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Combining the Demand Response of direct electric space heating and partial thermal storage using LP optimization
Electric Power Systems Research 106 (2014) 160–167
Contents lists available at ScienceDirect
Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Combining the Demand Response of direct electric space heating and partial thermal storage using LP optimization Mubbashir Ali a,∗ , Juha Jokisalo b , Kai Siren b , Matti Lehtonen a a b
Department of Electrical Engineering, Aalto University, Espoo, Finland Department of Energy Technology, Aalto University, Espoo, Finland
a r t i c l e
i n f o
Article history: Received 25 April 2013 Received in revised form 22 July 2013 Accepted 22 August 2013 Available online 19 September 2013 Keywords: Demand response Optimal control Partial electric storage space heating Linear programming
a b s t r a c t In this paper, we optimize the Demand Response (DR) control of partial storage electric space heating using a Linear Programming (LP) approach. The objective is to combine the DR control of direct electric space heating and partial thermal storage in order to minimize the total energy cost of customers without sacrificing user comfort. The proposed DR control is optimized according to the dynamic prices, which shifts the power demand from peak price periods to the cheapest hours. The optimal load shaping strategy is examined by performing simulations. The simulation results show that the partial heat storage together with thermal inertia of the house can offer much flexibility in DR control. The optimal DR control model can easily be integrated at the household level for better utilization of distributed energy resources under the Smart Grid scenario. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Power systems around the world are facing an increased challenge of the integration of intermittent renewable generation with various forms of distributed energy sources. This creates urgent requirements for the balancing and optimization of power system operations. One major technology which may respond to this challenge is Demand Response (DR) [1–4]. According to the Federal Energy Regulation Commission (FERC), Demand Response is the “Changes in electric usage by demand-side resources from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized” [5]. Therefore, intelligent load shaping will not only postpone the infrastructure investment, but would also create a more reliable system. According to the Finnish statistics (2012), around 80% of energy consumption in households is spent on heating [6]. Approximately, one quarter of the households utilize some form of electrical heating, which accounts for around 40% of all electricity consumed by the household sector [7]. Mainly, two types of electrical heating are currently employed: direct electric space heating, i.e. heating without thermal storage, and storage space heating. The storage space heating can be further classified into: partial storage space heating
∗ Corresponding author. Tel.: +358 50 4367307; fax: +358 9 47022991. E-mail addresses: mubbashir.ali@aalto.fi, mubbashir [email protected] (M. Ali). 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.08.017
and full storage space heating. The main difference between them is the storage capacity. The full storage space heating has the ability to store all the heat for the following day without significant storage losses. The space heating load is suited for DR application at household level for two reasons. First, space heating load constitues a major share of household load during winter and, secondly, the thermostatic controlled load can be curtailed, reduced or postponed as long as the user comfort is intact [8]. This flexibility can be unleashed by making the space heating load responsive either to price or by providing some incentives. However, all the DR actions must ensure that quality of service is not sacrificed. There has been a growing interest in the residential demand response and many researchers have turned to the household load management. For instance, the authors of [9–13] present an optimal operation of major household loads under Smart Grid scenario. A comprehensie overview of load managemnet practices is presented by Kostkova et al. [14]. An agent based system to simulate household DR is proposed in [15]. Gyamfi and Krumdieck [16] performed a scenario analysis to assess the DR potential during peak load periods. In [17], a pilot study has been performed at the household level to quantify the DR potential utilizing smart metre and token. Mohsenian-Rad and Leon-Garcia [18] present an optimal residential load control in Real Time Pricing (RTP) and Inclining Block Rate (IBR) environment. A price prediction filter, based on a prior knowledge of previous prices, is developed. A home energy management system is proposed by Pipattanasomporn et al. [19] to explore the DR potential at residential level. Gottwalt et al. [20] proposed an algorithm for demand side management at household level under time-of-use (ToU) prices to investigate the impact of variable prices
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Nomenclature hc Tmax Ca EH Emax H h i Ki Qi qi Qmax Qmi Qmmax Qsi S S0 Si t T x
heating power (kW) maximum allowed temperature variation (◦ C) heat capacity of the house (J/K) energy demand (kWh) of the period considered maximum energy demand (kWh) of a day thermal conductance of the house (W/K) scheduling interval (h) index of hours power price (D /kWh) of hour i heat released from the thermal masses of the building structures (kWh) at hour i average heat demand of the house (kWh) at hour i maximum heat that can be released from the thermal masses of the building structures (kWh) heat stored into the thermal masses of the building structures (kWh) at hour i maximum heat that can be stored into the thermal masses of building structures (kWh) heat stored into the thermal storage (kWh) at hour i net capacity of the thermal (tank) storage (kWh) initial level of storage (kWh) level of storage in the beginning of hour i time (s) temperature (◦ C) degree of storage (p.u.) penalty price (D /kWh) for altering the room temperature set point thermal time constant of the house (s)
on energy bills. Recently, many studies have primarily focused on the demand scheduling of major household appliances such as water heater in [21–23], AC in [24], HVAC in [25] and electric vehicles in [26,27]. However, the DR control of partial storage space heating load under dynamic pricing, despite being a major controllable household load, is virtually untreated in the literature. There exist literature [28,29] that deal with the optimal scheduling of storage, however the scheduling of storage is done in isolation of the thermal dynamics of the house. While, the studies pertaining to DR of direct electric heating load, such as [30,31] have not considered the additional thermal storage. Also, the user comfort has not been adequately addressed. This certainly indicates the lack of understanding about the DR potential of partial storage space heating load. We attempt to fill this gap by proposing a simple but optimal DR control of partial storage space heating load without sacrificing the user comfort. The objective is to develop an optimal heat load management that not only reduces the energy costs but also considers the possible compensation paid to the customers for employing the DR control. At present, many electric storage space heating consumers are charged according to the Time of Day distribution tariff [32].1 The existing ToU tariff helps the household consumers to charge the storage during night and release the stored heat during the day as required. However, the partial storage gets fully charged well before the cheaper tariff ends and is unable to coast the stored heat through the rest of the day with night charging alone. The irregular charging approach followed by partial storage
1 In Helsinki, for instance, the daytime distribution tariff is valid on weekdays from 7 a.m. to 8 p.m. The night time distribution is valid at other times. Night time tariff is 30% cheaper than day time tariff.
