Optimal Energy Management for Cooperative Microgrids With Renewable Energy Resources

Transcription

1 Optimal Energy Management for Cooperative Microgrids With Renewable Energy Resources Duong Tung Nguyen and Long Bao Le Abstract In this paper, we present an optimal energy management framework for a cooperative network of heterogeneous microgrids (MGs) where energy exchange among connected MGs is allowed to exploit the fluctuations of stochastic sources and demands. A multi-objective function is introduced to achieve an efficient tradeoff between low operation cost and good energy service for customers. The objective function captures the total cost of purchasing/selling power from/to the main grid, the start-up and shutdown costs, the operating cost of conventional generation unit, the payment for demand response load, the penalty cost for involuntary load curtailment, and renewable energy spillage. We propose to employ the scenario-based two-state stochastic optimization approach to deal with the uncertainties of renewable energy resources, load demand in the energy scheduling problem. The efficacy of the proposed energy management solution is demonstrated via numerical results. Index Terms Energy management system, cooperative network of microgrids, renewable energy, stochastic optimization. NOMENCLATURE ηi c, ηd i Charging/discharging efficiency coefficients of battery storage in MG i ρ s Probability of scenario s, s =, 2,..., NS b s,c, bs,d Binary variable capturing charging/discharging state, if charging/discharging C k (.) Production cost of unit k ($) CD k,t, CU k,t Shutdown/startup offer cost of unit k ($) d t Duration of time slot (hr) D s Load of MG i (kw ) DR k, UR k Ramp-down/ramp-up rate limit of unit k (kw ) DT k, UT k Minimum down/up time of unit k (hr) E cap i Capacity of battery storage in MG i (kw h) Ei max, Ei min Maximum/minimum energy stored in battery in MG i (kw h) e t Electricity price in time slot t ($/kw h) E s Energy stored in battery in MG i (kw h) e r Price of demand response load in MG i ($/kw h) i, j Microgrid index, i, j =, 2,..., NM I k,t Commitment state of unit k {, } k Conventional unit index, k =, 2,..., NG i NG i Number of conventional units in MG i NH Number of time slots N M Number of microgrids N S Number of scenarios Pk min, Pk max Minimum/maximum power generation of unit k (kw ) Pi,j,t s Power flow from MG i to MG j (kw ) The authors are with INRS-EMT, University of Quebec, Montréal, Québec, Canada. s: {duong.nguyen,long.le}@emt.inrs.ca. L. B. Le is the corresponding author. Maximum power exchange between MG i and main grid (kw ) P grid Scheduled power exchange between MG i and main grid (kw ) P shed,max Maximum load shedding in MG i (kw ) P s,pvs Solar power spillage in MG i (kw ) P s,pv Solar output power in MG i (kw ) P s,shed Load shedding in MG i (kw ) P s,ws Wind power spillage (kw ) P s,w Wind output power in MG i (kw ) P s,c, P s,d Charging/discharging power of battery in MG i (kw ) P c,max i, P d,max i P grid,max Maximum charging/discharging power of battery in MG i (kw ) Pk,t s Power generation of unit k (kw ) Pk,t s (m) Power generation of unit k from the m-th block of energy (kw ) upper bounded by Pk,t max(m) pv i Binary variable, if there is a solar source r, r s Offer and actual curtailment of demand response power in MG i (kw ) s Scenario index SD k,t, SU k,t Shutdown/startup cost of unit k ($) t Time slot index, t =, 2,..., NH Vt PV Cost of solar energy spillage ($/kw h) Vt W Cost of wind energy spillage ($/kw h) V ll Value of lost load for MG i ($/kw h) w i Binary variable, if there is a wind source y k,t, z k,t Start-up/shutdown indicator of unit k {, } I. INTRODUCTION There has been growing interest in integrating more distributed renewable energy resources into the future smart grid with advanced communications and control technologies. Deployment of microgrids (MGs) plays a key role in meeting this integration objective. In addition, MGs can enable more flexible energy management solution and enhanced reliability where an MG can be operated in either grid-connected mode or islanded mode. A typical MG would have the following basic components: renewable energy resources such as wind or solar generators, conventional generating units such as diesel generators, fuel cells, and energy storage facility. An efficient MG would be able to exploit local available renewable energy to supply its local power demand, to efficiently charge/discharge its storage facility, and to sell back surplus energy to the main grid during high-priced electricity period. There are some existing works on energy management and design mostly for a single MG system. In particular, Guan et al. proposed an optimal control scheme for a building MG []. In [2], the authors considered the energy storage

