A Scenario-Based Branch-And-Bound Approach for MES Scheduling in Urban Buildings Mainak Dan, Student Member, Seshadhri Srinivasan, Sr

A Scenario-based Branch-and-Bound Approach for MES Scheduling in Urban Buildings Mainak Dan, Student Member, Seshadhri Srinivasan, Sr. Member, Suresh Sundaram, Sr. Member, Arvind Easwaran, Sr. Member and Luigi Glielmo, Sr. Member

Abstract—This paper presents a novel solution technique for Storage Units scheduling multi-energy system (MES) in a commercial urban PESS Power input to the electrical storage [kW]; building to perform price-based demand response and reduce SoCESS State of charge of the electrical storage [kW h]; energy costs. The MES scheduling problem is formulated as a δ mixed integer nonlinear program (MINLP), a non-convex NP- ESS charging/discharging status of the electrical stor- hard problem with uncertainties due to renewable generation age; and demand. A model predictive control approach is used PTES Cooling energy input to the thermal storage [kW]; to handle the uncertainties and price variations. This in-turn SoCTES State of charge of the thermal storage [kW h]; requires solving a time-coupled multi-time step MINLP dur- δTES charging/discharging status of the thermal storage; ing each time-epoch which is computationally intensive. This T ◦C investigation proposes an approach called the Scenario-Based TES Temperature inside the TES [ ]; Branch-and-Bound (SB3), a light-weight solver to reduce the Chiller Bank computational complexity. It combines the simplicity of convex −1 programs with the ability of meta-heuristic techniques to handle m˙ C,j Cool water mass-flow rate of chiller j [kg h ]; complex nonlinear problems. The performance of the SB3 solver γC,j Binary ON-OFF status of chiller j; is validated in the Cleantech building, Singapore and the results PC Power consumed in the chiller bank [kW]; demonstrate that the proposed algorithm reduces energy cost by QC,j Thermal energy supplied by chiller j [kW]; about 17.26% and 22.46% as against solving a multi-time step heuristic optimization model. Energy Demands Index Terms—Multi-Energy Systems (MES), Mixed Inte- PL Electrical load demand [kW]; ger Nonlinear Program (MINLP), Scenario-Based Branch-and- QL Thermal load demand [kW]; Bound (SB3). Parameters −2 ◦ −1 HL Coefficient of heat loss [W m C ]; ◦ Tin/out Inlet/Outlet temperature of the TES [ C]; NOMENCLATURE V Volume of the TES [m3]; A Cross-sectional area of the TES [m2]; Dispatchable Generators CGR Market energy cost [$/kWh]; ∆t Sampling time [h]; PG,i Power generated by the generator i [kW]; ηESS Electrical storage efficiency; δG,i Binary ON-OFF status of the generator i; −1 ηTES Thermal storage efficiency; RG,i Ramp-rate of the generator [kW h ]; Cρ Specific heat capacity of the water [kJ kg−1 ◦C−1]; Cogeneration Units ρ Density of the water [kg m−3]; k Sampling index; PGT Power generated by the gas-turbine [kW]; arXiv:2003.03750v1 [eess.SY] 8 Mar 2020 Np Time horizon; δGT Binary ON-OFF status of the gas-turbine; −1 RGT Ramp-rate of the gas-turbine [kW h ]; QAC Thermal output of the absorption chiller [kW]; I.INTRODUCTION HE multi-energy systems (MES) is an emerging concept Utility Grid and Renewable Energy T wherein different energy vectors (e.g., thermal, electrical, gas and co-generation units) optimally interact at various PGR Power bought from the grid [kW]; levels in smart grid environments [1]. It is increasingly being PR Power generated by the photo-voltaic panel [kW]; recognized that a well-coordinated scheduling of different Mainak Dan is with the Interdisciplinary Graduate Program, Nanyang energy systems can reduce the energy cost, increase overall Technological University, Singapore. e-mail: [email protected]. efficiency, mitigate peak-demand and guarantee reliable power Seshadhri Srinivasan is with Berkeley Education Alliance for Research in delivery [2]. Key challenge here lies in optimally integrating Singapore (BEARS). e-mail : [email protected]. Suresh Sundaram is with the Department of Aerospace Engineering, Indian different energy vectors and networks (e.g., thermal and elec- Institute of Science, Bangalore, India. e-mail : [email protected]. tric) [3]. However, the presence of tight coupling between mul- Arvind Easwaran is with the School of Computer Science and Engineering, tiple energy vectors, components’ complex behaviours (e.g., Nanyang Technological University, Singapore. e-mail : [email protected]. Luigi Glielmo is with the Department of Engineering, University of Sannio, nonlinear, switching, and time-coupled), and many degrees Benevento, Italy. e-mail:[email protected] of freedom make the optimal scheduling problem intricate. 2

