Modeling and coordinated control for active power regulation of pumped storage‐battery integrated system under small‐disturbances

Multienergy complementation is an important means to improve the capacity of renewable energy consumption and the key to achieving the goal of “net zero” globally. The hydro–wind–photovoltaic‐storage hybrid system is an important technical approach, and in this system, pumped storage and battery energy storage are both key components for regulation. To study the problem of coordinated control of the two storage systems, a model of a pumped storage‐battery integrated system (PSBIS) for simulating small disturbances of pumped storage units and the battery charge and discharge characteristics was established by MATLAB/Simulink in this study firstly. Then, two control strategies (“priority regulation of pumped storage” and “priority regulation of battery storage”) are studied, and simulation calculations under ideal input and measured wind power disturbances are carried out to compare two control strategies by using the integrated system model under grid‐connected conditions. The simulation results revealed that the “priority regulation of pumped storage” control strategy has a better performance on active power balance, compared with the “priority regulation of battery storage” control strategy. This work could provide technical support for coordinated control of the practical PSBIS in the future.


| INTRODUCTION
It is proposed by the European Union that at least 27% of final energy consumption should be covered by renewable energy by 2030. 1 To achieve this goal, both wind power and photovoltaic installed capacity should continue to grow; China also proposes sustainable use of renewable energy and resources to achieve the goal of "net zero." However, wind power and photovoltaic power generation have the characteristics of randomness, volatility, and anti-peak regulation, requiring hydropower with strong regulation performance and special large-capacity energy storage devices for regulation. 2 The multienergy complementary system can coordinate the supply and demand of renewable energy, and also improve energy efficiency. 3 More specifically, the hydro-wind-photovoltaic-storage hybrid system is one of the feasible solutions, 4 and pumped storage and battery energy storage are both key components for regulation.
Pumped storage is the most mature large-scale energy storage method at present. 5 It is a key regulator for "net zero" targets and modern power systems because of its excellent regulating ability. Meanwhile, in recent years, the cost of battery energy storage has dropped rapidly, and commercial application has gradually matured. 6 Pumped storage systems integrated with batteries can increase the adjustable speed of active power on a timescale of milliseconds, improve the ancillary service performance, ensure the operation stability, and reduce the movements and wear of actuators of regulating systems of pumped storage units to increase the operation life. 7 Many scholars have studied the regulation of pumped storage or battery energy storage respectively. In Zhao et al., 8 a multiobjective optimization strategy to improve the regulation quality and stability of hydropower-dominated systems was proposed. In Yang et al., 9 the operation stability of a hydropower system was studied based on the combination of theory and experiment. In Al-Masri et al., 10 the impact of different photovoltaic models on a solar arraypumped storage integrated system was investigated by comparing the ecological benefits and reliability of the three photovoltaic models, and the best approach was validated in the Al-Wehda dam. In Ma et al., 11 the technoeconomic feasibility of solar-wind-battery storage integrated system was studied. In Shabani et al., 12 micropumped hydrostorage, and battery energy storage were operated respectively with wind and solar in a remote area in Sweden, and the economic benefits and reliability of the two approaches were compared.
However, little research was done on the combined regulation of pumped storage and battery energy storage. In Makinen et al., 13 a hydropower-battery integrated model in the simulation of grid frequency control was established. In Javed et al., 14 a pumped and battery storage hybrid system was proposed, and the battery is the auxiliary energy storage, and pumped storage is the main energy storage, and the performance indicators mainly based on the economy were analyzed. In Ma et al., 15 a pumped storage-battery system with a renewable energy system in Hongkong was studied, and economic benefits and technical viability were compared.
At present, there are some strategies and methods in the pumped storage-battery integrated system (PSBIS) to coordinate pumped storage and batteries to meet the regulation demand. In terms of performance: In Li et al., 16 a coordination method was proposed to shift peak load, respond to the wind power ramping, reduce the curtailment of wind, and steady the output of thermal units. In terms of economy: In Abdelshafy et al., 17 a novel energy management strategy was proposed to reduce investment costs and CO 2 emissions. In Ghanjati and Tnani, 18 an adapted energy management strategy was proposed for multiobjective optimization in economic aspects.
