2858 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 Robust Operation of Microgrids via Two-Stage Coordinated Energy Storage and Direct Load Control Cuo Zhang, Student Member, IEEE, Yan Xu, Member, IEEE, Zhao Yang Dong, Fellow, IEEE, and Jin Ma, Member, IEEE Abstract—This paper proposes a robust optimization approach for optimal operation of microgrids. The uncertain output variation of renewable energy sources (RESs) is addressed by collaboratively scheduling of energy storage (ES) and direct load control (DLC) through a two-stage complementary framework: an hour-ahead charging/discharging of ES and a quarter-hour-ahead activation of DLC. The objective is to maximize the total profit of the microgrid considering operation and maintenance costs of ES units, wind turbines and photovoltaics, and transaction with main grid and customer loads. Assuming the power output of RES randomly varies within a bounded uncertainty set, the problem is modeled to a two-stage robust optimization model and solved by a column-and-constraint generation algorithm. Compared with conventional operation methods, the ES and DLC are coordinated in different time-scales, and RES uncertainties are fully addressed during operation decision-making, ensuring the solutions to be optimal and robust for any realization of uncertainty. The proposed methodology is verified on the IEEE 33-bus distribution system through a wide range of different tests. Index Terms—Direct load control, distributed generation, energy storage, microgrid, operation planning, robust optimization. NOMENCLATURE A. Sets Br(i) Br(i, j) HQ Jch , Jdis ND /W T/PV /ES NT T UW T/PV B. Parameters CW T,OM , CPV ,OM Csell , Cbuy CD ,con , CD ,unc CES,ch , CES,dis E0,m Er,m Set of all the branches that connect to node i. Branch between node i and j. Set of all the quarters in the planned hour. Manuscript received March 6, 2016; revised June 28, 2016 and August 24, 2016; accepted November 4, 2016. Date of publication November 11, 2016; date of current version June 16, 2017. The work in this paper was supported in part by China Southern Power Grid Company through the Project WYKJ00000027, in part by the Australia-Indonesia Centre under a Tactical Research Project, in part by the University of Sydney under the Early Career Researcher Development grant, and in part by University of Sydney Bridging Grant. The work of C. Zhang is supported by Australian International Postgraduate Research Scholarship (IPRS), Australian Postgraduate Award (APA). Paper no. TPWRS-00358-2016. C. Zhang is with the School of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia (e-mail: cuo.zhang@ sydney.edu.au). Y. Xu is with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore (e-mail: eeyanxu@gmail.com). Z. Y. Dong is with the School of Electrical Engineering and Telecommunications, The University of NSW, Sydney, NSW 2052, Australia, and also with China Southern Power Grid Electric Power Research Institute, Guangzhou, 510000, China (e-mail: zydong@ieee.org). J. Ma is with the School of Electrical and Information Engineering, University of Sydney, Sydney, NSW 2006, Australia (e-mail: jma@sydney.edu.au). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPWRS.2016.2627583 Set of all the ES charging/discharging levels. Set of nodes that have loads/wind turbines/PVs/ES units, respectively. Number of all the time periods. Set of all the time periods. Uncertainty set for wind turbine/PV output power. Lch,m ,j , Ldis,m ,j KD ,con fc fc PW T,n ,t , PPV ,n ,t m ax m ax , Pdis,m Pch,m PD ,con , PD , unc m in/m ax m in/m ax PW T,n ,t , PPV ,n ,t rated rated PW T,n , PPV ,n ε ηch , ηdis μW T,l , μW T,u , O&M cost of wind turbine/PV ($/MWh). Price for selling/buying electricity to/from main grid ($/MWh). Price for selling electricity to controllable/uncontrollable load ($/MWh). O&M cost of ES during charging/ discharging ($/MWh). Initial energy stored in ES unit at node m. Rated energy which can be stored in ES unit at node m. Charging/Discharging power rate (% of rated power) of ES unit at node m on level j. Ratio of controllable load to total load, same as maximum demand cutting rate during DLC. Forecasted output power of wind turbine/PV at node n during period t. Rated charging/discharging power of ES unit at node m. Total controllable and uncontrollable load demand of microgrid. Minimum/Maximum foreca-sted output power of wind turbine/PV at node n during period t. Rated output power of wind turbine/ PV at node n. Maximum allowed bound gap. ES efficiency during charging/ discharging (ES total efficiency, η = ηch /ηdis ). Lower/Upper bound of wind 0885-8950 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. ZHANG et al.: ROBUST OPERATION OF MICROGRIDS VIA TWO-STAGE COORDINATED ENERGY STORAGE AND DIRECT LOAD CONTROL μPV , l , μPV ,u C. Variables KDLC,q PW T,n ,t , PPV ,n ,t Pb,t , Qb,t P0,b,t , Q0,b,t Pdef ,t , Psur,t PDLC,i,q , QDLC,i,q Vi,t αch,m ,j , αdis,m ,j turbine/PV output uncertainty budget. Demand cutting rate (% of total demand) for DLC during quarter-hour q. Uncertain output power of wind turbine/PV at node n during period t. Active/Reactive power through branch b during period t. Active/Reactive power through the lateral branch of branch b during period t. Power deficiency/surplus of microgrid during period t. Active/Reactive load demand at node i during hour quarter q under DLC. Voltage magnitude of node i during period t. Binary charging/discharging decisions of ES unit at node m on charging/ discharging level j. I. INTRODUCTION ITH large-scale installations of distributed generation, today’s distribution networks are now evolving from conventional passive systems to active decentralized systems such as microgrids. In order to reduce greenhouse gas emissions and alleviate the dependence on fossil fuels, renewable energy sources (RESs) such as wind and solar are dominantly adopted in today’s microgrids. However, unlike conventional controllable fossil-fuel generation, both wind turbines and solar photovoltaics (PVs) can only generate intermittent, volatile, and non-dispatchable power, which causes significant difficulties for microgrid operation [1], e.g. when the outputs of the wind turbines and PVs are excessively high, they may be curtailed; when they are low, the power from the microgrid itself may not meet load demands. To alleviate this problem, [1], [2] suggest integrating energy storage (ES) into the microgrid to achieve a “time-shifting” of energy, which allows the redundant energy produced by the wind turbines and PVs to be saved during low demand periods and released during peak demand periods. With this energy shifting, the microgrid operator can make more economic profits. Besides, as