2 2 sizing problem for a MG. An economic dispatch problem considering power reserve to ensure the stable operation of an MG was introduced in [3]. There are some recent works that consider the operation of multiple MGs. In [4], the authors proposed an agent-based intelligent energy management system to coordinate the operation of multiple MGs. However, to best of our knowledge, none of previous works have presented a concrete mathematical optimization model which consider energy exchange activities among connected MGs and investigate its impact on the optimal solution. The stochastic and intermittent nature of renewable energy resources can potentially result in costly operation of the MG if they are not managed efficiently. For example, if the local renewable energy is not sufficient to serve MG load in some particular high-price hours while the storage facility was not sufficiently charged during previous low-price hours then the MG needs to purchase expensive energy from the main grid or run local expensive power generators. In general, MG storage facilities can have limited capacity which may not be sufficient to absorb the fluctuation of local renewable energy sources. Due to the diversity in load patterns and renewable generation profiles of heterogeneous MGs, allowing energy exchange among MGs can potentially reduce the battery capacity requirement for the stable operation of MGs. Therefore, there can be significant benefits in cooperatively optimizing the energy management of multiple inter-connected MGs. This is exactly the design goal that we attempt to achieve in this work. The main contributions of this technical can be summarized as follows. We propose a comprehensive model for an optimal energy management of a cooperative network of heterogeneous MGs. The formulation aims to minimize a multi-objective cost function which accounts for the operating cost of conventional units, the cost for importing/exporting power from/to the main grid, the payment for demand response load, penalty costs of involuntary load shedding and wind/solar energy spillage. We employ the scenario-based two-stage stochastic programming approach to deal with the uncertainties of renewable energy resources and power demand in each MG. Then, we present numerical results to study the impacts of different design and system parameters on the optimal cost and to illustrate the advantages of applying the proposed control model for the cooperative network of heterogeneous MGs. The remaining of this technical report is organized as follows. The system model and solution approach are presented in Section II. Detailed problem formulation is described in Section III. Numerical results are provided in Section IV followed by conclusion in Section V. II. SYSTEM MODEL We consider a cooperative network of heterogeneous MGs which can be connected to the main grid and inter-connected with each other. If there exists a connection between a pair of MGs or between a MG and the main grid then the energy exchanges can occur via the connection lines. We assume that each MG contains the following basic elements: conventional generation units, renewable energy sources, and energy storage facility. The local power demand of each MG can be served Fig.. System model Power line Centralized Controller Control line by its local power sources, or by using power from the main grid or other MGs. The centralized controller is responsible for the energy scheduling within all MGs and for coordinating the energy exchange among MGs and the main grid. The generation cost for renewable energy sources is assumed to be zero. The energy management optimization is performed for one day, which is divided into 24 time slots each of which is one hour. The considered system model is illustrated in Fig.. A. Scenario-based Stochastic Optimization Approach In order to cope with the stochastic property of various parameters in the energy management problem, we employ the Monte Carlo simulation technique to generate scenarios that represent various uncertain factors including day-ahead forecast error of wind speed, solar irradiance, and the power demand [], [5] [9]. The number of generated scenarios is chosen sufficiently large to achieve an efficient energy scheduling solution. In general, the number of generated scenarios directly impacts the computation complexity of the underlying scenario-based stochastic optimization problem. For a largescale problem, a scenario reduction technique can be used to reduce number of scenarios, which consequently reduces the computational burden [9], []. The basic idea of scenario reduction is to eliminate scenarios with very low probability and to aggregate scenarios of close distances based on certain probability metric [], []. By using these scenario reduction techniques, one can obtain a smaller set of scenarios with corresponding probabilities [9], []. In this research work, we used GAMS/SCENRED [7] software to generate/reduce the set of scenarios and solve the underlying optimization problem. B. Modeling Microgrid Elements We describe the models for wind, solar power generation, and power demand in the following. ) Wind Power: We employ the following relationship between wind power and wind speed [2]

