Multiobjective optimal dispatch of microgrid based on analytic hierarchy process and quantum particle swarm optimization

0 Introduction

It is a well-known and recognized fact that renewable power generation is an effective means to resolve the global environmental concerns regarding fossil fuel consumption and energy crisis [1].Nowadays,a growing proportion of the generated renewable energy,such as wind and solar power,is employed to power loads via microgrids (MGs)rather than the traditional distribution grids [2-4].Therefore,optimal dispatch of the MGs is critical for promoting the application and accommodation of renewable energies [5].

Studies on the optimal dispatch of MGs have garnered attention in this regard [6].Several frameworks have been proposed for optimal dispatch to coordinate the output power of each MG unit and minimize its operational cost and pollutant emission [7,8].The mathematical models for optimal dispatch of the MGs are characterized by diversity and complexity,as numerous decision variables,constraint variables,and multiple subjects are involved [9].The multiobjective optimal dispatch scheme considers the economic cost,environmental concerns,and consistency of power supply.The economic cost is composed of operational,maintenance,and fuel costs of the distributed units.The environmental concerns and power supply consistency can be quantified by the pollution treatment costs and load interruption,respectively [10].It should be noted that conflicts between these multiple objectives pose considerable challenges to the optimal dispatch of the MGs.Some researchers have employed intelligent algorithms,such as the genetic algorithm,to obtain a series of paretooptimal solutions [11];however,decision makers still need to choose an optimal solution from the available solution set.In [12],the price penalty factor as well as linear weighting methods wasused to transform the multiple objectives into a single objective.Furthermore,the analytic hierarchy process (AHP) algorithm has shown adequate capability to determine the weight coefficients for the aforementioned intelligent algorithms [13-15].

The complexities in the mathematical models for optimal dispatch of the MGs necessitate studies on appropriate solution methodologies.The strong nonlinearities in the MG models challenge the traditional optimization algorithms but favor intelligent algorithms in some cases.The nondominated sorting genetic algorithm (NSGA-Ⅱ) was proposed to optimize the MG dispatch in [16].To solve the dual-objective optimization problem,the multiobjective bacterial colony chemotaxis (MOBCC) algorithm was employed to produce a pareto-optimal solution set with attractive simulation results in [17].

However,the multiple objectives of MG dispatch,with varying priorities,need to be studied in depth since as the concerns of various stakeholders should be appropriately considered.To fill this gap,an optimal dispatch model for the MG with varying subobjective priorities and their corresponding solution methodologies are studied in this work.The primary contributions of this study are as follows.First,a multiobjective optimal dispatch model for the standalone MG,which is composed of wind turbines (WTs),photovoltaics (PVs),diesel engine (DE) units,load,and battery energy storage system (BESS),is proposed.In this model,the economic cost,environmental protection,and power supply consistency are comprehensively taken into consideration,and the concerns of different stakeholders are expressed via varying priorities of the subobjectives.Second,the AHP algorithm is employed to reasonably evaluate the importance of various subobjectives by specifying weight coefficients for them.Furthermore,the quantum particle swarm optimization (QPSO) algorithm is proposed as the solution for improved convergence performance [18].Finally,simulation studies are performed on a test MG and the results are analyzed to draw conclusions.

The remainder of this paper is organized as follows.In Section 1,the multiobjective optimal dispatch model is proposed considering economic cost,environmental protection,and power supply consistency.The solution methodology based on the AHP and QPSO algorithms are described in Section 2.Case studies are conducted on a test system to validate the optimal dispatch model and solution methodology,which are described in Section 3.Finally,the conclusions are presented in Section 4.

1 Optimal dispatch model

In this work,the MG is considered to be in the islanded mode.The multiobjective optimal dispatch model addresses the multiple concerns of different stakeholders,such as the MG operator,end power users,and societies with environmental concerns.

1.1 Multiobjective optimization function

A multiobjective optimization function of the MG,denoted as F,is composed of three subobjectives,i.e.,F1,F2,and F3,and can be expressed as follows:

where F1 denotes the fuel as well as operation and maintenance (O&M) costs,and F2 and F3 denote the pollutant emission and load disruption costs,respectively.ω1,ω2,and ω3 are the weight coefficients of F1,F2,and F3,respectively,and are obtained by the AHP algorithm.As expressed in (2),F1 is composed of two parts,i.e.,fuel cost denoted as Cfuel(t) and O&M cost denoted as COM(t).