Fig. 1. 1-Capacity building model.
heating is very ineffective and needs refinement. We tackle this problem by optimally scheduling the partial storage using Linear Programming technique. The proposed DR control also efficiently utilizes the thermal inertia of the house along with the partial thermal storage. During critical periods, if necessary, heat is allowed to be released from the thermal masses of the building structures. The released heat is then restored to the thermal masses of house envelope depending on the price at the hour in question. However, the user comfort has been given the priority and the temperature variation band is not allowed to violate the user preference. Moreover, the daily heating energy requirement is not compromised. The simulation results show that LP can be an effective technique for DR control for a combination of direct and storage based electric space heating. The rest of the paper is organized as follows: in Section 2, Thermodynamic modelling of house and thermal storage is presented. Section 3 presents the DR control optimization and its implementation. In Section 4, we perform the case study and simulations to investigate the optimality of DR control model. Section 5 highlights the main conclusions of the paper. 2. System modelling 2.1. Simplified modelling of house thermal behaviour A simple model to estimate the indoor temperature in a dynamic situation is one-capacity model. In this model, the building fabric heat capacity and air heat capacity is lumped as one capacity Ca (Fig. 1) The indoor air node point is connected to the ventilation supply air temperature Ts through the ventilation air heat conductance Has , to the ground temperature Tg through the conductance Hag and to the external temperature Te through the combined conductance Hame of the external walls and the roof. The infiltration air flow is connected between the external temperature Te and indoor air temperature Ta . By this it is assumed that there is no warming of the infiltration air in the structures and the penetrating air flow has the temperature of the external air. In parallel with infiltration are the windows, which have a negligible thermal mass compared with the rest of the house envelope. To further simplify the model, a virtual conductance Hae between external and internal temperature node points is formed for infiltration heat capacity flow and windows heat conductance. Further, the heating power hc is assumed to be of convective nature and is thus allocated to the indoor air node point. Also, the effect of internal heat gains from the lighting, household appliances and occupancy is assumed to be included in the heat demand profile. If denotes the thermal time constant of the model house, then Eq. (1) can be solved analytically in order
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Fig. 2. Heating demand profiles used in the study for the simulations.
to obtain a causality between the indoor temperature and heating energy requirement. The energy balance for the indoor air node point is: hc = Ca
dTa + Hae (Ta − Te ) + Hame (Ta − Te ) dt (1)
Htotal = Hae + Hame + Hag + Has
(2)
Te ∼ = Tg , owing to the ventilated crawl space in the house
(3)
+
Si+1 = Si + Qsi − qi
+ Hag (Ta − Tg ) + Has (Ta − Ts )
Ta (t) = Ta (0) −
The energy stored at any instant can be given as:
Charging mode
Si+1 < Si
Discharging mode
where,
hc (Htotal − Has )Te Has Ts −t/ − − e Htotal Htotal Htotal
1 [ + (Htotal − Has )Te + Has Ts ] Htotal hc
Si+1 > Si
(6)
(4)
The hourly heating demand for a typical winter day is shown in Fig. 2. The thermodynamic parameter values for a 1-capacity model of a 180 m2 two-floor single-family house insulated according to the minimum requirements of the Finnish 2010 building code C3 [33] are shown in Table 1. The structures of the house are medium massive. With the parameters in Table 1, the thermal time constant is about 17 h.
• • • • • • •
S is the net storage potential Si is the level of storage in the beginning of hour i x denotes the degree of storage Emax is the maximum heat demand of a day Qsi is the energy loaded from grid to storage at hour i qi is the heat energy consumed at hour i i = (1, 2,. . ., h) represents the index of a hour
Depending on the optimization result, the amount of charging power within an hour varies and can in practical case be controlled by altering the duty cycle of the heating system within the hour.
2.2. Modelling an ideal thermal storage behaviour
2.3. Overall system model
The net thermal storage capacity can be expressed as a percentage of maximum demand of a day.