discussed in [2], [3], the ES can also provide other benefits such as mitigating the RES intermittency, improving power system reliability and so forth. As the price of ES continues to drop, it is now becoming popular to deploy ES in a microgrid for a better energy management purpose. However, ES also has clear drawbacks which hinder its effects, such as limited capacity and reduced lifetime due to frequent charging/discharging operations. In the literature, the ES operation can be optimized based on historical or predicted RES outputs [4]–[10]. As the major difficulty caused by RES is the stochastic power injections, uncertainty analysis and optimization methods are applied in the ES operation. For example, [11] suggests a probabilistic approach where different wind power levels are W 2859 produced with corresponding occurrence probabilities to simulate uncertain conditions. In [12], Monte-Carlo simulations are utilized to simulate wind power uncertainty data to improve solution robustness. [13] proposes a finite prediction error concept to involve RES uncertainties, so that the optimization process can be achieved with predictable RES profiles. On the other hand, with the increased controllability of the load in the smart grid, demand response is another solution to address the uncertainties arisen by RESs [1]. Demand response program can be classified, based on how load demands are changed, into price-based demand response and incentive-based demand response [14], [15]. Among all the demand response programs, direct load control (DLC) is incentive-based which directly shuts down the remote controllable and non-essential equipment such as air conditioners and water heaters, to maintain the power balance in a microgrid. Thus, DLC has stronger controllability and can respond faster to mitigate the uncertainties. Considering the complementary characteristics of the ES and the DLC, this paper proposes a two-stage coordinated operation strategy for robust operation of microgrids in the presence of uncertain renewable power outputs. In the first stage, ES units are scheduled to charge/discharge on an hourly basis. The optimization is based on one-hour ahead RES output predictions. In the second stage, DLC is then scheduled within each hour to complement the ES operation when the RES outputs deviate significantly from the prediction. In this strategy, the ES is operated to manage slow variations in the RES outputs and for larger economic benefits which DLC cannot achieve alone. On the other hand, the second stage DLC aims to balance the power within the microgrid when the outputs of RESs and ES are deficient, which can overcome the capacity limitation of ES. Besides, in particular, DLC can be activated in a relatively short time interval, therefore it can compensate the relatively long response time of the ES to manage fast RES power variation. The proposed collaborative scheduling of ES and DLC strategy is modeled as a two-stage robust optimization (TSRO) problem. Compared with conventional stochastic programming techniques which can only provide probabilistic guarantees for constraint satisfaction [11], [12], robust optimization can obtain an optimal solution within a deterministic uncertainty set by considering worst cases [16], [17]. In the literature, robust optimization has been successfully applied for unit commitment [16]–[18], microgrid planning [19], and ES planning [20] to handle RES uncertainties. However, its application in microgrid operation is relatively limited. In general, robust optimization has three major benefits. Firstly, it only needs modest data of uncertainty, such as the mean and the range of the uncertain variables. It is a significant advantage, considering that stochastic optimization is unable to provide reliable solutions when probability distribution functions are partially available or not available. Secondly, robust optimization is immune against any realization of the uncertainty in the uncertainty set. Since the robust optimization solutions are obtained according to the worst cases, constraints for all the uncertainty realizations are satisfied and the solutions are regarded robust. Thirdly, the un- Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. 2860 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 certainty sets support an efficient way in uncertainty modeling and the robust optimization is computationally efficient, while in the stochastic optimization, Monte Carlo sampling is very time consuming. Furthermore, the TSRO can improve the robustness through the second stage compensation operation. The major contribution in this paper can be summarized as follows: 1) A novel coordinated microgrid operation framework is proposed, which dispatches ES and DLC in different timescales to complement each other towards operational robustness. 2) A TSRO model is developed, which maximizes the total profit of the microgrid while satisfying operational limits with any realization of RES uncertainties. 3) A Lagrange-dual based column-and-constraint generation algorithm is applied to solve the proposed TSRO problem considering a variety of testing scenarios. The remainder of this paper is organized as follows. Section II describes the proposed two-stage microgrid operation strategy through cooperating ES and DLC. Section III presents the formulation of the microgrid operation optimization problem and Section IV supports the solution methodology of a TSRO. Section V carries out numerical simulations of the proposed optimization with different tests and demonstrates the results. At last, Section VI concludes the whole paper. II. TWO-STAGE COORDINATED MICROGRID OPERATION A typical microgrid consists of RES units, ES systems, as well as flexible loads. RESs like wind turbines and PVs can generate clean and low-cost power, ES units can alleviate energy management difficulties by charging/discharging energy to make an energy shift, and DLC can contribute in maintaining power supply and demand balance. Generally, the microgrid operator aims to maximize the total benefits from RES generation, ES scheduling and DLC, while satisfying the operational limits. To achieve optimal operation performance of microgrids, this paper seeks to coordinate ES and DLC to cooperatively handle RES uncertainties. Based on this, a two-stage operation strategy is proposed. It is assumed that ES units are invested and installed at the same locations with wind turbines and PVs. The ES operates to charge energy from the wind turbines and PVs, when the wind turbines and PVs generation exceeds the microgrid load. On the other hand, energy is discharged from the ES to the network when necessary, e.g. when the wind turbine and