Real-time scheduling strategy for microgrids considering operation interval division of DGs and batteries

1 Introduction

With the increasing penetration of renewable energy resources,the random and intermittent characteristics of such resources bring new challenges to the energy management system (EMS) of microgrids,particularly to the real-time scheduling strategy.

Several studies have been conducted on the EMS of microgrids in recent years.Deterministic scheduling model [1,2],stochastic dispatch model [3],and robust optimization model [4,5]have been established for microgrids to optimize the dispatch.However,these optimization approaches are all based on off-line algorithms and are difficult to apply to realtime scheduling given the real-time requirements.

The look-ahead scheduling of microgrids mainly focuses on the economy of the microgrid,whereas a realtime scheduling must consider the instantaneity in addition to the economy.Real-time scheduling algorithms can be divided into heuristic and algorithmic methods.In [6]and [7],a series of rules were formulated to handle the real-time scheduling problem via a heuristic algorithm.In [8],a deep reinforcement learning was applied to the real-time energy management of a microgrid.A real-time implementation of a multiagent-based game theory reverse auction model for microgrid market operations was proposed in [9].A real-time EMS whose objective was to minimize the effect of pulsed loads on the power system was presented in [10].In [11],a novel Lyapunov optimization framework based on the queueing theory was designed to solve the real-time scheduling model of microgrids.In [12],dayahead scheduling and real-time scheduling models were established,and different time-scale schedule schemes were respectively applied for cooling and electricity loads.In [13],a sliding-window approach for the real-time energy management of microgrids was devised.However,none of the real-time scheduling algorithms can meet both the economy and instantaneity requirements of scheduling simultaneously.Therefore,compromises have been made in most cases.

As none of these algorithms can separately resolve the contradiction between economy and computing time,two-layer scheduling [14-16],rolling scheduling [17],and dynamic programming [18-20]methods have been proposed to make use of offline algorithms to minimize the cost,whereas online algorithms are proposed to avoid the timeconsumption problem.In [14-16],a two-layer scheduling model was proposed,in which the day-ahead scheduling deploys the economic schedule in a one day horizon,and the real-time scheduling tracks the day-ahead schedule.A receding-horizon-based rolling schedule strategy was applied to solve the real-time scheduling problem in [17].In [18-20],an approximate dynamic programming was employed to derive a near optimal real-time scheduling policy.

Depending on the requirement of the economy and instantaneity in real-time scheduling,a new real-time scheduling strategy considering the operation interval division is proposed in this paper.Inspired by the twolayer and rolling scheduling methods,a three-layer rolling scheduling framework is applied to the scheduling strategy.In the proposed strategy,the aftereffect of the DGs in the microgrids is considered in the day-ahead/hours-ahead scheduling process.To track the day-ahead/hours-ahead schedule,the output ranges of the DGs are divided into several intervals in the real-time scheduling.Thus,the advantages of the day-ahead/hours-ahead scheduling and real-time scheduling are combined to optimize the final schedule.

The remainder of this paper is organized as follows.In Section 2,the rolling scheduling models are introduced.The real-time scheduling model of the microgrid is proposed in Section 3.Case study and simulation results are given in Section 4,followed by the conclusions in Section 5.

2 Models of rolling scheduling based on offline optimization

An off-line optimization is appropriate for the day-ahead scheduling and hours-ahead scheduling given the sufficient calculation time.

2.1 Rolling scheduling model framework

Fig.1 shows the data flow in the scheduling process of different time scales.

Fig.1 Data flow in optimal rolling scheduling

The real-time scheduling takes the real-time data,scheduled power purchased from the main grid,hours-ahead scheduling results,and state of charge (SOC) boundaries of the battery energy storage system (BESS) as input,and outputs the real-time scheduling results.If the real-time scheduling results violate the SOC boundaries,the realtime scheduling will refer to the database,obtain the hoursahead scheduling results of the corresponding case,replace the hours-ahead scheduling results with the new ones,and reschedule the modified real-time scheduling results.

To elaborate the rolling scheduling process,the time frame is depicted in Fig.2.In a real-time scheduling,the final scheduling results are outputted based on the dayahead and hours-ahead scheduling results.

Fig.2 Time frame of rolling scheduling

2.2 Day-ahead scheduling model

The day-ahead scheduling prepares a schedule covering the next day and submits the scheduled power purchase to the main grid.The actual power purchased from the main grid should be maintained within the envelope line range.Otherwise,the microgrid is required to pay the penalty.