The models of the house’s thermal behaviour (Section 2.1) and thermal storage (Section 2.2) are coupled together for optimal DR control system, see Fig. 3. The thermal storage S is charged by electrical power during cheapest hours to preserve the heat energy for later use. The power may also be directly delivered to the house for heating in case when storage level is too low to meet the heat demand qi . The thermal masses of the building structures would be utilized if the thermal storage is empty during peak electricity price periods. This heat released from the thermal masses of building structures is Qi . However, the released heat energy should be restored to the thermal masses of the building structure by taking the power from the electrical network Qmi during cheaper power price hours, either before or after the moment of heat releasing. The excessive utilization of thermal masses of the building structures is limited by the allowable variation band of indoor temperature Ta , which is set in this study to Tmax = ±2 ◦ C. The implementation of the optimal DR control is discussed in the following section.
S = [x][Emax ]
(5)
⎧ ⎨ x=0
No storage
x=1
Full storage
0≤x≤1
Partial storage
⎩
Table 1 Thermodynamic parameter used in simulation. Factors
Value
Ts Ca Hae Hame Has Hag
18 ◦ C 11,918 kJ/K 52.33 W/K 41.26 W/K 87.43 W/K 15.54 W/K
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Fig. 3. Schematic of system model.
3. Design of the optimal DR control
0 < Qi < Qmi ,
∀i = (1, 2, . . ., h)
3.1. DR control optimization
0 < Qmi < Qmmax ,
Maximum charging power Net storage capacity Quality of service Heating energy demand House cooling rate Maximum heat stored in the thermal masses of the building structures • Maximum heat released from the thermal masses of the building structures The optimal DR model is formulated as follows:
[Ki (Qsi + Qmi ) + (i )(Qi )]
(7)
i=1
Subjected to the following constraints
h
(Qsi + Qmi )≥EH − S0
(8)
i=1
j
[Qsi + Qi − qi ) > (−S0 )
Qm ∈ hc , ∃Qm Ca T
∀i = (1, 2, . . ., h)
(13)
Qmmax = Ca Tmax h
• • • • • •
h
(12)
Qmax = Ca Tmax
In this subsection, we optimize the electric space heating control using Linear Programming approach. The objective is to optimize the DR control of direct electric space heating and thermal storage in duo, to minimize the total energy cost without violating the indoor temperature limits. The objective function faces multiple constraints such as:
Minimize
Q ∈ hc , ∃Q Ca T
[Qi − Qmi ] = 0
(14)
i=1
where, • • • • • • • •
Ki is the power price (D /kWh) of hour i i is the penalty price (D /kWh) of hour i EH is the Energy demand (kWh) of the period considered h is the scheduling time interval (h) S0 is the initial level of storage at t = 0 (kWh) Pmax is the maximum power of the heating system (kW) t is the time step used in the calculations – hour in this case Qmax is the maximum heat that can be released from the thermal mass of the building structures (kWh) • Qmmax is the maximum heat that can be stored into the thermal mass of the building structures (kWh).
In (7), the first term (Qsi + Qmi ) is the electrical energy that must be bought from the power market at hour i. The penalty price, the latter term, is to make sure that thermal storage is used first. The direct control, i.e. releasing the heat out of house masses, is inevitable when the thermal storage is empty during critical periods. The penalty factor can take any value provided it
(9)
i=1
∀j = (1, 2, . . .h − 1) j
[Qsi + Qi − qi ) < (−S0 ),
(10)
i=1
∀j = (1, 2, . . .h − 1) 0 < (Qsi + Qmi ) < Pmax t,
∀i = (1, 2, . . ., h)
(11)
Fig. 4. An example of spot prices and system demand (normalized values; data from [34,35]).
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Fig. 5. DR control optimization of space heating with 40% thermal storage.
is smaller than the price difference of shifted hours; moreover, the aggregator2 companies may set and modify the penalty price based on contracts with consumers and it could be regarded as the compensation paid to the customers. However, the detailed subject of setting the penalty price is related to electricity markets and is not the focus of our work. The constraint (8) ascertains the minimum heat requirement. The constraint (9) guarantees the quality of service in case the heat is released from the house masses. The net storage capacity limit is enforced by constraint (10). The rated power of electric space heating is bounded by constraint (11). The constraints (12) and (13) bound the heat released and restored to the thermal envelope of the house respectively. Both of the constraints are formulated on the maximum allowable indoor air temperature change. While, the constraint (14) ascertains that the total heat taken from the thermal masses of the building structures to be restored within finite duration. 3.2. DR model implementation The implementation of this proposed optimal DR control does not require any additional expensive hardware. A two-way communication is needed between the load control centre and homes. The two-way communication infrastructure is required to be integrated with the existing thermostats to control the room temperatures and charging of the thermal storage. The aggregator company can perform a survey to record the customer occupancy, thermodynamic parameters of house and storage. The customer sets the desired indoor air temperature and allowable thermostat dead-band which is sent to the load control centre via communication channel. The load control centre optimizes the heat load management based on the Spot price/Penalty price and user preferences; and sends the signal to the smart thermostats to control the indoor air temperature and thermal storage charging accordingly. It is a rolling process and the aggregator companies compensate the customer for participating in the DR programme. The magnitude of DR depends on the customer’s preference and willingness to participate. The customers are free to set the priorities and preferences.