3 3 P W =, if v v in or v v out, P r v vin v r v in, if v in v v r, P r, otherwise. where P W is the wind output power, P r is the rated power of the wind generator; v r, v in, v out are the rated, cut-in, and cut-out wind speeds, respectively. Using this formula, we can calculate the output power of a wind generator based on wind speed data. We assume that the average wind speed in each time slot (ˆv t ) can be estimated with a high accuracy. Then, the actual wind speed can be expressed as v t = ˆv t + δ v t () where δ v t represents the wind speed estimation error. An autoregressive moving average model ARMA(,) is used to model wind speed forecast error [5]. The formula for the ARMA(,) model can be written as X(t) = αx(t ) + Z(t) + βz(t ). () Parameters for this ARMA model are taken from [5] where α =.98, β =.7 and Z(t) follows a Gaussian distribution with zero mean and standard deviation equal % of the wind speed forecast value. We assume that MGs are geographically close to each other; therefore, we can use the same wind speed estimation to calculate the wind power in each MG. 2) Solar Photovoltaic Power: Similar to wind power generation, we calculate the solar power as follows [4]: P s = η s SI (2) where η s denotes the conversion efficiency of the solar cell array (%), S is the array area (m 2 ), and I is the solar radiation (kw/m 2 ). In addition, we model the actual solar radiation I t in time slot t as I t = Ît + δ I t (3) where Ît is the forecast value and δ I t represents the forecast error. The solar irradiance forecast error is again assumed to follow a zero-mean normal distribution with the standard deviation of % of the predicted value. Similar to wind power case, we assume that we can use the same solar irradiance model to calculate the solar power in any MG. 3) Power Demand: We assume that the actual power demand D t can be modeled as D t = ˆD t + δ D t (4) where ˆD t is the forecast value and δt D is the forecast error. The load forecast error is assumed to follow a truncated normal distribution with zero mean and the standard deviation of 5% of the predicted value of power demand [], [5]. We will model the aggregated power demand for the whole system with a certain ratio for loads in MGs. C. Energy Management for Cooperative Microgrids We are interested in developing an efficient energy management for a cooperative network of interconnected MGs, which are supplied by different sources of energy including renewable energy, traditional power generators, and energy from the main grid. One of the key challenges of such energy management task is to deal with the intermittent nature of the renewable energy resources in a cost-efficient manner. In fact, if proper cooperation among the inter-connected MGs is performed then one can potentially exploit the energy exchange process among the MGs to minimize the amount of purchased energy from the main grid and/or to avoid producing energy by using expensive power generators. In other word, cooperation among MGs can enable us to mitigate the intermittent nature of renewable energy, which can translate into significant cost saving compared to the case where operation of MGs is optimized separately. This is especially important for the heterogeneous network of MGs where the available amount of energy from wind and solar power sources can be quite different over a 24-hour period (i.e., there is no solar power during night time while there is usually more wind power over night). III. PROBLEM FORMULATION We present how to employ the scenario-based two-stage stochastic programming to determine the optimal schedule for all elements in the network of MGs. The first-stage decision variables are the day-ahead schedule of energy exchange with the main grid for each MG (if there is a connection between them), and the day-ahead commitment statues for all conventional units. These decisions must be made before any uncertainties are unveiled, and they remain unchanged in the operating day. In the second stage, various decision variables are calculated when all the uncertainties are unveiled, and these second-stage decisions depend on the first-stage decisions. We denote all the second-stage variables with a superscript s. The objective function and all constraints of the underlying optimization problem are described in the following. A. Objective Function We are interested in minimizing the following objective function: ( ) NH NM NG min d t a i,m P grid e i t + (SU k,t + SD k,t ) t= i= + k= ( NS NH NM NGi ρ s s= +d t V ll P s,shed t= i= k= + w i d t Vt W P s,ws C(P s k,t) + d t e r r s + pv i d t V PV t ) P s,pvs. (5) This objective function comprises the total cost of purchasing/selling electricity from/to the main grid, the start-up and shut down costs, and the operating cost of generation units, payment for demand response customers, the penalty cost of curtailing involuntary load, and the penalty cost of spillage of wind and solar power. The operating cost of a conventional unit is represented by a piecewise linear function to approximate the its actual operating cost as follows [3]: N O,k C(Pk,t) s = d t m= λ k,t (m)p s k,t(m), k, t (6) Pk,t(m) s Pk,t max (m), k, t (7) P s k,t = N O,k m= P s k,t(m), k, t (8)

