Optimal Scheduling of Heat Pumps for Power Peak Shaving and Customers Thermal Comfort

Transcription

1 Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort Jocen L. Cremer, Marco Pau, Ferdinanda Ponci and Antonello Monti Institute for Automation of Complex Power Systems, E.ON Energy Researc Center - RWTH Aacen University, Matieustrasse 1, 5274 Aacen, Germany Keywords: Abstract: Demand Side Management, Heat Pump Sceduling, Power Peak Saving, Load Flexibility, Load Balancing, Mixed Integer Linear Programming. Final customers are expected to play an active role in te Smart Grid scenario by offering teir flexibility to allow a more efficient and reliable operation of te electric grid. Among te ouseold appliances, eat pumps used for space eating are commonly recognized as flexible loads tat can be suitably andled to gain benefit in te Smart Grid context. Tis paper proposes an optimization algoritm, based on a Mixed-Integer Linear Programming approac, designed to acieve power peak saving in te distribution grid wile providing at te same time te required termal comfort to te end-users. Te developed model allows considering a continuous operation mode of te eat pumps and different comfort requirements defined by te users over te day. Performed simulations prove te proper operation of te proposed algoritm and te tecnical benefits potentially acievable troug te devised management of te eating devices. 1 INTRODUCTION Wit te evolution towards te Smart Grid (SG) paradigm, new tecnologies and applications will be put in place to obtain a more efficient, reliable and sustainable utilization of te electric system assets. Some of te most important canges concern te distribution grid, were te penetration of Distributed Generation (DG) and oter Distributed Energy Resources (DERs) requires novel management tools to deal wit te increasing complexity of te network (Fan and Borlase, 29). Differently from te past, end-users are also expected to play an active role in te SG scenario. Many customers already evolved into te so-called prosumers, tanks to te installation of potovoltaic panels or small wind turbines in teir ouseold premises. From one side, tis goes in te direction of a more environmentally friendly system, on te oter and it also enables a better use of te network infrastructure if tese resources are suitably managed. Customers role, owever, is not only limited to te installation of generation units based on renewable energy sources, but also includes te possibility to support te grid operation by offering flexibility in te power demand. Te exploitation of te flexibility available on te customer side as been a ot researc topic in te last years. Several Demand Response (DR) and Demand Side Management (DSM) models ave been designed to acieve economic benefits or specific tecnical goals troug te control of different appliances (Balijepalli et al., 211; Caprino et al., 214; Klaassen et al., 216a). Even toug many callenges still prevent a wide diffusion of DR and DSM (suc as te lack of a suitable regulatory framework, or te absence of te metering and communication infrastructure), te benefits deriving from te application of tese scemes are well recognized (Strbac, 28). As a consequence, it is foreseeable tat suc applications will play a relevant role in future SGs. Nowadays, DR scemes are already deployed and well establised in te U.S. (US DoE, 26). From a market perspective te existing programs can be divided in two main categories: Price-based programs: customers are motivated to cange teir demand pattern in response to day aead or real-time price signals. According to tis model, utilities or energy aggregators cannot directly act on end-users appliances but tey motivate people to cange teir power consumption abits usually by offering iger prices in peak ours and lower prices during off-peak ours. Incentive-based programs: customers provide to utilities or energy aggregators te possibility to di- 23 Cremer, J., Pau, M., Ponci, F. and Monti, A. Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort. DOI: 1.522/ In Proceedings of te 6t International Conference on Smart Cities and Green ICT Systems (SMARTGREENS 217), pages ISBN: Copyrigt 217 by SCITEPRESS Science and Tecnology Publications, Lda. All rigts reserved

2 SMARTGREENS 217-6t International Conference on Smart Cities and Green ICT Systems rectly control or scedule some of teir appliances and are rewarded for tis service troug specific incentives in te tariff sceme. In tis case, tus, te DR program provider can manage te flexible loads allowed by te customer following is own needs, wile fulfilling some customer comfort requirements if tis is specified in te agreement. According to (FERC, 211), DR programs deployed in U.S. unlock a potential power peak reduction larger tan 53 GW. More tan 8% of tis peak reduction comes from incentive-based programs. Tis solution, despite being more invasive wit respect to te price-based alternatives, allows an optimum management of te load flexibility leading to te certain acievement of te desired targets. Given te invasiveness of tese scemes, incentivebased DR is usually implemented to control not critical siftable or interruptible loads, suc as eating devices, air conditioners and water eaters. In Europe, DR and DSM programs are still at an early stage. Tis is mainly because of te eterogeneity of te regulatory framework in te different countries and, sometimes, also witin te same country. Neverteless, tese services are recently being proposed more insistently and DR is regarded as a key tool to acieve te targets of at least 27% for renewable energy and energy savings by 23 (SEDC, 214). Tis paper proposes an optimization algoritm conceived to exploit te flexibility provided by eating devices, like eat pumps. Electro-termal devices are in fact becoming more and more used for space