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A Renewable Energy Integration Application in aMicroGrid Based on Model Predictive Control

Jingran Ma, Student Member, IEEE, Fang Yang, Member, IEEE, Zhao Li, Member, IEEE,and S. Joe Qin, Fellow, IEEE

Abstract—This paper investigates the application of modelpredictive control (MPC) method in a MicroGrid with distributedenergy resources (DERs), including distributed generators, ener-gy storage and demand response to achieve higher penetrationof renewable energy. A MicroGrid is an aggregation of networkthat is connected to a centralized grid and can be operatedautogenously. MPC utilizes a simulation model to make decisionson the amount of power that the MicroGrid should draw fromthe connected main grid and each DER respectively, in a way thatthe economical cost is minimized and all operational constraintsare satisfied. The potential of MPC is shown by simulations onan IEEE test feeder modeled on the OpenDSS simulator.

Index Terms—MicroGrid, renewable energy, model predictivecontrol, simulation, OpenDSS

I. INTRODUCTION

MOST of the world’s electricity system was built overthe last 40 to 60 years, so the aging electricity in-

frastructure is inefficient and increasingly unreliable. Theelectric system continues to be operated in the same way fordecades while new technologies have significantly changed theother industrial sectors. During high-demand period, utilitiescompanies typically rely on fast and flexible coal and gas-fired power stations, which are expensive and polluting. Thepenetration of renewable energy is still limited and the electricsystem still relies heavily on the fossil energy sources. Inorder to reach a low carbon economy and deal with aginginfrastructure and climate change, a strategic transformationof the electricity system is urgently required.

Thanks to the deregulation processes and implementation ofincentives in the energy sector, the usage of small distributedenergy resources (DERs) has recently received considerableattention. There are two types of DER in general: conventionaldispatchable distributed generation (DG) and non-dispatchableDG based on renewable energy sources, such as wind, solarand geothermal power. The economical and environmentalbenefits of integrating renewable energy into power systemshave been clearly demonstrated [1]. On the other hand, toincrease the penetration of intermittent energy resources whichfeature unpredictable behavior has become one of the biggestchallenges in smart grid.

J. Ma is with the Department of Chemical Engineering and MaterialsScience, University of Southern California, Los Angeles, CA, 90089 USA,During this work, he was a research intern with ABB US Corporate ResearchCenter, Raleigh, NC. e-mail: jingranm@usc.edu.

F. Yang and Z. Li are with ABB US Corporate Research Center, Raleigh,NC, 27606 USA e-mail: {fang.yang},{zhao.li}@us.abb.com.

S. J. Qin is with the Department of Chemical Engineering and MaterialsScience and Department of Electrical Engineering, University of SouthernCalifornia, Los Angeles, CA, 90089 USA e-mail: sqin@usc.edu.

Utility Grid

MicroGrid CentralMicroGrid CentralController (MGCC)MicroGrid

MC MC LC LC

DG / Microsources Controllable Loads

Fig. 1. Schematic diagram of a typical MicroGrid

Microgrids are increasingly being viewed as a meansto promote the deployment of DER, meanwhile improvingsystem reliability at the distribution level [2], [3]. Formedby a cluster of loads, small scaled generation units and/ordistributed energy storages, MicroGrids can be operated ingrid-connected or isolated-island mode, with the expectationto provide uninterrupted power supply to the loads. DERslocated near local loads can offer improved reliability andhigher energy quality, if they are properly operated [4], [5]. Atypical MicroGrid structure is illustrated in Fig. 1.

The MicroGrid Central Controller (MGCC) is one of themost critical components in a MicroGrid architecture [6]. Itcontrols the connection to the main grid, manages controllableloads and optimizes system operation based on information ofpower quality requirement, energy cost, demand-side requestsand special grid needs etc. It determines the amount of powerthat the MicroGrid should draw from the main grid andfrom each local DER respectively. The optimal (or near-optimal) decisions of power dispatch are made in a way thatcertain objectives are achieved, while a number of operationalconstraints need to be satisfied [7], [8]. In particular, theproblem becomes more complicated if the generation capacityof renewable energy sources is significant, which asks foradvanced modeling, optimization and control techniques [9].

