Abstract
Growing penetration of wind power challenges to power system security, since the conventional generators may not have sufficient capacity to compensate wind power fluctuation plus the reverse peak regulation. In this paper, the highcapacity pumpedstorage and fastresponse batterystorage are coordinated to compensate the variation of both wind power and load, aiming at shifting peak load, responding to wind power ramping, reducing the curtailment of wind and stabilizing the output of thermal units. A practical framework is designed for optimizing the operation of the hybrid system consisting of the wind, pumpedstorage, and battery storage, which can take full advantages of pumpedstorage and batterystorage. The detailed mathematical formulations of the pumpedstorage and batterystorage are built. Three cases are studied to demonstrate the advantages of the proposed coordination method.
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1 Introduction
With the largescale wind power grid integration, shifting peak load and responding to the wind power variations become challenging problems. Limited by the adjustable level and ramping rate, the conventional units may not have sufficient capacity to deal with these problems. Storage systems provide an effective way to settle both problems because they can quickly balance the power. However, the utilization of most storage systems is barricaded by the technoeconomical feasibilities [1]. For example, compressedair energy storage [2] and spinning flywheel are considerably complex in practice; the cost of largescale ultracapacitors is expensive. Pumpedstorage and batterystorage are two most mature and widespread technologies used in practice [3, 4].
Pumpedstorage is viewed as the most suitable storage technology to improve the wind power integration for its large capacity [5]. Various techniques have been developed to combine the wind and pumpedstorage. Some techniques aim to achieve maximum profit in electrical markets by using pumpedstorage as an ancillary service for balancing wind power and consumption [6, 7]. Pumpedstorage has proved to bring considerable profits as ancillary service in the electrical market. In recent years, with the increasing integration of the renewable sources, pumpedstorage plays an important role in keeping the security of power system by balancing the variations of renewable sources. It is used to balance renewable sources variations for islanded grids in [8,9,10]. The detailed mathematical model combing wind power and pumpedstorage has been proposed in [8, 9], and the operation strategy for hybrid windpumped storage has been investigated in [10]. [8,9,10] have provided valuable experiences in windpumped coordination in islanded grid. Later, the pumpedstorage system is used for a large system in [11]. The effective control methods to accommodate the wind power uncertainty and ensure the system security are investigated in [11]. The Pumpedstorage system shows good performances on accommodating the variability of the wind power.
Batterystorage is another kind of storage that has been widely used [12, 13]. It can be flexibly installed in every bus of grid and response to power requirement quickly in seconds. Batterystorage is widely used in the load leveling [14], frequency controlling [15], spinning reserves [16], compensating for generation variations [17] and smoothing the wind power output [18]. These literatures give good examples for applications of battery in microgrid.
Although there exist many methods and technologies for using pumpedstorage or batterystorage to accommodate the wind power variability. However, most literatures are the independent studies of pumpedstorage [19, 20] or batterystorage [21, 22], the two together are studied less. Reference [23] proposes a new method for weekly scheduling operating patterns of combining pumpedstorage and batterystorage. However, the operating characteristics of pumpedstorage and batterystorage, nodal power balance, system security are not considered, which will enlarge the deviation between the dispatch schedule and actual operation.
This paper investigates the optimal coordination of pumpedstorage and batterystorage considering the characteristics of pumpedstorage and batterystorage. The proposed method focuses on shaving peak load, reducing the curtailment of the wind power, stabilizing the output of thermal units and responding to the high ramping events of the wind power. The main contributions of this paper are as following:

A practical framework is designed for optimal operation of windpumped storagebattery storage hybrid system, which can take advantages of pumpedstorage and batterystorage.

The proposed framework can improve the computational efficiency. It’s not easy to solve the dispatch model, because it includes large scale mix variables and nonlinear constraints [24, 25]. This proposed operation framework not only reduces the scale of variables and constraints, but also limits the startstop times of the thermal units in IntraDay dispatching.