(1) Objective

The WT and PV generate power without fuel costs,and the wind and photovoltaic power should be considered with priority from an economic perspective.Accordingly,the operation costs of the WT and PV are omitted in this paper.The objective of the optimal day-ahead scheduling model is to minimize the total operation cost,which consists of costs associated with dispatchable DGs,BESS,and electricity purchase/sale.The objective function is expressed as:

where i and I represent the index and number of dispatchable DGs,respectively;k and K represent the index and number of BESSs,respectively;T is the number of time slots of scheduling horizon;d represents the index of the day-ahead scheduling,which will not be repeated in the following explanation for convenience;Pi(t) is the output power of DG i at time t;Pk(t) is the output power of BESS k at time t;Pgrid(t) is the power exchange between the microgrid and the main grid at time t;Ci(⋅) represents total operation cost function of DG i,whichconsists of the fuel cost,start-up cost,operation and maintenance cost,depreciation cost,and environmental cost;Ck(⋅) represents total operation cost function of BESS k,whichconsists of the operation and maintenance costs,and depreciation cost;Cgrid(⋅) represents net electricity purchase cost function,which includes the electricity purchase cost and sale revenue.Because the dayahead scheduling model is not the focus of this paper,the detailed calculation formulae and constraints,which can be found in [21],are not listed herein.

(2) Constraint

The day-ahead scheduling is subject to the power balance equation(2) and the reserve constraint(3).

where Pw(t) and Pp(t) are the output powers of WT and PV at time t,respectively;Pd(t) is the total load of the microgrid at time t;U i(t) is the binary on/off variable of DG i at time t;is maximum power limit of DG i;Δup,i is the ramp-up limit of DG i;SOC k(t) is the SOC value of BESS k at time t;is the minimum SOC bound of BESS k;Erated,k is the rated energy capacity(kWh) of BESS k;ηdhk, is discharge efficiency of BESS k;Δt represents the length of the scheduled time step;is the maximum discharging power bound of BESS k;is the maximum power limit that can be purchased from the main grid;Rs(t) is the total reserve of the microgrid at time t.

For the dispatchable DGs,the operation constraints,including the power,service time,and ramping limits,are represented in (4)-(7):

where is the minimum power limit of DG i;Ustart,i(t) and Ushut,i(t) are binary start-up variable of DG i (1 for startup and 0 otherwise) and binary shut-down variable of DG i,respectively;MOTi and MDTi are minimum up and down time of DG i;Δdowni, is the ramp-down limit of DG i.

For the BESSs,the SOC and the power should satisfy the constraints represented in (8)-(11):

where σk is the self-discharge rate of BESS k;Pch,k(t) and Pdh,k(t) are the charging and discharging powers of BESS k at time t;ηchk, is the charge efficiency of BESS k;is the maximum SOC bound of BESS k;is the maximum charging power bound of BESS k.SOCk(0) and SOC k(T) are the SOC values at the initial and end time in T of BESS k.

For the power purchased/sold from/to the main grid,the power exchange constraints are represented as follows(12):

where is the maximum power limit that can be sold to the main grid.

2.3 Hours-ahead scheduling model

An hours-ahead scheduling conducted every few hours (2 h in this study) gives a more accurate schedule,because the hours-ahead forecast is more accurate than the day-ahead one.

(1) Objective

Besides Ci(⋅),Ck(⋅),and Cgrid(⋅),the penalty cost for violating the envelope range is considered in the hoursahead scheduling.The objective function of the hours-ahead scheduling is expressed as:

where:

where h represents the index of the hours-ahead scheduling;Cpun(⋅) is the penalty cost function for violating the envelope range of ΔPup(t) and ΔPdown(t) are the upper and lower envelope ranges of respectively;pup(t) and pdown(t) are the penalty cost coefficients for violating the upper and lower envelope bounds of respectively.The penalty cost for violating the envelope range of is proportional to the market price in this study.

(2) Constraints

The hours-ahead scheduling should satisfy the constraints (2)-(12) similar to those of the day-ahead scheduling.Note that the battery SOC value at the end of the day is set equal to the one scheduled in the day-ahead scheduling.Therefore,the day-ahead scheduling for the next day will have a consistent energy stored in the schedule.

