Two-stage,Correction,Strategy-based,Real-time,Dispatch,for,Economic,Operation,of,Microgrids

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(1.Wenzhou Power Supply Company,State Grid Zhejiang Electric Power Co.,Ltd.,Wenzhou 325028,China;2.School of Electrical Engineering,Xi’an Jiaotong University,Xi’an 710049,China;3.School of Automation,Nanjing Institute of Technology,Nanjing 211167,China)

Abstract: Given the different energy rates of multiple types of power generation units,different operation plans affect the economy of microgrids.Limited by load and power generation forecasting technologies,the economic superiority of day-ahead plans is unable to be fully utilized because of the fluctuation of loads and power sources.In this regard,a two-stage correction strategy-based real-time dispatch method for the economic operation of microgrids is proposed.Based on the optimal day-ahead economic operation plan,unbalanced power is validly allocated in two stages in terms of power increment and current power,which maintains the economy of the day-ahead plan.Further,for operating point offset during real-time correction,a rolling dispatch method is introduced to dynamically update the system operation plan.Finally,the results verify the effectiveness of the proposed method.

Keywords: Real-time dispatch,day-ahead operation plan,economic operation,microgrid

With the development of the energy industry,generation technologies including wind power,photovoltaic power,and gas power have been widely used in the form of large-scale centralized power generation or small-scale distributed power generation[1-2].Among them,a variety of distributed generators and energy storage devices form microgrids[3].However,the coordinated operation among multiple distributed generators has a significant impact on the operating economy of microgrids.Therefore,it is crucial to study the economic operation strategy for microgrids.

Because of the different energy rate structures of multiple types of power generation technologies,operation plans can affect the economy of microgrid[4].Therefore,it is necessary to formulate an optimal operation plan according to energy rate structures and load changes.In terms of time scale,the economic dispatch of microgrid includes day-ahead dispatch[5-6]and real-time dispatch[7-8].Based on previous forecasting data,day-ahead dispatch can formulate operation plans for power sources for the next day.Ref.[9] proposed a day-ahead economic dispatching method for an energy coupling system,including hydrogen and natural gas,which reduced the total cost.Considering renewable generation,electricity price and power demand,Ref.[10]proposed an approximate dynamic dispatch method to improve economy under multiple operation conditions.Ref.[11] adopted a multi-stage optimization method to overcome uncertainties and realized the day-ahead economic dispatch.Scenario-based scheme is also one of the economic dispatch methods aimed at alleviating the problem of power fluctuations[12-13].However,due to load fluctuations and uncertainty of new energy power generation[14],the economy of day-ahead plan cannot be fully utilized for microgrids during real-time operation.Therefore,it is necessary to formulate an effective and economic real-time dispatch strategy,which can take full advantage of day-ahead plan.

Limited by the power forecasting technologies,accurate load and power generation estimation is challenging,and the work point of the generator may deviate from the original operation plan because of real-time power regulation.If the microgrids operate according to the day-ahead plan,the unbalanced power will be induced.Therefore,the output power of the generator should be adjusted to eliminate unbalanced power in the real-time dispatch.Ref.[15] established a real-time dispatch model and proposed a low-cost real-time operation scheme.To reduce the effect of wind power disturbances,a real-time dispatch method proposed in Ref.[16] struck a balance between the operational costs and wind power disturbance risks.For renewable energy generation uncertainty,Ref.[17]adopted stochastic dual dynamic programming and proposed a multistage programming method;however,the economy of day-ahead plan was neglected.The system operating costs were reduced by incorporating fluctuations into the frequency auxiliary service[18].For the above real-time dispatch method,however,the economy goal of the original day-ahead plan cannot be fully achieved.

To economically allocate the unbalanced power resulting from load fluctuations,a two-stage correction strategy-based real-time dispatch for economic operation of microgrids is proposed.First,based on a mathematical model of the main equipment,by minimizing the daily operating costs,the optimal day-ahead economic plan is obtained.Considering that the real-time adjustment capability of the equipment is limited by the power and ramp constraints,this study analyzes the maximal adjustable power and derives its mathematical expression under four scenarios.A two-stage real-time correction method is designed based on the day-ahead plan and maximal adjustable power,that is,the unbalanced power is allocated through the power increment and current power.The proposed real-time dispatch strategy can minimize the power generation costs (caused by the operating point deviating from the day-ahead plan) by utilizing the optimal day-ahead economic plan and the best regulation trend of the equipment.