A securityconstrained optimal dispatching problem of a hybrid system of wind, pumped storage, and battery storage is mathematically formulated, with the target of compensating the variation of wind power.
The rest of the paper is organized as follows: Section 2 presents the method outline of the proposed approach; Section 3 presents the detailed mathematic formulation; Section 4 analyses the coordinated framework and calculationbenefit of the proposed method; Section 5 applied the proposed method to modified 6bus system, IEEE 24bus system, IEEE 118bus system and concluding remarks are provided in Section 6.
2 Problem of coordinating of pumpedstorage and batterystorage
2.1 Issues brought by largescale wind power penetration
The wind power is featured with uncontrollability and unpredictability [26]. Hence, as largescale wind power increasingly penetrates power systems, many issues arise for system operators to keep the power balance.

1)
The large difference between peak and valley generations. Usually, the peak of the wind power appears at midnight, when the load is in the valley. It will enlarge the different between peak load and valley load, which is not easy to be compensated by conventional units, because the adjustment of conventional units may not cover the range from peak to valley.

2)
High ramping rate event. High rate power ramping up/down events of the wind power may occur unpredictably. However, the conventional units may not have enough regulation capacity. Hence, the curtailment of wind or load shedding will occur if the ramping events cannot be timely dealt with.

3)
Serious deviation from the forecast and real wind power. The wind power is not easy to be accurately forecasted as a load. It will burden the operators with large adjustment of units to compensate the deviation.
2.2 Positive roles played by coordinated pumpedstorage and batterystorage
Coordination of pumpedstorage and batterystorage provides an effective solution for the issues mentioned above. Pumpedstorage has the large capacity so that it has good ability to absorb the redundant power during offpeak periods and produce power during peak demand periods. Pumpedstorage can play the important role in shaving the peak load. However, the pumpedstorage is critical to geographical location and can’t respond to the fast ramps in the second timescale. For example, in Fig. 1, due to the capacity limit of transmission lines, the power cannot be transferred from pumpedstorage to every bus of the grid. Alternatively, batterystorage is a flexible and highspeed storage. Batterystorage is very suitable for responding the fast ramps in the second timescale. Hence, it is a good method to combine pumpedstorage and battery storage.
This paper proposes an optimization method to coordinate the pumpedstorage and batterystorage to achieve the four goals shown in Fig. 1.

1)
Stabilize the output of thermal units and reduce their frequency of startstop.

2)
Shave the peak load mainly using the pumpedstorage.

3)
Respond to the fast power ramping with the battery storage.