In this work, applying model predictive control (MPC)methodology to the renewable energy integration problem in

978-1-4673-2729-9/12/$31.00 ©2012 IEEE

2

Past Futureymax

y

Prediction horizon

ymin

umax

Measured

Predicted

Control horizon

maxCurrent move

Control horizon

k k+1 k+2 … … k+Npk+Nc

umin

Fig. 2. Basic MPC scheme

MicroGrids is explored. MPC has been shown as a successfulapproach by numerous industrial applications [10]. It is es-sentially an optimization based strategy in which a predictionmodel is employed to predict the behavior of the controlledplants over a finite receding horizon over future [11]. Asshown in Fig. 2 [12], in each discrete time step an open-loop optimal control problem is formulated by measured andpredicted inputs/outputs under certain objective function. Inthe optimal solution, only the control action for current timestep will be implemented on the plant. This routine is repeatedin subsequent intervals with new measurements and updatedplant information.

Modeling and optimization are two crucial componentsof MPC implementations. Given that short-term forecastingmethods for renewable energy resource output have beenextensively studied [13], [14], the scope of this paper isto demonstrate the effectiveness of MPC with a simulation-based model in solving the economic dispatch problems forMicroGrids with intermittent DGs. MPC is technically favor-able because it naturally incorporates prediction models andconstraints that can ensure the MicroGrid running along thedesired path.

The reminder of this paper is organized as follows. SectionII introduces the project structure. MPC problem formulationis described in section III. Section 4 introduces the OpenDSSsimulator and shows the simulation results conducted on it.The final section concludes the paper.

II. SYSTEM STRUCTURE

In this work, a simplified MicroGrid model with conven-tional dispatchable DGs, wind and solar generators, energystorages and a single bus connected to the distribution substa-tion is studied. The project system structure is illustrated inFig. 3.

Load Shape Predictions

GenerationForecasts

(Wind, Solar)

MicroGrid(OpenDSS)

PredictionNoise

MPC(Matlab)

Electricity cost Power loss (Objectives)

Power flow (Constraints)

Fig. 3. Project block diagram

Although not in the scope of this study, modeling theintermittent behaviors of DERs and load forecasting play im-portant roles in the success of MPC implementation. Utilizinghistorical data files of wind and solar outputs, we supposethe difference between the predicted and actual DER outputsis a white noise sequence. The load profiles are assumedto be following certain pattern. An optimization problem isformulated over the moving horizon for minimizing the totalelectricity generation cost. The optimal control actions areobtained by MPC controller out of this optimization withseveral constraints, and sent to the MicroGrid model beforeproceeding to the next time step.

The Microgrid is modeled in the OpenDSS simulationplatform and its specific configuration is described in thesection IV-A.

III. MPC PROBLEM FORMULATION

Based on the general MPC approach, the problem formaximizing the penetration of renewable energy resources,in other words, optimizing the generation cost (because thepower generated by local renewable DGs is much cheaper thandemanding from the main grid), is formulated in this section.

A. Objective Function

The length of prediction horizon Np and control horizonNc are set to be identical, i.e. Np = Nc = N . The time stepfor each interval is denoted as Δt. At the current time step k,the objective function to be optimized accounts for the totalgeneration cost in the prediction horizon, as Eq.(1).

minU

F (U, k) =

k+N−1∑t=k

(Cg(t) +∑m

Ccg,m(t)) (1)

where Cg(t) is the generation cost from the main grid, andis proportional to the power demand Pg(t). Ccg,m(t) is thecost of the mth conventional distributed generator in the Mi-croGrid, which is usually expressed as a quadratic polynomialwith respect to its power outputs Pcg,m(t).

Cg(t) = bg(t)Pg(t)Δt (2)

Ccg,m(t) = am + bmPcg,m(t)Δt+ cm(Pcg,m(t)Δt)2 (3)

Note that in Eq.(2), bg(t) is a time varying cost coefficient,indicating the rate depends on time-of-use.