4 4 where N O,k is number of blocks of energy for unit k and λ k,t (m) is the marginal cost of the m-th block of energy offered by unit k in time slot t ($/kw h) [3]. Constraints in the optimization problem are described in the following. B. Power Exchange with Main Grid The power exchange (P grid ) between MG i and the main grid in each time slot t is limited by the corresponding capacity of the line connecting them (if any). a i,m P grid,max P grid a i,m P grid,max, i, t. (9) where P grid is positive if MG i imports power from the main grid and P grid is negative if MG i exports its power to the main grid; a i,m is a binary variable which is equal to one if there is a connection between MG i and the main grid. C. Power Trading Limit between 2 Connected MGs The power exchange (Pi,j,t s ) between any two connected MGs i and j in any time slot must be less than the line capacity between them (if any), i.e., a i,j F max i,j Pi,j,t s a i,j Fi,j max, i, j, t () Pi,j,t s = Pj,, s i, j, t () where a i,j is a binary variable which is equal to one if there is a connection between MG i and MG j, and Fi,j max is the power line capacity of the line between MG i and MG j. The power exchange Pi,j,t s is positive if the power flows from MG i to MG j, and otherwise it is negative if the power is transferred from MG j to MG i. D. Constraints for Conventional Generation Units We impose the following constraints for conventional generation units [6], [2], [3]: t+ut k h=t Pk min I k,t Pk,t s Pk max I k,t (2) Pk,t s Pk,t s UR k ( y k,t ) + Pk min y k,t (3) Pk,t s Pk,t s DR k ( z k,t ) + Pk min z k,t (4) I k,t UT k y k,t ; t+dt k h=t I k,t DT k y k,t (5) y k,t z k,t = I k,t I k,t ; y k,t + z k,t (6) where I k,t represents the commitment state of unit k in time slot t, which is equal to one if unit k is committed to operate in time slot t, otherwise it is equal to zero. The power generation limit for each unit k is described in (2). Constraints (3)-(4) present the ramping up and down limits of unit k. Constraints (5) capture the minimum up and down time of unit k. A unit has to remain in ON/OFF status for at least UT k /DT k time slots after it is turned ON/OFF. The constraints (6) represent the relationship between the start-up indicator (y k,t ) and shutdown indicator (z k,t ) where y k,t = if the unit k is started up at time slot t and z k,t = if the unit k is shut down at time slot t [6]. Also, any unit cannot be started up and shut down simultaneously. Additional start-up cost and shut down cost constraints must be imposed as follows [6], [2], [3]: SU k,t CU k,t (I k,t I k,t ); SU k,t (7) SD k,t CD k,t (I k,t I k,t ); SD k,t. (8) E. Battery Constraints The charging/discharging power limits of battery in MG i are captured in (9). The limits and the dynamics of energy stored in a battery are described in (2)-(2) while constraints (22) capture the fact that a battery cannot be charged and discharged simultaneously in any time slot. P s,c bs,c P c,max i ; P s,d b s,d P d,max i (9) E+ s = E s + (ηi c Pd c t P d d t ηi d ), (2) E min i E s E max i (2) b s,c + bs,d = ; bs,c, bs,d {, }. (22) F. Involuntary Load Curtailment It is required that the total involuntary load curtailment (shedding) is less than the maximum allowed power shedding and the power demand in MG i in each time slot t as follows: P s,shed P shed,max, i, t, s. (23) P s,shed D, s i, t, s. (24) G. Demand Response Constraint Each MG can offer a certain amount of power r to participate in demand response program by curtailment and will receive corresponding payment for this participation, i.e., r s r, i, t, s. (25) The payment that an MG receives from the central controller for curtailment of the demand response load is much smaller than the penalty for involuntary load shedding which affects users comfort. H. Wind and Solar Power Spillage In each time slot, the wind/solar power spillage must be smaller than the maximum available wind/solar power, i.e., P s,ws P s,pvs P s,wind, i, t, s. (26) P s,solar, i, t, s. (27) I. Energy Balance Constraints for Each MG i For each MG, the total of power generation from local sources and battery charging/discharging power must be kept equal to the total of the local power demand and the power exchange with the main grid and other MGs. Therefore, the energy balance equation for each MG can be written as follows NG i k= P s k,t + (P s,wind +P grid P s,ws ) + (P s,solar P s,pvs ) (P s,c P s,d ) + P s,shed + r s = D s + j i a i,j P s i,j,t, i, j, t, s. (28) The optimization described above is a mixed integer linear program which can be solved efficiently by using commercial solvers such as CPLEX [8].