The intermittent renewable generation and pulsating demand and more often when MPC approach is used, the optimal add a new dimension to the problem. Therefore, novel control solution is guaranteed from only relatively small-scale convex approaches are required for scheduling MES. MINLPs. Emerging multi-time step MINLPs in EMS with Optimization models, scheduling techniques, and control large number of continuous and binary decision variables as approaches are widely investigated problems in energy man- well as non-convex constraints represent a difficult challenge agement system (EMS) related to MES. The energy hub and finding a feasible solution is computationally challenging (EH) concept proposed in [4] is a widely adopted model for [31]. Consequently, efficient solvers with fast convergence rate studying MES energy exchanges. The optimization approaches for MINLP model based MPC are required. for solving such models in the literature are categorised as: This investigation designs a MPC for scheduling MES (i) mathematical programming [5], [6], (ii) meta-heuristic [7], devices to perform price-based demand response (PBDR) and (iii) stochastic programming [8] and (iv) hybrid approach [9]. reduce operating cost. The scheduling problem is formulated Mathematical models for MES scheduling include the mixed as a non-convex MINLP-MPC model. In order to solve the integer linear programming (MILP) [10]–[15], which inher- problem, a novel light-weight solution method called the ently fits the MES operating modes and is widely used tool due scenario-based branch-and-bound (SB3) is proposed. The SB3 to its ability to include switching actions. Oversimplification is hybrid MINLP solver that integrates convergence efficiency of nonlinear behaviours by incorporating linear relaxation and of convex mathematical programming as well as the exhaustive the lack of scalability with the number of integer constraints searching capability of meta-heuristic solver. The main con- are the two shortcomings of the MILP models. The nonlinear tributions of this study are: (i) proposition of a light-weight programs [16], [17] and mixed integer nonlinear models solver called the scenario-based branch-and-bound (SB3) for (MINLP) [18], [19] comprehensively capture the complex scheduling MES devices, (ii) investigations into the existence behaviours of the MES. However, due to the non-linearity and conditions of the lower bound solution of the SB3 algorithm, non-convexity [9], [20], the existing commercial solvers for and (iii) demonstration of the SB3 approach in a pilot building, MINLP require more computation resources, solution time, which is a community microgrid and is responsible for supply- and are sensitive to initial conditions [21]. ing energy to the neighbouring buildings and office spaces. In The meta-heuristic techniques are often used to solve non- order to understand the efficiency, performance of the SB3 convex MINLPs with single as well as multiple objectives. algorithm is compared with performance of other MINLP There are several existing literature which have proposed solvers. modifications of meta-heuristic techniques to improve the convergence rate while solving economic load dispatch problem of EMS [7], [22]–[25]. However, their performances in non- convex MINLPs are dependent upon the quality of the initial solutions (seeds). As a result, the meta-heuristic approaches usually have large computation times, thereby making them unsuitable for real-time operations [26]. More recently, hybrid approaches that combine mathematical programming and meta-heuristic techniques have been proposed [9]. Though combined methods provide a sub-optimal solution, they solve complex problems in reasonable time and have the potential to address the non-linearity encountered in dispatch problems of smart-grid environments with distributed multi-energy sources. Still the aforementioned works have not considered intermittent behaviours in their analysis. Figure 1: Multi-Energy Systems Architecture of Cleantech Building, Singapore Two widely used methods for handling intermittent behaviours are stochastic programming (SP) [8], [27], [28] and model predictive control (MPC) [12], [29]. Typically SP solves The paper is organized as follows. Section II presents the a set of scenarios envisaged due to fluctuating behaviours from MES component models and the optimization problem. Sec- normal conditions [8], [30]. This requires solving multiple tion III describes the proposed SB3 algorithm and its different instances of MINLP model that leads to scalability issues. The components. with a mathematical analysis. The results are MPC on the other hand solves multi-time step problem con- provided in Section IV and conclusions in Section V. sidering the underlying disturbances and encapsulating complex behaviours. This boils down to a complex optimization II.MESMODELAND PROBLEM FORMULATION models. In addition, implementing MPC requires specialized hardware with commercial solvers which are cost-intensive. The energy hub model of the MES studied in this inves- A review of the literature reveals that MINLP models capture tigation is shown in Fig. 1. The supply from utility is the the complex MES behaviours [18], [19] and MPC approach is input to source energy demand. In addition, the electrical more suited for handling uncertainties. Although commercial energy is supplied by two dispatchable generators (DG), one solvers are available for solving MINLP problems, constraints gas turbine (GT) embedded within co-generation unit (CGU), on computational resources and light-weight solvers that can and a photo-voltaic panel. Similarly, thermal energy demand be ported into EMS control hardware are very much in demand is served by the five chillers and one absorption chiller (AC) 3 that resides inside the CGU. Steam generated from GT water- inpk k jacket is used to source the AC through heat recovery and QAC = βGTPGT. (7) system generator. The EH also includes electrical storage inpk system (ESS) and thermal energy storage (TES) for handling Moreover, the QAC is related to the cooling energy supplied intermittent behaviours. by the chiller using the equation

k inpk k Q = COPACQ = COPACβGTP , (8) A. Generator Operating Constraints (DG) AC AC GT k where COPAC is the coefﬁcient of performance of the AC for Suppose that the state of the generator is denoted by δG,i up down the given thermal load at time-instant k. Further, the cooling and the minimum up/down time by TG,i and TG,i , i.e. the minimum time the unit should stay in a particular state before energy supplied by the AC is limited through the following toggling to the other state. Thus, the temporal constraints constraints: associated with the generator during each sampling time k k k k δ Q ≤ Q ≤ δ Q , (9) are modelled as [12] GT AC AC GT AC

where [Q , QAC] are the limits of the thermal energy pro- δk − δk−1 ≤ δ (τ up ), AC G,i G,i G,i G,i (1a) duced by the AC. k−1 k down δG,i − δG,i ≤ 1 − δG,i(τG,i ), (1b) where i ∈ {1, . . . , ng} is the index of the generator, ng is the up up C. Chiller Bank (CB) number of generators, τ = k+1,..., min(k+T −1,Np), G,i G,i In addition to the AC, there is a CB consisting of five and τ down = k +1,..., min(k +T down −1,N ), respectively. G,i G,i p chillers whose mass-flow rates are controlled using a super- Similarly, the generation limits and ramp-rate of the generators visory controller and the outlet temperature is maintained at are modelled as, a pre-defined set-point using closed-loop controls. Following k k k [32], the cooling energy supplied from the CB is given by δG,i P G,i ≤ PG,i ≤ δG,i P G,i (2a) k k−1 k k k |PG,i − PG,i | ≤ RG,i, ∀i (2b) QC,j = γC,j m˙ C,j Cρ∆TC, ∀j ∈ {1, . . . , nc}, (10) k where PG,i and RG,i are the power provided by the generator k th k where m˙ C,j is the mass-flow rate of the j chiller and γC,j and the ramp-rate limit of the generator i, and P G,i and P G,i th denotes the corresponding ON/OFF operation and ∆TC is denote lower and upper generation limits of the i generator. the temperature difference between the inlet and outlet of the The generation cost is given by [12] chiller. The electrical power consumed by CB is given by k k X QC,j ng P = . (11) k X k k 2 k C C P = δ A P + B P + C , COPC,j G,i G,i G,i G,i G,i G,i G,i (3) j∈{1,...,nc} i=1 In addition, the mass-flow is bounded by where AG,i, BG,i and CG,i are coefficients. k k k γC,j m˙ C,j ≤ m˙ C,j ≤ γC,j m˙ C,j , (12) B. Cogeneration Units (CGU) where m˙ C,j and m˙ C,j denote the lower and upper bound on the chiller mass-flow rates. Similar to the generator, the constraints associated with GT’s minimum up/down time are defined during each sampling time k as: D. Energy Exchanged with the Utility Grid k The power exchanged with the utility grid PGR is con- δk − δk−1 ≤ δ (τ up ) GT GT GT GT (4a) strained by lower (P GR) and upper bound (P GR) on the k−1 k down consumption given by δGT − δGT ≤ 1 − δGT(τGT ), (4b) k up up down − P GR ≤ PGR ≤ P GR. (13) where τGT = k + 1,..., min(k + TGT − 1,Np), and τGT = k +1,..., min(k +T down −1,N ), respectively. The physical The cost of power exchanged with the utility grid is time- GT p varying and and modelled as, bounds and the ramp-rate constraints are modelled as k k k CGR = CD + CRT, (14) k k k k k δGTP GT ≤ PGT ≤ δGTP GT (5a) where CD and CRT denote the day-ahead and real-time k k−1 demand-based price of energy respectively at time instant k. |PGT − PGT | ≤ RGT, (5b) k where PGT is the power generated by the gas-turbine and RGT models the ramp-rate constraint. In addition, [P GT, P GT] E. Thermal Energy Storage (TES) denotes the generation limits of the gas-turbine whose cost Following [33], the TES temperature dynamics is is given by nc ! k+1 µ X k k k k k HLA TTES = m˙ C,j γC,j Tin − TTES + TTES 1 − 2 V ρ V ρCρ k k k k j=1 C P = δ AGTP + BGTP + CGT , (6) GT GT GT GT HLA where AGT,BGT and CGT are coefficients. To increase + Tamb , (15) energy efficiency, the heat recovered by the water jacket of V ρCρ k the GT is used to feed the absorption chiller along with boiler. T TES ≤ TTES ≤ T TES , k k k Considering that the heat energy provided by the GT depends where, Tin,TTES and Tamb denote the inlet temperature of linearly on the power generated, we have the TES, inlet temperature and the ambient temperature in ◦C. 4