4)
Reduce the curtailment of the wind with the combination of pumpedstorage and batterystorage.
3 Mathematical formulation of the coordinated model
In this section, the components of the power system, including the thermal units, the wind farms, the pumpedstorage and the batterystorage are introduced first. Based on these component models, the DayAhead and IntraDay dispatch models are formulated.
3.1 The basic dispatch models
The proposed dispatch model minimizes the total system cost throughout the operational horizon. As shown in (1), the total system cost contains four parts: the operational cost of thermal units, startup and shutdown cost of the thermal units, the startup cost of pumpedstorage units, and the penalty cost of wind power curtailment. The operation cost of the thermal unit is calculated by (2). To accommodate the wind power as much as possible, wind power is considered as free here.
Where, FC is the total system cost. N_{ F }, N_{ H }, N_{ w } are the number of thermal units, pumpedstorage units, and wind farms, respectively. T is the number of time periods in the scheduling horizon. \( {d}_{i,t}^F \) is the state of thermal unit i in the time period t, \( {d}_{i,t}^F=1 \) denotes the unit is on and \( {d}_{i,t}^F=0 \) denotes the unit is off. \( {P}_{i,t}^F \) is the active power of thermal unit i in the time period t. \( {f}_{i,t}\left({P}_{i,t}^F\right) \) is the operational cost of thermal unit i in time period t. \( {d}_{j,t}^{out} \) is the generating state of pumpedstorage unit j in the time period t, \( {d}_{j,t}^{out}=1 \) denotes the unit is in generating state and \( {d}_{j,t}^{out}=0 \) denotes the unit is not in generating state. \( {d}_{j,t}^{in} \) is the pumping state of pumpedstorage unit j in the time period t, \( {d}_{j,t}^{in}=1 \) denotes the unit is in pumping state and \( {d}_{j,t}^{in}=0 \) denotes the unit is not in pumping sate. \( {C}_{i,t}^U \) and \( {C}_{i,t}^D \) are the startup and shutdown cost of thermal unit i in the time period t. C^{H} is the startup cost of pumpedstorage. \( {P}_{w,t}^{W, cur} \) is the curtailment of wind power of wind turbine w in the time period t. γ is the penalty coefficient of wind curtailment. a_{ i }, b_{ i }, c_{ i } are the coefficients of the operational cost of thermal unit i.
The proposed dispatch objective is subject to the following practical constraints.
1) System operation constraints
Where, S_{ F }, S_{ H }, S_{ B }, S_{ N } are the set of thermal units, pumpedstorage, batterystorage and buses, respectively. N_{ M } is the number of nodes. P^{W, av} is the available wind power. θ_{m, n, t} is the voltage angle in degrees with subscriptions m and n denoting the nodal number and t denoting the time period. U_{m, t} is the voltage magnitude (p.u) of node m in the time period t. \( {P}_{m,t}^{L, pre} \) is the prediction load of node m in the time period t. \( {\overline{P}}_{i,t}^F \) and \( {\underline{P}}_{i,t}^F \) are maximum and minimum real power of thermal unit i in the time period t respectively. \( {P}_{j,t}^{H, out} \) is the generated power of pumpedstorage unit j in the time period t, and its maximum and minimum value are \( {\overline{P}}_{j,t}^{H, out} \) and \( {\underline{P}}_{j,t}^{H, out} \) respectively. \( {P}_{j,t}^{H, in} \) is the pumped power of pumpedstorage unit j in the time period t, and its maximum and minimum value are \( {\overline{P}}_{j,t}^{H, in} \) and \( {\underline{P}}_{j,t}^{H, in} \) respectively. \( {d}_{k,t}^{ch} \) is the charging state of batterystorage unit k in the time period t, \( {d}_{k,t}^{ch}=1 \) donates the unit is in charging and \( {d}_{k,t}^{ch}=0 \) donates the unit is not in charging. \( {d}_{k,t}^{dis} \) is the discharging state of batterystorage unit k in the time period t, \( {d}_{k,t}^{dis}=1 \) donates the unit is in discharging and \( {d}_{k,t}^{dis}=0 \) donates the unit is not in discharging. \( {P}_{k,t}^{B, ch} \) is the charged power by batterystorage unit k in the time period t, its maximum and minimum value are \( {\overline{P}}_{k,t}^{B, ch} \) and \( {\underline{P}}_{k,t}^{B, ch} \). \( {P}_{k,t}^{B, dis} \) is the discharged power by batterystorage unit k in the time period t, its maximum and minimum value are \( {\overline{P}}_{k,t}^{B, dis} \) and \( {\underline{P}}_{k,t}^{B, dis} \) respectively. \( {R}_t^{up} \) and \( {R}_t^{down} \) are the up and down spinning reserves of systems in the time period t respectively.