The remainder of this paper is organized as follows.Section 2 establishes mathematical models of the devices and designs the optimal day-ahead operation plan.Section 3 proposes the two-stage correction strategy-based real-time dispatch method for economic operation of microgrids.The proposed method is verified by a microgrid case in Section 4,and Section 5 draws the main conclusions.

2.1 Mathematical models of generation units

A microgrid generally consists of traditional power generation,renewable energy generation,and energy storage devices[19-21].For better reliability of power supply,it is necessary for the microgrids to connect to the utility grid[22].The structure of a typical microgrid including multiple power sources is shown in Fig.1,and the main equipment models are as follows.

(1) Micro gas turbine (MGT)

wherePMGT,i,tandSMGT,iare the output power and rated capacity,respectively;ηMGT,i,tis the power generation efficiency;VMGT,i,tis gas consumption;Ai,kis thek-thorder coefficient;andqis the calorific value of natural gas.

(2) Permanent magnet synchronous generator(PMSG)

wherevi,tis the wind speed;andare the starting,rated,and safe wind speed,respectively.

(3) Photovoltaic power generation (PV)

wherePPV,i,t,GAC,i,t,andTc,i,tare the power,light intensity,and temperature,respectively;andkTis the temperature coefficient.The superscript “Stc”represents the standard conditions.

(4) Energy storage system (ESS)

whereSBat,i,tis the capacity;,andδBat,iare the charging efficiency,discharging efficiency and self-discharge rate,respectively.

2.2 Optimal day-ahead economic operation plan

Using the complementary characteristics of various energy prices,the system economy can be improved by optimizing the output power of each generation unit.As shown in Fig.2,to increase the consumption of new energy,the wind power and photovoltaic power are obtained first.Subsequently,the day-ahead operation plan for MGT and the power shortage is obtained.Unbalanced power can be eliminated by abandoning the wind,photovoltaic,or battery storage sources,and purchasing electricity from the utility grid,i.e.,meeting the load balance constraint.Finally,the operation cost is calculated and optimized,and the minimal operating cost and optimal operation plan is obtained.

Fig.2 Optimal day-ahead economic operation plan

In this study,the optimization object is to minimize the operating costCs,such that

whereCEle,tis the electricity price at timetandCLngis the unit price of natural gas.

To ensure the safe operation,the operating constraints in Eqs.(7) and (8) should be met.

(1) Load constraint

wherePGrid,tandPLoad,tare the purchased power and the total day-ahead forecasting load,respectively.

(2) Equipment constraints

Because the accurate information of load and power generation cannot be obtained in advance,there will be a large power shortage between the real-time load and day-ahead plan of generation units during real-time operation.Therefore,a two-stage correction method is designed to revise the day-ahead plan and realize economic allocation of the unbalanced power.

3.1 Real-time operation correction strategy

Based on the optimal day-ahead economic operation plan,Fig.3 shows the flowchart of the two-stage correction strategy.Firstly,to evaluate the regulation ability of the equipment,the maximal adjustable power is calculated considering the rated power and ramp power of the generation unit.Thereafter,according to the current work point and the remained regulation power,the correction state of the device can be obtained.The real-time correction strategy then starts to allocate the system’s unbalanced power through two stages.When all power shortage is eliminated,the system carries out the revised operation plan.

Fig.3 Flowchart of two-stage real-time correction strategy

3.2 Maximal adjustable power

The aim of the real-time correction strategy is to economically change the original output power predetermined by the day-ahead plan.Therefore,at any moment,the revised output power of the equipment includes three parts,i.e.,the current power,power increment of the day-ahead plan,and real-time correction power.The total power at the next moment,determined by the above three parts,must meet the power and ramp constraints.As a consequence,it is essential to first analyze the maximal adjustable power and evaluate the regulation ability considering the power increment.

For a positive increment power (day-ahead plan) att+Δt,Fig.4 demonstrates the relationship between the maximal adjustable power and two constraints.Under the power and ramp constraints,it is evident that the maximal upward adjustable power (overlap area)includes both the types of constraints;which constraint is valid,depends on the output power.