5 5 IV. NUMERICAL RESULTS We consider a network of three MGs, namely MG, MG2, and MG3. The parameters of wind generator is retrieved from [2] as follows: v r = 2m/s, v in = 3m/s, v out = 3m/s, and P r = kw. We use the historical wind speed data [6] as the forecast values for wind speed. We use the average solar irradiance for August 2 [5] as the forecast values of solar irradiance. The parameter for PV source is taken from [2] where η = 5.7% and S = 7 m 2. We assume that MG has one wind generator and no PV source; MG2 has one PV source, no wind source; and MG3 has both wind generator and PV source. Wind power and solar power are calculated from the wind speed and solar irradiance using (II-B), (II- B2). Load data is taken from [] where we scale the load value so that the average power demand of the system is equal to the average renewable energy generation in the base case. The wind power forecast for one wind generator, solar power forecast for one solar generator, and the forecast of total load in the system is shown in Fig. 2(a). We assume that the load distribution among MGs is.3:.3:.4. Power (kwh) Fig. 2. Price ($) wind solar load (a) Wind power, solar power, and total load prediction (b) Day-ahead electricity price Forecast values of wind/solar power, total load, and electricity price The electricity price is the day-ahead pricing data retrieved from PJM [9] in a typical day of August 2 as shown in Fig.2(b). For simplicity, we assume that the prices for importing and exporting the power from/to the main grid are the same. The cost for demand response load is assumed to be $/MW h, the penalty cost of lost load is $/MW h, the cost for wind power spillage, and solar power curtailment are set equal to $5/MW h. We assume that each MG has one conventional unit where each conventional unit k offers a single block of energy at the cost of λ k,t [3] where the parameters for distributed generators are taken from Table I of [2] for microturbines and fuel cell. Each MG is assumed to have one battery storage of capacity 3 kw h where the charging/discharging power ratings are set to kw. Minimum and maximum energy stored in one battery are 6 kw h and 27 kw h, respectively. The maximum involuntary load curtailment for each MG is set equal to 5 kw, the voluntary load for demand response offered by each MG is % of the load forecast value for the corresponding MG. We assume that three MGs are all inter-connected to each other and they are also connected to the main grid. The maximum power exchange with the main grid is set equal to 2 kw. The lines between any two MGs are assumed to be the same, which is 5 kw in the base case. The Monte Carlo simulation method is used to generate 2 scenarios with equal probability to represent the uncertainties of wind speed, solar irradiance, and the total system load. GAMS/SCENRED [7] is used to reduce number of scenarios and to solve the underlying large-scale MILP optimization problem. We fix the renewable energy production profiles, and change the load factor to see its impact of different renewable energy penetration levels on the total optimal cost. We define load factor as the ratio between the average load forecast over the average of the total renewable energy production during the optimization horizon. Optimal cost ($) Fig UF =.3 UF =.6 UF =. UF =.5 UF = Number of reduced scenarios Optimal gap (%) (a) Absolute cost UF =.3 UF =.6 UF =. UF =.5 UF = Number of reduced scenarios (b) Optimal cost difference (%) Relationship between number of reduced scenarios and optimal cost Figs. 3(a), 3(b) show the impact of number of reduced scenarios on the optimal cost. We can see that as the number of scenarios is 8 or larger, the optimal cost is almost the same. The optimal gap presented in Fig.(3(b)) shows the difference between the optimal cost and the cost achieved with the corresponding number of reduced scenarios. As suggested by these figures, number of reduced scenarios is set equal to 8 to obtain other numerical results, which would achieve reasonably accurate results with manageable computation burden. It can be observed that when the load factor is small, e.g., the load factor =.5 or, no conventional units need to be operated because the high start-up cost and the operating cost of these units make it more preferable to import power from the main grid. Moreover, when the load factor is small, the system load can be served by the renewable energy. When