The load balance constraint (3) indicates that the power generated at each bus meets the demand at that node and the losses. The generated power contains four parts: thermal power \( {d}_{m,t}^F{P}_{m,t}^F \), pumpedstorage power \( \left({d}_{m,t}^{out}{P}_{m,t}^{H, out}{d}_{m,t}^{in}{P}_{m,t}^{H, in}\right) \), batterystorage power \( \left({d}_{m,t}^{ch}{P}_{m,t}^{B, ch}{d}_{m,t}^{dis}{P}_{m,t}^{B, dis}\right) \) and wind power \( \left({P}_{m,t}^{W, pre}{P}_{m,t}^{W, cur}\right) \).
The system upward spinning reserve requirement (4) ensures that the upward reserve provided by the thermal unit, pumpedstorage and batterystorage can meet the upregulation requirement of the systems.
The system downward spinning reserve requirement (5) ensures that the downward reserve provided by the thermal unit, pumpedstorage and batterystorage can meet the downregulation requirement of the systems.
2) System security constraints
\( {\overline{U}}_m \) and \( {\underline{U}}_m \) are the maximum and minimum voltage magnitude (p.u) of node m respectively. \( {\overline{\theta}}_{m,n} \) and \( {\underline{\theta}}_{m,n} \) are the maximum and minimum voltage angle (degree) difference between node m and n respectively. P_{m, n, t} is the active power of line from bus m to bus n in the time period t. \( {\overline{Pf}}_{m,n} \) is the flow limit of the line from bus m to bus n.
The constraints (6)–(8) require that all the electrical equipment works at the rated voltage magnitude; the difference of voltage angle between both ends of a line does not exceed the given range; and the power flow through the line does not exceed its capacity.
3) Thermal units’ constraints.
Thermal units are subject to limits on their min/max output capacity (9), ramp up/down limits (10) and (11), minimum up/down time (12) and (13).
\( {T}_{i,t}^{on}/{T}_{i,t}^{off} \) are the continuous on/off time of thermal units. \( {\underline{T}}_i^{on}/{\underline{T}}_i^{off} \) are the minimum on/off time of thermal units. \( \Delta {P}_i^F \) is the ramping rate of thermal unit i.
4) Wind power constraints.
The actual wind power equals to the available wind power minus the wind curtailment as (14). The wind curtailment limit (15) ensures that the wind curtailment is no larger than the forecasted wind power. In this paper, the wind is allowed to be curtailed to ensure the power balance.
Here, \( {P}_{w,t}^{W, av} \) and \( {P}_{w,t}^{W, pre} \) are the available wind power and prediction wind power of wind farm w in the time period t.
5) Pumpedstorage constraints.
The pumpedstorage unit constraints include (16)–(22) as described in [12]. The units for power generation and water reserve level are unified to be MWh. Constraint (16) is the hydro water reserve capacity balance. Δt is the time interval between t1 and t. It equals to 1 h in this paper. Constraint (17) is the total volume of the water reserve. Constraints (18) and (19) describe the upper and lower bounds of the power absorbed and generated by the pumpedstorage units. Constraints (20) and (21) give the initial and target water level for the pumpedstorage units. Constraint (22) ensures that the pumpedstorage units cannot absorb and generate electricity at the same period.
C_{j, t} is the water reserve of pumpedstorage station j in the time period t. \( \overline{C} \) and \( \underline{C} \) are the maximum and minimum of water reserve respectively. C_{j, begin} and C_{j, last} are the initial and target water reserve of pumpedstorage station j respectively. η^{in} and η^{out} are the efficiency of pumping and generating cycle of pumpedstorage units respectively.
6) Batterystorage constraints.
The batterystorage unit constraints include (23)–(28). Constraints (23) and (24) are the power capacity limits of the batterystorage. Constraint (25) is the conversion relationship between energy and power. Constraint (26) describes the energy capacity of the battery. Constraint (27) requires the energy stored in the battery at the end of the day (period T) equals to the initial energy. Constraint (28) ensures that the batterystorage units cannot discharge and charge electricity at the same period.
Where, E_{k, t} is the energy charge of batterystorage k in the time period t. E_{k, 0} is the initial state of charge (SOC) of batterystorage k in the time period t. \( {\overline{E}}_k \) is the capacity of batterystorage k. η^{ch} and η^{dis} are the efficiency of charging and discharging cycle of batterystorage respectively.
3.2 Dayahead dispatch model
Batterystorage do not appear in the optimization in the DayAhead dispatch model. Fix \( {d}_{k,t}^{ch}=0 \), \( {d}_{k,t}^{dis}=0 \), k ∈ S_{ B }, t ∈ T and then solve the DayAhead optimization problem consisted of (1)–(22). Then the optimal plan is obtained, which contains the following results:

1)
Unit commitment and economic dispatch plan of thermal units \( \left({d}_{i,t}^F,{P}_{i,t}^F\right) \).

2)
Pumpedstorage plan \( \left({d}_{j,t}^{in}{P}_{j,t}^{H, in},{d}_{j,t}^{out}{P}_{j,t}^{H, out}\right) \).

3)
Wind curtailment \( {P}_{w,t}^{W, cur} \).
3.3 Intraday dispatch model
In the IntraDay dispatch model, the unit commitment of thermal units are fixed, and the IntraDay model consisted of (1)–(28) is rolling computed hourly based on the feedback information of the grid. Pumpedstorage and batterystorage are fully coordinated to cope with the wind power variation in the IntraDay dispatch. The following results are obtained to control the units:

1)
Economic dispatch command of thermal units \( {P}_{i,t}^F \).

2)
Pumpedstorage command \( \left({d}_{j,t}^{in}{P}_{j,t}^{H, in},{d}_{j,t}^{out}{P}_{j,t}^{H, out}\right) \).

3)
Batterystorage command \( \left({d}_{k,t}^{ch}{P}_{k,t}^{B, ch},{d}_{k,t}^{dis}{P}_{k,t}^{B, dis}\right) \).

4)
Wind curtailment \( {P}_{w,t}^{W, cur} \).
These results are used to dispatch the units to shift the peak load, respond to the high rate power ramping events, reduce the curtailment of wind and stabilize the output of thermal units. The units are dynamically optimized across the complete time horizon of interest.
4 Coordinated framework and calculationbenefit analysis for the proposed coordinated dispatch method
4.1 Coordinated framework of pumpedstorage and batterystorage
Figure 2 depicts the proposed framework to coordinate pumpedstorage and batterystorage. It is a closedloop dispatch process including DayAhead and IntraDay dispatch as follows.

1)
DayAhead dispatch. It is a unit commitment model including multitime period Alternating Current Optimal Power Flow with security constraints (Shorted as UCACOPF model). Thermal units, wind farms, and the pumpedstorage are optimized together. The DayAhead dispatch is to make schedules to balance the shorttime forecast wind power and load. The model considers the security constraints and the pumpedgenerated process of the pumpedstorage. Due to the limited capacity, batterystorage is only used in the IntraDay dispatch, but not used for the DayAhead plan. The scheduling plan from DayAhead is regarded as the base plan for Intraday dispatch.

2)
IntraDay dispatch. It is an economic dispatch model considering Alternating Current Optimal Power Flow with security constraints (Shorted as EDACOPF model). To avoid frequent start or stop of the thermal generators, unit commitment schedule is fixed in DayAhead dispatch and kept unchanged at this stage. The EDACOPF model is a rolling computation per hour to modify the base plan from DayAhead. The IntraDay dispatch is to make schedules to balance the veryshorttime (HourAhead or MinuteAhead) forecast wind power and load. Due to the forecast accuracy of HourAhead or MinuteAhead is higher than that of DayAhead, the errors of DayAhead forecast are balanced by the rolling dispatch in IntraDay. The thermal units, wind farms, pumpedstorage and batterystorage are optimized together according to the system operation conditions, such as the load and wind power. The outputs of this model are used to control the thermal units, wind farms, pumpedstorage and batterystorage.
There are three major advantages of the proposed framework in Fig. 2.

1)
The twostage optimal dispatch consists of the DayAhead stage and rolling IntraDay stage. It is a closedloop dispatch process to compensate the forecast inaccuracy of both wind power and load. It avoids the large power flow transfer in the realtime operation. Besides, UCACOPF with secure constraints is considered to enhance the quality of the scheduling.

2)
Batterystorage does not participate in power balancing at the DayAhead stage. It can reduce the required battery capacity. Also, this strategy can reduce the optimization variables and constraints of UCACOPF problem.