2 An aggregator is a company which acts on behalf of group of customers to purchase electricity and allow them to take part in Demand Response (DR) activities.
Nonetheless, the proposed load shaping strategy can bring the optimal DR of space heating load. 4. Case study: optimizing the partial storage space heating load A case study is performed in order to investigate the DR optimization model. An analysis of DR potential of space heating load with different degree of storage size is done. The simulations are performed for an unusual winter day (February 22, 2010). On that day, the spot prices showed a lot of volatility while outdoor temperature was rather low. In Nordic power market the hourly power prices are known one day ahead. The extreme prices in power market usually have a positive correlation with the system peak demand (Fig. 4). The thermal buffers in the house could have played a major role in alleviating the critical situations depicted in Fig. 4. Next, we optimize the DR control of partial storage space heating using LP tool of Matlab.3 The optimization results for different storage sizes are illustrated in Figs. 5–8. As can be seen from Fig. 5, the larger the thermal storage the more is the flexibility in heat load management. With bigger size thermal storages, the heat is not taken from the thermal masses of the building structures. Instead, the scheduling of thermal storage is such that the stored heat in the storage tank coast the peak price periods easily and thus the heat transfer between the building structures and indoor air is prevented. The room temperature set point remains constant hence indicating no loss of comfort. On the contrary, in the case of small storages (S ≤ 20%), the DR optimization model unleashes the full potential of space heating load by utilizing the heat stored in the storage as well as in the building structures. It should be noticed that the thermal masses of building structures is only used during peak price periods (Figs. 6 and 7) and they collaborated with the thermal storage only when the storage capacity is not big enough to coast the peak price period. The heat stored/released in the thermal mass of the building structures is basically governed by thermostat set point. Although, utilizing the thermal masses of building structures results in the change in indoor temperature; however, there is a minimal loss of comfort
3
Matlab V7.9 (R2009b).
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Fig. 6. DR control optimization of space heating with 20% thermal storage.
as the room air temperature dead-band stayed within the allowable limit (±2 ◦ C). The deviation of set point from the desired value changes the heat demand of that hour. This change in heat demand is illustrated as Modified Demand (Figs. 5–8) i.e. the hourly electrical energy to be supplied from the grid. It should be noted that the demand and modified demand are same in Fig. 5 unlike other cases (Figs. 6–8). This is because of having enough thermal storage to coast the stored heat without altering the indoor temperature set point. Also, to be noted that sum of heat stored and released from the thermal masses of the building structures is zero, which means no compromise on daily energy requirement. In case of zero storage, the DR control manages the direct electric space heating load by varying the set point within allowable temperature dead band (Fig. 8). The preheating of house envelope is done optimally, before the occurrence of peak periods. In all of the cases, the thermal comfort has not been violated as the room temperature dead-band altered within acceptable limits.
The optimal control effectively bridges the DR potential of direct electric space heating and thermal storage. The effect of thermal storage on the flexibility of DR control is evident from the simulation results. The DR potential of sufficient storage level is tremendous, nonetheless minimum storage capacity is much more useful than having no storage at all. The bigger storages have more flexibility to respond to the price variation, while the low capacity storages tend to operate close to, and between their extreme limits. The economic benefits of the DR control are calculated and compared with the case of no optimization at all (Table 2). The ‘Limited DR control’ refers to the strategy with NO thermostat set point control. That means the thermal masses of the building structures were unutilized in that strategy. It should be noticed that partial storage space heating load can bring significant demand response potential in spite of having low size storage. Of course, the savings will change depending on the hourly spot prices. The DR combination of direct electric heating and thermal storage proves to be more economical, and savings are significant. It should be noted that the
Fig. 7. DR control optimization of space heating with 10% thermal storage.
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Fig. 8. DR control optimization of direct electric space heating.
Table 2 Comparison of wholesale energy cost savings under different DR strategies. DR Strategies
Optimal DR control (with dead-band control) Limited DR control (without dead-band control)
Energy cost savings (%) No storage
10% storage
20% storage
40% storage
5.51 0
26.65 21
38.2 32.8
46 46
results in Table 2 reflect the percentage energy savings under different control profiles in the example case only. The absolute analysis of retailers/aggregators and customers costs and benefits requires an analysis of extensive data set and is beyond the scope of this paper.
5. Conclusion This study focused on the combined Demand Response potential of the direct electric space heating and partial thermal storages. A price-based optimal control model was proposed and verified by simulations. The results show that the optimal DR control using LP approach is feasible: it will reduce the energy payment of the house, benefit the aggregator companies and indirectly reduce the market power. The DR optimization model is realistic and requires reasonable computational effort. The duo of direct electric heating and thermal storage in tandem brings the best possible DR under the smart grid scenario. The results of the paper can be used for optimizing the control of this kind of heating loads in the cases of variable but predictable electricity prices, like is the situation in Nordic electricity market. The optimization method can also be used in analysing the performance and cost efficiency of various size heat storages. According to the simulations performed, the utilization of thermal inertia of the house masses is beneficial with relatively small heat storages only and there is a limit to the storage size beyond which utilization of thermal inertia is not beneficial for hourly level demand response optimization. In our example case, this storage size was about 40% of the full day heat demand. The future research would focus on employing the optimal DR control to complex building structures having multiple thermal zones using smart thermostats.