PV outputs are lower than the load and the electricity price is high. As a result, the microgrid can decrease the energy purchase from the main grid, which in turn increases the final profits. Thus, in the microgrid operation strategy, the ES aims to cooperate with wind turbine and PV uncertain outputs to maximize the profits for the microgrid operators. Since frequent changes of ES states lead to reduced lifetime and increased operation and maintenance (O&M) cost, ES should operate to change states between charging and discharging at a relatively long interval to minimize its O&M cost [3]. Considering this characteristic of the ES, in the proposed Fig. 1. A two-stage coordinated microgrid strategy. strategy, the states of ES units are planned in a relatively long timescale, which is set as one hour ahead in this paper, and ES units act hourly with the forecasted RES outputs. Within each operation hour, the states of the ES units are fixed. This ES operation is regarded as the first stage operation. It is emphasized that the predicted RES outputs according to the weather forecast can be in a reasonably accurate range, but still vary randomly from the expectation. Thus, once the uncertain output power deviates from the prediction heavily within an hour, the financial benefits may be deteriorated and operational limits of the microgrid may not be guaranteed. To operate the microgrid robustly against the uncertain RES outputs, a second stage operation is designed in this paper, in which the DLC is implemented to complement the ES operation. As DLC is relatively faster, it can act in a shorter timescale which is set to one quarter-hour in this paper. It aims to modify the load demands when the RES outputs have significant deviations from the hour-ahead expected values. A quarter-hour RES prediction is applied in this stage as well. However, unlike the first stage issue, this prediction accuracy can be much higher as the prediction lead-time is much shorter, meaning the uncertainty is much lower. As a result, the power supply of the ES units and RESs can fulfill the requirement of the responded load, which results in more profits. Fig. 1 shows the structure of the proposed two-stage microgrid operation strategy. In the microgrid, RES generation, ES and responsive loads can coordinate to maximize the operator’s benefits. RES outputs, ES states and load demand data can be collected by measurement equipment and smart meters and they are applied in the computation procedure as optimization parameters. The proposed computation procedure is described in Sections III and IV. With the operation decisions optimized from the procedure, ES operates to change charging/discharging states in the first stage and DLC operates in the second stage. III. MATHEMATICAL MODELING The proposed strategy aims to maximize the profit by coordination of ES and DLC and ensures operational constraints against RES uncertain outputs. The profit is the total revenues from selling electricity to customers and the main grid minus the total costs on ES, wind turbine and PV’s O&M and buying electricity from the main grid. In this section, the proposed Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. ZHANG et al.: ROBUST OPERATION OF MICROGRIDS VIA TWO-STAGE COORDINATED ENERGY STORAGE AND DIRECT LOAD CONTROL two-stage microgrid operation strategy is modeled mathematically with a profit objective and operational constraints. A. Economic Model of Energy Storage As discussed above, the ES O&M cost is related to ES charging/discharging states, i.e. the energy ES stores and releases, so this cost must be considered when the operation is optimized. In this paper, a practical ES O&M cost model is developed and applied in the profit maximization. For the sake of modeling, it is assumed that each ES unit has a dummy owner which can be the microgrid operator itself or a private entity in practice. As a result, the microgrid operator can trade with these ES owners. When an ES unit discharges power to the network as a generator, the microgrid operator needs to pay for the electricity. On the other hand, when an ES unit charges power from the network as a load, the microgrid operator earns money from the ES owners for selling electricity. The prices of these two kinds of electricity transaction can be designed as pricedis ($/MWh) and pricech ($/MWh). pricedis is positive for the payment and pricech is negative for the revenue of the microgrid operator. In [3], all the costs for ES, including the investment cost, the replacement cost and the charging/discharging cost, can be transformed into an O&M cost for analysis simplification, expressed as CES,OM ($/MWh). To apply this O&M cost model in the proposed strategy optimization, this cost is modified and divided into two parts as CES,dis ($/MWh) and CES,ch ($/MWh) for discharging and charging electricity respectively, which are constant. Considering the transaction concept described above, they can be pricedis and pricech respectively. The following relationship should be satisfied for cost equality, CES,dis Edis + CES,ch Ech = CES, OM Estored . (1) Considering the characteristics of ES, the following equations need to be satisfied, Estored = ηdis Edis = ηch Ech , ηdis > 1, ηch < 1. (2) where Estored , Edis , Ech represent the energy stored, the energy discharged and the energy charged by ES for a cycle, respectively. The cycle means the period starting from some certain energy being charged and ending in this certain energy being discharged. Substituting (2) into (1), we have CES,ch CES,dis + = CES,OM . ηdis ηch (3) Thus, CES,dis and CES,ch can be designed by using (3) and the proposed ES transaction model is developed as above. This ES economic model is applied in the proposed microgrid operation optimization. B. Operation Model of Energy Storage After the economic model of the ES cost is developed, a complementary operational model of the ES is developed here. Considering that the operation states of the ES units are fixed during the planned hour in the first stage, a discrete charging/discharging model is developed in this paper. 