3)
The unit commitment of thermal units is kept unchanged at the IntraDay stage. This strategy ensures the thermal units do not frequently startstop in operation. Also, the variables and constraints of EDACOPF model are greatly reduced, and the burden of calculation is relieved.
In summary, the flowchart of the coordinated dispatch method with pumpedstorage and batterystorage is as shown in Fig. 3.
4.2 Calculationbenefit analysis for the proposed coordinated dispatch method
The mathematical formulation of the optimization problem introduced in Section 3 is a largescale, multidimensioned, mixedintegral, nonconvex, and nonlinear constrained problem, which is hard to solve. Especially, the number of discrete variables is a major influencing factor on computational difficulty. Seen from Section 3, the basic model includes large scale discrete variables, including the state of the thermal unit, pumpedstorage and batterystorage of T time periods. Therefore, the computational burden of the basic model is heavy. So, the coordinated dispatch model divides the basic model into two subproblems, DayAhead dispatch model and IntraDay dispatch model. Accordingly, the discrete variables in each subproblem will decrease, which will reduce the computational burden.
To show the advantages of the proposed coordinated dispatch model in the improvement of computational efficiency, the variables of the basic and coordinated dispatch models are listed in Table 1. Then, the calculationbenefit analysis is conducted via comparing the number of variables in both models. The model that has the fewer variables will has better performances in computational efficiency.
As shown in Table 1, only part of discrete variables of the basic model are included in the subproblems of the coordinated model. To show the calculating amount of basic and coordinated dispatch models more clearly, Table 2 compares their variables number.
As shown in Table 2, the IntraDay model has the same continuous variables as the basic model. Hence, as for the continuous variable, the advantage of the coordinated model is not obvious. However, as for the discrete variable, the advantage of the coordinated model is obvious, especially when the number of thermal unit and battery is large. For example, suppose N_{ F } = 54, N_{ H } = 1, N_{ B } = 5 (N_{ B } is the number of batterystorage), T = 96, the number of the discrete variable in the basic model, DayAhead model, and IntraDay model are 6336, 5376, and 1152 respectively. Therefore, the computational time is greatly reduced by using the coordinated model.
5 Numerical simulation
The coordinated dispatch of pumpedstorage and batterystorage are simulated in three systems: 6bus system, IEEE 24bus system, and IEEE 118bus system from MatPower 5.0 [27]. In the simulations, the thermal units output, pumpedstorage output, batterystorage output as well as wind curtailment are recorded to verify the coordinated dispatch method.
For verifying the advantages of proposed method, the indexes in Table 3 are used, measuring the performances in stabilizing the output of thermal units, shaving the peak load, and reducing the curtailment of wind power.
The difference between peak and valley of three cases are calculated as following. PeakValley 1, PeakValley 2, and PeakValley 3 represent the difference between peak and valley of case 1, case 2, and case 3 respectively.
Besides, to demonstrate the contributions of the combining of the pumpedstorage and batterystorage, three cases below have been studied in all the three systems.
Case 1: Only the thermal units and the wind power units are dispatched without the assistance from pumpedstorage units and batterystorage.
Case 2: The thermal units, the wind power units, and the pumpedstorage units are dispatched. The batterystorage are not dispatched.
Case 3: The thermal units, wind power units, pumpedstorage units and batterystorage units are dispatched in coordination.
The solution method is discussed in following contents. Cplex Optimizer can provides flexible, highperformance mathematical programming solvers, for linear programming, mixed integer programming, quadratic programming, and quadratically constrained programming problems with millions of constraints and variables.
In this paper, the proposed model is a mixed integer nonlinear programming (MINLP) problem, which can be solved by Cplex solver, the core algorithm is branch and bound algorithm. All the experiments are implemented on the Matlab platform with Cplex Optimizer, at Intel Core 1.70GHz with 4GB memory.
5.1 Simulation of 6bus system
A.Description of the simulation system.
As shown in Fig. 4, the 6bus system includes three thermal units at bus 1, bus 2 and bus 3, one wind farm at bus 5, one pumpedstorage unit at bus 4 and one batterystorage at bus 5.
F1, F2, and F3 represent thermal units, H represents pumpedstorage units, W represents the wind farm, and B presents the batterystorage. Loads are connected to the bus 4, bus 5, and bus 6. Their load proportionality factors are 0.2, 0.4, and 0.4. The parameters including thermal units, pumpedstorage, batterystorage, transmission lines, load, and the wind are given in [27, 28] (http://www.eirgrid.com/operations/systemperformancedata/windgeneration/), respectively. The penalty coefficient of wind curtailment is 10 $/MWh in this example.
Three cases mentioned at the beginning of Section 5 are simulated, denoted as 6case 1, 6case 2, and 6case 3 in 6 bus test system.
B. Simulation results of 6bus system

1)
Results of 6case 1
The simulation results of 6case 1 are shown in Fig. 5ad, including the thermal units’ output and wind curtailment in both DayAhead and InterDay dispatch. In this case, in order to balance the power at peak load time, F1 has to start instead of F2 in 11th and 14th time periods. Because the maximum output of F2 and F3 couldn’t supply the peak load, but meanwhile starting up F1, F2 and F3 will result in plenty of wind curtailment. Figure 5c indicates that the output of F3 is varied to response the load and the wind. In Fig. 5d, the wind accepted by the system is much less than the available wind. It indicates wind curtailment is large without the adjustment of storages. Besides, due to the inaccurate forecasting of the wind, the DayAhead plan is departures from the actually available wind power. Also seen from Fig. 5d, the departures are reduced by rolling correction in the IntraDay model.