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Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr
Combining the Demand Response of direct electric space heating and partial thermal storage using LP optimization Mubbashir Ali a,∗ , Juha Jokisalo b , Kai Siren b , Matti Lehtonen a a b
Department of Electrical Engineering, Aalto University, Espoo, Finland Department of Energy Technology, Aalto University, Espoo, Finland
a r t i c l e
i n f o
Article history: Received 25 April 2013 Received in revised form 22 July 2013 Accepted 22 August 2013 Available online 19 September 2013 Keywords: Demand response Optimal control Partial electric storage space heating Linear programming
a b s t r a c t In this paper, we optimize the Demand Response (DR) control of partial storage electric space heating using a Linear Programming (LP) approach. The objective is to combine the DR control of direct electric space heating and partial thermal storage in order to minimize the total energy cost of customers without sacrificing user comfort. The proposed DR control is optimized according to the dynamic prices, which shifts the power demand from peak price periods to the cheapest hours. The optimal load shaping strategy is examined by performing simulations. The simulation results show that the partial heat storage together with thermal inertia of the house can offer much flexibility in DR control. The optimal DR control model can easily be integrated at the household level for better utilization of distributed energy resources under the Smart Grid scenario. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Power systems around the world are facing an increased challenge of the integration of intermittent renewable generation with various forms of distributed energy sources. This creates urgent requirements for the balancing and optimization of power system operations. One major technology which may respond to this challenge is Demand Response (DR) [1–4]. According to the Federal Energy Regulation Commission (FERC), Demand Response is the “Changes in electric usage by demand-side resources from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized” [5]. Therefore, intelligent load shaping will not only postpone the infrastructure investment, but would also create a more reliable system. According to the Finnish statistics (2012), around 80% of energy consumption in households is spent on heating [6]. Approximately, one quarter of the households utilize some form of electrical heating, which accounts for around 40% of all electricity consumed by the household sector [7]. Mainly, two types of electrical heating are currently employed: direct electric space heating, i.e. heating without thermal storage, and storage space heating. The storage space heating can be further classified into: partial storage space heating
∗ Corresponding author. Tel.: +358 50 4367307; fax: +358 9 47022991. E-mail addresses: mubbashir.ali@aalto.fi, mubbashir [email protected] (M. Ali). 0378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.epsr.2013.08.017
and full storage space heating. The main difference between them is the storage capacity. The full storage space heating has the ability to store all the heat for the following day without significant storage losses. The space heating load is suited for DR application at household level for two reasons. First, space heating load constitues a major share of household load during winter and, secondly, the thermostatic controlled load can be curtailed, reduced or postponed as long as the user comfort is intact [8]. This flexibility can be unleashed by making the space heating load responsive either to price or by providing some incentives. However, all the DR actions must ensure that quality of service is not sacrificed. There has been a growing interest in the residential demand response and many researchers have turned to the household load management. For instance, the authors of [9–13] present an optimal operation of major household loads under Smart Grid scenario. A comprehensie overview of load managemnet practices is presented by Kostkova et al. [14]. An agent based system to simulate household DR is proposed in [15]. Gyamfi and Krumdieck [16] performed a scenario analysis to assess the DR potential during peak load periods. In [17], a pilot study has been performed at the household level to quantify the DR potential utilizing smart metre and token. Mohsenian-Rad and Leon-Garcia [18] present an optimal residential load control in Real Time Pricing (RTP) and Inclining Block Rate (IBR) environment. A price prediction filter, based on a prior knowledge of previous prices, is developed. A home energy management system is proposed by Pipattanasomporn et al. [19] to explore the DR potential at residential level. Gottwalt et al. [20] proposed an algorithm for demand side management at household level under time-of-use (ToU) prices to investigate the impact of variable prices
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Nomenclature hc Tmax Ca EH Emax H h i Ki Qi qi Qmax Qmi Qmmax Qsi S S0 Si t T x
heating power (kW) maximum allowed temperature variation (◦ C) heat capacity of the house (J/K) energy demand (kWh) of the period considered maximum energy demand (kWh) of a day thermal conductance of the house (W/K) scheduling interval (h) index of hours power price (D /kWh) of hour i heat released from the thermal masses of the building structures (kWh) at hour i average heat demand of the house (kWh) at hour i maximum heat that can be released from the thermal masses of the building structures (kWh) heat stored into the thermal masses of the building structures (kWh) at hour i maximum heat that can be stored into the thermal masses of building structures (kWh) heat stored into the thermal storage (kWh) at hour i net capacity of the thermal (tank) storage (kWh) initial level of storage (kWh) level of storage in the beginning of hour i time (s) temperature (◦ C) degree of storage (p.u.) penalty price (D /kWh) for altering the room temperature set point thermal time constant of the house (s)
on energy bills. Recently, many studies have primarily focused on the demand scheduling of major household appliances such as water heater in [21–23], AC in [24], HVAC in [25] and electric vehicles in [26,27]. However, the DR control of partial storage space heating load under dynamic pricing, despite being a major controllable household load, is virtually untreated in the literature. There exist literature [28,29] that deal with the optimal scheduling of storage, however the scheduling of storage is done in isolation of the thermal dynamics of the house. While, the studies pertaining to DR of direct electric heating load, such as [30,31] have not considered the additional thermal storage. Also, the user comfort has not been adequately addressed. This certainly indicates the lack of understanding about the DR potential of partial storage space heating load. We attempt to fill this gap by proposing a simple but optimal DR control of partial storage space heating load without sacrificing the user comfort. The objective is to develop an optimal heat load management that not only reduces the energy costs but also considers the possible compensation paid to the customers for employing the DR control. At present, many electric storage space heating consumers are charged according to the Time of Day distribution tariff [32].1 The existing ToU tariff helps the household consumers to charge the storage during night and release the stored heat during the day as required. However, the partial storage gets fully charged well before the cheaper tariff ends and is unable to coast the stored heat through the rest of the day with night charging alone. The irregular charging approach followed by partial storage
1 In Helsinki, for instance, the daytime distribution tariff is valid on weekdays from 7 a.m. to 8 p.m. The night time distribution is valid at other times. Night time tariff is 30% cheaper than day time tariff.