3

The decision variable in Eq. (1) U is a vector containingcontrol actions in the entire control horizon,

U(t) =[u(k)T u(k + 1)T · · · u(k +N − 1)T

]T(4)

For any single time step, the control signal u(t) includespower outputs of all controllable generators as well as energystorages. For simplicity, it is assumed only one conventionalgenerator and one energy storage in the MicroGrid.

u(t) = [Pg(t) Pcg(t) Pes(t)]T (5)

where Pg(t), Pcg(t) and Pes(t) denote the power from maingrid, conventional DG and energy storage, respectively.

B. Constraints

The optimization problem subjects to the following con-straints for t ∈ [k, k +N − 1].

1) Real power balance:

Pg(t) + Pcg(t) + Pes(t) = P̂l(t)−∑

P̂r(t)− P̂loss(t) (6)

where P̂l(t) and P̂loss(t) are the forecasts of total loads andreal power losses respectively. P̂r(t) is the predicted outputfrom renewable energy resources, such as wind and solargenerators.

2) Physical capacity: The power generated by each con-trollable generator should be within its maximum capacity.

Pcg(t) ≤ Pcg,max (7)

Since all loads must be energized, there is no constraintimposed on Pg . As an isolated MicroGrid is studied, the supplycapacity of the main electricity grid can be treated as infinitelarge.

The energy storage has its maximum rates in both chargingand discharging modes. The stored energy in energy storageWes(t) should be below its rated kWh value. Only steady-statebehavior of energy storages is considered here.

Pes char,max ≤ Pes(t) ≤ Pes disc,max (8)

0 ≤ Wes(t) ≤ Wes,max, t = k + 1, k + 2, · · · , k +N (9)

Wes(t+ 1) = Wes(t)− Pes(t) ·Δt, (10)

3) Power flow equations: A feasible control action shouldsatisfy the power flow equations. The voltage magnitude andangle at each bus can be determined by he well-knownNewton-Raphson method. From the complex power balanceequation at bus i (non-slack bus),

Si = Pi + jQi = Vi

∑k

Y ∗ikV

∗k (11)

Resolving into the real and imaginary parts, the mismatchequations are

ΔPi = −Pi+∑k

|Vi||Vk|(Gik cos(θik) +Bik sin(θik)) (12)

ΔQi = −Qi +∑k

|Vi||Vk|(Gik sin(θik)−Bik cos(θik))

(13)

where Gik and Bik are the corresponding elements of thesystem nodal admittance matrix Y ∗. The system Jacobianmatrix is factorized as

J =

⎡⎢⎣∂ΔP

∂|V |∂ΔP

∂θ∂ΔQ

∂|V |∂ΔQ

∂θ

⎤⎥⎦ (14)

The initial guess of unknown |Vi0| and θi0 is usually madeas a ”flat start” in which all voltage magnitudes are set to 1.0p.u. and all voltage angles are set to zero. The power flowsolution can be obtained by the following iterations,

|V |m+1 = |V |m +Δ|V |θm+1 = θm +Δθ

(15)

where the incremental guess is given by[Δ|V |Δθ

]= −J−1

[ΔPΔQ

](16)

The iteration continues until a termination criterion isreached, e.g. the norm of ΔP and ΔQ are below specifiedthresholds.

It should be noted that in this work, the realization of thepower flow equations is through the use of the OpenDSS simu-lator, instead of being explicitly formulated in the optimizationscheme. Doing this in practice may bring problem becausein iterations it requires considerable time and computationalcost to run the simulator many times. Therefore, systemidentification technique is usually employed to obtain input-output models out of experimental data, i.e. the work in [15].

4) Voltage limit: In the converged power flow solutions,all bus voltages need to be maintained within permitted range.Typically, the range of [Vmin, Vmax] = [0.95, 1.05] in p.u. valuecan ensure normal system operations.