2)
Results of 6case 2
The results of the 6case 2 are shown in Fig. 6af. Compared with the results in Fig. 5, thermal units F1 and F2 need not startstop with the help of pumpedstorage. In addition, the IntraDay curve of F2 is the same as the DayAhead curve in Fig. 6b. It means that the output of F2 needn’t change its plan during the whole day due to the adjustment of pumpedstorage, which greatly relieves the operators from frequently changing the scheduling plan. Figure 6d shows the optimal pumping and generation plan of the pumpedstorage. The pumpedstorage is optimized over the entire time horizon, so that the pumpedstorage can have enough space to store or generate power when needed. Seen from Fig. 6d, the pumpedstorage absorbs power at valley periods and generates power at peak periods, which lowers the level of peak load while enhances the level of valley load. So the pumpedstorage plays an important role in shifting the peak load. Figure 6e is the curve of the water reserve. As we can see from Fig. 6e, the reserve reaches to its maximal level during 5th to 12th periods. The pumpedstorage no longer has space to absorb the surplus wind power. Therefore, the wind power is curtailed during 5th to 12th periods in Fig. 6f. However, seen from the Fig. 6f, the wind curtailment of 6case 2 is less than 6case 1.

3)
Results of 6case 3
The results of the 6case 3 are shown in Fig. 7ag. The IntraDay output curve of F3 is more stable than that in the Figs. 5 and 6. It indicates that the batterystorage partly share the fluctuation and ramping of wind power, which avoids the thermal unit from frequently adjusting. So the efficiency of the thermal unit is enhanced. Figure 7d shows the optimal charging and discharging process of battery storage and its state of charge is shown in Fig. 7f. In Fig. 7f, the batterystorage reaches its top capacity to decrease wind curtailment during the 5th to 12th periods. Therefore, compared with the results in Fig. 6f, the wind curtailment is decreasing with the help from the battery storage during the 5th to 12th periods, shown in Fig. 7g.
C. Comparative analysis.
The comparative results of the above three cases are gathered in Table 4. The Wind Curtailment of the dispatch day (W_Cur), StartStop times of thermal units (S_T), and the difference between Peak and Valley (PV) can be seen from Table 4.
The comparison results are analysed as follows.
1) Comparison results of the difference between peak and valley load.
Figure 8 compares the difference between peak and valley, which is undertaken by thermal units. PeakValley 1, PeakValley 2, and PeakValley 3 are calculated by the method referred at the beginning of Section 5.
As shown in Fig. 8, the PeakValley 1 is 182 MW, PeakValley 2 is 153 MW and PeakValley 3 is 148 MW. By optimally using the pumpedstorage, the peakvalley is decreased by 29 MW, which is 15.9% of PeakValley 1. Therefore, the pressures of balancing the power between peak and valley are greatly lightened. Also, we can see the PeakValley 3 is not improved greatly than Peakvalley 2, which indicates that the task of shifting load is not mainly undertaken by batterstorage due to the limitation of its capacity.
2) Comparison results on the smooth output of thermal unit.
In Table 3, the startstop times of F1 and F2 are decreased from 2 to 0 with the adjustment of storages. The outputs of the F3 are compared in Fig. 9.
Seen from Fig. 9, with the helping of storages, the curves of 6case 2 and 6case 3 are smoother than that of 6case 1, especially during the 9th to 23rd periods. The differences between the maximum and minimum output of F3 are 54 MW, 53 MW, and 44 MW, respectively. The difference is reduced 10 MW by the fast adjustment of batterystorage, which indicates that batterystorage plays important role in compensating the ramping events.
3) Comparison results of wind curtailment.
In Table 3, the wind curtailment is greatly reduced by the helping of the storages. The proportions of wind curtailment in the three cases are 12.1%, 6.5%, and 4.6%, respectively. The proportion of wind curtailment is decreased by 7.5% with the help of storages, which has a considerable economic.
5.2 Simulation of IEEE 24bus system
In IEEE 24bus system, there is one pumpedstorage, one batterystorage, and one wind farm. The pumpedstorage connects at bus 15, the battery and wind farm connects to the same bus 18. Also, three cases referred at the beginning of Section 5 are simulated, denoted as 24case 1, 24case 2, and 24case 3 in this section.
For brevity, only the results of difference between peak and valley load, wind curtailment are analysed here.
1) Comparison results of the difference between peak and valley load.
Figure 10 compares the difference between peak and valley.