0 < µ < 1 deﬁnes the fraction of chilled water shared between H. Renewable Energy Source (RES) CB and TES. The energy stored in the TES is modelled as The uncertain renewable generation due to the photo-voltaic k k+1 k k c +k panels is given by P , which is directly fed into the model SoC = SoCTES + δTESηTESP ∆t (16a) R TES TES from the renewable energy sources present in the system. k 1 −k + (1 − δTES) d PTES∆t + HLA∆T, ηTES SoC ≤ SoCk ≤ SoC , (16b) TES TES TES I. Load Balance Constraints k +/−k where SoCTES and PTES denote the thermal storage, the k k The MES has to meet the electrical (PL ) and thermal (QL) power exchanged (charging/ discharging) with the TES, re- loads; the balance constraints at a given time instant k are spectively, and ∆T is the difference between the ambient and ng k k X k k k k k k k +k the TES’s internal temperature. The binary variable δTES mod- PL = δG,iPG,i + δGTPGT + PR + PGR − δESSPESS c d els the charging/discharging operations and 0 < ηTES, ηTES < i=1 1. The storage power is also constrained by the physical limits k −k k k − (1 − δESS)PESS − PC − PAC, (23a) of the TES which is given by nc k X k k k −k k +k QL = QC,j + QAC − (1 − δTES)PTES − δTESPTES (23b) k k k − (1 − δTES) P TES ≤ PTES ≤ δTES P TES, (17) j=1 where [P TES, P TES] denote the limits on PTES. J. Cost Function F. Electrical Storage Systems (ESS) The objective is to reduce the energy costs and peak-demand The state-of-charge (SoC) of the ESS is modelled as [29]: by scheduling the different energy vectors so as to minimize

n k+1 k k c +k g SoCESS = SoCESS + δESSηESSPESS∆t k X k k k k k J = C(PG,i) + C(PGT) + CGRPGR + C(PESS). (24) 1 k k − k i=1 + (1 − δESS) d PESS∆t − ηlossSoCESS (18a) ηESS k SoCESS ≤ SoCESS ≤ SoCESS, (18b) k +/−k K. MPC Optimization Model where SoCESS is state of charge, PESS is the power ex- k changed with storage (charging/ discharging) and δESS the Considering a prediction horizon Np, the MES scheduling binary variable indicating the charging operation and 0 < problem can be deﬁned on the decision vector over the time c d k,Np k+1 k+Np ηESS, ηESS, ηloss < 1. There exist an upper bound (P ESS) and horizon {k + 1, . . . , k + Np} as u = [u ,..., u ] k lower bound (P ESS) on the PESS so that with

k k k k k k k k k k k k − (1 − δ ) P ≤ P ≤ δ P ESS. (19) ESS ESS ESS ESS u = [PG,i,...,PG,ng ,PGT,QAC, m˙ C,1,..., m˙ C,nc ,PESS,PTES, P k , δk , . . . , δk , δk , δk , δk , γk , . . . , γk ]. (25) In addition, an ESS cost has been considered based on the GR G,1 G,ng GT ESS TES C,1 C,nc k k k k charging-discharging cycle to understand the effect of storage s = [TTES, SoCESS, SoCTES] denotes the state variables of degradation in scheduling MES [34], the system. The MPC optimization model for time-epoch k is given by k +k k −k ! k+Np k cESS δESSPESS (1 − δESS)PESS X k C(PESS) = + − − , M : min J 2n × capESS uk,Np τESS τESS k=k+1 (20) +/− s. t. constraints (1), (2), (4), (5), (8), (9), (10) − (12), (15), where, τESS is the average number of time instants for (16), (17), (21), (18a), (19), (23); charging/discharging, n is the average number of charging- k k k k k discharging cycles before ESS reaches to its end of life, Binary constraints δG,i, δGT, δESS, δTES, γC,j ∈ B, ∀k ∈ {k + 1, .., k + Np}. (26) capESS is the capacity and cESS is the purchase as well as installation cost of the ESS. Eqn. (26) implementing the MPC aims to obtain a control approach to perform PBDR by scheduling MES devices with ﬂuctuating renewable generation, demand and energy prices. G. Energy Exchanged with the Utility Grid The MINLP-MPC optimization problem M possesses non- k The power exchanged with the utility grid PGR is con- convexity, which needs to be solved over a prediction horizon strained by lower (P GR) and upper bound (P GR) on the with ramp rate constraints of the generation units (2b) and consumption given by (5b) and time-coupled bilinear storage dynamics (15). Thus, k − P GR ≤ PGR ≤ P GR. (21) solving the problem directly with existing MINLP solvers such The cost of power exchanged with the utility grid is time- as BARON, Counene and other meta-heuristic algorithms is varying and and modelled as, computationally intensive, which makes their adoption in a k k k CGR = CD + CRT, (22) real-time EMS challenging [21], [31]. Also, heuristic solvers k k where CD and CRT denote the day-ahead and real-time are only suitable for off-line computations due to their slow demand-based price of energy respectively at time instant k. convergence. 5

III.THE PROPOSED SB3 ALGORITHM (ii) Convex Relaxation:: The main challenge in the MINLP The proposed light-weight solver, Scenario-based Branch- problem is the nonlinear constraints that needs to be relaxed and-Bound (SB3), illustrated in Fig. 2 aims to address the without oversimplifying the analysis. The most restrictive aforementioned challenges. Widely used approaches to solve constraints are the bilinear one in eqn. (15) and ramp rate the MINLP are the generalized Benders decomposition, the constraints in eqn. (2b) and (5b). Usual approaches such as outer approximation, the generalized outer approximation, and SQP or a MILP formulation based on big-M method have the extended cutting plane approach [35]. These methods been used [12]. We use a polyhedral over approximation to linearize the MINLP by pivoting the binary constraints that simplify the bilinear dynamics as a box constraint. In order leads to a sequential quadratic programming (SQP) or MILP to replace the bilinear term, we consider an auxiliary variable k k k k k formulation. In contrary, the proposed algorithm is accumula- ξj such that γC,j = 1 ⇔ ξj =m ˙ C,j TTES. The modiﬁed TES tion of the following idea: dynamics are given by:

(i) to fix the valid binary decision variables to prior values N ! c ξk m˙ k T k with a priori knowledge and provide a set of scenarios k+1 X j C,j in k UA TTES = − µ + +TTES(1− )+φ (27) V ρ V ρ V ρCρ by partially partitioning into a set of NLP sub-problems, j=1 followed by convex relaxation of the NLP sub-problems k k k k UA where γ = 1 ⇔ ξ =m ˙ T and φ = Tamb . Then C,j j C,j TES V ρCρ into a set of quadratic programming (QP) sub-problems the following constraints, also known as McCormick envelopes over a prediction horizon as shown in Fig. 2, k defined on ξj turns the problem with a bilinear term into a (ii) to use the resulting schedules from the scenario block convex relaxed one: as initial seeds to hot-start the MINLP solver, an improved real-coded genetic algorithm (iRCGA) to obtain k k k k k k k ξj ≥ m˙ C,j TTES + T TESm˙ C,j − T TESm˙ C,j , (28a) scheduling for the first-time instant. k k ξk ≤ m˙ k T k + T m˙ k − T m˙ k , (28b) The approach leads to a hierarchical problem with less compu- j C,j TES TES C,j TES C,j k k k k k k k tational complexity. The proposed algorithm is proposed with a ξj ≥ m˙ C,j TTES + T TESm˙ C,j − T TESm˙ C,j , (28c) motivation to find reasonable acceptable sub-optimal solution k k k k k k k ξj ≤ m˙ C,j TTES + T m˙ C,j − T m˙ C,j . (28d) with a lower computational time. This section describes the TES TES steps of the SB3 algorithm. McCormick envelopes provide a computationally fast convex relaxation of the bilinear terms compared to other existing methods. Similarly, using the epigraph technique, the ramp rate constraints are modelled as:

k k−1 k PG,i − PG,i − RG,i ≤ εG,i, (29a) k k−1 k PG,i − PG,i − RG,i ≥ εG,i, (29b) k k−1 k PGT − PGT − RGT ≤ εGT, (29c) k k−1 k PGT − PGT − RGT ≥ εGT. (29d) k k where, εG,i, εGT ≥ 0. The introduction of the constraints (28), linear TES dynamics (27) and (29) makes the non-convex NLP to have only linear constraints. Figure 2: Schematic diagram of SB3 algorithm Definition 3: A Scenario P(b`) is convex relaxation of the NLP obtained by pivoting the binary variables to a valid string b` followed by the relaxation of the non-linear constraints A. STEP 1: Scenario Generation and Branch-and-Bound - using Eqns. (28) and (29). Seeds for MINLP Solver The set of convex QP sub-problems by pivoting the binary n The importance of this step is to provide initial seeds to decision variable to a valid binary string b` ∈ B b and convex hot-start the iRCGA MINLP solver, which is intrinsically a relaxation is given by, population-based direct-search algorithm. The master problem k+Np ng ! M is divided into a set of convex QP problems by performing X k X k k P(b`) : min J + λ1 εG,i + λ2εGT (30) two operations sequenttially: (i) NLP partitioning and (ii) k,Np ub k=k+1 i=1 convex relaxation as discussed below. ` s. t. constraints (1), (2a), (29a), (29b), (4), (29c), (29d), (5a), (8), (i) NLP Partitioning: Partitioning is an efficient technique for handling the combinatorial complexity of the problem. We (9), (10) − (12), (23), (16), (17), (27), (28), (18a), (19), (21), k k k k k define the following: Binary constraints δG,i, δGT, δESS, δTES, γC,j ∈ b` Definition 1: A partial partition of the M is a set of Ns ∀k ∈ {k + 1, . . . , k + Np} NLP sub-problems with Ns ≤ Nq for which the definition where, λ1 and λ2 are penalty factors. Epigraph terms in of partition holds. objective function in P(b`) of eqn. (30) takes care of the Definition 2: A valid binary string b` from the partial partition error introduced due to convex relaxation of the ramp-rate is the binary decision with l0-norm kb`k0 ≤ nb, for which the constraints. The problem P(b`) of eqn. (30) can be solved by combinatorial constraints in M are satisfied. nb is the total general QP solvers efficiently to find initial seeds for iRCGA number of binary decision variables in M. solver. 6