In terms of engineering practice, at present, because the power system has higher requirements for the regulation capacity and operation intensity of pumped storage plants, a small number of hydropower plants or pumped storage plants have been integrated with battery energy storage. For example, pilot constructions and operations are carried out in Forshuvud Hydropower Plant in Sweden (2019), 19 Bavaria Pumped Storage Project in Germany, and Vogelgrun Hydropower Plant in France (2018). 20 The State Grid Corporation of China has also recently launched related research projects, aiming for the integration of small and medium size pumped storage and battery energy storage systems. Meanwhile, the US Department of Energy released a prospective research report in 2019, 21 while most countries currently have no practical projects.
In brief, the above studies could be improved in the following aspects: (1) Most of the multienergy complementary systems adopt pumped storage or battery energy storage separately to balance renewable energies, making the regulation of the two energy storage components relatively isolated. Moreover, there is a lack of research on the mathematical model and control strategy of the PSBIS. Therefore, research on the modeling of the PSBIS should be carried out. (2) In the studies for combined regulation of pumped storage and battery energy storage, most are based on long-term research on economic benefits, ecological benefits, and feasibility, while the research on refined power regulation with a time scale of seconds is relatively insufficient. Therefore, it is of significance to study the active power regulation characteristics and control strategies of the PSBIS based on the time scale of seconds.
Aiming at the above problems, in this work, the model of the PSBIS is established based on MATLAB/ Simulink, for simulating small disturbances of pumped storage units and the battery charge and discharge characteristics. Then, the dynamic response characteristics of the integrated system are studied under gridconnected conditions, and the two control strategies for active power regulation ("priority regulation of pumped storage" and "priority regulation of battery storage") are compared. This work could provide technical support for the regulation of practical PSBIS in the future.
The main novelty and contributions of this study are as follows: (1) The model of the PSBIS has been built, for simulating small disturbances of pumped storage units and the battery charge and discharge characteristics, providing a tool for performance prediction to support engineering practices. Although previously there are several independent models for pumped storage systems and independent models for batteries, there are few integrated models of the PSBIS. (2) Two control strategies for active power regulation, "priority regulation of pumped storage" and "priority regulation of battery storage," are proposed. Simulation and quantitative assessment are carried out under ideal input and measured wind power disturbances to display the performance of the proposed strategies.
The paper structure is as follows: In Section 2, the mathematical modeling of the PSBIS for simulation is established. In Section 3, strategies of coordinated control and performance evaluation indexes are introduced. In Section 4, the effects of active power balance under five strategies are compared and analyzed. In Section 5, the conclusions and limitations are given.
2 | MATHEMATICAL MODELING FOR SIMULATION 2.1 | Pumped storage system A pumped storage system can be regarded as a complex system composed of a hydraulic system, mechanical system, and electric power system. According to the control theory, pumped storage units under the power generation condition can be simplified as a turbine regulation system, including five subsystems: speed governor, water diversion system, surge tank, pump turbine, and generator. 22 The turbine regulation system is very complex, with nonlinear and nonminimum phase characteristics. [23][24][25] In the PSBIS, pumped storage units need to control the external power change in real-time. Therefore, a PI speed governor model is selected in this study, as shown in Figure 1, and the transfer functions of the speed governor, 26 water diversion system, 27 and surge tank are as follows: where P is active power (input) and Y is guide vane opening (output); k p and k i are respectively turbine governor parameters for the proportional and integral term; T y is servo time constant.
where Q is flow (input), and H is water head (output); T w is water flow inertia time constant; T e is water flow elastic time constant; T wt is diversion tunnel water flow inertia time constant; T s is surge tank time constant; a is the elastic coefficient of pressure pipeline, taken as 0.5; f t is the frictional drag coefficient.
At present, the main method to study the transient process of pumped storage plants is to quantitatively describe the steady-state working characteristics of turbines through turbine characteristic curves. However, the study in this paper focuses on small disturbances, and the error when using the linear model is in the allowed range. The formulas are as follows: In summary, a model of the pumped storage system can be established as shown in Figure 2.