2861 In this model, the maximum output power an ES unit can generate at a node, i.e. the maximum discharging power, is divided into several levels (10 levels in this paper simulation). Each level represents a percentage of the maximum discharging power – this is aligned with industry-grade ES discharging controller which needs a set-point to control the discharging level. For the sake of the optimization purpose, a binary decision variable is used to denote each level: 1 for the ES unit discharging the corresponding power of the level, and 0 for no operating. Thus, for a specified ES unit at the node m, the planned discharging power is calculated as follows, m ax αdis,m ,j Ldis,m ,j . (4) PES,dis,m = Pdis,m j ∈J d i s Similarly, several levels (e.g. 10) for charging power of each ES unit are derived and their corresponding binary decision variables are defined. The planned charging power of the ES unit at the node m is derived as m ax αch,m ,j Lch,m ,j . (5) PES,ch,m = Pch,m j ∈J c h With these binary variables and the pre-designed charging/discharging levels, this operational model can be optimized to decide the ES charging/discharging power to maximize the profit with the proposed ES economic model. C. Operation Model of Direct Load Control A profit-based DLC derived by [21] is used to coordinate with the first stage ES operation and to compensate profits for the microgrid operator in the second stage. In this model, the total loads can be divided into two groups, controllable loads, i.e. DLC loads and uncontrollable loads. The ratio of the controllable loads to the total loads is PD ,con . (6) KD ,con = PD This ratio also represents the maximum percentage of the load demands which can be controlled. Thus, the fixed and uncontrollable load demands can be calculated as PD ,unc = (1 − KD ,con ) PD . (7) During a certain hour quarter of DLC, the controllable loads can be cut off by a cutting percentage, KDLC,q . It aims to keep the microgrid power independently balanced as much as possible with assisting the ES operation. Besides, during this process of optimizing KDLC,q , the total profit can be maximized by modifying the transaction with the main grid. In this paper, KDLC,q is a continuous and adjustable variable optimized in the second stage. However, this variable can also be discrete when loads are clustered (say, loads can be clustered into several groups, e.g. several houses can have only one DLC switch). Therefore, the load demand during DLC for each node can be calculated as PDLC,i,q = (1 − KDLC,q ) PD ,i , ∀i, q. (8) Assume that for each node, the power factor is fixed. Thus, the reactive power of each node during DLC is expressed as QDLC,i,q = (1 − KDLC,q ) QD ,i , ∀i, q. (9) Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. 2862 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 The controllable loads can be cut off by remote switches with the help of smart meters. During the DLC, these customers with the cut-off loads can use limited power, even no power. Normally, to make up the loss for the controllable load customers, the microgrid operator offers a lower electricity price, i.e. DLC load price CD ,con for these customers than the normal price CD ,unc for the customers of the uncontrollable loads. The microgrid operator can reset CD ,con to modify the number of the customers who agree to join in the DLC group [21]. For example, the microgrid operator can reduce CD ,con to involve more loads as controllable loads with the customers’ agreement, so that more loads can be cut off for the modifying load demands purpose. However, considerably surplus controllable loads mean a much lower overall revenue from the customers, since the DLC load price is much lower. Thus, the microgrid operator should design the DLC load price based on the cautious expectation of the DLC capacity. m in m ax PW T,n ,t ≤ PW T,n ,t ≤ PW T,n ,t , ∀n, t (20) m in m ax PPV (21) ,n ,t ≤ PPV ,n ,t ≤ PPV ,n ,t , ∀n, t m ax αch,m ,j Lch,m ,j Pb+1,t = Pb,t − P0,b+1,t − Pch,m m ax + Pdis,m j ∈J c h αdis,m ,j Ldis,m ,j − PDLC,i,q j ∈J d i s + PW T,n ,t + PPV ,n ,t , b ∈ Br (i) , ∀i, t, q (22) Qb+1,t = Qb,t − Q0,b+1,t − QDLC,i,q , b ∈ Br (i) , ∀i, t, q (23) Vi+1,t = Vi,t − Rb Pb,t + Xb Qb,t , b ∈ Br (i, i + 1) , ∀i, t V0 (24) PDLC,i,q = (1 − KDLC,q ) PD ,i , ∀i, q (25) D. Optimization Model of Microgrid Operation QDLC,i,q = (1 − KDLC,q ) QD ,i , ∀i, q (26) The objective is to maximize the total profit of the microgrid considering O&M costs o ES units, wind turbines and PVs, transaction with main grid and loads. The objective and constraints are formulated as follows, 1 − V m ax ≤ Vi,t ≤ 1 + V m ax , ∀i, t (27) P1,t = Pdef ,t − Psur,t , Pdef ,t ≥ 0, Psur,t ≥ 0, ∀t (28) (10) min CES + CW T + CPV + Cgrid − Crev m ax s.t. CES = CES,ch Pch,m αch,m ,j Lch,m ,j + CES,dis m ∈N E S m ax Pdis,m m ∈N E S j ∈J c h αdis,m ,j Ldis,m ,j (11) j ∈J d i s PW T,n ,t NT CW T = CW T,OM (12) n ∈N W T t∈T CPV = CPV ,OM PPV ,n ,t NT (13) n ∈N P V t∈T Cgrid = Cbuy Pdef ,t t∈T NT − Csell Psur,t t∈T Crev = CD ,unc (1 − KD ,con ) NT (14) PD ,i i∈N D + CD ,con (KD ,con − KDLC,q ) q ∈HQ PD ,i 4 αch,m ,j ∈ {0, 1} , αdis,m ,j ∈ {0, 1} , ∀m, j αch,m ,j + αdis,m ,j ≤ 1, ∀m j ∈J c h ∪J d i s m ax − E0,m ≤ ηch Pch,m m ax − ηdis Pdis,m (15) i∈N D (16) (17) αch,m ,j Lch,m ,j j ∈J c h αdis,m ,j Ldis,m ,j ≤ Er,m − E0,m , ∀m j ∈J d i s (18) 0 ≤ KDLC,q ≤ KD ,con , ∀q (19) The objective function (10) considers all the costs and the revenues during the microgrid operation. Equations (11)–(15) are the calculation functions of these costs and revenues, i.e. the O&M costs of the ES, wind turbine and PV respectively, the transaction with the main grid including the electricity payment and the electricity revenue, and the revenue of selling electricity to the demand customers. The objective is to maximize the profit, which is equivalent to minimize the total costs minus the total revenues. Constraint (16) describes the first stage decision variables for the ES operations are binary for all the charging/discharging levels. Constraint (17) guarantees that only one charging/discharging level is planned to be operated for each ES unit. Constraint (18) limits the maximum charging/discharging power of each ES unit with the consideration of the battery efficiency. Constraint (19) expresses the allowed range of the load cutting during DLC. Constraints (20) and (21) describe that due to the uncertain nature of the wind and solar power, the outputs of the wind turbines and PVs vary randomly in the ranges of the forecasted lower and upper bounds. Constraints (22)–(24) are the linearized distribution load flow (Dist-Flow) equations. The Dist-Flow model is originally proposed in [22] and linearized in [23]. It has been proved efficient for microgrid modeling [19]. Note that the power loss is not considered here since compared with the other cost terms in (10) it is minor to make a notable difference. Moreover, its inclusion may introduce non-linear terms and add difficulty for developing numerical algorithm. Equations (25) and (26) represent the load demands during each quarter of the hour with the consideration of the planned DLC. Constraint (27) guarantees the voltage magnitude of each node is kept within the allowed maximum deviation from the nominal value. Constraint (28) denotes the