1) Branch-and-Bound (B2) for Scenario Generation: The and mutation (e.g., simple, heuristic, and arithmetic crossover binary decision variables that ensures feasibility plus optimal- etc., and binary mutation, Gaussian mutation etc. respectively) ity from step III-B of previous instant’s scheduling problem (Ref. supplementary material for detail discussion). As the is given as the input to the B2 step. The B2 expands each number of feasible scenarios are large in number, solving node of the tree by pivoting the binary variables considering the problem using mathematical optimization techniques for only the temporal constraints. The purpose of expanding the each of the initial seed is computationally intensive. In these branches of the tree based on the binary temporal variables circumstances, population based direct searching ability of is to provide a feasible scenario over the prediction horizon. meta-heuristic techniques from a small set of initial seeds are At the leaf nodes, the convex MPC problems of eqn. (30) more efficient to find the solution of the MINLP problem. generated after pivoting and relaxation are solved. The B2 RCGA over GA is selected as it does not need phenotype procedure in association with QP keeps track of feasibility to genotype conversion and hence it converges faster. Due of the scenarios in terms of temporal, operating, physical as to natural representation, one can achieve high precision and well as equality constraints for the current prediction horizon. easy to integrate constraints in string representation. String A scenario is considered to be infeasible if there exist no length used in RCGA is small and computationally faster [26], solution of the QP problem at the leaf nodes and subsequently [36]. The availability of multiple initial seeds provide iRCGA the corresponding scenario is pruned. The procedure repeats to search exhaustively through the search-space. Typically, in until a user-defined maximum number of feasible scenarios are RCGA, different crossover and mutation techniques are widely obtained. The solution of MPC from each unpruned branch used for generating off-spring vectors and for preserving acts as initial seed to hot-start MINLP solver which solves M diversity. Practice shows that selection of the crossover and only for the current time-instant. The following example is mutation is problem dependent [36]. Therefore, in order to used to illustrate the working principle of the aforementioned enhance the performance of conventional RCGA, we use an B2 process. adaptive selection technique that increases RCGA’s capability to tackle both continuous and integer variables simultaneously, without any relaxation. The selection of crossover and mutation techniques on basis of objective function value guides the algorithm towards faster convergence than using a particular crossover and mutation. We call the RCGA with multiple genetic operators selected using an adaptive selection technique as iRCGA. The detail of iRCGA algorithm can be found in the supplementary material for readers’ understanding. iRCGA is a population based direct search MINLP solver. In our approach, iRCGA solves a single instant MINLP instead of a multi-time step MPC problem. The solution of iRCGA, thus found, can lead to binary variables of incompatible temporal constraints over the prediction horizon considered Figure 3: Illustration of B2 step in SB3 algorithm for scenario earlier in section III-A. The feasibility verification step of generation the proposed SB3 algorithm ensures that the solution found from iRCGA has temporal constraint compatibility over the Illustrative example: Let us consider a 2 DG and 1 GT system prediction horizon. Although feasibility verification follows up up up similar approach of section III-A, it tries to check existence of with Np = 1 in which, TG,1 = 2,TG,2 = 2,TGT = 2 and down down down a single scenario, which produces a feasible QP solution over TG,1 = 2,TG,2 = 2,TGT = 2. The solution from the previous instant is considered as (x∗, b∗), where b∗ = [1 1 0] the prediction horizon instead of finding a set of scenarios. up up It is to be noted that it only verifies the existence of feasible with recorded consecutive ON-OFF time as τG,1 = 2, τG,2 = down binary variables and the existence of such scenario does not 1, τGT = 1. In Fig, 3, the branches define the feasibility of the binary variables subject to the temporal constraints of the necessarily guarantee the existence of MINLP solution over system only. However the existence of the solution of the QP the prediction horizon. If temporal constraint feasibility is problems after convex relaxation decides the feasible scenario. achieved, the solution from iRCGA is implemented at that time-instant. In case of failure, the iRCGA is iterated again The branch associated with the binary variables b1 is pruned as it does not converge to a feasible solution. The solutions for an alternative solution. associated with the branches b2, b3 and b4 act as initial seeds for the MINLP solver. C. Lower Bound Estimation of the SB3 Algorithm This two stage decision problem requires QP to provide B. STEP 2: Solution of the MINLP solver with Feasibility good initial conditions for the MINLP solver. The following Verification theorem provides the conditions under which the QP is able To solve the MINLP, we propose a novel improved real- to produce lower bound solution (LBS) to M. coded genetic algorithm (iRCGA), a meta-heuristic optimiza- Notation: We define single instances of M and P(b`) at time tion method which extends the capability of RCGA by pro- instant k as Mk and Pk. To simplify our analysis, we use the viding adaptive selection for the genetic operators– crossover following notations: f(·) denotes the objective function, the set 7 of inequality constraints of Mk are denoted by the function M k P P∗ ∗ P g and those of P by g . The real decision variables kx − x k2 ≤ Ω, ν ≤ Ω˜ν , kdk2 ≤ Ω˜d. mc are denoted by x ∈ X ⊆ R with mc is the number of n ˜ ˜ ˜ real variables and the binary variables by b ∈ B b . Without Considering Ω = max{Ωd, Ων }, from the necessary condi- P∗ P∗ P∗ loss of generality, the equality constraints are replaced with tions of optimality for the KKT point (x , b ), λ with ∗ corresponding appropriate inequality constraints for ease of dual solution being λP , we have the analysis. ∗ ∗ ∗ ∗ ∗ P P X P P P Theorem 1. Suppose ηM is the optimal solution of Mk and ∇f(x , b ) + B d + λj ∇gj (x , b ) = 0, P∗ k ∗ j η is the LBS for a given set of scenarios Ns with P (b ) be- ∗ ∗ ∗ ∗ ∗ P P X P P P ing the corresponding scenario. Then ηP is a LBS to Mk if =⇒ k∇f(x , b ) + λj ∇gj (x , b )k2 ≤ kBk2kdk2 Mk allows a convex continuous SQP relaxation with optimal j ∗ ∗ ˜ solution with xP , bP and there exists Ω ≥ 0 such that ≤ MB Ω (35) the following condition holds: where kBk2 ≤ MB is the bound on the Hessian. Considering the primal feasibility condition, Ω ≥ max{MB Ω,˜ (1 + M∇g)Ω,˜ (1 + M∇g)MλΩ˜}, ∗ ∗ P P P P ∗ ∗ ∗ ∗ where kBk2 ≤ MB , k∇gj (X , b )k2 ≤ M∇g, |λj | ≤ P P P P P P T P gj (x , b ) + ∇gj (x , b ) d ≤ ν Mλ, ∀j ∈ {1, ...nc}. P P∗ P∗ P P∗ P∗ T P =⇒ gj (x , b ) ≤ −∇gj (x , b ) d + ν ∗ P P P∗ P∗ P P∗ P∗ P Proof: Let η be the LBS obtained by solving the dual of =⇒ kgj (x , b )k2 ≤ k∇gj (x , b )k2kdk2 + ν k P (b`) computed as, ˜ ≤ Ω(1 + M∇g) (36) P∗ T P η ≤ inf max min f(x, b`) + λ g (x, b`) P `∈Ns λ x∈X From dual feasibility condition, λj ≥ 0, ∀j holds. Considering (31) the complimentary slackness condition, we have and [x∗, b∗] and λ∗ denote the corresponding primal solu- ∗ ∗ ∗ ∗ tion and Lagrange multipliers of the inequality and equality λP gP (xP , bP ) + λP ∇gP (xP , bP )Td = λP νP constraints, respectively. The Lagrangian of Mk is given by j j j j j P P P∗ P∗ P P P∗ P∗ T P P =⇒ λj gj (x , b ) = −λj ∇gj (x , b ) d + λj ν M T M L = f(x, b) + λ g (x, b). (32) P P∗ P∗ P P P P∗ P∗ =⇒ kλj gj (x , b )k2 ≤ kλj k2 kν k2 + k∇gj (x , b )k2kdk2 Let us consider that ˜x denotes the solution obtained by fixing ≤ (1 + M∇g)MλΩ˜ (37) the binary variable to b` in (32) from the scenario set {b`, ` = 1,...,Ns} and the corresponding solution is an upper bound Thus the SQP relaxation in (34) produces a close proximal to the problem Mk with objective value as η˜ [35]. Thus, solution of (33) to an accuracy Ω such that the following necessary conditions holds, M∗ T M η ≤ inf max min f(x, b`) + λ g (x, b`) ≤ η,˜ `∈Ns λ x∈X (33) Ω ≥ max{M Ω,˜ (1 + M )Ω,˜ (1 + M )M Ω˜} (38) ∗ B ∇g ∇g λ where, ηM is the optimal solution of Mk. Defining d = P∗ M∗ [dc | db] = [x − ˜x | b − b`], the trust-region continuous with η ≤ η ≤ η˜. (38) provides a lower bound accuracy SQP approximation [37] of Mk around [˜x, b`] with convex measurement to the optimality of the problem. The low value relaxation is given by, of Ω indicates the possibility of improving optimality of the solution. ♦ T 1 T P k min ∇f(˜x, b`) d + d Bd + σν The Corollary 1 relates KKT points of SQP and P . d,νP 2 P P T P s. t. g (˜x, b`) + ∇g (˜x, b`) d ≤ ν 1 (34) Corollary 1. For sufficiently large value of the penalty factor kdk∞ ≤ ∆, x + dc ∈ X , b + db ∈ {b`, ` = 1,...,Ns} k σ and for some b = b`, the KKT points of P coincides with where σ is a positive penalty term and νP = that of the SQP relaxed problem with d = 0 and νP = 0, P P T P max 0, kg (˜x, b`) + ∇g (˜x, b`) dk∞ . B is the quassi- where d is distance measurement in SQP formulation and ν Newton approximaion of the hessian of the Lagrangian. The is the penalty factor for constraint violation. solution from (34) provides a LBS to (32) due to convex continuous relaxation. The SQP formulation allows for Proof: The KKT conditions of Pk at the optimal solution point handling the infeasible constraints including the temporal are given by constraints as well as temporal search subspace. After a ∗ ∗ X ∗ P ∗ ∗ P ∗ ∗ certain number of iterations, it provides a solution denoted by ∇f(x , b ) + λ ∇g (x , b ) = 0, g (x , b ) ≤ 0 P∗ P∗ ∗ ∗ j j j x , b which is closer to (x , b ) by construction [37]. j It is to be mentioned that pivoting the binary variable to ∗ ∗ P ∗ ∗ λj ≥ 0, λj gj (x , b ) = 0, ∀j. (39) a particular value of binary variables produces a convex continuous optimization problem of (33). We define the Similarly, the KKT conditions of the SQP after a finite following number of iteration (iter) are given by 8

Table II: Comparison of price-based demand response (PBDR) Piter Piter iter iter X Piter P Piter Piter performance ∇f(x , b ) + B d + λj ∇gj (x , b ) = 0 j Control approach without storage with storage iter X Piter Heuristic 19.57 10.46 σ = λj BB-MINLP 76.06 92.58 j SB3-MPC 82.37 96.78 P Piter Piter P Piter Piter T iter Piter gj (x , b ) + ∇gj (x , b ) d ≤ ν 1 solves the MINLP problem M for multiple time-steps (pre- Piter Piter Piter Piter Piter T iter λj g(x , b ) + ∇g(x , b ) d = 0 diction horizon) with receding horizon approach, (ii) branch- Piter and-bound MINLP (BB-MINLP) with MPC, (iii) SB3 based λj ≥ 0, ∀j (40) iter MPC: it is the feedback control law computed in receding Now using the conditions that diter = 0, νP = 0 and and iter + horizon manner solving the MINLP problem using the SB3 σ ∈ R in (39), we can rewrite the KKT conditions as, approach assuming accurate forecasts on renewable generation