eating, also tanks to te support of recent regulations aimed at improving te energy efficiency in te residential sector. Tanks to te relatively slow dynamics of termal penomena, electric eat pumps can be operated flexibly, tus offering a great potential for te deployment of DSM and DR scemes designed for teir management (Arteconi et al., 213). Te goal of te optimization algoritm ere presented is twofold. Te main objective is to minimize te power peaks on te grid, but te eat pumps sceduling is performed also in order to guarantee te termal comfort required by te end-users. In te following, Section 2 sows ow te flexibility given by eat pumps can be used for DSM purposes and points out te differences between te proposed approac and tose already available in literature. In Section 3, te designed optimization algoritm is presented and te constraints taken into account in te used model are described. Section 4 presents te application of te proposed optimization algoritm in different case studies, igligting te tecnical benefits potentially acievable troug te devised eat pumps management. Section 5 finally summarizes te obtained results and concludes te paper. 2 USE OF HEAT PUMPS FOR DEMAND SIDE MANAGEMENT Te flexibility provided by eating systems as been studied and evaluated in several works, proving tat a large potential exists for te application of DR scemes based on te management of electro-termal devices (Klaassen et al., 216b; Capman et al., 216). As a consequence, large efforts ave been focused on tis researc field, dealing wit different aspects like te modelling of te termal system (Good et al., 213; Akmal and Fox, 216) or te estimation of te eating demand (Kouzelis et al., 215) in order to design tailored DR scemes. Many of te DSM and DR programs proposed in te literature refer to te pricebased model and aim at minimizing te costs incurred by te final customer. Terefore, te developed models are usually conceived as a service to te customer, wile te utilities can address teir needs (in terms of grid management) by sending different price signals over te time and relying on te response of te users to te varying prices. In (Molitor et al., 211), different price scemes are used as input to an optimization algoritm running at te end-user premises for te sceduling of eat pumps. Results sow tat te optimal sceduling leads to a reduction of te energy consumption of te customer, but tis is obtained at te expense of a termal discomfort. In (Loesc et al., 214), an evolutionary algoritm is proposed to scedule te eat pump so to minimize te costs for te user, given te price of te energy in te spot market. Here utilities can also define power limitations in specific periods of te day for solving possible contingencies in teir grid and carge penalties to te customer if suc limitations are not respected. Te algoritm is able to exploit te flexibility provided by te eating system and to minimize te user costs, but a direct link to te termal comfort delivered to te customer is missing. Te proposal in (Battarai et al., 214) also tries to combine te objective of minimizing te costs for te customer wit a service tat is oriented to te distribution grid management. A two-step optimization process is presented, were te first step gives te sceduling of te eat pumps (minimizing te costs) wile te second step cecks possible voltage problems in te grid and, in case, sifts te eat pumps operation to te following time slots. Again, customer discomfort is in general possible in case of reallocation of te eat pumps operation. Heat pump flexibility is directly used to improve te operation of distribution 24

3 Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort grids in (Csetvei et al., 211). A metod to define local price signals for te end-users is presented, were additional costs are added to te spot market prices if overload conditions exist. Te price signals are ten used to determine te set point temperature of te eat pumps. Te metod allows eliminating te overloads, but customer discomfort can still arise during overload periods. To avoid termal discomfort for te end-user, some proposals include in te optimization model constraints on te indoor temperature provided to te customer. In (De Angelis et al., 213), temperature boundaries are considered in a ome energy management system wic is used to scedule te operation of flexible loads (including eat pumps) and possible storage systems. Te objective is to reduce te costs for te customer, so utilities can pursue teir goals only by setting different price signals over te time. In (Nielsen et al., 212), instead, te price-based sceme is compared to two different DR approaces were te power consumption or te temperature set point of te eat pump are directly controlled by te DR provider. Te objective is in tis case to minimize te costs for te energy aggregator (wic is providing te DR program), wile minimizing te discomfort for te customers by keeping teir ome temperature between te considered boundaries. Similarly to te case of te eat pumps, (Li et al., 217) propose an algoritm to manage air conditioners by acting on te temperature set points in order bot to reduce energy consumption and to provide te interruptibility of te load as DR service. In tis case, no fixed temperature boundaries are used, but te control sceme was tested in te field and tuned according to te customers feedback in order to minimize teir termal discomfort. All tese approaces, wile proposing solutions to make DR and DSM programs more attractive for te final customer, do not allow to fully exploit te available flexibility for enancing te efficiency of te electric system operation. As described in (Strbac, 28) and reported in (US DoE, 26), one of te main benefits for te system would be te power peak minimization. By minimizing te power peaks in te grid, utilities can minimize