relationship between the power flow from the main grid and transacted electricity, where P1,t means the power transformed from the main grid to the microgrid. It is noted that Pdef ,t > 0 means the microgrid buys Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. ZHANG et al.: ROBUST OPERATION OF MICROGRIDS VIA TWO-STAGE COORDINATED ENERGY STORAGE AND DIRECT LOAD CONTROL electricity from the main grid and Psur,t > 0 means the microgrid sells electricity to the main grid. Note that the first stage ES operation acts hourly and the operation time is set to 1 hour. Thus, the first stage time summation is 1 hour and it can be hidden in (11), (15) and (18). Equations (10)–(28) make up a mixed-integer linear programming (MILP) with uncertain variables. Herein, the ES charging/discharging operations are the first stage decisions and the DLC cut-off rates are the second stage decisions in this twostage optimization problem. IV. ROBUST COORDINATION MODEL In order to make the solutions robust against the uncertain RES output power, a TSRO model is developed to coordinate the ES and DLC in the different time-scales. A. Two-Stage Robust Optimization Model In the robust optimization modeling, uncertain variables are searched first within uncertainty sets to form a worst case and then these variables are fixed and applied in optimization as parameters. The solution obtained with the worst uncertainty case is robustly optimal for all the possible uncertainty cases produced by the uncertainty sets, thus all uncertainty cases are fully addressed during the optimization. The proposed microgrid operation model is converted to a TSRO model, which can be formulated in the following compact matrix form: min cT x + max min dT y + eT u (29) s.t. Ax ≥ b (30) x u y y ∈ O (x, u) = {F x + Gy ≤ v, Hx + Iy + Ju = w} (31) u∈U (32) The objective described in (29) is modeled in a “min-maxmin” optimization form. The first “min” is to minimize the first stage costs by optimizing the first stage variable set x. The “max” is to find the worst uncertainty case u in the given uncertainty set U by maximizing the minimization of the second stage objective. The second “min” is to minimize the second stage costs by optimizing the second stage variable set y. It can be seen that the worst case from the uncertainty set is obtained by maximizing the minimal second stage costs, which guarantees the solution robustness. The three types of variables at different stages are classified as follows. 1) x represents a set of decision variables in the first stage operation which are not subject to the uncertain variables or the adjustment variables in the second stage. Considering the unadjustable characteristic of these decision variables, they can be regarded as the “here-and-now” decisions. In the proposed strategy model formulated in Section III-D, x indicates the vector of the binary variables for all the ES operation levels, i.e. αch and αdis . Besides, their constraints (16)–(18) are grouped in (30). 2863 2) y stands for a group of adjustable variables in the second stage including the quarter-hour ahead DLC controllable variables, KDLC and dependent variables, P, Q, V. Herein, KDLC for each quarter hour can be optimized in the second stage after the realization of the uncertain variables, and they are referred as the “wait-and-see” decisions. Constraint (31) indicates that y must be adjusted in the feasible set, O(x, u) which is based on the first-stage decision variable set x and any single case of uncertainty variable group u. O(x, u) is defined by constraints (19), (22)–(28). 3) u stands for the uncertainty variables which are the outputs of the wind turbines and the PVs, i.e. PW T and PPV . Constraint (32) means that with the predicted wind and solar power, the uncertain variables vary in uncertainty sets which support the worst case during the robust optimization process. In other words, with (32) as the constraint, the minimization of the second stage objective is maximized. The uncertainty sets are made up by allowed uncertain ranges for uncertainties and they limit the uncertainties to make the optimization problem practical. In this paper, two polyhedral uncertainty sets are formulated for the wind and solar power respectively as follows, UW T = {PW T,n ,t ∈ Rn w t : PW T,n ,t 1 μW T,l μW T,u , fc nn nt PW T,n ,t n ∈N t∈T WT m in PW T,n ,t m ax PW T,n ,t PW T,n ,t , ∀n, t}, (33) UPV = {PPV ,n ,t ∈ Rn p v : PPV ,n ,t 1 μPV ,l μPV ,u , fc nn nt PPV ,n ,t n ∈N t∈T PV m in PPV ,n ,t m ax PPV ,n ,t PPV ,n ,t , ∀n, t}. (34) m in m ax m in m ax PW T,n ,t , PW T,n ,t , PPV ,n ,t , PPV ,n ,t are forecasted generation interval (lower and upper bounds) of the wind turbine and PV outputs at a node n during a period t. They can be obtained from interval forecasting tools [24]. These bounds represent the constraints (20) and (21) for each single uncertain variable. In practice, they are obtained from the hour-ahead forecasts. Furthermore, a budget of uncertainty is a user-defined parameter in pair of μl and μu to limit the overall uncertainty. They are lower and upper bounds of a summation of the ratios between the actual RES outputs and the forecasted outputs, averaged by the total numbers of periods nt and RES units nn . This pair is an indicator for measuring the uncertainty caused by inaccurate wind and PV generation forecasting. For example, if both μl and μu are 100%, it means that the overall hourly forecast is accurate. Otherwise, it means the overall hourly forecast has an average accuracy between μl and μu . This budget should be designed considering a few aspects such as the historical data (e.g. the accuracy statistics of the forecasting tools) and the expectation of the solution robustness. For example, it should have a larger range to improve the robustness if heavy uncertainties are predicted to occur. Besides, if the budget is not set up large enough, realization of the uncertainties may be out of the Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. 