Fig. 1. 1-Capacity building model.
heating is very ineffective and needs refinement. We tackle this problem by optimally scheduling the partial storage using Linear Programming technique. The proposed DR control also efficiently utilizes the thermal inertia of the house along with the partial thermal storage. During critical periods, if necessary, heat is allowed to be released from the thermal masses of the building structures. The released heat is then restored to the thermal masses of house envelope depending on the price at the hour in question. However, the user comfort has been given the priority and the temperature variation band is not allowed to violate the user preference. Moreover, the daily heating energy requirement is not compromised. The simulation results show that LP can be an effective technique for DR control for a combination of direct and storage based electric space heating. The rest of the paper is organized as follows: in Section 2, Thermodynamic modelling of house and thermal storage is presented. Section 3 presents the DR control optimization and its implementation. In Section 4, we perform the case study and simulations to investigate the optimality of DR control model. Section 5 highlights the main conclusions of the paper. 2. System modelling 2.1. Simplified modelling of house thermal behaviour A simple model to estimate the indoor temperature in a dynamic situation is one-capacity model. In this model, the building fabric heat capacity and air heat capacity is lumped as one capacity Ca (Fig. 1) The indoor air node point is connected to the ventilation supply air temperature Ts through the ventilation air heat conductance Has , to the ground temperature Tg through the conductance Hag and to the external temperature Te through the combined conductance Hame of the external walls and the roof. The infiltration air flow is connected between the external temperature Te and indoor air temperature Ta . By this it is assumed that there is no warming of the infiltration air in the structures and the penetrating air flow has the temperature of the external air. In parallel with infiltration are the windows, which have a negligible thermal mass compared with the rest of the house envelope. To further simplify the model, a virtual conductance Hae between external and internal temperature node points is formed for infiltration heat capacity flow and windows heat conductance. Further, the heating power hc is assumed to be of convective nature and is thus allocated to the indoor air node point. Also, the effect of internal heat gains from the lighting, household appliances and occupancy is assumed to be included in the heat demand profile. If denotes the thermal time constant of the model house, then Eq. (1) can be solved analytically in order
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Fig. 2. Heating demand profiles used in the study for the simulations.
to obtain a causality between the indoor temperature and heating energy requirement. The energy balance for the indoor air node point is: hc = Ca
dTa + Hae (Ta − Te ) + Hame (Ta − Te ) dt (1)
Htotal = Hae + Hame + Hag + Has
(2)
Te ∼ = Tg , owing to the ventilated crawl space in the house
(3)
+
Si+1 = Si + Qsi − qi
+ Hag (Ta − Tg ) + Has (Ta − Ts )
Ta (t) = Ta (0) −
The energy stored at any instant can be given as:
Charging mode
Si+1 < Si
Discharging mode
where,
hc (Htotal − Has )Te Has Ts −t/ − − e Htotal Htotal Htotal
1 [ + (Htotal − Has )Te + Has Ts ] Htotal hc
Si+1 > Si
(6)
(4)
The hourly heating demand for a typical winter day is shown in Fig. 2. The thermodynamic parameter values for a 1-capacity model of a 180 m2 two-floor single-family house insulated according to the minimum requirements of the Finnish 2010 building code C3 [33] are shown in Table 1. The structures of the house are medium massive. With the parameters in Table 1, the thermal time constant is about 17 h.
• • • • • • •
S is the net storage potential Si is the level of storage in the beginning of hour i x denotes the degree of storage Emax is the maximum heat demand of a day Qsi is the energy loaded from grid to storage at hour i qi is the heat energy consumed at hour i i = (1, 2,. . ., h) represents the index of a hour
Depending on the optimization result, the amount of charging power within an hour varies and can in practical case be controlled by altering the duty cycle of the heating system within the hour.
2.2. Modelling an ideal thermal storage behaviour
2.3. Overall system model
The net thermal storage capacity can be expressed as a percentage of maximum demand of a day.