power losses, improve te voltage profile in te grid, reduce te risk of contingencies and postpone network reinforcement in areas wit increasing connected power. At system level, tis also leads to avoid te use of expensive generation units during peak ours and to reduce te needed spinning reserve, tus minimizing te overall costs. For tis reason, differently from te oter proposals available in te literature, te DSM model ere presented performs an optimal day aead sceduling Figure 1: Example of user-defined comfort requirement. of te eat pumps for minimizing te power peaks on te grid over te day. Te minimization is performed by taking into account user-defined requirements in terms of termal comfort, so tat bot utilities and end users can take advantage from te proposed DSM program. Furter reward to te final customers could be also defined, in terms of incentives in teir tariff, to make te DSM sceme more appealing, depending on te savings te utilities estimate to acieve from te application of tis optimization on a large scale. 3 MODEL FORMULATION Tis section presents te formulation used for te proposed DSM model. First, te termal model, consisting of comfort constraints, boundary constraints, energy balance equations and eat pump equations/constraints, is described. Ten, te optimization algoritm designed to perform te day aead sceduling of te eat pumps in te considered grid is presented. 3.1 Termal Model Comfort constraints Tey are used in te model to guarantee te comfort requirements of te residents living in eac ouse. In te proposed DSM sceme, users coose te reference temperature tey want to ave (it can also vary during te day) and provide a certain boundary around suc reference temperature. Figure 1 sows an example of possible temperature requirement for a customer. Te comfort constraints are tus defined so tat, for every time period t, te indoor temperature is always witin te permitted range. Indicating wit Γ LB and ΓUB te lower and te upper bound, respectively, of te temperature in ouse at time t, te following olds: T IN Γ LB, t (1a) T IN Γ UB, t (1b) 25

4 Power [W] SMARTGREENS 217-6t International Conference on Smart Cities and Green ICT Systems were T IN is te variable associated to te indoor temperature of ouse at time t. Boundary constraints Tey are added to define te initial and final states of te temperature for te daily optimization. Given a starting temperature Γ INI, te temperature at time t = is: T IN, = ΓINI (2) wile at te final time period f, te indoor temperature is bounded wit te inequality constraint: T IN,f ΓREF,f, (3) were Γ REF,f,f 2 is te reference temperature of ouse at t = f. Suc a coice is done in order not to ave a final temperature too close to te lower bound, since tis would force to turn on te eat pump at te beginning of te following day (tus removing any flexibility for te first time steps of te subsequent day aead sceduling). = ΓUB,f +ΓLB Energy balance Te energy balance equation defines ow te indoor temperature canges over te time due to te eat provided by te eat pump and te eat loss to te outdoor environment. Te used equation is based on te model described in (De Angelis et al., 213) and it is: T IN = T IN 1 + µ HS t ( Q HP γ AR Q LS ), t (4) were t is te duration of te time period between two consecutive discrete time steps, µ HS and γ AR are specific parameters, namely te ouse indoor air mass and te air eat capacity, and Q HP and Q LS are variables indicating te eat flow given by te eat pump and te eat loss, respectively. Te indoor air mass µ HS is a parameter tat depends on te size and geometrical caracteristics of te ouse (see (De Angelis et al., 213) for more details) and, combined wit te air eat capacity γ AR, appears as a termal energy storage for te ouse, tus affecting te dynamics of te termal penomena. Te eat losses are instead defined troug te following relationsip: Q LS = κhs (T 1 IN ΓOT 1 ), t (5) Suc losses depend on a eat loss factor κ HS and on te temperature difference between te indoor and te outdoor temperature Γ OT 1. As for Q HP, more details will be provided in te following paragrap were te used eat pump model is fully described m m Continuous HP operation m2 Air mass flow [kg -1 ] Binary HP operation Figure 2: Power demand of te eat pump in binary or continuous mode. Heat pump model Tis model as to link te delivered eat Q HP to te electrical power P HP required to produce suc eat, and as to account for all te possible constraints present in te eat pump operation. In te literature, eat pumps are often considered to work at a fixed power and tus a simple binary variable is adopted to define if teir status is on or off. In some papers, a multi-operation mode is instead defined by considering different discrete air mass flows to wic different electrical powers are consequently associated. In tis case, binary variables are introduced for eac discrete operation mode, ence determining an increasing complexity of te optimization problem. In tis paper, a continuous operation mode of te eat pump is considered. Tis means tat te eat pump can generate any value of air mass flow included in te range between a minimum and a maximum limit. Te electrical power needed to generate te output air mass flow can be described troug a function, wic can be in first approximation linearised troug a given number of linear segments. Figure 2 sows an example of linearised curve mapping te air mass flow to te required electrical power, wic as been obtained using eat pump data given in (De Angelis et al., 213). In Figure 2, it is possible to observe tat tree operation modes are defined: te first one, named m, is a discrete value corresponding to te minimum air mass flow of te eat pump; te second one, m1, is associated to te first segment of te curve; te last one, called m2, is linked to te upper segment of te curve and arrives till te maximum air mass flow for te eat pump. As it will be sown in te following, suc a solution can be implemented in te optimization algoritm by using integer variables for eac operating mode, wile just one binary value is used to determine te status (on or off) of te eat pump. Figure 2 also sows te possible limits present in te definition of a simple binary operation mode for te eat pump. In fact, in suc a case a single operating point of te eat pump as to be decided, wic does not reflect te actual operation mode of many eat pumps. 26