In Fig. 10, the PeakValley 1 is 1422 MW, PeakValley 2 is 1249 MW and PeakValley 3 is 1208 MW. Compared to PeakValley 1, PeakValley 2 has decreased 173 MW, which is over 12% of PeakValley 1. And compared to PeakValley 2, PeakValley 3 has decreased 41 MW, which is 3% of PeakValley 2. Therefore, the pressures of balancing the power between peak and valley are greatly lightened by optimally using the pumpedstorage.
2) Comparison results of wind curtailment.
Figure 11 compares the wind curtailment of the three cases.
As shown in Fig. 11, in 24case 1, wind curtailment occurs in many time periods. However, in 24case 2 and 24case 3, wind curtailment only occurs in the 3rd time period. The total wind curtailment of 24case 1, 24case 2, and 24case 3 is 571 MW, 53 MW and 12 MW, respectively. Therefore, wind curtailment can be greatly reduced by using the pumpedstorage and further reduced by using batterystorage.
5.3 Simulation of IEEE 118bus system
In IEEE 118bus system, there is one pumpedstorage, one batterystorage, and one wind farm. The pumpedstorage and wind farm connects to the same bus 54, the battery connects to bus 30. Also, three cases mentioned at the beginning of Section 5 are simulated, denoted as 118case 1, 118case 2, and 118case 3 in this 118 bus test system.
For brevity, only the results of difference between peak and valley load and wind curtailment are analysed here.
1) Comparison results of the difference between peak and valley load.
Figure 12 compares the difference between peak and valley of IEEE 118bus system. In Fig. 12, the PeakValley 1, PeakValley 2 and PeakValley 3 are 4228 MW, 4184 MW, and 4128 MW, respectively. Therefore, the pressures of balancing the power between peak and valley are lightened by optimally using the pumpedstorage and batterystorage.
2) Comparison results of wind curtailment.
Figure 13 depicts the wind curtailment of the three cases. In Fig. 13, the maximum of wind curtailment in 118case 1 reach 286 MW, which is nearly double of wind curtailment in 118case 3 in the 6th time period. The together wind curtailment in three cases are 664 MW, 358 MW and 290 MW, respectively. Therefore, pumpedstorage and batterystorage in 118case 2 and 118case 3 can reduce the wind curtailment and save energy.
6 Conclusion
In this paper, a detailed mathematical formulation coordinating the pumpedstorage and batterystorage problem is proposed to accommodate the reverse peak regulation and variability characters of the wind power. The proposed method can be extended to any combination of highcapacity and fastresponse energy storages. Based on the characters of pumpedstorage and batterystorage, a practical framework for the optimal operation of DayAhead plan and IntraDay scheduling is designed. Three cases have been used to study the advantages of the coordination of pumpedstorage and batterystorage in three test systems. The simulation results demonstrate that the coordination method has good performance in the aspects of shifting peak load, responding to the wind power ramping, reducing the curtailment of wind and steadying the output of thermal units.
Further, there are still some works that need to develop in the future research.

1)
Further, improve the computational efficiency of the coordinated dispatch model. The coordinated dispatch is a largescale, multidimensioned, discrete, nonconvex, and nonlinear constrained problem, which requires faster and more accurate method to solve.

2)
Add AGC (Automatic Generation Control) control part into the coordinated dispatch. The proposed method only includes DayAhead and IntraDay dispatch, while not including the realtime dispatch. Adding AGC control part will form a more complete dispatch system, including Dayahead, IntraDay, and realtime dispatch.

3)
Consider the influence of different kinds of battery storage in the coordinated dispatch model, especially the parameters of capacity and response time.
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This work was supported in part by the National Key Research and Development Program of China (2016YFB0900101) and in part by the National Natural Science Foundation of China (51377027).
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JL conceived and designed the study. JL and SW performed the experiments. JL, SW and LY wrote the paper. JL, SW, LY and JF reviewed and edited the manuscript. All authors read and approved the manuscript.
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Li, J., Wang, S., Ye, L. et al. A coordinated dispatch method with pumpedstorage and batterystorage for compensating the variation of wind power. Prot Control Mod Power Syst 3, 2 (2018). https://doi.org/10.1186/s4160101700749
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DOI: https://doi.org/10.1186/s4160101700749