| Battery storage system
Since the characteristic curves of battery charge and discharge are nonlinear, it is complicated to establish a model that can reflect the complete and accurate charging and discharging process of batteries. 31 The equivalent circuit model can reflect the change in the state of charge (SOC) and the dynamic performance of batteries, and the modeling is not complex. [32][33][34][35] Therefore, the RINT equivalent circuit model is adopted in this study.
One-machine equivalent model is adopted in the battery storage system. In simpler terms, the same type of batteries with the same performance are adopted throughout the system, and all batteries are in the same working state at every moment. Therefore, when establishing the model, firstly build the single model, and then combine the single cells in series and parallel to establish the model of energy storage battery packs. The equivalent circuit of energy storage battery packs is shown in Figure 3.
The ampere-hour integration method is adopted to estimate the SOC in this study, and the formula is as follows: where C N is the rated capacity of the battery; η is the efficiency of charge and discharge; and i is electric current.
The SOC, capacity, and voltage functions of the energy storage battery pack are as follows: where Q B is the quantity of electricity; E m is electromotive force; I in is input current; I T is the current of a single battery; U T is the voltage of a single battery; R T is the internal resistance of a single battery; N p is the number of parallel batteries; and N s is the number of batteries in series.

| Integrated system and parameter values
The modeling of the PSBIS adopts a transfer function method that can reflect the internal characteristics of each subsystem itself and continue to expand. The equations in the above literature only build the independent system model for pumped storage systems or battery systems. In this section, based on the two subsystem models, an integrated Simulink model of the PSBIS is established by using the AC bus topology, as shown in Figure 4. According to the practical projects of the PSBIS in the world, 19,20 the capacity ratio of battery storage plants and pumped storage plants is generally 5%-10%. Therefore, the installed capacity of the battery storage power station is taken as 5% of the installed capacity of the pumped storage system in this study, and parameter settings in the PSBIS are shown in Table 1.

| STRATEGIES OF COORDINATED CONTROL
In this section, five control strategies are designed to study the regulation quality of the PSBIS, as shown in Table 2. The details are described in the following sections.

| "Priority regulation of pumped storage" strategy
The PSBIS realizes real-time regulation for the deviation of external power, and the power deviation is the input signal. The "priority regulation of pumped storage" strategy can be described as follows: The power deviation is first input to the pumped storage system for regulation, and then the deviation part of the power is input to the battery storage system for further regulation.
In Figure 5, P p,in is the active power input into the pumped storage system; P p,out is the active power output by the pumped storage system; P b,in is the active power input into the battery storage system.

| "Priority regulation of battery storage" strategy
The "priority regulation of battery storage" strategy can be described as follows: The power deviation is first input to the battery storage system for regulation, and then the deviation part of the power is input to the pumped storage system for further regulation.
In Figure 6, P b,out is the active power output by the battery storage system.

| Conventional strategies
Three conventional strategies are introduced in this section.
The "simultaneous regulation of battery and pumped storage" strategy can be described as follows: The power deviation is simultaneously input to the battery storage system and pumped storage system for regulation according to the capacity ratio.
In Figure 7, K 1 is the proportion of the pumped storage system in the capacity of the PSBIS, K 1 = 20/21; K 2 is the proportion of the battery storage system in the capacity of the PSBIS, K 2 = 1/21.
The "regulation of pumped storage alone" strategy can be described as follows: The power deviation is the only input to the pumped storage system for regulation.  The "regulation of battery storage alone" strategy can be described as follows: The power deviation is the only input to the battery storage system for regulation.

| Performance evaluation indexes
Two evaluation indexes for comparing the two control strategies are selected as follows: where δ is the energy deviation coefficient, an index that the smaller, the better; P MW is reference power F I G U R E 6 Energy control module of the "priority regulation of battery storage" strategy.
where E p is penalty energy, an index that the smaller, the better. It represents cumulative energy deviation between reference and simulation; P pu is reference power deviation (pu); P a,pu is the active power of the PSBIS (pu).

| SIMULATION AND ANALYSIS
In this section, the active power of the PSBIS under different inputs is mainly studied. The input is the power deviation signal, and there are two groups of input signals, that is, ideal input and practical input.
The specific settings are as follows: (1) Ideal input (2) Practical input Four groups of measured wind power deviation signals are selected, and each power reference length is 600 s. Considering different distribution characteristics of wind power deviation, the histogram of measured wind power deviation signals is shown in Figure 8, including unimodal, skewed, and bimodal distributions. 36