5 Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort Relying on te described continuous operation, te generated eat is defined as: Q HP = γ AR F,m,t HP ( Γ HP Γ RF ) 1, t (6) m were Γ HP is te output temperature of te eat pump (assumed as constant) and Γ RF 1 is te reference temperature of te ouse at te time step t 1. It is wort noting tat a rigorous definition of te generated eat Q HP would require te use of te actual indoor temperature T 1 IN in (6) in place of te reference temperature Γ RF 1. However, suc a solution would lead to a nonlinear relationsip and for tis reason it is ere approximated by using te constant value given by Γ RF 1. Tis approximation is considered acceptable since te indoor temperature is constrained to be close to te reference temperature due to te comfort constraints previously defined. Te oter term appearing in (6), namely F,m,t HP, is te additional air mass flow of mode m wit respect to te upper bound air mass flow of mode m 1. As for te first operating mode m, te air mass flow is constrained by te following equality constraint: F HP,m,t = y Φ,m, t. (7) were Φ,m is te minimal air mass flow of te eat pump. Te air mass flow of mode m is tus eiter or Φ,m depending on te binary decision variable y. Te additional air mass flows of all oter operating modes m are instead constrained by te following inequality constraints: F HP,m,t y Φ UB,m, m / {m}, t (8) were Φ UB,m is te upper bound of te additional air mass flow of te linearised segment associated to mode m. Given tese definitions of te additional air mass flows, te required power of te eat pump is directly mapped to te air mass flow by means of te following equation: P HP = m β m F HP,m,t, t (9) were te parameter β m is te power per air mass flow associated to eac mode m. Te total power of te eat pump is tus determined by taking te sum of all te additional air mass flows F,m,t HP multiplied by te respective parameter β m over all te operating modes m. Te proposed formulation works properly for increasing values of β m (β m β m1 β m2...) as in Figure 2. In fact, since te following optimization operates to minimize te used powers, tis ensures tat te modes will be automatically selected by te solver in te order m = {m,m1,m2...}. A furter aspect considered in eat pump model is te possible presence of time constraints. Tese constraints account for te minimum (or maximum) times te equipment as to operate or ave to be turned off since, usually, many operational switces result in inefficiency and mecanical stress. In (Hedman et al., 29), several different metods to account for time constraints in anoter sceduling problem (te unit commitment problem) were proposed and examined. Results of suc work are ere adapted to te eat pump sceduling problem. In tis case, only a minimum number of time periods τ, during wic te eat pump as to be turned on, is implemented (e.g., no minimum turn-off time) by te two following constraints: Z y y 1, t (1) Z y,τ, t,τ {t,,min(t + τ MIN (11) 1,f)}. Note, te switcing variable Z 1 is a bounded continuous variable. Terefore by using tese time constraints, te introduction of new binary variables is not required. More binary variables would result in a larger branc and bound tree and tus in a more complicated problem. As a result, te complexity of te problem decreases by using te inequality constraints proposed in (1) and (11). 3.2 Te Optimization Algoritm As discussed in Section 2, te objective of te DSM ere proposed is to minimize te power peaks in te grid. To acieve tis target, Quadratic Programming (QP) could be used to minimize te squared power resulting on te monitored network over all te time periods. However, if binary variables are included in te problem, QP approaces lead to very ig computational burden and execution times. For tis reason, in te proposed approac, te objective function as been linearised as presented in te following. Tis, togeter wit te linear constraints defined in Section 3.1, allows obtaining a linear problem tat can be solved more easily troug a Mixed Integer Linear Programming (MILP) formulation. In tis way, execution times can be reduced, wic is an essential aspect wen dealing wit large optimization problems (in tis scenario, wen optimizing te eat pump operation of a large number of ouses). Te basic idea used ere to linearise te objective function is to discretize te power consumption at time t troug a given number of blocks b and to assign increasing weigts to blocks associated to iger levels of power (see Figure 3); in tis way, te minimization of te weigted blocks leads to avoid 27