Piter Piter X Piter P Piter Piter and demand, i.e., less than 2% error, (iv) SB3 based MPC with ∇f(x , b ) + λj ∇gj (x , b ) = 0 forecast errors: it is the 24 hour feedback control law obtained j by solving the MES scheduling problem using SB3 but with iter X Piter P Piter Piter σ = λj , gj (x , b ) ≤ 0 forecast errors of 2% and 10% to study the robustness, and j (v) performance of SB3 based MPC without (case 1) and with Piter Piter Piter Piter λj g(x , b ) = 0, λj ≥ 0, ∀j (41) (case 2) energy storage components. In addition, the sensitivity iter Thus using (38), for diter = 0, νP = 0 and and of the proposed SB3 algorithm is also analysed by varying the iter ∗ σiter ∈ R+, Ω ≥ 0. Thus, ∃ bP = bP , at which the maximum number of scenarios during optimization. In our study, a sampling time of 0.5 h with 10 h prediction KKT conditions of both QP and SQP approaches coincide. ♦ horizon and 24 h control horizon is selected. Further, the renewable energy source is non-dispatchable and the peak- IV. RESULTS demand period is from 10 AM (10:00 h) to 5.00 PM (17:00 h) computed from daily load-curve as shown in supplementary Table I: Rating of different MES components material. The user-deﬁned number of scenarios is kept at 20 for all the simulations to keep the simulation time tractable. Component Rating Constraints The heuristic optimization is considered with multi-time step PV Panel 165 kW 2 units and Non-dispatchable receding horizon approach however, its large computational Electrical Storage 300 kW h SoC: 30-90%, P = [−30, 200] kW s time hinders its implementation in real-time systems [9], [26]. Generator Units 1.2 MW 2 units, P = 400, P = 1200 kW g g Note on forecasting: Implementing MPC for scheduling Gas turbine 1 MW P = 250 - P = 1000 kW GT GT MES components requires forecasts on renewable generation Thermal Vector 5400 RT 5 chillers, CoP = [2.8-3.3] and demand. Meta-Cognitive Fuzzy Inference System (McFIS) Absorption chiller 350 RT Q = 200, Q = 350 RT AC AC is a neuro-fuzzy inference approach, which is based on an TES 2000 RTh SoC = [100, 7000] kW h, T adaptive sequential learning algorithm that starts approximat- P =[-1000, 3000] kW T ing a non-linear function with zero fuzzy rule and develops the necessary number of fuzzy rules depending upon the information contained in the training samples (historical forecasting data). A detailed analysis of the forecasting methodology using McFIS can be found in [38].

A. Demand Response The PBDR based scheduling of MES heuristic optimization (RCGA), BB-MINLP and the SB3 approach is studied. Fig. 4 (a) shows the normalized energy price for 24 h which are high during peak-periods i.e., 10 AM (10:00 hr) to 5.00 PM (17:00 hr). It can be observed in Fig. 4(b) and 4(c) as well as in Tab. II that during peak-hours the SB3 based MPC reduces energy utilization from utility grid by 82.37% and 96.78% in case study 1 and 2, respectively. Whereas, heuristic method Figure 4: Demand response performance: SB3 v. heuristic– reduces only 19.57% and 10.46%, respectively as a result of (a) electricity tariff, (b) case study 1: without storage unit, (c) pre-mature termination and BB-MINLP reduces 76.06% and case study 2: with storage unit 92.58%, respectively. Thus SB3-MPC provides a promising improvement in demand response with respect to the heuristic The PBDR performance of the proposed SB3 is illustrated algorithm as well as the BB-MINLP. on the CleanTech building, Singapore whose MES architecture is shown in Fig. 1. The ratings and operating limits of the B. Storage Management and Cost-efﬁcient MES Scheduling MES components are shown in Tab. I. The following control Flexibility provided by storage devices can be used to strategies are compared: (i) heuristic optimization: The RCGA augment capacity and deal with uncertain elements more 9

Figure 5: (a) ESS and (b) TES management Figure 8: Electrical sources scheduling: case study 2 - with storage unit

Figure 9: Chiller bank scheduling: case study 2 - with storage unit local energy source utilization increased during peak-periods Figure 6: Electrical sources scheduling: case study 1 - without as shown in Fig. 6(c) and Fig. 8(c) compared to heuristic algo- storage unit rithm in Fig. 6(a) and Fig. 8(a). A close inspection reveals that the CB is used more during the lower price periods; whereas, effectively. The case-study considered has both electrical and its usage reduces during high price periods, as depicted in thermal storage, the variations in SoC of the thermal and Fig. 7 and Fig. 9. Similarly, CGU is used more during high- electrical storage are shown in Fig. 5. It can be verified price periods compared to other local generation units due to that the SB3 based MPC increases the SoC of the storage its ability to supply electrical and thermal energy simultane- devices during off-peak load periods when the price is low and ously. As a result, the SB3-MPC provides 17.26% and 22.46% discharges it during peak-demand periods. As against this, the cost-efficient scheduling as against heuristic optimization in heuristic control and BB-MINLP both under utilize the storage case study 1 and 2, respectively. BB-MINLP also utilizes local units during peak-price hours. BB-MINLP restricts the use of energy sources more during peak-price hours as shown in the storage units due to presence of storage degradation costs. Fig. 6(b) and Fig. 8(b). Due to under-utilization of the storage A poor demand response performance of heuristic algorithm units by BB-MINLP in presence of degradation costs reduces as well as its incapability of scheduling the local generation the overall cost. The cost-efficiency of BB-MINLP is found units during peak-price hours have been caused due to its pre- to be 2% more than the proposed SB3-MPC approach with mature simulation termination at maximum iteration. storage unit. However, it can be verified from Fig !6 that during The MES component schedules are shown in Fig. 6, 7 low price hours BB-MINLP is unable to utilize the utility grid without storage units and in Fig. 8, 9 with storage units. The at its maximum potential. As a consequence, SB3 achieves 3% SB3-based MPC schedules local energy sources strategically more cost-effectiveness over BB-MINLP in absence of storage depending on the price vector to minimize the cost. Further, units.