Fig.4 Maximal adjustable power (positive power increment)

Considering the sign of the power increment and maximal adjustable power,a total of four cases are shown in Fig.5,where,Ri,up,andRi,downare the rated power,cut power,upward,and downward ramp rate,respectively.For positive power increment,the upward adjustable power can be written as

Fig.5 Calculation of maximal adjustable power

Similarly,maximal downward adjustable powercan be calculated by

3.3 Equipment correction state matrix

Under the effect of the power and ramp constraints,the calculated maximal adjustable power may be 0.Further,during the correction process,if the adjustable power of a device is exhausted,it should exit subsequent unbalanced power distribution.Therefore,some devices do not at all or partially provide regulation services.The equipment correction state matrix is

whereei,Xis the correction state in theX-th stage,andei,X=1 represents participation in correction,otherwise,ei,X=0.

3.4 Correction coefficient and correction amount

For the most economic trend of power regulation,while operating during the whole day,the original day-ahead power increment represents the most economical trend.Therefore,the unbalanced power is allocated according to the power increment using the correction coefficientin Eq.(14) in the first correction stage.However,power increment of some device may reach its maximal adjustable power before the power balance is completely eliminated.Therefore,the second correction stage starts and the remaining unbalanced power is allocated according to the current output power using the correction coefficientin Eq.(15).

3.5 Real-time update of correction state matrix,correction coefficient,and correction amount

EXneeds to be initialized first,as shown in Fig.6,before the real-time correction strategy starts.According to Eq.(14),in the first correction stage,if the output power is equal to that at the next dispatch moment,the device need not to participate in the first unbalanced power allocation.Therefore,for the initialization ofEI,the correction state parameters of the such devices are set to 0.Similarly,for the initialization ofEII,since the equipment whose states are set to 0 (during theEIinitialization) have an ability to be adjusted in the second stage,their state parameters are set to 1.

Fig.6 EX initialization and update

Limited by the maximal adjustable power,some equipment may exhaust the adjustable power while the system is still under power shortage.The remained power shortage should be calculated again between other devices with adjustment ability.The correction amountCi,Xcan be expressed as

According to Eqs.(10),(12),and (17),the corrected output powercan be calculated as in Eq.(18).Meanwhile,the correction state matrixEXcan be updated as in Eq.(19).

To this end,according to Eqs.(17)-(19),the unbalanced power can be allocated andEXcan be updated,as shown by Algorithm 1 (Fig.7).

Fig.7 Allocation algorithm of unbalanced power

As for switching between the two stages,there is a dependence onEIand the remaining unbalanced power.In the first correction stage,whenis equal to 0,it indicates that the system power is balanced,and the real-time correction ends.IfEIis updated to a null matrixO,it means that the devices participating in the correction have all reached the upper limit of their adjustment capabilities under the unbalanced power distribution method in Eq.(14).At this time,the correction method in Eq.(15) needs to replace that in Eq.(14),that is,the second stage correction starts.

Based on the above steps,the proposed strategy can generally be described as follows.

(1) The first correction stage:allocating the unbalanced power by power increment.

(2) The second correction stage:if the power shortage cannot be completely allocated in the first stage,the system switches to the second stage and allocates the remaining unbalanced power according to the current output power.

3.6 Real-time correction strategy based on rolling dispatch technology

With the above real-time correction strategy,the problem of power shortage is solved effectively and the load balance constraint is satisfied.However,the economy of real-time correction may decline in comparison to the original optimal day-ahead plan.The reasons are the work point of the device deviating from the predetermined plan and this deviation accumulating over time.In addition,the real-time correction changes not only the output power but also the adjustable ability,which increases the operating cost due to the exhaustion of adjustable power.Therefore,a dynamic rolling dispatch method is adopted to update the generator’s operation plan in time,to ensure sufficient adjustable power.

Modifying the objective function in Eq.(6) as 24 h afterk-th hour yields

Fig.8 demonstrates the rolling dispatch technique and real-time correction process.At thek-th hour,the current day-head operation plan is only used for real-time correction within the first hour,and the equipment operate according to the revised plan.Meanwhile,the parameterkscrolls backward one hour,and the subsequent 24 h operation plan is remade according to current output power.Finally,the real-time correction algorithm is repeated and the day-ahead plan is created until out of service.

Fig.8 Process of rolling dispatch

To verify the correctness and effectiveness of the proposed real-time dispatch strategy,the studied microgrid shown in Fig.1 is established in Matlab,whose equipment parameters are shown in Tab.1.

Tab.1 Equipment parameters

Due to the peak and valley characteristics of the load,the time-of-day tariff in Eq.(21) is often used to alleviate the power supply pressure.The electricity price curve is shown in Fig.9a.

