 Original Research
 Open Access
A coordinated dispatch method with pumpedstorage and batterystorage for compensating the variation of wind power
 Jinghua Li^{1}Email author,
 Sai Wang^{1},
 Liu Ye^{1} and
 Jiakun Fang^{1}
https://doi.org/10.1186/s4160101700749
© The Author(s) 2018
 Received: 16 April 2017
 Accepted: 4 December 2017
 Published: 19 January 2018
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.
Keywords
 Pumpedstorage
 Batterystorage
 Hybrid energy system
 Economic dispatch
 Renewable energy
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 [8–10]. 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]. [8–10] 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.

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
 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
 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
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.
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.
\( {\overline{U}}_m \) 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.
\( {T}_{i,t}^{on}/{T}_{i,t}^{off} \) 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.
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.
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.
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
 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
 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
 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.
 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.
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.
The variables of the basic and coordinated dispatch models
Model  Discrete variable  Continuous variable  

Basic  \( {d}_{i,t}^F \), \( {d}_{j,t}^{in} \), \( {d}_{j,t}^{out} \), \( {d}_{k,t}^{ch} \), \( {d}_{k,t}^{dis} \)  \( {P}_{i,t}^F \), \( {P}_{j,t}^{H, in} \), \( {P}_{j,t}^{H, out} \), \( {P}_{k,t}^{B, ch} \), \( {P}_{k,t}^{B, dis} \), \( {P}_{w,t}^{W, cur} \), U_{m, t}, θ_{m, n, t}  
Coordinated  DayAhead  \( {d}_{i,t}^F \), \( {d}_{j,t}^{in} \), \( {d}_{j,t}^{out} \)  \( {P}_{i,t}^F \), \( {P}_{j,t}^{H, in} \), \( {P}_{j,t}^{H, out} \), \( {P}_{w,t}^{W, cur} \), U_{m, t}, θ_{m, n, t} 
IntraDay  \( {d}_{j,t}^{in} \), \( {d}_{j,t}^{out} \), \( {d}_{k,t}^{ch} \), \( {d}_{k,t}^{dis} \)  \( {P}_{i,t}^F \), \( {P}_{j,t}^{H, in} \), \( {P}_{j,t}^{H, out} \), \( {P}_{k,t}^{B, ch} \), \( {P}_{k,t}^{B, dis} \), \( {P}_{w,t}^{W, cur} \), U_{m, t}, θ_{m, n, t} 
Comparison of the variable number of basic and coordinated dispatch models
Number  Basic model  Coordinated model  

DayAhead  IntraDay  
Discrete variable  \( {\displaystyle \begin{array}{l}\Big({N}_F+2\times {N}_H\\ {}+2\times {N}_B\Big)\times T\end{array}} \)  (N_{ F } + 2 × N_{ H }) × T  (2 × N_{ H } + 2 × N_{ B }) × T 
Continuous variable  \( {\displaystyle \begin{array}{l}\Big({N}_F+2\times {N}_H\\ {}+2\times {N}_B\\ {}+{N}_W+\\ {}2\times {N}_M\Big)\times T\end{array}} \)  \( {\displaystyle \begin{array}{l}\Big({N}_F+2\times {N}_H\\ {}+{N}_W+2\times {N}_M\Big)\times T\end{array}} \)  \( {\displaystyle \begin{array}{l}\Big({N}_F+2\times {N}_H+2\times {N}_B\\ {}+{N}_W+2\times {N}_M\Big)\times T\end{array}} \) 
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.
The advantages and corresponding indexes of the optimization method
Advantages  Stabilize the output of thermal units  Shave the peak load  Reduce the curtailment of wind power 
Indexes  The StartStop times of thermal units  The difference between Peak and Valley  The wind curtailment 
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.
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.
 1)
Results of 6case 1
 2)
Results of 6case 2
 3)
Results of 6case 3
C. Comparative analysis.
Comparison results of the three cases of 6bus system
W_Cur(MW)  S_T  P_V(MW)  