The power outputs of PVs and WTs are mainly determined by solar radiation and wind velocity [19,20];therefore,no fuel costs are introduced by the PVs and WTs.With regard to the fuel cost of DE units,a quadratic function of the power output is employed as follows [21]:

where Cfuel,DE(t) is the fuel cost of the DE,PDE(t) is the power output of the DE,and α,β,and γ are the fuel cost coefficients.In addition to the Cfuel(t),the COM(t) of WTs,PVs,DEs,and BESS are considered and evaluated as follows:

where ζi,OM and Pi(t) are the O&M coefficient (OMC) and t-th power output of the i-th distributed generator (DG),respectively.The pollutant emission cost of the DE is defined as

where τj and σj are the cost and emission coefficients of the j-th pollutant,respectively.Moreover,the load disruption cost is as expressed below:

where Ploss(t) is the interrupted load in the t-th hour,and kloss is the penalty coefficient for load interruption.In the following case studies,the priorities of the critical and noncritical loads are considered by assigning different penalty coefficients.The noncritical loads will be interrupted first,and the penalty factor for the critical loads will be higher than those for the noncritical loads.

1.2 Constraints

The equality constraint shown in (7) represents the power balance among the load,DGs,and BESS.

Here,PBESS(t) is the output power of the BESS in the t-th hour and is positive when the BESS discharges or negative otherwise;PL(t) is the load in the t-th hour.The inequality constraints shown in (8) specify the maximum and minimum power constraints of the DGs.

where Pimin and Pimax are the permissible minimum and maximum power outputs of the i-th DG,respectively.In addition,the constraints with regard to the power and state of charge (SOC) of the BESS are considered as specified in(9) [22,23].

where is the power limit of the BESS.SOCmin and SOCmax are the permissible minimum and maximum values of the SOC to protect the BESS from overcharge or overdischarge,respectively.

2 Solution methodology

The multiobjective optimal dispatch model specified in Section 1 is described in this section.First,the AHP algorithm is used to determine the weight coefficients of the subobjectives since it can effectively address multiattribute decision-making problems.The QPSO algorithm is then employed to solve the multiobjective optimization model.

2.1 AHP algorithm

Taking the economic cost,environmental conservation,and power supply consistency into consideration,reasonable weight coefficients of the subobjectives,i.e.,ω1,ω2,and ω3 are proposed by the AHP algorithm,which is composed of the following steps [24-26]:

1) Establishment of the hierarchical AHP model

2) Creation of judgment matrices

3) Calculation of the weight coefficients

4) Consistency checking

The AHP model for optimal dispatch of the MG is summarized in Table1.

Table1 Hierarchical AHP model of MG optimal dispatch

Objective layer Criteria layer Attribute layer Optimal dispatch strategy Economic cost Cfuel COM Environmental conservation CCO2 CSO2 CNOX Power supply consistency Cload

Here,CCO2,CSO2,and CNOX are the costs of CO2,SO2,and NOX emissions,respectively;Cload is the cost of load disruption.The judgment matrices are obtained by pairwise comparisons of the importance of factors from the same layer.The weight coefficient of each factor is determined by calculating the eigenvalue and eigenvector of the corresponding judgment matrix.The consistency ratio (CR)index is calculated for consistency checking;a CR less than or equal to 0.1 is considered acceptable in this work.

2.2 QPSO algorithm

The particle swarm optimization (PSO) algorithm generates a group of random initial solutions and searches for the optimal solution by iterative computations.However,the PSO has difficultly in converging to a global or even a local optimal solution [27].The QPSO,however,has been determined to have the advantage of fast convergence rate,and its fitness value is better than that of the traditional PSO [28,29].Hence,the QPSO is introduced to solve the optimization problem in this work.

In QPSO,each particle is considered to be in a quantum state and formulated using a wave function of the Schrodinger equation.The particles will eventually converge to a certain region owing to the local attractor,which is defined as follows [30]:

where i,j,and d denote the number of particles,number of dimensions of the solution space,and number of iterations,respectively;pi,j(d) is the local attractor.Pi,j(d) and Gj are the personal best (pbest) position of the particle and global best (gbest) position of the swarm,respectively.φi ,j ( d) is a random number with a uniform probability density function(PDF) on interval (0,1).

In the solution space,the particles converge to the center of the well according to the PDF given by the quantum well and wave function.All particles are then updated using the following equations [31]:

whereXi,j(d+1)is thepositionofparticleiin the(d+1)-th iteration;βisthe contraction-expansionfactor,whichcan control the convergence speed of the QPSO;Cj(d) is the centerofthebestposition oftheswarm;u i,j( d)isa random numberwitha uniformPDF ontheinterval(0,1);dmax is the maximum iteration number;M is the total number of particles that represent the potential solutions.The flowchart for optimal dispatch based on the AHP and QPSO is graphically shown in Fig.1.