Vmin ≤ Vi(t) ≤ Vmax (17)

Note that in a practical application there should also beconstraints on current, i.e., Ii(t) ≤ Irated,i(t). For simplicityand the lack of rated current parameters, the current constraintsare not included in the optimization.

IV. SIMULATION STUDIES

The Matlab optimization toolbox is used to solve thisnonlinear constrained optimization problem in the above sec-tion using interior point algorithm. Matlab and OpenDSS areintegrated to a co-simulation scheme, where Matlab takescharge optimization and control, and OpenDSS simulates thedistribution network.

A. OpenDSS Simulator

The OpenDSS (Open Distribution System Simulator, usedversion 7.4) is developed by Electric Power Research Institute(EPRI) as a comprehensive open-source simulation tool forelectric utility distribution systems [16]. It aims at providinga flexible research platform and a foundation for specialdistribution applications such as DG analysis. It can be usedas either a stand-alone executable program or an in-processCOM server to be driven from external software programs.

4

Wind farmsEnergy storage

Distributed generator

Solar photovoltaics

Distributed generator

Fig. 4. Modified IEEE 13 node test feeder

1) IEEE 13 node system: The IEEE 13 node radial testfeeder system which is one of the benchmark systems in theOpenDSS software package, is selected as the testing systemfor this work. It is a three-phase unbalanced system, whoseparameter specification and power flow for the base case canbe retrieved from [17]. Originally there is no DG installed inthe network. Additional DSS scripts as described in AppendixA are added to the feeder model for modification as shown inFig. 4. There are two capacitors installed at bus 675 (3 phases)and 611.C and a load locates at the bus 670 invisible in Fig.4, which is connected between bus 632 and 671.

2) Distributed generators: As shown in Fig. 4, one conven-tional dispatchable distributed generator, one wind generatorand one solar generator are added to the system, specifyingtheir rated capacities and the buses to which they are connect-ed. The conventional DG output in kW Pcg is to be passed bythe controller in Matlab in each time step. The wind and solargenerator daily outputs would follow the multiplication ofrated kW values and duty schedules generated from historicaldata files. Wind output is essentially a stochastic disturbanceand solar power contributes only during day time.

3) Energy storage: In OpenDSS, the energy storage ele-ment is essentially treated as a special class of generator thatcan be designated to either produce power (in dischargingmode) or consume power (in charging mode) with its powerrating and stored energy capacity.

The working mode of energy storage is set as discharg-ing/charging depending on the positive/negative sign of thedemanded power Pes(t), and the discharging/charging rate inkW (|Pes(t)|) is passed from Matlab to the OpenDSS modelin each time step.

The energy storage module is used in a snapshot mode tocompute the power flow for a deterministic state. This meansthat its dynamic transient behavior is not considered at present.The default value of 90% for both charging and dischargingefficiency is applied, making a nominal round trip efficiency of81%. The energy storage is placed at the center of MicroGrid,with the hope to conveniently compensate for short term power

0 3 6 9 12 15 18 21 240

0.2

0.4

0.6

0.8

1

1.2

Time (hr)

Load

Lev

el

Fig. 5. Load level daily schedule

variations caused by intermittent generations.4) Load schedule: A loadshape object is defined for varying

loads in OpenDSS to carry out real-time simulations. The loadschedule is stored in a data set, as shown in Fig. 5. The levelindicates the ratio of current and maximum load. White noisewith standard deviation of 0.025 is added to the load level toaccount for the load estimation error.

B. Simulation Results

A 24 hour simulation is conducted on the MicroGrid modeldescribed above. The length of prediction horizon is set as4, meaning an one-hour ahead prediction is applied. Thecontribution to loads from each energy source is shown inthe stacked graph as Fig. 6. Power from main grid followsthe load variation because the main grid is treated as a swingsource. Conventional distributed generator and energy storageare used as auxiliary resources to maintain the power balanceand as assets to optimize the total generation costs. It can beseen that the conventional DG is mainly utilized during thepeak hours (8 : 00 − 18 : 00) when higher price is appliedto the grid power. The behavior of energy storage is subjectto a slow-charging fast-discharging pattern, which allows it tocompensate to unpredictable change of renewable outputs andavoid sacrificing the power stability.