6case 1  458  2:2:0  182 
6case 2  246  0:0:0  153 
6case 3  174  0:0:0  148 
The comparison results are analysed as follows.
1) Comparison results of the difference between peak and valley load.
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.
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.
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.
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.
2) Comparison results of wind curtailment.
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.
 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.
Declarations
Acknowledgements
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).
Authors’ contributions
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.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
 David, L. (2010). The energy storage problem. Nature, 463(7), 18–20.Google Scholar
 Li, R., Chen, L., Yuan, T., et al. (2016). Optimal dispatch of zerocarbonemission micro energy internet integrated with nonsupplementary fired compressed air energy storage system. Journal of Modern Power Systems & Clean Energy, 4(4), 566–580.View ArticleGoogle Scholar
 Mohammadi, S., Mozafari, B., Solymani, S., et al. (2014). Stochastic scenariobased model and investigating size of energy storages for PEMfuel cell unit commitment of microgrid considering profitable strategies. IET Generation Transmission and Distribution, 8(7), 1228–1243.View ArticleGoogle Scholar
 Zhang, N., Kang, C. Q., Kirschen, D. S., et al. (2013). Planning pumped storage capacity for wind power integration. IEEE Transactions on Sustainable Energy, 4(2), 393–401.View ArticleGoogle Scholar
 Van MEERWIJK, A. J. H., BENDERS, R. M. J., DAVILAMARTINEZ, A., et al. (2016). Swiss pumped hydro storage potential for Germany’s electricity system under high penetration of intermittent renewable energy. Journal of Modern Power Systems & Clean Energy, 4(4), 542–553.View ArticleGoogle Scholar
 Hozouri, M. A., Abbaspour, A., FotuhiFiruzabad, M., et al. (2015). On the use of pumped storage for wind energy maximization in transmissionconstrained power systems. IEEE Transactions on Power Systems, 30(2), 1017–1025.View ArticleGoogle Scholar
 Wu, C. C., Lee, W. J., & Cheng, C. L. (2008). Role and value of pumped storage units in an ancillary services market for isolated power systems—Simulation in the Taiwan power system. IEEE Transactions on Industry Applications, 44(6), 1924–1929.View ArticleGoogle Scholar
 Caralis, G., & Zervos, A. (2007). Analysis of the combined use of wind and pumped storage systems in autonomous Greek Islands. IET Renewable Power Generation, 1(1), 49–60.View ArticleGoogle Scholar
 Papaefthymiou, S. V., Karamanou, E. G., Papathanassiou, S. A., et al. (2010). A windhydropumped storage station leading to high RES penetration in the autonomous island system of Ikaria. IEEE Transactions on Sustainable Energy, 1(3), 163–172.View ArticleGoogle Scholar
 Papaefthimiou, S., Karamanou, E., Papathanassiou, S., et al. (2009). Operating policies for windpumped storage hybrid power stations in island grids. IET Renewable Power Generation, 3(3), 293–307.View ArticleGoogle Scholar
 Khodayar, M. E., Abreu, L., & Shahidehpour, M. (2013). Transmissionconstrained intrahour coordination of wind and pumpedstorage hydro units. IET Generation Transmission and Distribution, 7(7), 755–765.View ArticleGoogle Scholar
 Wang, Y., Zhou, Z., Botterud, A., et al. (2016). Stochastic coordinated operation of wind and battery energy storage system considering battery degradation. Journal of Modern Power Systems & Clean Energy, 4(4), 581–592.View ArticleGoogle Scholar
 Li, X. J., Yao, L. Z., & Hui, D. (2016). Optimal control and management of a largescale battery energy storage system to mitigate fluctuation and intermittence of renewable generations. Journal of Modern Power Systems & Clean Energy, 4(4), 593–603.View ArticleGoogle Scholar
 Papič, I. (2006). Simulation model for discharging a leadacid battery energy storage system for load leveling. IEEE Transactions on Energy Conversion, 21(2), 608–615.View ArticleGoogle Scholar
 Pascal, M., & Rachid, C. (2009). Optimizing a battery energy storage system for frequency control application in an isolated power system. IEEE Transactions on Power Systems, 24(3), 1469–1477.View ArticleGoogle Scholar
 Li, J. H., Wen, J. Y., Cheng, S. J., et al. (2014). Minimum energy storage for power system with high wind power penetration using pefficient point theory. Science China Information Sciences, 57, 128202:1–128202:12.Google Scholar
 Maly, D. K., & Kwan, K. S. (1995). Optimal battery energy storage system (BESS) charges scheduling with dynamic programming. IEE Proceedings: Science, Measurement & Technology, 142(6), 453–458.Google Scholar
 Li, X. (2012). Fuzzy adaptive Kalman filter for wind power output smoothing with battery energy storage system. IET Renewable Power Generation, 6(5), 340–347.View ArticleGoogle Scholar
 Chazarraa, M., PérezDíaza, J. I., GarcíaGonzález, J., et al. (2016). Modeling the realtime use of reserves in the joint energy and reserve hourly scheduling of a pumped storage plant. Energy Procedia, 87, 53–60.View ArticleGoogle Scholar
 Kusakana, K. (2016). Optimal scheduling for distributed hybrid system with pumped hydro storage. IET Renewable Power Generation, 111, 253–260.Google Scholar
 Kusakana, K. (2015). Optimal scheduled power flow for distributed photovoltaic/wind/diesel generators with battery storage system. Renew Energy, 9(8), 916–924.Google Scholar
 Duggal, I., & Venkatesh, B. (2015). Shortterm scheduling of thermal generators and battery storage with depth of dischargebased dost model. IEEE Transactions on Power Systems, 30(4), 2110–2118.View ArticleGoogle Scholar
 Kumano J, Yokoyama A (2014) Optimal weekly operation scheduling on pumped storage hydro power plant and storage battery considering reserve margin with a warge penetration of renewable energy. Paper presented at 2014 international conference on power system technology, Chengdu, 20–22 October 2014.Google Scholar
 Liang, R. H. (2000). A noise annealing neural network for hydroelectric generation scheduling with pumpedstorage units. IEEE Transactions on Power Systems, 5(3), 1008–1013.MathSciNetView ArticleGoogle Scholar
 Tsoi, E., & Wong, K. P. (1997). Artificial intelligence algorithms for short term scheduling of thermal generators and pumpedstorage. IET Generation Transmission and Distribution, 144(2), 193–200.View ArticleGoogle Scholar
 Li, J. H., Fang, J. K., Wen, J. Y., et al. (2015). Optimal tradeoff between regulation and wind curtailment in the economic dispatch problem. CSEE Journal of Power and Energy Systems, 1(4), 52–60.Google Scholar
 Zimmerman, R. D., MurilloSanchez, C. E., & Thomas, R. J. (2011). Mat power: Steadystate operations, planning and analysis tools for power systems research and education. IEEE Transactions on Power Systems, 26(1), 12–19.View ArticleGoogle Scholar
 Reza, K., & Mahmoud, R. H. (2013). Unit commitment in presence of wind power plants and energy storage. International Journal of Smart Electrical Engineering, 2(4), 187–193.Google Scholar