2.4 Database of rescheduled hours-ahead scheduling

Since prediction errors are inevitable,the hours-ahead schedule should be adjusted in the real-time scheduling.The real-time scheduling,however,can not reschedule from a global optimal perspective because of the real-time requirements.To this end,the hours-ahead scheduling as an off-line optimization can consider possible situations in advance,where any significant SOC deviation from the hours-ahead schedule is considered.Fig.3 shows the calculation process of the hours-ahead scheduling under significant SOC deviation conditions at time t.First,the hours-ahead scheduling passes the scheduling results to the marginal cost method.Second,the marginal cost method adjusts the schedule to find the maximum allowable SOC deviations at time t and outputs the adjusted results including the total cost and SOC boundaries.Third,taking the SOC boundaries as the initial data,the hours-ahead scheduling reschedules to obtain a new schedule.Finally,the rescheduled hoursahead scheduling results are stored in the database if the total cost and the start-up and shut-down schedules satisfy where CMC and CRE are total costs in the marginal cost method and hours-ahead rescheduling,respectively;Ui,MC(t) and Ui,RE(t) are binary on/off variable of DG i at time t in the marginal cost method and hours-ahead rescheduling,respectively.Otherwise,the value of Ui,MC(t) is replaced by Ui,RE(t),and the marginal cost method readjusts the schedule.

The objective of the marginal cost method is to determine the SOC boundaries at time t.The marginal cost at time t denoted by λ(t) can be calculated using the Lagrange duality [16]and equal incremental method [22],and the corresponding power at time t is denoted by PMC(λ,t).

Fig.3 Flowchart of hours-ahead scheduling in situations with SOC boundaries

The upper SOC deviation is calculated by.

where ΔSOCup,k(t)is the upper SOC deviation at time t in the marginal cost method.

Considering the SOC physical limit,the upper SOC deviation should be substituted in (16):

The upper SOC boundary at time t is represented in:

where SOCup,k(t) is the final upper SOC boundary at time t in the marginal cost method.

Similarly,the lower SOC boundary at time t is represented in:

where ΔSOCdown,k(t) and SOCdown,k(t) are the lower SOC deviation and boundary,respectively,at time t in the marginal cost method.

3 Model of real-time scheduling

The real-time scheduling strategy proposed in this paper is based on the day-ahead and hours-ahead scheduling.The output power of the dispatchable DGs is divided into two intervals:an output power interval that can track the hoursahead schedule (defined as CI1 for ease of description) and an output power interval with the physical limits (CI2).Similarly,the output power of the BESSs is divided into two intervals:a power interval satisfying the SOC boundaries (BI1) and a power interval with the physical limits (BI2).The power purchased/sold from/to the main grid is divided into two intervals:a power interval within the envelope range (GI1) and a power interval with the physical limits (GI2).

3.1 Objective

The objective of the real-time scheduling is expressed as:

where ΔPadj1, i(t) and ΔPadj2, i(t) are the adjusted powers in CI1 and CI2,respectively,of DG i at time t;ΔPadj1, k(t) and ΔPadj2, k(t) are the adjusted powers in BI1 and BI2,respectively,of BESS k at time t;ΔPadj2, grid(t) and ΔPadj2, grid(t) are the adjusted powers in GI1 and GI2,respectively,at time t;Uadj,l(t) is the binary variable of load l at time t;Creali1, (⋅) and Creali2, (⋅) are the adjustment cost functions of power in CI1 and CI2,respectively,of DG i in real-time scheduling;Crealk1, (⋅) and Crealk2, (⋅) are the adjustment cost functions of power in BI1 and BI2,respectively,of BESS k in real-time scheduling;Crealgrid1, (⋅) and Crealgrid2, (⋅) are the adjustment cost functions of power in GI1 and GI2,respectively,in real-time scheduling.Creall, (⋅) is the load shedding cost function of load l in realtime scheduling.

The cost function of the real-time scheduling consists of two parts:the cost scheduled as per the hours-ahead scheduling results and the cost for adjustment.

3.2 Interval division

The power intervals of Pi(t),Pk(t),and Pgrid(t) are represented in (20).

where and are CI1 and CI2,respectively;and are BI1 and BI2,respectively;are GI1 and GI2,respectively.

The boundaries of each interval are represented in (21).

The power intervals of Pk(t) and Pgrid(t) are relatively easy to understand,whereas the power intervals of Pi(t) require more description.

CI2 is the power interval considering the physical limits of the dispatchable DGs,e.g.,the minimum and maximum output power limits and ramping limits.CI1 is within the interval CI2,and the output power in CI1 can track the hours-ahead schedule.Fig.4 shows the schematic of the power interval division of the dispatchable DGs.