2864 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 uncertainty sets and the robustness may not be ensured which may lead to reduced profits and/or violation of the limits. It is emphasized that the budget is enlarged when μl falls and μu rises, so that the final optimization solutions are robust against more uncertain cases but will be more conservative (i.e. less profits). Therefore, its value should be designed by the operator with consideration of the balance between robustness and conservativeness. It should be noticed that, the “wait-and-see” decisions which can be adjusted in the second stage can improve the objective value when the worst case does not occur. In other words, the worst-case-based profit may be improved by the second stage decisions according to the realization of the uncertainty so that the conservativeness can be reduced. According to the characteristics of the “min-max-min” form and its corresponding variables, the proposed two-stage optimization objective (10) can be rewritten in a TSRO form as the following, min CES + α d i s ,α c h max min P W T ,P P V K D L C ,V ,P ,Q ∈O CW T + CPV + Cgrid − Crev . (35) It can be seen that the O&M cost of the ES units are minimized by the binary decision variables αch and αdis in the first stage, while the other economic terms are optimized by the adjustable variable KDLC with the uncertainty variables PW T and PPV in the second stage. In addition, the ES operation decisions are the optimized solutions for the hour-ahead microgrid operation planning, and the DLC decisions are modified further based on the quarter-hour ahead RES forecasts during the planned hour. B. Column-and-Constraint Generation (C&CG) Algorithm To solve a TSRO problem, two decomposition methodologies are widely applied for unit commitment problems and planning problems. One is an Benders decomposition with dual-cutting [16] and the other one is using a column-and-constraint generation (C&CG) algorithm to solve TSRO problems which can be regarded as a primal cutting plane algorithm [25]. It is concluded in [25] that the convergence speed of C&CG is much faster than that of Benders decomposition. Therefore, C&CG is applied in this paper. In C&CG algorithm, the TSRO problem is divided into a master problem and a slave one which can formulate the first and the second stages respectively. The master problem is, min cT x + λ (36) s.t. Ax ≥ b, (37) λ ≥ dT yl∗ + eT u∗l , ∀u∗l ∈ S, (38) x Fx + Gyl∗ ≤ v, Hx + Iyl∗ + Ju∗l = w, ∀u∗l ∈ S. (39) (40) Since in the proposed planning model, x is a set of binary decision variables, the master problem is a MILP. In this problem, an optimal solution can be derived as (x∗ , λ∗ ) with a set of fixed uncertainty variables u∗l obtained from the slave problem. It is denoted that the solution, x∗ is the current optimal solution of the first-stage planning and it is used for solving the slave problem. In addition, yl∗ corresponding to each uncertainty result is optimized as well. But, it is emphasized that only the final x∗ which is the “here-and-now” decision is optimized as the final planning solution, since other decision variables treated as “wait-and-see” decisions can be modified further during the planning hour. On the other hand, a slave problem is expressed as, S (u, x∗ ) = max min dT y + eT u (41) s.t. F x∗ + Gy ≤ v, (42) Hx∗ + Iy + Ju = w, (43) u ∈ U. (44) u y It is noticed that exactly solving the slave problem is significantly challenging with a polyhedral uncertainty set [25]. To solve the slave problem, the authors of [16] applied an outer approximation approach; in [18], a strong duality of the slave problem is utilized to produce a bilinear problem; furthermore, [25] suggested to use Karush-Kuhn-Tucker conditions and a big-M constraints approach to transfer the bilinear problem into a MILP. In this paper, the classic Lagrange dual is proposed to make a strong duality. Thus, the “max-min” form optimization is changed into a bilinear maximization problem as the follows, max (F x∗ − v)T ϕ + (w − Hx∗ − Ju)T ρ + eT u (45) s.t. GT ϕ − I T ρ + d = 0, ϕ ≥ 0, ρ free. (46) u ,ϕ,ρ Here ϕ and ρ are the dual variables of the second stage variables y, this duality can be solved by non-linear and bilinear solvers such as SCIP [26]. By maximizing the duality, the worst case is searched with a corresponding uncertainty variable u∗ as a slave problem solution. Besides, u∗ is added into a slave solution set S, for the master problem. After solving the slave problem, new second-stage variables are generated and supported with their constraints (38)–(40) together to the master problem. The implemented C&CG algorithm in this paper is shown in Fig. 2. V. NUMERICAL RESULTS A. Test System In this paper, an IEEE 33 bus radial distribution system is applied to demonstrate the proposed approach. The system topology is shown in Fig. 3 and its data are obtained from [27]. The voltage level is 12.66 kV with an allowed maximum voltage deviation as 0.05 p.u. The rated power and energy data for the ES units, wind turbines and PVs used in the case study are shown in Tables I and II. Note that optimal placement of distributed generation is out of the scope of this paper. A recent reference and related literature review can be found in [28]. The ES units modeled in this paper can be Zn/Br battery sets which are Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. ZHANG et al.: ROBUST OPERATION OF MICROGRIDS VIA TWO-STAGE COORDINATED ENERGY STORAGE AND DIRECT LOAD CONTROL 2865 TABLE III PARAMETERS FOR MICROGRID OPERATION TESTS Parameter Value ($/kWh) Parameter Value ($/kWh) 0.015 0.07 0.06 0.1 C ES,dis C ES,ch C WT,OM C PV,OM 0.051 −0.02 0.01 0.01 C sell C buy C D, con C D, unc TABLE IV UNCERTAINTY BUDGET SETS UNDER TESTS Fig. 2. C&CG algorithm. Test No 1 2 3 4 5 6 μ WT, l μ WT, u μ PV, l μ PV, u 95% 105% 97.5% 102.5% 90% 110% 95% 105% 85% 115% 92.5% 107.5% 80% 120% 90% 110% 75% 125% 87.5% 112.5% 70% 130% 85% 115% TABLE V SOLUTION RESULTS FOR BASE CASE UNDER DIFFERENT UNCERTAINTY SETS Test No ES Discharging Fig. 3. ES 1 ES 2 ES 3 ES 4 DLC under 0–15 min Worst Case 15–30 min 30–45 min 45–60 min Profit under Worst Case ($) Iteration Number Solution Time (s) Test microgrid topology. 1 2 3 4 5 6 0% 0% 20% 30% 0% 46% 0% 3% 192.39 5 61.39 10% 0% 20% 20% 0% 0% 0% 6% 187.94 5 15.96 0% 10% 40% 20% 0% 43% 0% 2% 184.45 3 12.04 10% 0% 20% 30% 0% 39% 0% 2% 179.86 3 13.84 10% 0% 40% 30% 0% 38% 31% 0% 177.30 3 18.34 10% 0% 40% 30% 0% 38% 0% 0% 174.29 2 7.01 TABLE I ES DATA ES ID Node No Rated Stored Energy (MWh) Rated Power (MW) 2 1 1 1 1.5 1 1 1 1 2 3 4 6 18 24 32 Charging Efficiency η c h Discharging Efficiency η d i s 0.9 1.2 B. Initial Tests TABLE II RES DATA Wind Turbines Data Node No 6 18 24 This simulation is conducted on a 64-bit PC with 3.30-GHz CPU and 8 GB RAM using Yalmip [29] toolbox in the MATLAB platform. Both the bilinear slave problem and the MILP master problem are solved by SCIP solver [26]. The terminal gap of the robust optimization is set as 0.01. PVs Data Rated Power (MW) Node No Rated Power (MW) 2 1 1 18 24 32 0.5 0.5 0.5 commonly applied in practical distribution networks, since they have low O&M costs and relatively high efficiency [3]. Table III lists the economic parameters for the microgrid operation and the average transaction price. A base system state is considered for the initial tests. The base state has a relatively low energy storage as 1.4 MWh stored in total, 35% of the wind turbine rated power, 90% of the PV rated power and 100% of the load demand indicating a peak hour condition. For this system state, a range of different budget sets are considered, which are listed in Table IV. For the six uncertainty sets, six corresponding tests are implemented by using the C&CG algorithm to solve the TSRO model. The six initial tests results are given in Table V which shows the ES discharging status at the first stage, the DLC results under the worst case, the profit under the worst case, the iteration number and solution time. Taking Test 1 as an example, see the second column of Table IV, μW T,l and μW T,u are the lower and upper budget bounds for wind turbine uncertain output respectively, which means the average forecast accuracy ratio of the actual wind Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. 