C. Robustness, Sensitivity Analysis To study the MPC’s robustness, forecast errors of 2% and 10% was introduced. Our study, as recorded in Tab. III, revealed that with a forecast error of 10%, the change in savings and PBDR were around 2.5% and 1.77% respectively Figure 7: Chiller bank scheduling: case study 1 - without against SB3-based MPC’s performance on actual demand. storage unit This showed the proposed method’s robustness to forecast Table IV: Change in demand response w.r.t scenarios (in %) Table III: Performance of SB3 with forecast errors (FE) Scenario 30 40 50 60 Control approach Change in demand-response Change in cost Case study 1 ±0.6 ±0.1 ±0.4 ±1.00 SB3-MPC with 2% FE ±0.08% ±1.21% Case study 2 ±1.0 ±2.0 ±1.7 ±0.7 SB3-MPC with 10 % FE ±1.77% ±2.34% Runtime (s) 12.48 15.97 22.04 25.48 10

Table V: Runtime of the SB3 with various prediction horizon ACKNOWLEDGEMENT Np 20 30 40 50 60 This research is supported by the National Research Runtime (s) 7.01 7.8 8.7 9.8 10.26 Foundation, Prime Ministers Office, Singapore under its uncertainties. In addition, PBDR performance of the SB3 is Energy NIC grant (NRF Award No.: NRF-ENIC-SERTD- analyzed for both case study 1 and 2, by varying the maximum SMESNTUJTCI3C-2016). number of scenarios. Tab. IV records the change in PBDR for different number of scenarios considering the outcome REFERENCES with 20 scenarios as the base performance. Analysis suggests [1] S. Clegg and P. Mancarella, “Integrated electrical and gas network that variation in number of scenarios has an negligible effect flexibility assessment in low-carbon multi-energy systems,” IEEE Trans- actions on Sustainable Energy, vol. 7, no. 2, pp. 718–731, apr 2016. on the SB3’s performance, whereas the runtime increases [2] A. Sheikhi, M. Rayati, and A. M. Ranjbar, “Demand side management significantly with increasing number of scenarios. The iRCGA for a residential customer in multi-energy systems,” Sustainable cities solver has the capability of population based direct search and society, vol. 22, pp. 63–77, 2016. [3] G. Mavromatidis, “Model-based design of distributed urban energy method, which reduces the dependency of the initial number systems under uncertainty,” Ph.D. dissertation, ETH Zurich, 2017. of scenarios in the end result. [4] F. Kienzle, P. Ahcin, and G. Andersson, “Valuing investments in multi- energy conversion, storage, and demand-side management systems under uncertainty,” IEEE Transactions on sustainable energy, vol. 2, no. 2, pp. 194–202, 2011. D. Computation Performance [5] M. Ameri and Z. Besharati, “Optimal design and operation of district heating and cooling networks with cchp systems in a residential complex,” Energy and Buildings, vol. 110, pp. 135–148, 2016. The SB3’s computation performance was studied on 10 tri- [6] P. Mancarella and G. Chicco, “Real-time demand response from energy als using simulations for 24 h duration. The average execution shifting in distributed multi-generation,” IEEE Transactions on Smart time for different prediction horizons are shown in Tab. V. Grid, vol. 4, no. 4, pp. 1928–1938, 2013. [7] Z. Bao, Q. Zhou, Z. Yang, Q. Yang, L. Xu, and T. Wu, “A multi time- The average execution time of heuristic is found to be 5437 scale and multi energy-type coordinated microgrid scheduling solution- s when the maximum number of iteration considered is 5000. part ii: optimization algorithm and case studies,” IEEE transactions on Therefore, the computational time is higher while solving the power systems, vol. 30, no. 5, pp. 2267–2277, 2015. [8] A. Dolatabadi, M. Jadidbonab, and B. Mohammadi-ivatloo, “Short-term problem with receding horizon approach. The approximate scheduling strategy for wind-based energy hub: A hybrid stochastic/igdt time for BB-MINLP with MPC approach to solve the problem approach,” IEEE Transactions on Sustainable Energy, 2018. is around 720 s whereas, the computation time of the SB3 is [9] B. Morvaj, “Holistic optimisation of distributed multi energy systems for low carbon urban areas,” Ph.D. dissertation, ETH Zurich, 2017. around 10 s even with a 30 h prediction horizon. This shows [10] S. Sudtharalingam, “Micro combined heat and power units in the uk: the SB3-based MPC’s capability to be used as a real-time Feasibility assessment using real time pricing and analysis of related scheduler in place of multi time-step heuristic methods and policies,” 2012. [11] F. De Angelis, M. Boaro, D. Fuselli, S. Squartini, F. Piazza, and BB-MINLP solver. Q. Wei, “Optimal home energy management under dynamic electrical and thermal constraints,” IEEE Transactions on Industrial Informatics, vol. 9, no. 3, pp. 1518–1527, 2013. [12] F. Verrilli, S. Srinivasan, G. Gambino, M. Canelli, M. Himanka, C. D. V. CONCLUSIONS Vecchio, M. Sasso, and L. Glielmo, “Model predictive control-based optimal operations of district heating system with thermal energy storage This investigation presented a novel scheduling algorithm and flexible loads,” IEEE Transactions on Automation Science and Engineering, vol. 14, no. 2, pp. 547–557, apr 2017. for Multi-Energy Systems (MES) that performs PBDR. The [13] C. Shao, X. Wang, M. Shahidehpour, X. Wang, and B. Wang, “An formulation led to a MES scheduling problem with mixed milp-based optimal power flow in multicarrier energy systems,” IEEE integer nonlinear program (MINLP), a NP-hard problem. To Transactions on Sustainable Energy, vol. 8, no. 1, pp. 239–248, 2017. [14] S. Pal and R. Kumar, “Electric vehicle scheduling strategy in residential reduce computation complexity, the proposed SB3 solver demand response programs with neighbor connection,” IEEE Transac- utilizes the McCormick’s bi-linear relaxation and epigraph tions on Industrial Informatics, vol. 14, no. 3, pp. 980–988, 2018. technique, followed by integrating the simplicity of convex [15] A. Jindal, N. Kumar, and J. J. Rodrigues, “A heuristic-based smart hvac energy management scheme for university buildings,” IEEE Transactions programs and the ability of meta-heuristic optimization to on Industrial Informatics, 2018. solve complex nonlinear problems. This study also investi- [16] M. Yazdani-Damavandi, N. Neyestani, G. Chicco, M. Shafie-khah, and gated the existence conditions of the lower bound solution of J. P. S. Catalo, “Aggregation of distributed energy resources under the concept of multienergy players in local energy systems,” IEEE the problem while solved with the SB3 method. The approach Transactions on Sustainable Energy, vol. 8, no. 4, pp. 1679–1693, Oct was demonstrated on a pilot building in Singapore, a test-bed 2017. for MES. Our results showed that the SB3-MPC reduced cost [17] M. Moeini-Aghtaie, A. Abbaspour, M. Fotuhi-Firuzabad, and E. Ha- jipour, “A decomposed solution to multiple-energy carriers optimal by approximately 17.26% without storage and 22.46% with power flow,” IEEE Transactions on Power Systems, vol. 29, no. 2, pp. storage when compared with multi-time step dynamic MINLP 707–716, 2014. solved using heuristic optimization. Moreover, SB3-MPC also [18] X. Zheng, G. Wu, Y. Qiu, X. Zhan, N. Shah, N. Li, and Y. Zhao, “A minlp multi-objective optimization model for operational planning of a achieved promising demand response over BB-MINLP solver. case study cchp system in urban china,” Applied Energy, vol. 210, pp. Although the proposed method has produced sub-optimal 1126–1140, 2018. solution compared to BB-MINLP, it showed robustness to [19] P. Gabrielli, M. Gazzani, E. Martelli, and M. Mazzotti, “Optimal design of multi-energy systems with seasonal storage,” Applied Energy, 2017. forecast errors and has lower computation time significant. [20] L. Mencarelli, “The multiplicative weights update algorithm for mixed Studying the role of market strategies in MES scheduling integer nonlinear programming: theory, applications, and limitations,” and extension of this work in multi-objective optimization Ph.D. dissertation, Universite´ Paris-Saclay, 2017. [21] S. Burer and A. N. Letchford, “Non-convex mixed-integer nonlinear pro- framework for planning and scheduling are the future course gramming: A survey,” Surveys in Operations Research and Management of this investigation. Science, vol. 17, no. 2, pp. 97–106, 2012. 11