Fig.4 Schematic of the power interval division of the dispatchable DGs

From Fig.4,CI2 of DG i at time t is In addition to the physical limits,CI1 should consider the schedule at time t+1.Explicitly,the output power of DG i at time t is in the interval CI1 if the output power of DG i at time t+1 can return to the hours-ahead schedule after the power adjustment at time t.The lower boundary of CI1 of DG i at time t is and the higher boundary is

3.3 Real-time scheduling process

In the grid-connected microgrid,the power adjustments include Pw(t),Pp(t),Pi(t),Pk(t),Pgrid(t),and Pl(t) in the real-time scheduling.As illustrated previously,the output power of the dispatchable DGs in the interval CI1 can track the hours-ahead schedule in the following time,whereas it cannot do so when outside this interval.Since the hoursahead schedule is optimized considering a much longer period,the power in CI1 should be adjusted first compared with that outside CI1.Similarly,the output power of the BESSs outside the interval BI1 can increase the cost from a global optimal perspective,and therefore,the power in BI1 should be prioritized during the adjustment compared with that outside BI1.As for the power purchased/sold from/to the main grid,a penalty cost must be paid for the power outside the interval GI1,and thus,the power adjustment cost in GI1 is lower than that outside GI1.The WT and PV generate power without fuel costs,and the wind and photovoltaic power should be considered with priority from an economic perspective.To improve the reliability of the grid-connected microgrid,the penalty cost associated with the load shedding is much greater than those associated with the other regular adjustments in this study.In conclusion,the adjustments of the power in the intervals CI1,GI1,and BI1 in the real-time scheduling should take priority,followed by the power in intervals CI2,GI2,and BI2.The load shedding and renewable energy curtailment are the last choice.

The adjustment order of the output powers in the different intervals is set either based on the special requirements of the microgrid or in accordance with the marginal cost order.In this study,the adjustment order is based on the marginal cost order and the effect of tracking the hours-ahead schedule.

Fig.5 shows the adjustment order of the output powers in the real-time scheduling.ΔP is the predicted deviation in the net load,and Δ ＞P 0 is taken as an example to illustrate the flowchart.When Δ ＞P 0,the adjustment order to increase the output power is as follows:① Power in CI1,BI1,and GI1;② Power in CI2,BI2,and GI2;③ Load shedding.If the load shedding is implemented,the power should be reduced in reverse order until achieving a power balance.The adjusted results will be outputted if the SOC satisfies SOCdown,k (t ) ＜SOC k (t ) ＜SOCup,k (t) or if the number of iterations is greater than one (Iter ＞1).Otherwise,the adjustment will be recalculated based on the hours-ahead schedule in the database.When Δ ＜P 0,the adjustment is similar,and the steps are not repeated herein for conciseness.

The power in CI1,BI1,and GI1 increases in ascending cost order and reduces in descending cost order.The rules are also applicable to the power during CI2,BI2,GI2,and load shedding.The detailed operations of each DG and BESS are not provided in this paper because of space limitations.

Fig.5 Flowchart of the real-time scheduling

4 Case study

The rolling scheduling models were implemented in C++ using the solver CPLEX 12.5 on a PC with an Intel Core(TM) i7-4790 CPU and 8 GB of RAM,and the realtime scheduling model was solved using a heuristic model.The time consumed for the real-time scheduling was less than 1.0×10-3 s,which meets the instantaneity requirement of real-time scheduling.

4.1 Structure of test microgrid

Fig.6 shows the configuration of a modified microgrid [14].The microgrid is connected to the main grid,and it is composed of 13 loads,a battery ESS (BESS),and several DGs including a wind turbine (WT),photovoltaic (PV) system,microturbine (MT),fuel cell (FC),and diesel engine (DE).The MT,FC,and DE are considered dispatchable DGs,whereas the WT and PV are nondispatchable DGs because of their random characteristics.

Fig.6 Configuration of the microgrid system

Fig.7 shows the forecasted and actual outputs of the PV,WT,and load in a typical day.The time-of-use prices in Beijing,as listed in Table1,are used as the microgrid purchase and sale prices.

Fig.7 Forecasted and actual outputs of PV,WT,and load in a typical day

Table1 Time-of-use prices

Type Critical peak period Peak period Flat period Valley period Time of use 11:00-13:00 20:00-21:00 10:00-15:00 18:00-21:00 7:00-10:00 15:00-18:00 21:00-23:00 23:00-7:00 Purchase price/RMB·kWh-1 1.52 1.39 0.87 0.38 Sale price/RMB·kWh-1 0.81 0.81 0.81 0.30

Table2 lists the main parameters of the DGs and BESS.The battery has a capacity of 320 kWh,and its maximum,minimum,and initial SOC values are 100%,25%,and 47%,respectively.The capacity limit at the PCC is 500 kW.These data are obtained from previous papers [14,23-27]and tests conducted in Yanqing New Energy Park,Beijing,which are listed in [21].We assume that the penalty cost for surpassing GI1 is 50% of the market price.