The models of the house’s thermal behaviour (Section 2.1) and thermal storage (Section 2.2) are coupled together for optimal DR control system, see Fig. 3. The thermal storage S is charged by electrical power during cheapest hours to preserve the heat energy for later use. The power may also be directly delivered to the house for heating in case when storage level is too low to meet the heat demand qi . The thermal masses of the building structures would be utilized if the thermal storage is empty during peak electricity price periods. This heat released from the thermal masses of building structures is Qi . However, the released heat energy should be restored to the thermal masses of the building structure by taking the power from the electrical network Qmi during cheaper power price hours, either before or after the moment of heat releasing. The excessive utilization of thermal masses of the building structures is limited by the allowable variation band of indoor temperature Ta , which is set in this study to Tmax = ±2 ◦ C. The implementation of the optimal DR control is discussed in the following section.
S = [x][Emax ]
(5)
⎧ ⎨ x=0
No storage
x=1
Full storage
0≤x≤1
Partial storage
⎩
Table 1 Thermodynamic parameter used in simulation. Factors
Value
Ts Ca Hae Hame Has Hag
18 ◦ C 11,918 kJ/K 52.33 W/K 41.26 W/K 87.43 W/K 15.54 W/K
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Fig. 3. Schematic of system model.
3. Design of the optimal DR control
0 < Qi < Qmi ,
∀i = (1, 2, . . ., h)
3.1. DR control optimization
0 < Qmi < Qmmax ,
Maximum charging power Net storage capacity Quality of service Heating energy demand House cooling rate Maximum heat stored in the thermal masses of the building structures • Maximum heat released from the thermal masses of the building structures The optimal DR model is formulated as follows:
[Ki (Qsi + Qmi ) + (i )(Qi )]
(7)
i=1
Subjected to the following constraints
h
(Qsi + Qmi )≥EH − S0
(8)
i=1
j
[Qsi + Qi − qi ) > (−S0 )
Qm ∈ hc , ∃Qm Ca T
∀i = (1, 2, . . ., h)
(13)
Qmmax = Ca Tmax h
• • • • • •
h
(12)
Qmax = Ca Tmax
In this subsection, we optimize the electric space heating control using Linear Programming approach. The objective is to optimize the DR control of direct electric space heating and thermal storage in duo, to minimize the total energy cost without violating the indoor temperature limits. The objective function faces multiple constraints such as:
Minimize
Q ∈ hc , ∃Q Ca T
[Qi − Qmi ] = 0
(14)
i=1
where, • • • • • • • •
Ki is the power price (D /kWh) of hour i i is the penalty price (D /kWh) of hour i EH is the Energy demand (kWh) of the period considered h is the scheduling time interval (h) S0 is the initial level of storage at t = 0 (kWh) Pmax is the maximum power of the heating system (kW) t is the time step used in the calculations – hour in this case Qmax is the maximum heat that can be released from the thermal mass of the building structures (kWh) • Qmmax is the maximum heat that can be stored into the thermal mass of the building structures (kWh).
In (7), the first term (Qsi + Qmi ) is the electrical energy that must be bought from the power market at hour i. The penalty price, the latter term, is to make sure that thermal storage is used first. The direct control, i.e. releasing the heat out of house masses, is inevitable when the thermal storage is empty during critical periods. The penalty factor can take any value provided it
(9)
i=1
∀j = (1, 2, . . .h − 1) j
[Qsi + Qi − qi ) < (−S0 ),
(10)
i=1
∀j = (1, 2, . . .h − 1) 0 < (Qsi + Qmi ) < Pmax t,
∀i = (1, 2, . . ., h)
(11)
Fig. 4. An example of spot prices and system demand (normalized values; data from [34,35]).
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Fig. 5. DR control optimization of space heating with 40% thermal storage.
is smaller than the price difference of shifted hours; moreover, the aggregator2 companies may set and modify the penalty price based on contracts with consumers and it could be regarded as the compensation paid to the customers. However, the detailed subject of setting the penalty price is related to electricity markets and is not the focus of our work. The constraint (8) ascertains the minimum heat requirement. The constraint (9) guarantees the quality of service in case the heat is released from the house masses. The net storage capacity limit is enforced by constraint (10). The rated power of electric space heating is bounded by constraint (11). The constraints (12) and (13) bound the heat released and restored to the thermal envelope of the house respectively. Both of the constraints are formulated on the maximum allowable indoor air temperature change. While, the constraint (14) ascertains that the total heat taken from the thermal masses of the building structures to be restored within finite duration. 3.2. DR model implementation The implementation of this proposed optimal DR control does not require any additional expensive hardware. A two-way communication is needed between the load control centre and homes. The two-way communication infrastructure is required to be integrated with the existing thermostats to control the room temperatures and charging of the thermal storage. The aggregator company can perform a survey to record the customer occupancy, thermodynamic parameters of house and storage. The customer sets the desired indoor air temperature and allowable thermostat dead-band which is sent to the load control centre via communication channel. The load control centre optimizes the heat load management based on the Spot price/Penalty price and user preferences; and sends the signal to the smart thermostats to control the indoor air temperature and thermal storage charging accordingly. It is a rolling process and the aggregator companies compensate the customer for participating in the DR programme. The magnitude of DR depends on the customer’s preference and willingness to participate. The customers are free to set the priorities and preferences.
2 An aggregator is a company which acts on behalf of group of customers to purchase electricity and allow them to take part in Demand Response (DR) activities.