2866 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 TABLE VI SYSTEM STATES FOR COMPREHENSIVE TESTS Test No Fig. 4. Load Demand (%) ES Stored Energy (MWh) Wind Turbine Output Rate (%) PV Output Rate (%) 100% 100% 100% 100% 100% 100% 100% 100% 50% 50% 50% 50% 50% 50% 50% 50% 2.7 2.7 2.7 2.7 0.8 0.8 0.8 0.8 2.7 2.7 2.7 2.7 0.8 0.8 0.8 0.8 95% 25% 95% 25% 95% 25% 95% 25% 95% 25% 95% 25% 95% 25% 95% 25% 90% 90% 10% 10% 90% 90% 10% 10% 90% 90% 10% 10% 90% 90% 10% 10% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Illustration of the worst case in wind turbine uncertainty set. power to the forecasted one can vary between 95% and 105%, and μPV , l and μPV ,u are those for PV output. For the illustration purpose, under this uncertainty set, the predicted wind power output, the uncertain range, and the calculated worst case by the TSRO of the wind turbine at Node 6 are shown in Fig. 4. Note that the uncertainty range is set up as the grey area based on the forecasted value with the allowed maximal deviation and the red curve presents this worst case found in the solution process. The worst case corresponds to maximizing the minimization of the second stage objective, i.e. “max-min”. It can be seen that the uncertainty variable of each period reaches the boundaries for this uncertainty budget. However, it is found that the uncertainty variables may not always lay at the boundaries for other uncertainty budgets. With this uncertainty budget, the ES operation states, i.e. discharging rates, are shown in the second column of Table V and they are the two-stage strategy hour-ahead decisions. The ES units are planned to act these operation states in the following hour. Besides, under the worst case, the DLC 15min decisions, i.e. the controllable load cutting rates, are also given. It is emphasized that the actual decisions are optimized 15-min ahead with the realization of the uncertainties and taken into effect for the corresponding 15-min interval. The profit under the worst case is calculated as well, but note that the actual profit would be calculated according to the actual DLC and the realization of the uncertainties. According to the solution results for the other five uncertainty sets, it can be seen that as the uncertainty size increases, the optimal solutions are more conservative. In Table IV, it is demonstrated that from Test 1 to Test 6, the budget size is enlarged, as a result, the overall profit decreases. For a large budget robust optimization, although the expected profit is relatively low, the solution can fit more uncertain conditions, which means more robust. Thus, it is noted that for increasing robustness purpose, a large uncertainty size can be selected by the microgrid operator to plan the ES hour-ahead operation, and a slightly conservative but more robust planning solution can be prepared for operation. However, with more accurate predictions of wind speeds and solar irradiance given by modern weather forecasting systems, a relatively small uncertainty budget size can be enough. In terms of solution efficiency, all the solutions are obtained within 5 iterations. Besides, the minimal solver time is only System States TABLE VII ES OPERATION PLANNING RESULTS Test No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Operation States, % of Rated Power ES 1 ES 2 ES 3 ES 4 0% −50% 0% −50% 0% −20% 0% −20% 60% −10% 10% −10% 0% −10% 10% −20% 20% −10% 0% −30% 20% −20% 0% −20% 60% 20% 40% −10% 60% 20% 30% −10% 0% −50% 0% −50% 0% 0% 0% 0% 40% 0% 40% −50% 40% 0% 0% 0% 0% 0% 0% −50% 0% 0% 0% 0% 10% 0% 0% −10% 100% 0% 50% 0% Iteration Solution Time (s) 4 3 3 3 4 2 3 2 3 3 4 4 3 3 5 3 21.82 11.72 10.22 13.34 26.13 23.47 10.35 1.87 3.54 3.39 8.87 8.47 9.01 3.49 24.22 2.97 7.01 seconds, the maximal one is only 61.39 seconds and the average one is 21.43 seconds, which is feasible for the hourahead optimization. In practice, for extra larger systems, more powerful solvers can be used to further speed up the solution process. C. Comprehensive Tests To comprehensively examine the proposed methodology, a range of different load/ES/RES system states are tested here. These system states make up 16 tests and they are shown in Table VI. For the uncertainty sets of robust optimization, 0.9 and 1.1 are set as the lower and upper budget bounds for the wind turbine output, while 0.95 and 1.05 are for PV output. Table VII demonstrates the robust optimization solutions of the proposed microgrid operation for all the 16 tests. For the ES operation states, negative values stand for discharging power Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. ZHANG et al.: ROBUST OPERATION OF MICROGRIDS VIA TWO-STAGE COORDINATED ENERGY STORAGE AND DIRECT LOAD CONTROL and positive values for charging power during the planned hour. It is seen that for the high wind turbine and PV output tests (1, 5, 9 and 13), some ES units are planned to be charged since the power supply is greater than the load demands. It can also be noticed that during the off-peak period, more energy is charged into the ES units with the adequate power supply, from the Tests 9 and 13. The results of Tests 11 and 15 show that although the PV outputs are low, the ES units are charged as well due to sufficient power supply generated by the wind turbines to the only half demands. Besides, when the wind turbine output levels are low (Tests 2, 4, 6, 8, 12 and 16), some ES units are planned to be discharged, for the wind turbines are main distributed generators in the microgrid and the power supply is insufficient. For Tests 10 and 14, No.1 ES is discharged but NO.2 ES is charged, because the power unbalance conditions in the areas around Buses 6 and 18 are quite different. To keep all the voltages within the allowed range, these two ES are operated differently. Last but not least, it is noted that for Tests 3 and 7, the ES units