Fig.1 Flowchart for MG optimal dispatch based on AHP and QPSO algorithms

3 Simulation studies

3.1 Information of test system

A test MG system,as shown in Fig.2,is applied in this work for the case study.The PVs,DE,WTs,and BESS are included to power the load,which is composed of critical and noncritical loads.

Fig.2 Schematic of a standalone MG for case study

The capacities of the PVs,i.e.,PV1,PV2,PV3,and PV4 are 12 kW,10 kW,8 kW,and 10 kW,respectively.The rated power and permissible minimum output of the DE is 30 kW and 9 kW,respectively.The detailed parameters of the WTs are denoted by WT1,WT2,WT3,WT4,WT5,and WT6,as specified in Table2.

Table2 Parameters of the WTs

Parameters WTs WT1 WT2 WT3 WT4 WT5 WT6 Cut-in speed (m/s) 4 4 3 3 3 3 Rated speed (m/s) 12 12 10 10 8 8 Cut-out speed (m/s) 24 24 25 25 20 20 Rated power (kW) 10 10 8 8 7 7

The OMCs of the PVs,WTs,DE,and BESS used in this study are 0.0096 ¥/kWh,0.0296 ¥/kWh,0.0880 ¥/kWh,and 0.0027 ¥/kWh,respectively.The emission and cost coefficients of the various pollutants are listed in Table3.

Table3 Emission and cost coefficients of pollutants

Pollutants Emission coefficient(g/kWh)Cost coefficient(¥/kg)CO2 649 0.210 SO2 0.206 14.842 NOX 9.890 62.946

A 24 hour simulation was conducted in steps of 1 hour.The hourly meteorological data employed in the simulations,such as temperature,radiation intensity,and wind speed,are summarized in Table4.

Table4 Hourly meteorological data employed in the simulations

Time (h) Temperature(°C)Radiation intensity(kW/m2) Wind speed (m/s)1 13.9 0 4.05 2 12.1 0 5.16 3 11.5 0 4.92 4 11.3 0 6.71 5 12.7 0 7.88 6 13.4 0 7.3 7 13.2 0 7.87 8 14.2 0.004 7.6 9 14.4 0.1406 10.3 10 16.8 0.3899 6.28 11 17.3 0.7029 10.42 12 17.8 0.8345 9.29 13 18.8 1.044 7.63 14 20.9 0.7673 8.65 15 20.1 0.9872 7.27 16 20.7 0.7392 3.75 17 20.3 0.4633 4.15 18 20.2 0.2378 4.52 19 18.5 0.0259 3.48 20 16.3 0 3.17 21 16.2 0 2.9 22 15.2 0 2.44 24 14.2 0 4.41 24 14.6 0 3.59

Based on the meteorological data,the available power values of the WTs and PVs are calculated and illustrated in Fig.3.

The hourly varying load,which is composed of critical and noncritical components,is employed in this study.The load and its critical component are shown in Fig.4.

Fig.3 Available power of PVs and WTs

Fig.4 Hourly varying load and its critical component

3.2 Simulation results and analyses

The optimal dispatch for the test system involves two basic steps.First,the weight coefficients of the criteria layer,i.e.,the weight coefficients of the subobjectives,are determined by the AHP algorithm.Then,the QPSO algorithm is used to determine the solutions of the optimal dispatch strategy.It should be noted that different stakeholders of the MGs give different priorities to the subobjectives.Seven sets of priorities of the weight coefficients can thus be proposed for the optimal dispatch model of the MGs,namely case 1:ω1＞ω2＞ω3,case 2:ω1＞ω3＞ω2,case 3:ω2＞ω1＞ω3,case 4:ω2＞ω3＞ω1,case 5:ω3＞ω2＞ω1,case 6:ω3＞ω1＞ω2,and case 7:ω1=ω2=ω3.In this work,all of these cases have been considered,and the corresponding weight coefficients are determined using the AHP algorithm.Consider case 1 as an example;the weight coefficients of the attribute and criteria layers are calculated successively.The results of pairwise comparisons and weight coefficients of the attribute layer by the AHP are shown in Table5.

The weight coefficients of the criteria layer,i.e.,ω1,ω2,and ω3 are further derived based on the pairwise comparisons,whose computational results are summarized in Table6.