To encourage electricity customers to use clean energy,natural gas often adopts tiered prices according to Eq.(22) and price curve as shown in Fig.9b.

Fig.9 Price curves

4.1 Day-ahead dispatch

To minimize operating costs,a modified particle swarm algorithm[23],with excellent searching performance,is used in this study.Fig.10 shows the solved optimal day-ahead plan whose operating cost is 2 102 $.During periods,such as 0-8 h and 12-15 h,there is a lower purchasing cost of electricity.As a result,the MGT maintains a low-power operation,reducing the operating cost,while the increasing load is completely assumed by the utility grid,at a lower electricity price.

Fig.10 Optimal operation plan solved by day-ahead dispatch

4.2 Real-time dispatch

Limited by load/generation forecast technologies,the real-time load often deviates from the day-ahead forecast load.To simulate the random load fluctuation,the real-time load is obtained by superimposing random disturbances on the day-ahead forecast load.It is worth noting that the real-time load can only be obtained within a few minutes,using ultra-short-term load forecast,which is usually more accurate than the day-ahead data.Fig.11 shows the prediction errors between the day-ahead forecast load and real-time load.If the day-ahead plan shown in Fig.10 is strictly carried out,a series of low frequency load shedding events or high frequency generator tripping events will arise from the unbalanced power.

Fig.11 Day-ahead forecast load vs.real-time operation load

To verify the effectiveness of the proposed method,three correction methods are designed.

Case 1:All unbalanced power is compensated by the grid;MGT adopts the day-ahead plan.

Case 2:All unbalanced power is compensated by MGT;grid adopts the day-ahead plan.

Case 3:The grid and MGT both adopt the two-stage real-time correction method,and their output is the real-time correction amount,calculated by the two-stage correction method superimposed on the day-ahead plan generated by rolling dispatch.

In addition,the fluctuations of load,wind power,and photovoltaic power are the same in all the cases.Fig.12 shows real-time dispatch results of the three cases,and the operating costs are shown in Tab.2.

Fig.12 Real-time dispatch results

Tab.2 Operating costs of three cases

For case 1,all the unbalanced power is fully undertaken by the grid,and the MGT adopts the day-ahead plan.According to Fig.12a,MGT’s output power is consistent with the day-ahead plan in Fig.10.While the grid power is significantly higher than the day-ahead plan,the operating cost is reduced by reducing the power purchased from the grid during the high electricity price period [see 10-11 h and 17-22 h in Fig.10].For the real-time operation in case 1,because the unbalanced power is fully undertaken by the grid,purchasing more power will greatly increase the system operation cost during the high electricity price period,in Fig.12a.Therefore,the daily operating cost of case 1 is the largest among the three methods.

For case 2,all unbalanced power is undertaken by the MGT,and its output power increases during high electricity price period,reducing the operating cost.However,during the low electricity price period,case 2 still uses MGT to correct the unbalanced power [see 22 h in Fig.12b].In addition,for the medium electricity price period,case 2 still maintains the original day-ahead plan.Compared with case 1,case 2 reduces the operating cost to a certain extent,but there is a potential to further improve the economy of the real-time operation.

A common reason for the restriction of the economy in cases 1 and 2 is that the current operating point of the equipment has already deviated from the optimal day-ahead plan.As a result,if the equipment still runs according to day-ahead plan,the original economy of day-ahead plan cannot be realized.Therefore,rolling dispatch should be used to renew the optimal economic operation plan within the next 24 hours based on the current operating conditions.

For case 3,according to Eq.(14),the device with the larger power increments undertakes more load fluctuation in the first stage,such as in 5-7 h in Fig.12c.According to Eq.(15),the larger output power means to assume more unbalanced power.For example,the MGT’s output power in the day-ahead plan is large,and hence it is significantly increased during 8-21 h in Fig.12c.In addition,since the rolling dispatch updates the operation plan in time,the effect of work point deviation is significantly reduced.Therefore,the proposed real-time correction method can ensure safe operation and maintain the economy of the original day-ahead plan.

Due to unforeseen load fluctuations,the inappropriate power correction of optimal day-ahead plan induces extra costs and impairs the economic operation.This paper proposes an economic real-time dispatch method for microgrids.The unbalanced power is effectively allocated in the terms of economic trends,which significantly saves the operating cost.The rolling dispatch can update the optimal day-ahead plan in time to solve the deviation of output power.The proposed real-time correction strategy realizes the economic and safe operation.