optimal scheduling for distributed hybrid system with pumped hydro storage
Energy Convers Manage
Energy management supporting high penetration of solar photovoltaic generation for smart grid using solar forecasts and pumped hydro storage system
Renewable Energy
Residential electricity cost minimization model through open well-pico turbine pumped storage system
Appl Energy
A novel pumped hydro-energy storage scheme with wind energy for power generation at constant voltage in rural areas
Renewable Energy
Hybrid DG-PV with groundwater pumped hydro storage for sustainable energy supply in arid areas
J Storage Mater
Cited by (44)
Spatiotemporal distribution pattern and analysis of influencing factors of pumped storage power generation in China
2024, Journal of Energy StorageOptimizing pumped-storage power station operation for boosting power grid absorbability to renewable energy
2024, Energy Conversion and ManagementDesign and performance assessment of a pumped hydro power energy storage connected to a hybrid system of photovoltaics and wind turbines
2023, Energy Conversion and Management