Table5 Pairwise comparisons and weight coefficients of the attribute layer

Factors Factors Weight coefficients Cfuel COM CCO2 CSO2 CNOX Cload Cfuel 1 3////0.7500 COM 1/3 1////0.2500 CCO2//1 5 3/0.6556 CSO2//1/5 1 3/0.1578 CNOX//1/3 1/3 1/0.1866 Cload/////1 1.0000

Table6 Pairwise comparison and weight coefficients of criteria layer

Factors Factors Weight coefficients CR F1 F2 F3 F1 1 3 5 0.6333 0.0372 F2 1/3 1 3 0.2605 F3 1/5 1/3 1 0.1062

Note that the CR of case 1 is 0.0372,which is less than 0.1;therefore,the consistency of the weight coefficients in Table5 is acceptable.

The remaining six sets of priorities of the weight coefficients are similarly analyzed,and ω1,ω2,and ω3 are accordingly specified by employing the AHP algorithm.Then,the optimal dispatch models with different sets of weight coefficients are solved based on the QPSO algorithm;these computational results are listed in Table7.

It can be seen that the consistency can be verified and accepted for all cases since the CRs are all less than 0.1.Meanwhile,the solution methodology based on the AHP and QPSO present attractive capabilities and adaptability for MG dispatch considering multiple concerns.Moreover,it is clearly illustrated that the priorities of the subobjectives produce different results for the objective function F.Hence,comprehensive investigations and assessments are needed to propose reasonable priorities for the subobjectives that can be accepted by multiple stakeholders.

Table7 Optimization results for various subobjective priorities

Cases Priorities Results ω1 ω2 ω3 F/¥ CR 1 ω1＞ω2＞ω3 0.6333 0.2605 0.1062 247.4652 0.0372 2 ω1＞ω3＞ω2 0.6555 0.1578 0.1867 232.2314 0.0281 3 ω2＞ω1＞ω3 0.4055 0.4796 0.1150 257.9295 0.0280 4 ω2＞ω3＞ω1 0.1062 0.6333 0.2605 249.6452 0.0372 5 ω3＞ω2＞ω1 0.1578 0.1875 0.6555 179.9897 0.0281 6 ω3＞ω1＞ω2 0.1062 0.2605 0.6333 186.5540 0.0372 7 ω1=ω2=ω3 0.3333 0.3333 0.3333 225.0007 0.0000

In addition to the objective function F,the decision variables,such as outputs of the DE,discharge/charge power of the BESS,and disrupted load,are solved by the QPSO algorithm,for example,ω1 = 0.1578,ω2 = 0.1875,and ω3 = 0.6555 in case 5.The computational results of the decision variables are shown graphically in Fig.5,and the BESS capacity is 96 kW.Further,the influences of different BESS capacities on the optimal dispatch are studied.Figs.6 and 7 show the dispatch results for BESS capacities of 48 kW and 192 kW,respectively.

First,the optimal dispatch provides the prerequisite for complete accommodation of the PVs and WTs.Second,as illustrated in Figs.5,6,and 7,different BESS capacities have different influences on the optimal dispatch results.The BESS mitigates the imbalance between the power demand and power supply resulting from fluctuations of the PVs,WTs,and load.When the total power generated by the PVs and WTs is greater than that required for the load,

Fig.5 Outputs of BESS and DE corresponding to the optimal result

Fig.6 Optimal result with 48 kW BESS capacity

Fig.7 Optimal result with 192 kW BESS capacity

the redundant power is absorbed by the BESS.Otherwise,the BESS discharges and provides supplementary power.Moreover,the DE operates as a standby when necessary to address power shortages within its capacity.For example,the total power of the WTs and PVs at 16:00 in Fig.5 is 31.3317 kW,which is less than that required for the load;consequently,the BESS discharges the additional 19.2 kW of power,and the DE outputs a rated power of 30 kW.However,the load cannot be completely powered in this situation,and the noncritical load of 4.4683 kW is thus disrupted.

4 Conclusion

In this study,a multiobjective optimal dispatch model has been developed for a standalone MG.During the development of the model,multiple objectives regarding the economic costs,pollutant emissions,and power supply consistency are comprehensively considered.A solution methodology based on the AHP and QPSO algorithms is then developed.First,the weight coefficients of each objective are determined by the AHP,and the optimal dispatch strategy among these is derived using the QPSO algorithm.The optimized results of the multiple objectives with different weight coefficients are determined,and the output power values of the PVs,WTs,BESS,and DE are obtained.Thus,it can be concluded from these case studies that the BESS and DE prompt consistency in the power supply and accommodation of renewable energy in the dispatch of the MGs.The MG grid structure was not considering in this study.And there were some limitations in reliability study.In the future,we will continue to study the multiobjective optimal dispatch model and solution methodology by evaluating cases for systems that are closer to engineering reality.

Acknowledgments

This work was supported by State Grid Corporation Science and Technology Project (520605190010).

Declaration of Competing Interest

We declare that we have no conflict of interest.