6 6 the load factor is high, e.g., when load factor is equal to 4, all conventional units needed to be online (committed to ON for the whole operation day). This is because total renewable wind generator, battery energy storage, and imported power from the grid are not sufficient to meet the required high demand. The impact of line capacity and the load factor on the optimal cost is presented in Figs. 4(a), 4(b) where we vary the line capacity in [, 3] kw and the load factor values are equal to.5,,.5, and 2. Relative saving is calculated with respect to the case where the line capacity is zero (i.e., no power exchange among MGs). It can be observed that the total optimal cost reduces as the line capacity increases before getting saturated, which demonstrates benefit of power exchanges among MGs. This is because the larger line capacity is, the more surplus power can be exchanged among MGs. Optimal cost ($) Fig Saving (%) Load factor =.5 Load factor =. Load factor =.5 Load factor = 2. Line capacity (kw) (a) Absolute cost Load factor =.5 Load factor =. Load factor =.5 Load factor = Line capacity (kw) (b) Relative saving Impact of line capacity and load factor on optimal cost Figs. 5(b), 5(a) show the impact of line capacity and forecasting uncertainty of load, wind irradiance, and solar irradiance on the optimal cost where the uncertainty factor UF represents the scaling factor for the standard deviation of the forecast errors of wind speed, solar irradiance, and power demand with respect to the base case described in Section II. We can observe from this figure that the optimal cost increases when the uncertainties increases (or UF increases). Battery storage facility enables stored energy to be discharged during high-price hours or when the output of renewable energy sources is small. Figs. 6(a), 6(b) show the impact of battery capacity of each MG on the optimal cost. This figure reveals that the cost saving increases when the battery capacity becomes larger. The relative savings with respect to the case where there is no battery storage can be quite significant (more than % for sufficiently large load factor and battery capacity). Optimal cost ($) Fig UF =.3 UF =.6 UF =. UF =.5 UF = Line capacity (kw) Saving (%) (a) Absolute cost UF =.3 UF =.6 UF =. UF =.5 UF = Line capacity (kw) (b) Relative Saving Impact of line capacity and uncertainty level on optimal cost Figs. 7(a), 7(b), 7(c) show the various profiles in terms of total power exchange with the main grid. Line capacity of zero (kw) means no power exchange among MGs is allowed. These figures reveal the positive impacts of allowing power exchange among MGs and large battery storage capacity on the profile of power exchange with the main grid. The negative value of imported power means that the power is exported to the main grid. The scheduled unit commitment statuses of conventional units with different load factors are presented in Figs. 8(a), 8(b), 8(c). We have indeed performed simulations for other values of load factor and found that when the load factor is sufficiently small, no conventional unit needs to be turned ON during the operating day, e.g., when load factor =. On the other hand, when the load factor is large, all three conventional units have to be ON during the operating day to meet high load demand, e.g., when the load factor = 3. Due to the power limit of the lines connecting MGs with the main grid, if the total system load is high, we need to bring some conventional units online. The generating unit in MG (U) has lowest operating cost while the generating unit in MG 3 has the highest operating cost; therefore, U is scheduled to operate more frequently than U2 and U3. Furthermore, Fig. 2(a) shows that the renewable energy generation is small during the period between 5 P.M and 9 P.M, and the period between A.M and 7 A.M; therefore, the conventional units tend to be committed in these periods to meet the high power demand. V. CONCLUSION We have proposed an optimization framework for energy management in a cooperative network of microgrids. The uncertainties in power demand, wind/solar power generation are