6 SMARTGREENS 217-6t International Conference on Smart Cities and Green ICT Systems Figure 3: Te weigt α b of te energy E b,t in box b. te allocation of flexible load consumption in periods were power peaks are occurring. Tese blocks can be interpreted as boxes tat can be filled wit energy up to teir respective capacity ε UB b. Eac energy box b is tus a continuous variable (indicated in te following wit E b,t ) tat is lower bounded by and upper bounded troug tis inequality constraint: E b,t ε UB b t (12) were ε UB b is te maximum capacity of te energy box, wic, in general, can be different for eac block b. For eac time step t, te sum of all te energy boxes is related to te power consumption in tat period by means of: E b,t b tp HP + ε GD t t (13) were εt GD is te energy consumption at time t given by all te non-sceduled loads in te grid and P HP is te already mentioned power consumption of te eat pumps for eac ouse. Given te above definition of te energy boxes and considering all te constraints introduced in te problem, te optimization used to scedule te eat pumps is a centralized algoritm wit te following objective function: minimize y, F HP,m,t t α b E b,t b s.t. Eqs. (1) (13). were te optimization decisions are te binary variables y and te continuous variables F,m,t HP. As it can be observed, te designed algoritm is tus a centralized approac were te eat pumps of eac ouse included in te problem are sceduled witin te same DSM optimization procedure. Similarly to te case of te additional air mass flows, for te Table 1: Parameters of te eat pump. Mode m m m1 m2 m (Wkg 1 ) m (kg 1 ) β HP Φ UB proper functioning of te metod it is crucial tat te weigt α b is increasing (α b1 α b2 α b3...). In tis case, indeed, te boxes will be selected (or filled wit energy ) by te solver in te order b = {b1,b2,b3...}. Te box approac is reasonable since te target is only te cut of te igest peak. Tis approac allows to be tailored to te considered scenario. For example, te discretization in te energy level can be modified, or any arbitrary strong functions (e.g., exponential to te power x, etc.) can be linearized by setting te values of te weigts α b accordingly. Differently from oter proposals available in literature and, in general, from price-based DSM scemes, te proposed centralized approac also allows avoiding tat possible ig power peaks are simply sifted from a time to anoter due to te similar response of te customers to te DSM inputs. 4 TESTS AND RESULTS 4.1 Tests Setup Te proposed optimization algoritm as been tested considering different scenarios were te DSM provider wants to minimize te power peak of te grid using te flexibility provided by 6 residential ouses endowed wit electric eat pumps. Te time orizon for te sceduling is one day. Te initial time of te sceduling problem is midnigt and te day is separated in 96 time periods resulting in a discretization time step of t = 15min. For te sake of simplicity, in te simulation it is assumed tat all ouses ave te same eat pump tat can continuously operate in 3 different modes. However, te algoritm obviously allows for te implementation of eat pumps wit different caracteristics for eac ouse. Te parameters of te eat pump model are stated in Table 1 and are derived from (De Angelis et al., 213). It is wort reminding tat mode m is te operating start point, wile te linear operating segments m1 and m2 offers continuous operation of te eat pump as depicted in Figure 2. Te output temperature of te eat pump as been cosen as Γ HP = 3 C and te minimal time period te eat pump as to run is τ = 2 (corresponding to a minimal operation time of 3min). As sown in Figure 4, in te proposed DSM sceme, te inputs needed for te optimization algoritm are: 28

7 Indoor air mass [1 3 kg] Temperature [ C] Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort a forecast of te inflexible load in te grid a forecast of te outdoor temperature te termal comfort required by te customers, togeter wit eat pumps and building caracteristics. As for te inflexible load profile in te grid, statistical data are often available (for example at substation level) regarding te aggregated power consumption in different periods of te year and for different types of day (e.g. working or weekend day). In te following simulations, te aggregated profiles of residential ouses ave been taken from te standard load profile of 212 (Bundesverband der Energie- und Wasserwirtscaft) using an average consumption of 2 kw/year per customer. Two different periods of te year, namely a working day in May and one in December, ave been simulated, and te corresponding load profiles ave been assumed as inflexible load for te residential customers. In addition, te presence of industrial consumers as been also considered. Tis contributes to give te final sape of te forecast inflexible load, as it will be sown in te next subsection wen presenting te simulated scenarios. For te forecast of te outdoor temperature, te actual temperature of a day in May is used in a first simulation, wile te actual temperature of a day in December is used to simulate a second scenario. Te used temperature profiles are presented in Figure 5. Te termal comfort of te 6 ouses differs from ouse to ouse and individual parameter sets (as described in te previous section) ave to be taken into account. For te case studies presented ere, te relevant parameters are sampled based on 5 different temperature profiles and 12 different building caracteristics. Figure 5 sows te 5 different temperature profiles (te reference temperature is always te mean upper bound lower bound outdoor temperature Time [] Figure 5: Upper and lower temperature bounds of te residents and outdoor temperature. value of te upper and lower bound). As starting point for te simulation, te initial indoor temperature Γ INI is assumed to be equal to te reference temperature of te first time period. Te 12 building types differ in te indoor air mass and te eat loss factor (Figure 6). Te parameters are calculated based on te geometric dimensions of te ouse (De Angelis et al., 213). As an example, let us consider a ouse aving te lengt ξ HS 1 = 2m, ξ HS 2 = 2m, te eigt ξ HS 3 = 4m, a roof pitc of σ HS = 4 and η W I = 6 windows, eac one wit an area of Λ W I = 1m 2. Te termal transmittance for walls and windows are assumed ν WA =.15Wm 2 K 1 and ν W I = 1Wm 2 K 1, respectively. Te eat loss factor in tis example ouse is calculated as follows: κ HS = ν WA ( 2 (ξ HS 1 + ξ HS 2 ) ξhs 3 η WI Λ W I) + η WI ν W I Λ WI = kJ 1 (14) C By using te density of te air ρ AR = 1.241kgm 3 at standard conditions, te total air mass is: ( ( ) 2 µ HS = ρ AR ξ HS 1 ξ HS 2 ξ HS ξ HS 1 ξ HS 2 tan(σ )) HS = 3946 kg. (15) For all te 6 residential ouses, te indoor air masses and eat loss factors are presented in Figure Heat loss factor [kj -1 C -1 ] Figure 4: Overall model of te designed DSM sceme. Figure 6: Indoor air masses and eat loss factors of te residential ouses. 29