Nonetheless, the proposed load shaping strategy can bring the optimal DR of space heating load. 4. Case study: optimizing the partial storage space heating load A case study is performed in order to investigate the DR optimization model. An analysis of DR potential of space heating load with different degree of storage size is done. The simulations are performed for an unusual winter day (February 22, 2010). On that day, the spot prices showed a lot of volatility while outdoor temperature was rather low. In Nordic power market the hourly power prices are known one day ahead. The extreme prices in power market usually have a positive correlation with the system peak demand (Fig. 4). The thermal buffers in the house could have played a major role in alleviating the critical situations depicted in Fig. 4. Next, we optimize the DR control of partial storage space heating using LP tool of Matlab.3 The optimization results for different storage sizes are illustrated in Figs. 5–8. As can be seen from Fig. 5, the larger the thermal storage the more is the flexibility in heat load management. With bigger size thermal storages, the heat is not taken from the thermal masses of the building structures. Instead, the scheduling of thermal storage is such that the stored heat in the storage tank coast the peak price periods easily and thus the heat transfer between the building structures and indoor air is prevented. The room temperature set point remains constant hence indicating no loss of comfort. On the contrary, in the case of small storages (S ≤ 20%), the DR optimization model unleashes the full potential of space heating load by utilizing the heat stored in the storage as well as in the building structures. It should be noticed that the thermal masses of building structures is only used during peak price periods (Figs. 6 and 7) and they collaborated with the thermal storage only when the storage capacity is not big enough to coast the peak price period. The heat stored/released in the thermal mass of the building structures is basically governed by thermostat set point. Although, utilizing the thermal masses of building structures results in the change in indoor temperature; however, there is a minimal loss of comfort
3
Matlab V7.9 (R2009b).
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Fig. 6. DR control optimization of space heating with 20% thermal storage.
as the room air temperature dead-band stayed within the allowable limit (±2 ◦ C). The deviation of set point from the desired value changes the heat demand of that hour. This change in heat demand is illustrated as Modified Demand (Figs. 5–8) i.e. the hourly electrical energy to be supplied from the grid. It should be noted that the demand and modified demand are same in Fig. 5 unlike other cases (Figs. 6–8). This is because of having enough thermal storage to coast the stored heat without altering the indoor temperature set point. Also, to be noted that sum of heat stored and released from the thermal masses of the building structures is zero, which means no compromise on daily energy requirement. In case of zero storage, the DR control manages the direct electric space heating load by varying the set point within allowable temperature dead band (Fig. 8). The preheating of house envelope is done optimally, before the occurrence of peak periods. In all of the cases, the thermal comfort has not been violated as the room temperature dead-band altered within acceptable limits.
The optimal control effectively bridges the DR potential of direct electric space heating and thermal storage. The effect of thermal storage on the flexibility of DR control is evident from the simulation results. The DR potential of sufficient storage level is tremendous, nonetheless minimum storage capacity is much more useful than having no storage at all. The bigger storages have more flexibility to respond to the price variation, while the low capacity storages tend to operate close to, and between their extreme limits. The economic benefits of the DR control are calculated and compared with the case of no optimization at all (Table 2). The ‘Limited DR control’ refers to the strategy with NO thermostat set point control. That means the thermal masses of the building structures were unutilized in that strategy. It should be noticed that partial storage space heating load can bring significant demand response potential in spite of having low size storage. Of course, the savings will change depending on the hourly spot prices. The DR combination of direct electric heating and thermal storage proves to be more economical, and savings are significant. It should be noted that the
Fig. 7. DR control optimization of space heating with 10% thermal storage.
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Fig. 8. DR control optimization of direct electric space heating.
Table 2 Comparison of wholesale energy cost savings under different DR strategies. DR Strategies
Optimal DR control (with dead-band control) Limited DR control (without dead-band control)
Energy cost savings (%) No storage
10% storage
20% storage
40% storage
5.51 0
26.65 21
38.2 32.8
46 46
results in Table 2 reflect the percentage energy savings under different control profiles in the example case only. The absolute analysis of retailers/aggregators and customers costs and benefits requires an analysis of extensive data set and is beyond the scope of this paper.
5. Conclusion This study focused on the combined Demand Response potential of the direct electric space heating and partial thermal storages. A price-based optimal control model was proposed and verified by simulations. The results show that the optimal DR control using LP approach is feasible: it will reduce the energy payment of the house, benefit the aggregator companies and indirectly reduce the market power. The DR optimization model is realistic and requires reasonable computational effort. The duo of direct electric heating and thermal storage in tandem brings the best possible DR under the smart grid scenario. The results of the paper can be used for optimizing the control of this kind of heating loads in the cases of variable but predictable electricity prices, like is the situation in Nordic electricity market. The optimization method can also be used in analysing the performance and cost efficiency of various size heat storages. According to the simulations performed, the utilization of thermal inertia of the house masses is beneficial with relatively small heat storages only and there is a limit to the storage size beyond which utilization of thermal inertia is not beneficial for hourly level demand response optimization. In our example case, this storage size was about 40% of the full day heat demand. The future research would focus on employing the optimal DR control to complex building structures having multiple thermal zones using smart thermostats.
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