An ordinary control strategy is implemented to comparewith MPC, in which no prediction effect is incorporated. Thecontroller makes decision to achieve minimum cost only basedon the current measurements. The total electricity generationcost is shown in Fig. 7. The advantage of MPC appearsfrom 8 a.m. the generation cost begins to increase, showingthe capability of MPC to foresee the price change and takeappropriate actions in advance.

Fig. 8 shows the bus voltages in the MPC test. The voltagesare repeatedly measured after the convergence of power flowin each time step with under the control inputs given by MPC.All bus voltages are within the feasible region showing thatthe voltage constraints are always satisfied.

5

Time (hr)

Pow

er o

utpu

t (kW

)

3 6 9 12 15 18 21 24−0.5

0

0.5

1

1.5

2

2.5

3

3.5

4Energy StorageSolar PowerWind PowerConventional DGMain Grid

Fig. 6. Generation output profiles under MPC

0 3 6 9 12 15 18 21 241

2

3

4

5

6

7

Time (hr)

Cos

t (10

3 $)

OrdinaryMPC

Fig. 7. Generation cost comparison between ordinary control strategy andMPC

V. CONCLUSIONS AND FUTURE WORK

In this paper, we studied the renewable energy integrationproblem in a MicroGrid taking advantage of MPC method.With a prediction model embedded, MPC is capable of re-ducing the generation cost over a future horizon. A numberof constraints can be naturally satisfied to ensure the powerquality and network stability.

In a co-simulation framework, Matlab optimization tool-box is used to solve the nonlinear optimization problemand OpenDSS is the platform to simulate virtual distributionsystem model with renewable energy resources and energystorage installed.

The demonstrating work can be continued and extended inthe following directions:

1) Although modeling for the wind and solar generators isnot the focus of this work and we assume accurate modelsare available by certain techniques, incorporating the forecastmodels that are not built from historical data to optimizationin MPC is still challenging.

2) In addition to steady-state, taking in to account dynamicbehavior of devices such as energy storages is of significance.

650 633 634 671 645 692 675 611 652 670 632 680 6460.9

1

1.1Phase A

Vol

ts (

pu)

650 633 634 671 645 692 675 611 652 670 632 680 6460.9

1

1.1Phase B

Vol

ts (

pu)

650 633 634 671 645 692 675 611 652 670 632 680 6460.9

1

1.1Phase C

Vol

ts (

pu)

Node number

Fig. 8. Bus voltage distribution measured after convergence of each powerflow calculation

3) Due to the complexity of power flow equations, theoptimization cannot be readily formulated as a programmingproblem that can be analytically solved. Therefore, the non-linear optimization executed by the Matlab built-in functionsusually gives local optima and it requires a deep look into theiterations to track the searching trajectory of optimal solutions.

APPENDIX AOPENDSS SCRIPTS TO MODIFY IEEE TEST FEEDER

A. Distributed Generators! 24HOURS SOLAR RAMP SCREENNew Loadshape.SolarRamp npts=96 Interval=(1 4 /)mult= (file= SolarRamp.csv)

! 24HOURS WIND OUTPUT SCREENNew Loadshape.WindRamp npts=96 Interval=(1 4 /)mult= (file= WindRamp.csv)

! GENERATOR DEFINITIONSNew Generator.ConGen Bus1=680.1.2.3 Phases=3 kV=4.16 pf=1 Model=1New Generator.SolarGen Phases=2 Bus1=684.1.3 kV=4.16 kW=300 PF=1Duty=SolarRampNew Generator.WindGen Phases=2 Bus1=646.2.3 kV=4.16 kW=300 PF=1Duty=WindRamp

B. Energy Storage! ENERGY STORAGE DEFINITIONNew Storage.ES1 Phases=3 Bus1=632 kV=4.16 kWRated=100kWhRated=200 stored=50

C. Load Schedule! LOADSHAPE DEFINITIONNew Loadshape.LoadSchedule npts=96 Interval=(1 4 /)mult= (file= LoadSchedule.csv)! LOAD DEFINITIONNew Load.675a Bus1=675.1 Phases=1 Conn=Wye Model=1 kV=2.4kW=485 kvar=190 Duty=LoadSchedule

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ACKNOWLEDGMENTS

The authors would like to thank Dr. Xiaoming Feng, Dr. Vaibhav Donde,James Stoupis and Xianda Deng for their valuable help and comments.