8 Temperature [ C] Power [kw] SMARTGREENS 217-6t International Conference on Smart Cities and Green ICT Systems 6. Te set of ouses used in te simulation as been obtained using all te possible combinations between te 5 termal comfort profiles (Fig. 5) and te 12 different ouse caracteristics (Fig. 6). During te presentation of te test results, te benefits provided by te proposed DSM model are analyzed by comparing te results of te described optimization algoritm to tose of two different simulations. In te first case, te term of comparison is given by a simulation were te target of te internal control system of te eat pump is to keep te indoor temperature as close as possible to te reference temperature Γ RF for all te time periods. Tis simulation as been run separately for eac HP by using a QP approac tat minimizes te squared difference of te indoor temperature of te ouse wit respect to te reference temperature selected by te customer, according to: minimize y, F HP,m,t ( T IN Γ RF ) 2 t s.t. Eqs. (1) (11) (16) Tis comparison aims at igligting te advantages offered by te proposed DSM sceme wit respect to a scenario in wic no DSM is applied. In te following, tis operation mode of te HP will be referred to as internal HP control. In te second case, te DSM model as been approximated by using te same model presented in Section 3 but excluding multiple HP modes m. Tus, HP operation is only valid in mode m = {m} (by using te equality constraint Equation (7)) and Equation (8) is not required any more in te optimization. In tis comparison, te binary operation of te eat pump is selected to ave an air mass flow of Pi UB m = 647kg 1 and a power per air mass flow β m = 1.25Wkg 1. Tis value is te mean air mass flow of te continuous eat pump model. Tis scenario allows sowing te different results acievable wen considering a more realistic (continuous) operation mode of te eat pump rater tan a simplified binary version. 4.2 Simulation Results To assess te benefits provided by te proposed DSM sceme, a first simulation scenario, using as input te outdoor temperature of a day in May (see Fig. 5), as been considered. In tis test case, it is assumed tat te optimization as to be performed in a portion of a LV grid were all te 6 ouses are equipped wit an electric eat pump. In addition, an industrial load is also taken into account, wic operates at {1.5kW,8kW} and switces wit a period of 4, starting wit 8kW at midnigt. Tis scenario can be representative, for example, of a distribution feeder tat supplies te simulated 6 ouses. At te ouseold level, te results for an example ouse are presented in Figure 7. Te comparison of te sceduled powers of te eat pump, for te case of internal HP control and for te DSM wit binary and continuous HP operation mode, is presented in te upper part of te figure, wile te respective indoor temperatures are presented in te bottom part. In te case of temperature minimization in te internal control system of te eat pump, obviously te indoor temperature follows closely te reference temperature. It can be observed tat more power is required in te morning, wen te desired reference temperature increases, and tat te eat pump works regardless of te loading conditions of te grid. Wit te DSM, since te optimization algoritm fosters te power consumption in some time periods more tan in oters, te full range of te specified temperature bounds is used. However, it is possible to observe tat te temperature always falls witin te range accepted by te customer. In particular, morning ours (wen te loading of te grid is lower) are used to store termal energy in te ouse, wile during peak ours te operation of te eat pump is minimized in order not to aggravate te situation in te grid (wile providing to te customer te required comfort). Te main differences between te binary and te proposed continuous HP operation mode are from an energy consumption perspective. Indeed, it is possible to see tat te continuous model leads to operate te eat pump at lower power levels and for a longer time during te day. Tis allows better modulating te power before peak ours, wen te storage of termal energy is needed, and during peak ours, wen, wile respecting te customer termal requirements, te operation of te eat pump as to be minimized. In addition, operating te HP at its lower bound also Time [] DSM wit binary HP DSM wit continuous HP internal HP control temperature bounds TUB Figure 7: Heat pump consumptions and temperature profiles for one example ouse in te first simulation scenario. 3

9 Power [kw] Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort Table 2: Results on te daily energy consumption, first simulation scenario. case HP consumption increase (kw) (%) Example ouseold DSM - continuous HP DSM - binary HP internal HP control Overall scenario DSM - continuous HP DSM - binary HP internal HP control allows using te most efficient operation points of te HP, and tis implies a significant reduction in te overall energy consumption for te end-user. Table 2 sows te results related to te energy consumption for bot te example ouseold presented in Fig. 7 and for te overall scenario. It is possible to see tat a simplified binary model of te HP clearly leads to a larger energy consumption, wic may be not acceptable for te final customers. Te results obtained at te grid level are sown in Figure 8. Wereas for all te cases te inflexible industrial and residential loads are te same, te flexible parts differ depending on te HP sceduling. In tis