7 7 Saving ($) Fig. 6. Saving (%) Load factor =.5 Load factor =. Load factor =.5 Load factor = 2. Load factor = Battery capacity (kwh) (a) Absolute saving Load factor =.5 Load factor =. Load factor =.5 Load factor = 2. Load factor = Battery capacity (kwh) (b) Relative saving Impact of line capacity and uncertainty level on optimal cost unit commitment, IEEE Trans. Power Syst., vol. 22, no. 2, pp. 8 8, May 27. Imported power (kw) Imported power (kw) Battery kwh, line kw Battery kwh, line 5 kw Battery 3 kwh, line kw Battery 3 kwh, line 5 kw (a) Load factor =.5 Battery kwh, line kw Battery kwh, line 5 kw Battery 3 kwh, line kw Battery 3 kwh, line 5 kw (b) Load factor =. considered in our proposed system model. Numerical results are presented to illustrate the impacts of system parameters on the optimal cost. The results confirm that by applying our proposed energy management scheme, significant cost saving can be achieved compared to the case where each MG optimizes its operation separately. REFERENCES [] X. Guan, Z. Xu, and Q. S. Jia, Energy-efficient buildings facilitated by microgrid, IEEE Trans. Smart Grid, vol., no. 3, pp , Dec. 2. [2] S. X. Chen, H. B. Gooi, and M. Q. Wang, Sizing of energy storage for microgrids, IEEE Trans. Smart Grid, vol., no. 4, pp , Mar. 22. [3] S. J. Ahn, S. R. Nam, J. H. Choi, and S. I. Moon, Power scheduling of distributed generators for economic and stable operation of a microgrid, IEEE Trans. Smart Grid, vol. 4, no., pp , Mar. 23. [4] H. S. V. S. K. Nunna, and S. Doolla, Demand response in smart distribution system with multiple microgrids, IEEE Trans. Smart Grid, vol. 3, no. 4, pp , Dec. 22. [5] M. E. Khodayar, M. Shahidehpour, and L. Wu, Enhancing the dispatchability of variable wind generation by coordination with pumped-storage hydro units in stochastic power systems, IEEE Trans. Power Syst., early access, vol. PP, no. 99, pp., 23. [6] S. Bahramirad, W. Reder, and A. Khodaei, Reliability-constrained optimal sizing of energy storage system in a microgrid, IEEE Trans. Smart Grid, vol. 3, no. 4, pp , Dec. 22. [7] Q. Wang, Y. Guan, and J. Wang, A chance-constrained two-stage stochastic program for unit commitment with uncertain wind power output, IEEE Trans. Power Systems, vol. 27, no., pp , Feb. 22. [8] J. G. Gonzalez, R. M. R. de la Muela, L. M. Santos, and A. M. Gonzalez, Stochastic joint optimization of wind generation and pumped-storage units in an electricity market, IEEE Trans. Power Systems, vol. 23, no. 2, pp , May 28. [9] W. Lei, M. Shahidehpour, and L. Tao, Stochastic security-constrained Imported power (kw) Fig Battery kwh, line kw Battery kwh, line 5 kw 8 Battery 3 kwh, line kw Battery 3 kwh, line 5 kw (c) Load factor = 2. Comparison of profiles of power exchange with the main grid [] J. Dupacov, N. Grwe-Kuska, and W. Rmisch, Scenario reduction in stochastic programming: An approach using probability metrics, Math.Program, pp , 23. [] J. Wang, M. Shahidehpour, and L. Zuyi, Security-constrained unit commitment with volatile wind power generation, IEEE Trans. Power Syst., vol. 23, no. 3, pp , Aug. 28. [2] M. Carrion, and J. M. Arroyo, A computationally efficient mixedinteger linear formulation for the thermal unit commitment problem, IEEE Trans. Power Syst., vol. 2, no. 3, pp , Aug. 26. [3] J. M. Morales, A. J. Conejo, and J. Perez-Ruiz, Economic valuation of reserves in power systems with high penetration of wind power, IEEE Trans. Power Syst., vol. 24, no. 2, pp. 9 9, May 29. [4] R. Palma-Behnke, C. Benavides, F. Lanas, B. Severino, L. Reyes, J. Llanos, and D. Saez, A microgrid energy management system based on the rolling horizon strategy, IEEE Trans. Smart Grid,, early access, vol. PP, no. 99, pp., 23. [5] d ata/nsrdb/99-2/hourly/siteonthefly.cgi?id = [6] ftp://ftp.ncdc.noaa.gov/pub/data/noaa/2/ [7] GAMS/SCENRED Documentation [online]. Available: [8] CPLEX Solver [Online]. Available: [9]

8 8 U U U (a) Load factor =.5 U U2 U (b) Load factor = 2. U U U (c) Load factor = 2.5 Fig. 8. Scheduled unit commitment statuses of conventional units