| Result of "priority regulation of pumped storage"
The change curves of the active power of the PSBIS under the "priority regulation of pumped storage" strategy are shown in Figures 9-13. The black solid is the active power of the PSBIS, and the red dotted line is the reference power deviation.
The results of four ideal inputs are shown below: (1) Step input (shown in Figure 9): The PBSIS has a good performance on active power balance under the step (A) and (C) input, as shown in Figure 9A,C. Whereas under the step (B) input, as shown in Figure 9B, since the installed capacity of the battery storage system is 10 MW, it cannot regulate the part of the power deviation exceeding 10 MW, making the power balance time about 20 s longer compared to the step (A) and (C) input. (2) Ramp input (shown in Figure 10): It can be seen that there is almost no difference between the active power curve and the power deviation curve of the PSBIS under small disturbances. (3) Sine input (shown in Figure 11): It can be seen that the regulation of the pumped storage system has a long delay, and due to the long regulation time, the active power is not regulated to the peak value of the reference power deviation before the next round of regulation. Furthermore, after the combined regulation of the battery storage system, the active power can better balance the power deviation. Comparing the sine (A) and (C) input, as shown in Figure 11A,C, it can be found that when the change of the power deviation exceeds the installed capacity of the battery storage system, the PSBIS has a worse performance on active power balance. (4) Sawtooth input (shown in Figure 12): The active power curve of the pumped storage system changes on a ramp at first and then slows down slightly when it approaches the target value. The simulation results are similar to the sine input, and the PSBIS has a good performance on active power balance.
Under the practical input (shown in Figure 13), since the power deviation is initially regulated by the pumped storage system and then further regulated by the battery storage system, the part of the power deviation exceeding the installed capacity of the battery storage system is less.
Meanwhile, the characteristics of the battery storage system that can realize rapid active power regulation enable the PSBIS to quickly balance active power under the "priority regulation of pumped storage" strategy. Under the four-practical input, the active power output curve only has a small gap with the power deviation curve where the power deviation changes greatly.
In brief, the PSBIS has a good performance on active power balance under the "priority regulation of pumped storage" strategy.

| Result of "priority regulation of battery storage"
The change curves of the active power of the PSBIS under the "priority regulation of battery storage" strategy are shown in Figures 14-18. The black solid is the active power of the PSBIS, and the red dotted line is the reference power deviation. When the size of the power deviation is different, the performance of the "priority regulation of battery storage" strategy is also different: (1) When the power deviation does not exceed the installed capacity of the battery storage power system, the PSBIS is only regulated by the battery storage system, and the pumped storage system does not participate in the regulation, for example, Figure 14A, Figure 15A, Figure 16B and Figure 17B. Similar to the results of the "priority regulation of pumped storage" strategy, the PSBIS has a good performance on active power balance. (2) When the power deviation exceeds the installed capacity of the battery storage power system, for example, Figure 14B,C, the regulation time for the PSBIS to balance active power is about 100 s longer compared with the "priority regulation of pumped storage" strategy since the installed capacity of the battery storage system is 10 MW, and the part of the power deviation exceeding 10 MW cannot be regulated. Under the ramp (B) and (C) input, as shown in Figure 15B,C, the active power curve of the PSBIS has a large gap with the reference power deviation curve at its peak. Similarly, the PSBIS has a worse performance on active power balance compared with the "priority regulation of pumped storage" strategy under the sine (A), (C), sawtooth (A), and (C) input, as shown in Figure 16A,C, and 17A,C.
There is a big gap between the "priority regulation of pumped storage" strategy and the "priority regulation of battery storage" strategy under practical input. There are peaks with large power deviation in the four-practical input (shown in Figure 18), leading to the worse performance of the power regulation at the single peak and double peaks under the "priority regulation of battery storage" strategy.
By comparing the time domain diagrams under the two control strategies, it can be seen that the PSBIS has a better performance on active power balance under the "priority regulation of pumped storage" strategy.

| Result of conventional strategies
The change curves of the active power of the PSBIS under the "priority regulation of battery storage" strategy are shown in Figures 19 and 20. In Figure 19, the black solid is the active power of the PSBIS, and the red dotted line is the reference power deviation. In Figure 20, the blue solid is the active power of the pumped storage system under the "regulation of pumped storage alone," and the orange solid is the active power of the battery   storage system under the "regulation of battery storage alone." Under conventional strategies, the pumped storage system and the battery storage system do not complement each other's advantages, but their disadvantages are obvious. The battery storage system has a better performance on active power balance than the pumped storage system, but the capacity of the battery storage system is limited, thus restricting the regulation performance. Therefore, the disadvantages of the conventional strategies on active power balance are shown, especially when compared to the strategies proposed in this work.