[22] J. Sun, V. Palade, X.-J. Wu, W. Fang, and Z. Wang, “Solving the Mainak Dan received his bachelors and masters de- power economic dispatch problem with generator constraints by random gree in electronics and tele-communication engineer- drift particle swarm optimization,” IEEE Transactions on Industrial ing with specialization in control engineering from Informatics, vol. 10, no. 1, pp. 222–232, 2013. Jadavpur University in 2014 and 2016, respectively. [23] A. Askarzadeh, “A memory-based genetic algorithm for optimization Currently he is working towards his doctorate in of power generation in a microgrid,” IEEE transactions on sustainable philosophy with Interdisciplinary Graduate Program, energy, vol. 9, no. 3, pp. 1081–1089, 2017. Nanyang Technological University, Singapore from [24] A. Shefaei and B. Mohammadi-Ivatloo, “Wild goats algorithm: An 2016. His research interest lies in the problem area evolutionary algorithm to solve the real-world optimization problems,” of model predictive control, optimal control, mixed IEEE Transactions on Industrial Informatics, vol. 14, no. 7, pp. 2951– integer optimization techniques, energy management 2961, 2017. systems. [25] J. Reynolds, M. W. Ahmad, Y. Rezgui, and J.-L. Hippolyte, “Operational supply and demand optimisation of a multi-vector district energy system using artificial neural networks and a genetic algorithm,” Applied energy, vol. 235, pp. 699–713, 2019. [26] M. Dan, S. Srinivasan, and S. Sundaram, “A hybrid cross-entropy guided Dr. Seshadhri Srinivasan is currently with Berke- genetic algorithm for scheduling multi-energy systems,” in 2018 IEEE ley Education Alliance for Research in Singapore, Symposium Series on Computational Intelligence (SSCI). IEEE, 2018, Singapore working on building automation, optimal pp. 1807–1814. control, fault-diagnosis, and smart grids. Prior to [27] D. Huo, C. Gu, K. Ma, W. Wei, Y. Xiang, and S. Le Blond, “Chance- joining BEARS, he was working with the University constrained optimization for multienergy hub systems in a smart city,” of Sannio, Italy, Technical University of Munich, IEEE Transactions on Industrial Electronics, vol. 66, no. 2, pp. 1402– Germany, Tallinn University of Technology, Estonia, 1412, 2019. and ABB Corporate Research Center at Bangalore. [28] P. Zhao, C. Gu, D. Huo, Y. Shen, and I. Hernando-Gil, “Two-stage He is a member of the IEEE CSS standing commit- distributionally robust optimization for energy hub systems,” IEEE tee on standards. Transactions on Industrial Informatics, 2019. [29] A. Maffei, S. Srinivasan, P. Castillejo, J. F. Mart´ınez, L. Iannelli, E. Bjerkan, and L. Glielmo, “A semantic-middleware-supported receding horizon optimal power flow in energy grids,” IEEE Transactions on Industrial Informatics, vol. 14, no. 1, pp. 35–46, 2018. [30] X. Cao, J. Wang, and B. Zeng, “Networked microgrids planning through Dr. Suresh Sundaram received the B.E degree in chance constrained stochastic conic programming,” IEEE Transactions electrical and electronics engineering from Bharathi- on Smart Grid, 2019. yar University in 1999, and M.E (2001) and Ph.D. [31] L. Liberti, N. Mladenovic,´ and G. Nannicini, “A recipe for finding good (2005) degrees in aerospace engineering from Indian solutions to minlps,” Mathematical Programming Computation, vol. 3, Institute of Science, India. He worked as an Asso- no. 4, pp. 349–390, 2011. ciate Professor with School of Computer Science [32] K. Deng, Y. Sun, S. Li, Y. Lu, J. Brouwer, P. G. Mehta, M. Zhou, and and Engineering, Nanyang Technological University, A. Chakraborty, “Model predictive control of central chiller plant with Singapore till Oct 2018. Currently he is working thermal energy storage via dynamic programming and mixed-integer as Associate Professor in Department of Aerospace, linear programming,” IEEE Transactions on Automation Science and Indian Institute of Science, Bangalore, India. His Engineering, vol. 12, no. 2, pp. 565–579, 2014. research interest includes flight control, unmanned [33] A. C. Celador, M. Odriozola, and J. Sala, “Implications of the modelling aerial vehicle design, machine learning, applied game theory, optimization, of stratified hot water storage tanks in the simulation of chp plants,” and computer vision. Energy Conversion and Management, vol. 52, no. 8-9, pp. 3018–3026, 2011. [34] L. M. I. Sampath, A. Krishnan, K. Chaudhari, H. B. Gooi, and A. Ukil, “A control architecture for optimal power sharing among interconnected microgrids,” in 2017 IEEE Power & Energy Society General Meeting. Dr. Arvind Easwaran is an Associate Professor IEEE, 2017, pp. 1–5. in the School of Computer Science and Engineer- [35] T. Lehmann, “On efficient solution methods for mixed-integer nonlinear ing at Nanyang Technological University (NTU), and mixed-integer quadratic optimization problems,” Ph.D. dissertation, Singapore. He is also a Cluster Director for the 2013. Future Mobility Solutions research programme at the [36] S. Suresh, H. Huang, and H. Kim, “Hybrid real-coded genetic algorithm Energy Research Institute in NTU. He received a for data partitioning in multi-round load distribution and scheduling in PhD degree in Computer and Information Science heterogeneous systems,” Applied Soft Computing, vol. 24, pp. 500–510, from the University of Pennsylvania, USA, in 2008. nov 2014. In NTU, his research focuses on the design and [37] O. Exler, T. Lehmann, and K. Schittkowski, “A comparative study analysis of real-time and cyber-physical computing of sqp-type algorithms for nonlinear and nonconvex mixed-integer systems, including their application in domains such optimization,” Mathematical Programming Computation, vol. 4, no. 4, as automotive, manufacturing and urban energy systems. pp. 383–412, 2012. [38] M. Dan and S. Srinivasan, “A comparative study: Adaptive fuzzy inference systems for energy prediction in urban buildings,” arXiv preprint arXiv:1809.08860, 2018. Dr. Luigi Glielmo holds a laurea degree in Elec- tronic Engineering and a research doctorate in Au- tomatic Control. He taught at University of Palermo, at University of Naples Federico II and then at University of Sannio at Benevento where he is now a professor of Automatic Control. His current research interests include singular perturbation methods, model predictive control methods, automotive controls, deep brain stimulation modeling and control, smart-grid control. He seated in the editorial boards of Dynamics and Control and IEEE Transaction on Automatic Control, and has been chair of the IEEE Control Systems Society Technical Committee on Automotive Controls. He has been head of the Department of Engineering of University of Sannio from 2001 to 2007.