are not to be operated, since the power is almost balanced and the unbalance for some certain periods can be solved by the DLC and the power flow from the main grid. Furthermore, the iteration number and the solution time are shown in Table VII as well. The average time is 11.43 seconds, which again demonstrates the high solution efficiency of the algorithm. VI. CONCLUSION This paper developed a novel approach to plan a cooperation of ES and DLC in microgrids by applying a TSRO with consideration of uncertain renewable energy. In the proposed microgrid operation strategy, the ES states are optimized to charge or discharge power an hour ahead in the first stage operation and an assistant quarter-of-hour-ahead DLC is applied in the second stage to make power balanced and profits maximum. The optimization objective is to maximize the microgrid profits on the revenues from the customers after covering the O&M costs of ES units, wind turbines and PVs and the transaction with the main grid. The TSRO is solved by C&CG algorithm with the polyhedral uncertainty sets. In the robust optimization, the uncertain nature of the wind and solar power is fully involved through the uncertainty sets and the worst cases given by the uncertain variables are generated and used to make the final solution robust for all the uncertain conditions. The proposed planning methodology is verified on a 33-bus microgrid network with different specific tests and the characteristics of the uncertainty budgets are analyzed. The tests results indicate the good robustness and efficiency of the two-stage coordinated microgrid operation strategy. It is concluded that the proposed two-stage ES and DLC coordination strategy is suitable for practical microgrid operation planning. REFERENCES [1] P. Denholm, E. Ela, B. Kirby, and M. Milligan, “The role of energy storage with renewable electricity generation,” Nat. Renew. Energy Lab., Golden, CO, USA, NREL Rep. TP-6A2-47187, 2010. [2] A. Nasiri, “Integrating energy storage with renewable energy systems,” in Proc. 34th Annu. Conf. IEEE Ind. Electron., 2008, pp. 17–18. 2867 [3] P. Poonpun and W. T. Jewell, “Analysis of the cost per kilowatt hour to store electricity,” IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 529– 534, Jun. 2008. [4] S.-H. Jang, J.-B. Park, J. H. Roh, S.-Y. Son, and K. Y. Lee, “Short-term resource scheduling for power systems with energy storage systems,” in Proc. IEEE Power & Energy Soc. General Meeting, 2012, pp. 1–7. [5] S. 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Wong, “Probabilistic forecasting of wind power generation using extreme learning machine,” IEEE Trans. Power Syst., vol. 29, no. 3, pp. 1033–1044, May 2014. [25] B. Zeng and L. Zhao, “Solving two-stage robust optimization problems using a column-and-constraint generation method,” Oper. Res. Lett., vol. 41, pp. 457–461, 2013. [26] T. Achterberg, “SCIP: Solving constraint integer programs,” Math. Program. Comput., vol. 1, pp. 1–41, 2009. Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply. 2868 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 32, NO. 4, JULY 2017 [27] B. Venkatesh, R. Ranjan, and H. Gooi, “Optimal reconfiguration of radial distribution systems to maximize loadability,” IEEE Trans. Power Syst., vol. 19, no. 1, pp. 260–266, Feb. 2004. [28] C. Zhang, Y. Xu, Z.Y. Dong, and J. Ma, “A composite sensitivity factor based method for networked distributed generation planning,” in Proc. 19th Power Syst. Comput. Conf., Jun. 2016, pp. 1–7. [29] J. Löfberg, “YALMIP: A toolbox for modeling and optimization in MATLAB,” in Proc. IEEE Int. Symp. Comput. Aided Control Syst. Des., 2004, pp. 284–289. Cuo Zhang (S’15) received the B.E. (Hons.) degree in electrical (power) engineering in 2014 from the University of Sydney, Sydney, Australia, where he is currently working toward the Ph.D. degree in electrical engineering. His current research interests include power system planning and operation, voltage stability and control, smart grids, renewable energy systems, and applications of optimization theory in these areas. He received the 2014 University Medal, the 2013 University Academic Merit Prize from the University of Sydney, and the 2015 Top Final Year Student Award from Engineers Australia. Yan Xu (S’10–M’13) received the B.E. and M.E degrees from South China University of Technology, Guangzhou, China in 2008 and 2011, respectively, and the Ph.D. degree from The University of Newcastle, Australia, in 2013. He is now a Nanyang Assistant Professor at the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore. His research interests include power system stability and control, power system optimization, microgrid, and smart grid data-analytics. Zhao Yang Dong (M’99–SM’06–F’17) received the Ph.D. degree from the University of Sydney, Australia in 1999. He is with the University of NSW. His immediate role is Professor and Head of the School of Electrical and Information Engineering in the University of Sydney. He is also with China Southern Power Grid Electric Power Research Institute. He was previously Ausgrid Chair and Director of the Centre for Intelligent Electricity Networks, the University of Newcastle, Australia. He also worked with Transend Networks (now TASNetworks), Australia. His research interest includes Smart Grid, power system planning, power system security, renewable energy systems, electricity market, and computational intelligence and its application in power engineering. He is an editor of the IEEE TRANSACTIONS ON SMART GRID, IEEE PES LETTERS, and IET Renewable Power Generation. Prof. Dong is a Fellow of IEEE. Jin Ma (M’06) received the B.S. and M.S. degrees in electrical engineering from Zhejiang University, Hangzhou, China, the Ph.D. degree in electrical engineering from Tsinghua University, Beijing, China, in 1997, 2000, and 2004, respectively. From 2004 to 2013, he was a Faculty Member of the North China Electric Power University. Since September 2013, he has been with the School of Electrical and Information Engineering, University of Sydney, Sydney, NSW, Australia. His major research interests include load modeling, nonlinear control system, dynamic power system, and power system economics. He is the member of CIGRE W.G. C4.605 “Modeling and aggregation of loads in flexible power networks” and the corresponding member of CIGRE Joint Workgroup C4-C6/CIRED “Modeling and dynamic performance of inverter based generation in power system transmission and distribution studies.” He is a registered Chartered Engineer in the U.K. Authorized licensed use limited to: the Leddy Library at the University of Windsor. Downloaded on February 16,2022 at 01:09:51 UTC from IEEE Xplore. Restrictions apply.