| Quantitative evaluation
The energy deviation coefficient (ζ) and penalty energy (E p ) under the two different control strategies of the PSBIS are shown in Tables 3 and 4.
It can be seen that the energy deviation coefficient (ζ) and penalty energy (E p ) under the "priority regulation of pumped storage" strategy are smaller than under the "priority regulation of battery storage" strategy, and most of them even have an order of magnitude difference. Only when the power deviation is small and does not exceed the installed capacity of the battery storage system, the difference between the two control strategies is not significant. However, at this time, the pumped storage system does not participate in regulation under the "priority regulation of battery storage" strategy.
The reasons for the above are as follows: (1) The power regulation range of the pumped storage system is large, but the regulation speed is not as fast as that of the battery storage system. (2) The power regulation speed of the battery storage system is fast, but the peak value of power regulation is limited compared with the pumped storage system. (3) The "priority regulation of pumped storage" strategy develops the respective advantages of the pumped storage system and the battery storage system. First, the pumped storage system is adopted to balance the active power deviation in a large range, and then the battery storage system is adopted for balancing fast and finely. In brief, the "priority regulation of pumped storage" control strategy has a better performance on active power balance compared with the "priority regulation of battery storage" control strategy.

| CONCLUSIONS
The main contributions and work of this study are as follows: (1) The model of the PSBIS has been built, for simulating small disturbances of pumped storage units and the battery charge and discharge characteristics. (2) Two control strategies for active power regulation, "priority regulation of pumped storage" and "priority regulation of battery storage," are proposed. Simulation and quantitative assessment are carried out under ideal input and measured wind power disturbances. It was shown that the "priority regulation of pumped storage" control strategy has a better performance on active power balance compared with the "priority regulation of battery storage" control strategy.
This study also has several limitations, and the following issues need to be further explored: (1) In terms of numerical models, the pumped storage plants model and the battery energy storage model can be simulated more refined in the characteristic simulation: For example, the linear turbine model is represented by six transfer coefficients and is only suitable for small disturbances. If a large disturbance needed to be studied, the dynamic input of the characteristic curves of turbines in the model needs to be considered. Moreover, the equivalent circuit in the battery energy storage model can be more refined, and the steady-state and transient characteristics of the battery are suggested to be considered. (2) In terms of control strategy, the study on the control strategy of the pumped storage-battery integrated system can be further carried out: In this study, only the two control strategies ("priority regulation of pumped storage" and "priority regulation of battery storage") are compared. In the future, more practical control strategies can be proposed according to the characteristics of pumped storage units and batteries, to improve the complementation advantage of the pumped storage and battery system. (3) In terms of performance evaluation, only the regulation rapidity of the integrated system is compared, and its stability and economic benefits, etc., do not be considered. Further studies on these issues are meaningful for future work.
NOMENCLATURE a varying coefficient of the transfer function for elastic water hammer C N rated capacity of the battery E′ d , E′ q d-axis and q-axis components of transient electromotive force E″ d , E″ q d-axis and q-axis components of subtransient electromotive force E f excitation electromotive force E m electromotive force e y , e x , e h partial derivatives of the turbine power output for the guide vane opening, speed, and head e qy , e qx , e qh partial derivatives of the turbine discharge for the guide vane opening, speed, and head f t frictional drag coefficient h/H water head i electric current I d , I q d-axis and q-axis components of the armature current I in input current I T the current of a single battery K ef excitation system gain k i the integral coefficient in the governor k p the proportional coefficient in the governor m turbine dynamic torque M inertia coefficient of the synchronous generator N p number of parallel batteries N s number of batteries in series P active power P a,MW active power of the PSBIS (MW) P a,pu active power of the PSBIS (pu) P b,in active power input into the battery storage system P b,out active power output by the battery storage system P e electromagnetic air gap power P m mechanical power output P MW reference power deviation (MW) P pu reference power deviation (pu) P p,in active power input into the pumped storage system P p,out active power output by the pumped storage system q/Q the flow of the turbine Q B quantity of electricity R T the internal resistance of a single battery