Table2 Main parameters of DGs

Type MT FC DE WT PV BESS Lower limit (kW) 5 4 4 0 0 -80 Upper limit (kW) 80 80 60 150 100 80

4.2 Simulation results

Fig.8 shows the day-ahead scheduling results.Most of the energy is supplied by the main grid (PCC).The MT and FC start up at noon when the load and price are high.The DE is kept in standby owing to its high operation cost.The BESS charges at valley periods and discharges at critical peak periods.To verify the effectiveness of the proposed strategy,the realtime scheduling results are depicted in Fig.9.

Fig.8 Day-ahead schedule of the microgrid in the grid-connected mode

Fig.9 Real-time schedule of the microgrid in the gridconnected mode

Comparing the real-time scheduling results with the day-ahead ones,we find that the real-time schedule tracks the rolling schedule results (including day-ahead scheduling and hours-ahead scheduling) overall.The unbalanced power is mainly absorbed by the PCC and the BESS.Fig.10 shows a comparison of the SOCs between the real-time and day-ahead schedules,along with the lower and upper boundaries of the SOCs calculated in the hours-ahead scheduling.

As shown in Fig.10,the SOCs of the real-time schedule are between the lower and upper boundaries,in which the BESS can operate economically in the real-time scheduling.The SOC deviations between the real-time and day-ahead schedules are significant between hours 12 and 19 because of the prediction errors of the renewable energies and loads.However,the deviations do not require immediate modification,because the SOCs of the real-time schedule are between the lower and upper boundaries.

Fig.11 shows the electricity generated by the DGs and PCC at different intervals in a day.

Fig.10 Comparison of SOCs between real-time and day-ahead schedule

Fig.11 Electricity generated by the DGs and PCC at different intervals during T

As shown in Fig.11,most of the energy is supplied by the renewable generators,the BESS in BI1,the dispatchable DGs in CI1,and PCC in GI1,which means that the realtime scheduling can track the hours-ahead schedule well.The electricity supplied by the PCC in GI2 is 16.6 kWh,because the gaps between the prediction and actual values are large enough to exceed the PCC envelope range.

4.3 Economic analysis

To analyze the economic impact of the proposed method in this paper,the proposed method and the conventional method without considering the interval division of the DGs and batteries are compared in terms of the cost.Table3 lists the results.

Table3 Operation costs of the microgrid during T

Method MT(RMB)FC(RMB)DE(RMB)BESS(RMB)PCC(RMB)Total cost(RMB)Proposed method 454.4 300.9 0 199.1 2721.0 3675.4 Conventional method without interval division 488.2 289.6 0 202.5 2718.4 3698.7

From Table3,the cost of the MT is higher than that of the FC,because the MT generates more electricity,as shown in Fig.11.The cost of the DE is zero,because it kept on standby consistently.The BESS can shift energy from valley periods to peak periods to save the total operation cost,which will increase its maintenance and depreciation expenses.The load is mainly supplied by the main grid through the PCC,and hence,its cost is the highest.With the proposed method in this paper,the total operation cost is 3675.4 RMB,a reduction of 23.3 RMB compared with the conventional method without the interval division.

5 Conclusions

In this study,a real-time scheduling strategy for microgrids based on off-line optimization was developed to optimize the microgrid schedule.The major contributions of this paper can be concluded as follows:

(1) Rolling scheduling models,including day-ahead scheduling and hours-ahead scheduling,were established.The day-ahead scheduling makes a schedule covering the next day,and the hours-ahead scheduling makes the schedule more accurate.

(2) The possible deviations in the real-time schedule could be considered in the hours-ahead scheduling,and the lower and upper boundaries of the SOC could be calculated in advance.

(3) A real-time scheduling model based on the dayahead and hours-ahead scheduling was established,and the output power of the DGs was divided into two intervals in terms of the ability to track the hours-ahead schedule.

(4) Simulations were implemented on a grid-connected microgrid comprising a WT,PV,BESS,MT,DE,and FC.The schedule results indicated that the proposed realtime schedule strategy is effective from both economic and instantaneity perspectives.

Acknowledgments

This work was supported by the National Key R&D Program of China (2018YFA0702200) and the Fundamental Research Funds of Shandong University.

Declaration of Competing Interest

We declare that we have no conflict of interest.