scenario, all te ouses are equipped wit eat pumps, so a large amount of flexible energy is available. As a consequence, te final curve of aggregated power is mainly determined by te allocation of tis flexible energy, rater tan by te sape of te fixed load. In te case of temperature minimization using te internal control of te HP, large power peaks are obtained. Te reason for tese peaks is te presence of similar comfort profiles for many customers (see Fig. 5), wic leads to te simultaneous operation of te eat pumps. Even toug tese peaks are originated by te particular termal requirements used for te test, tis kind of problem is likely in a scenario wit large penetration of electric HPs managed in a decentralized way. In fact, end-users can ave same requirements Time [] fixed power industrial fixed power residents internal HP control DSM wit binary HP DSM wit continuous HP Figure 8: Aggregated power in te grid for te first simulation scenario. Table 3: Tecnical benefits wit te DSM at peak times, first simulation scenario. case max. peak power at 6: HP cut (kw) (kw) (%) internal HP control DSM - binary HP DSM - continuous HP in some periods of te day (e.g. due to similar working ours or consequently to te weater conditions) or price-based DSM programs can lead to a similar reaction of te customers. Tis would bring te simultaneous operation of te eat pumps, tus determining a significant impact on te aggregated power demand. Te use of a centralized optimization approac leads significant benefits in tis perspective, allowing to acieve power peak saving. Fig. 8 clearly sows tat a muc flatter demand profile is obtained tanks to te application of te DSM. Table 3 reports te numeric results for te maximum power peaks originated by eac HP control. It is possible to see tat a reduction of te power peak larger tan 6% is obtained for te DSM wit continuous HP operation mode. Since te actual potential of te DSM sceme is only to manage te HP power, Table 3 also sows te results in terms of flexible energy tat is sifted troug te DSM to avoid te power peaks. Considering te power peak time for te case of internal HP control, almost 74% of te flexible power can be reallocated troug te DSM sceme (tis reduction is calculated considering only te part of te load associated to te HP operation). Te continuous HP operation mode provides larger improvements due to its flexibility in coosing te HP operation point and its better efficiency wit respect to te binary HP. To evaluate te potential of te proposed DSM sceme even wen less flexible energy is available, a second test case as been run considering a scenario wit 24 residential ouses, among wic only 6 are endowed wit electric HPs. Tis test case could be representative, for example, of a MV/LV substation tat subtends four different feeders. Due to te assumed scenario, also te industrial load as been scaled up to consider four feeders, and power levels equal to {6kW,32kW} ave been assumed using te same operation cycles as te previous test. Wile te same considerations as te previous case old wen looking at te single ouseold, different results can be found wen considering te aggregated power at grid level. Fig. 9 sows te obtained power profiles for te different HP operation modes. In tis case, te level of te fixed load is relevant wit respect to te flexible power associated to te HPs, tus te profile of te aggregated power is strongly affected by its sape. Noneteless, it is possible to observe tat, 31

10 Power [kw] Power [kw] SMARTGREENS 217-6t International Conference on Smart Cities and Green ICT Systems Time [] fixed power industrial fixed power residents internal HP control DSM wit binary HP DSM wit continuous HP Figure 9: Aggregated power in te grid for te second simulation scenario. wen no DSM is applied, te tree additional power peaks brougt by te customer termal requirements are still evident and give te largest power peaks over te day. In case of DSM, a power profile as flat as te one obtained in te previous test scenario cannot be found due to te relatively low amount of flexible energy. However, it is possible to note tat te DSM sceme accomplises its task of power peak minimization by reducing te HP use at te peak ours and sceduling te operation of te HPs during off-peak periods. Tis beaviour is clearly depicted in Figure 1, wic sows te distribution of te HPs operation over te day for te two DSM scemes. It is possible to observe tat, in te case of continuous HPs, all te devices are activated in te period of lowest power consumption (4: - 6:), wile only a minimum set of HPs is sceduled to operate during peak ours, like at 12: or at 2:. Fig. 1 also permits underlining once more te advantages of te continuous HP mode wit respect to te binary model. In te latter case, in fact, despite a generally lower use of te HPs (because tey generally operate at iger power), te same or a larger number of HPs is running during peak periods, wic implies a larger additional power due to te fixed power cosen to represent te binary beaviour. Tis is also reflected in Table 4, wic sows te obtained values of power peak, Operating Heat Pumps [%] Time [] DSM wit binary HP DSM wit continuous HP Figure 1: Distribution of te HP operation for te second simulation scenario. Table 4: Tecnical benefits wit te DSM at peak times, second simulation scenario. case max. peak HP power operating HPs (kw) (kw) internal HP control DSM - binary HP DSM - continuous HP te corresponding quote brougt by te HPs, and te number of HPs operating at tat time. Moreover, even in tis scenario, te binary HP model proves to be less efficient tan te continuous one, wit an increase in te overall energy consumption (for all te 6 ouses) larger tan 36%. To furter confirm te results acieved until now, te last scenario as been simulated again considering as outdoor temperature a day in December (see Fig. 5). Te first consideration in tis test case concerns te DSM wit binary HPs: in tese conditions te optimization algoritm is unable to find a feasible solution, because wit te considered operating power is not possible to fulfil te termal comfort requirements during te canges in te reference temperature. Tis outcome igligts once again te possible drawbacks associated to te introduction of tis simplification in te HP model. Focusing on te oter two HP sceduling criteria, Figure 11 sows te results obtained for te aggregated power at grid level. Comparing tese results wit tose obtained in te same scenario in May (Fig. 9), it is immediate to verify tat a larger amount of HP energy results on top of te inflexible base load. Tis is a consequence of te colder outdoor temperature, wic forces te HPs to run more frequently in order to provide te required termal comfort to te customers. Looking at te sceduling of te single ouseolds, in te case of DSM wit continuous HP, 5 ouses out of 6 require to ave te HP running at all te time steps, and 13 ouses need an operating HP for at least 23 ours. Tese effects are automatically propagated to te results of te ag fixed power industrial internal HP control Time [] fixed power residents DSM wit continuous HP Figure 11: Aggregated power in te grid for te tird simulation scenario. 32

11 Optimal Sceduling of Heat Pumps for Power Peak Saving and Customers Termal Comfort Table 5: Tecnical benefits wit te DSM at peak times, tird simulation scenario. case max. peak HP power operating HPs (kw) (kw) internal HP control DSM - continuous HP gregated power. As sown in Table 5, in fact, te level of power and te number of operating HPs during te peak time is significantly larger tan in te previous simulation scenario. Noneteless, despite tis sligt degradation of te DSM performance, it is still possible to notice as te proposed DSM sceme allows optimizing te sceduling of te HPs, reducing as muc as possible te operation at te peak time and filling te valleys during off-peak ours. In comparison to te case of internal HP control, a reduction of te power peak and of te overall energy consumption larger tan 9% and 2%, respectively, is obtained also in tis last scenario. Finally, as for te computational cost for te proposed metod, we can state tat it is relatively low. Te test cases were solved on a standard laptop using CPLEX in GAMS 24.8 on an Intel i7(2.9 GHz) macine wit 16 GB RAM. Te termination criteria for te DSM wit binary and continuous operation mode was set to a computation time of 24 s and 12 s, respectively; tus, bot optimizations were not solved to global optimality. Tis is reasonable since sub-optimal solutions from te grid perspective are acieved quickly. Table 6 sows te results related to te first presented simulation scenario. Note, before te relative gap is calculated all separate parameters and products of multiple parameters tat arise in te objective function are subtracted from te objective function. Interestingly, te more detailed te HP model, te smaller gets te relative gap. Tis means tat a more realistic model (continuous HP operation) decreases te computational complexity of te problem. As for te internal HP control case, were te temperature differences are minimized, a QP optimization is solved for eac ouse (in total 6). Te termination criteria of eac optimization was set to a computation time of 3 s. Te relative gap of te 6 QPs varies muc, but te majority was solved to global optimality. Table 6: Computational results. case time relative gap (s) (%) internal HP control 1922 differs DSM wit binary HP DSM wit continuous HP CONCLUSIONS Tis paper presented an optimization algoritm designed to define te day aead sceduling of eat pumps for acieving power peak saving in te electric grid. Te conceived approac exploits te flexibility given by te eating devices on te customer side to obtain te minimization of te power peaks, wile providing te required termal comfort to te final users. Performed tests prove tat te proposed approac allows combining te benefits for te utilities wit te service for te customer, wic obtains te required temperature over te day and a minimization of te energy consumption. Moreover, te advantages brougt by te proposed continuous operation model of te eat pump, wit respect to te simplified case of binary operation of te eat pump, are presented. Tis work will be used as a starting point for furter developments in tis field. In particular, a deeper study on te impact of te customer flexibility on te final results and te evaluation of te possible drawbacks led by te unavoidable uncertainties present in te used model (e.g. outdoor temperature, knowledge of te building parameters, etc.) will be object of future studies. Te possible use of dedicated termal storage will be also object of future work, since it can significantly increase te available flexibility leading to potential improvements in te acievable results and in te design of te DSM sceme. Te integration of additional ome appliances in te proposed management algoritm can be a furter step for te design of a complete DSM program fully exploiting te flexibility offered by residential customers. ACKNOWLEDGEMENTS Tis work was supported by FLEXMETER, wic is an EU Horizon 22 project under grant agreement no REFERENCES Akmal, M. and Fox, B. (216). Modelling and simulation of underfloor eating system supplied from eat pump. In 216 UKSim-AMSS 18t International Conference on Computer Modelling and Simulation (UKSim), pages Arteconi, A., Hewitt, N., and Polonara, F. (213). Domestic demand-side management (dsm): Role of eat pumps and termal energy storage (tes) systems. Applied Termal Engineering, 51(1): Balijepalli, V. S. K. M., Pradan, V., Kaparde, S. A., and Sereef, R. M. (211). Review of demand response 33

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