REFERENCES

[1] X. Liu and B. Su, “Microgrids: an integration of renewable energy tech-nologies,” in China International Conference on Electricity Distribution,(CICED), 2008.

[2] B. Lasseter, “Microgrids [distributed power generation],” in IEEE PowerEngineering Society Winter Meeting, 2001, pp. 146–149.

[3] R. Lasseter, A. Abbas, C. Marnay, J. Stevens, J. Dagle, R. Guttromson,A. S. Meliopoulos, R. Yinger, and J. Eto, “Integration of distributedenergy resources: The certs microgrid concept,” California EnergyCommission, P500-03-089F, oct. 2003.

[4] R. Yokoyama, T. Niimura, and N. Saito, “Modeling and evaluation ofsupply reliability of microgrids including pv and wind power,” in IEEEPower and Energy Society General Meeting, july 2008.

[5] A. Tsikalakis and N. Hatziargyriou, “Centralized control for optimizingmicrogrids operation,” in IEEE Power and Energy Society GeneralMeeting, july 2011.

[6] S. Mohagheghi and F. Yang, “Applications of microgrids in distribu-tion system service restoration,” in IEEE PES Innovative Smart GridTechnologies (ISGT), jan. 2011.

[7] A. Hawkes, “Optimal selection of generators for a microgrid underuncertainty,” in IEEE Power and Energy Society General Meeting, july2010.

[8] D. Olivares, C. Canizares, and M. Kazerani, “A centralized optimalenergy management system for microgrids,” in IEEE Power and EnergySociety General Meeting, july 2011.

[9] S. Lu, M. Elizondo, N. Samaan, K. Kalsi, E. Mayhorn, R. Diao, C. Jin,and Y. Zhang, “Control strategies for distributed energy resources tomaximize the use of wind power in rural microgrids,” in IEEE Powerand Energy Society General Meeting, july 2011.

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[17] D. T. F. W. Group, IEEE 13 Node Test Feeder, IEEE PES DistributionSystem Analysis Subcommittee, 2001.

Jingran Ma received his B.S. and M.S. degree in Automatic Control fromTsinghua University in Beijing, China, in 2006 and 2008, respectively. Heis currently a Ph.D. candidate in Chemical Engineering at the University ofSouthern California, Los Angeles, CA. His research interests include buildingenergy efficiency, power system modeling and control, model predictivecontrol and system identification.

Fang Yang is a Sr. R&D engineer with ABB US Corporate ResearchCenter in Raleigh, North Carolina. Her research interests include distributionautomation, power system reliability analysis, and application of artificialintelligence techniques in power system control.

Zhao Li joined ABB Corporate Research in Raleigh, North Carolina in 2007,where he is currently a Software Architect. His research interests include theapplication of software technologies in process automation and power systems,performance analysis, and information system design and tuning.

S. Joe Qin is the Fluor Professor at the Viterbi School of Engineering atUniversity of Southern California and Chang Jiang Professor affiliated withTsinghua University by the Ministry of Education of China. Prior to joiningUSC he held the Paul D. and Betty Robertson Meek and American PetrofinaFoundation Centennial Professorship in Chemical Engineering at University ofTexas at Austin. He obtained his B.S. and M.S. degrees in Automatic Controlfrom Tsinghua University in Beijing, China, in 1984 and 1987, respectively,and his Ph.D. degree in Chemical Engineering from University of Marylandat College Park in 1992. Dr. Qin’s research interests include process control,model predictive control, process monitoring, fault detection and diagnosis,control performance monitoring, process optimization, semiconductor processoptimization, system identification and building energy efficiency.