Impacts of Optimization Interval on Home Energy ... - IEEE Xplore

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CSEE JOURNAL OF POWER AND ENERGY SYSTEMS, VOL. 1, NO. 2, JUNE 2015

Impacts of Optimization Interval on Home Energy Scheduling for Thermostatically Controlled Appliances Zhaoguang Pan, Student Member, IEEE, Qinglai Guo, Senior Member, IEEE, Hongbin Sun, Senior Member, IEEE

Abstract—Home energy management systems (HEMS) have attracted much attention in recent years for energy efficiency and cost savings. Home energy scheduling is an important function of the HEMS, especially for thermostatically controlled appliances (TCAs). Optimization interval is a basic parameter in home energy scheduling, a topic that has been seldom studied before. This paper studies the impacts of optimization interval on home energy scheduling taking into consideration four scheduling strategies for TCAs. A tracking strategy is developed to arrive at a suboptimal solution while avoiding unacceptable solving time. The impact mechanism of optimization interval is analyzed. The optimization interval takes into account the scheduling ability of HEMS, flexibility of TCAs, the feasibility of scheduling, scheduling performances, user experiences, and model accuracy. The flexibility of TCAs, which depends on optimization interval, is defined and modeled. Two time division methods are proposed, namely, consistent interval division method (CIDM) and inconsistent interval division method (IIDM). Numerical simulation is carried out to verify the analysis. The results show that optimization interval impacts the flexibility, feasibility, and performance of scheduling. The proposed tracking strategy is seen as an effective method for HEMS. Index Terms—HEMS, optimization interval, scheduling, TCAs.

I. I NTRODUCTION S the global energy crisis and climate change become increasingly urgent, there is a need to take further action in improving energy efficiency of household appliances for reducing CO2 emission. Residential homes now consume a significant share of energy [1], being very low in efficiency due to poor management. In addition, rising energy costs have become major concerns for consumers. Smart homes, equipped with smart appliances, such as thermostatically controlled appliances (TCAs), time-shiftable appliances (TSAs), interruptible appliances, distributed generations (DGs), and energy storage systems (ESS) [2] have become popular around the world because they hold the promise to improve the quality of life through energy savings and efficiency. These smart

A

Manuscript received February 5, 2015; revised May 9, 2015; accepted May 11, 2015. Date of publication June 30, 2015; date of current version May 22, 2015. This work was supported in part by National Key Basic Research Program of China (973 Program) (2013CB228202), the National Natural Science Found for Innovative Research Groups (51321005). Z. Pan, Q, Guo, and H. Sun are all with the Department of Electrical Engineering, State Key Laboratory of Power Systems, Tsinghua University, Beijing 100084, China ([email protected]). Digital Object Identifier 10.17775/CSEEJPES.2015.00024

appliances and systems are also called demand side resources. They have the flexibility to be scheduled to reduce costs and improve energy efficiency while satisfying user experience. Demand response (DR) [3] can be used to take advantage of smart appliances and encourage users to shift loads from peak time to off-peak time to relieve the operational challenge. The research field of home energy management systems (HEMS) [4]–[6] has attracted attention in recent years because homeowners are often faced with difficult decisions on how to optimize energy while using a vast array of household appliances without the benefit of smart decision making tools. In general, they are not equipped to respond to dynamic pricing, intermittent renewable energy generation, and other technical aspects of energy saving in real time. Thus, HEMS has been developed as a tool to help users manage and schedule their appliances automatically. One of the main functions of HEMS is home energy scheduling, which decides when and how appliances work in advance. Among smart appliances, TCAs usually consume the most energy, while having greater flexibility for deriving potential benefits from scheduling. Typical TCAs include heating, ventilating, and air-conditioning (HVAC) systems, air conditioners (ACs) and electric water heaters (EWH), which are common household appliances. Much research has been conducted on TCA scheduling or control to save costs or provide services. In [7] a heuristic algorithm is proposed that schedules TCAs based on price and consumption forecasts taking into consideration users’ comfort settings. Electric water heaters for demand response are modeled in [8] using the PDE method. Reference [9] presents design considerations for a centralized load controller to TCAs for continuous regulation reserves, while [10] demonstrates the potential for providing intra-hour load-balancing services using aggregated HVAC loads. Reference [11] investigates the frequency regulation service through control of fans in commercial building HVAC systems. The scheduling of more appliances, including TCAs has also received extensive study. Reference [12] uses a dynamic programming approach to solve a mixed integer linear programming (MILP) model, including a water heater and thermal energy storage. In [13] particle swarm optimization is used to coordinate residential distributed energy resources, including space conditioning and water heating. The optimal residential load control with price prediction is studied in [14] to achieve a desired trade-off between minimizing the electri-

c 2015 CSEE 2096-0042 ⃝

PAN et al.: IMPACTS OF OPTIMIZATION INTERVAL ON HOME ENERGY SCHEDULING FOR THERMOSTATICALLY CONTROLLED APPLIANCES

-city payment and minimizing the waiting time, including heating. Reference [15] investigates the energy-scheduling problem for a household with solar-assisted thermal load and factors in renewable energy and price uncertainty, including HVAC and water 1heating system. The focus of much of the research to date has been on the models, strategies, or algorithms of home energy scheduling. However, little attention has been paid to the optimization interval. Different papers have adopted different intervals, such as 5 min [16], 15 min [12], [17], and 1 hr [17], [18]. In spite of these works, the impacts of optimization interval still remain unclear. In fact, optimization interval is one of several key parameters in scheduling. 1) The discretization method is widely used in modeling, in which the interval is the basic parameter with regards to model accuracy. Optimization interval also decides the scale of the scheduling problem, which impacts the solving time. 2) The home energy scheduling covers different energy sectors, such as electricity, heating and cooling, and the dynamics of each of these sectors varies considerably. For example, the indoor temperature dynamics of a home is much slower than its electric dynamics. These dynamics are related to optimization interval. 3) Different from traditional thermal units, demand side resources are highly dependent on time constraints, such as the TCAs and TSAs. This is due to the fact that integral or summation is the main feature of these appliances. Time constraints are also related to the optimization interval. Therefore, the optimization interval has significant impact on home energy scheduling. Research on the impact of optimization interval is a necessary preliminary step toward developing advanced HEMS methods. This paper explores the impacts of optimization interval on the home energy scheduling specifically for TCAs. ACs are chosen as typical TCAs to explain the impact mechanism and for simulation purposes. Four strategies are used to solve the scheduling problem. The impacts of optimization interval on these strategies are studied. The impact mechanism is concluded into five categories. Two time decision methods are proposed. The main contributions of this paper can be summarized as follows. 1) The importance of optimization interval in HEMS is identified, an area seldom studied before. Optimization interval reflects the scheduling ability of HEMS and is a key parameter. 2) The impact mechanism of optimization interval is studied, including the flexibility of TCAs, the feasibility of scheduling, scheduling performance, users’ experience and model accuracy. Flexibility of TCAs is defined and modeled by using the flexible temperature zone, which depends on the optimization interval. 3) A tracking strategy is developed to solve the scheduling of TCAs. The tracking strategy can arrive at a suboptimal and practical solution quickly and avoid the unacceptable solving time when the MILP solving methods are used. 4) Two time division methods are proposed to study the impacts of optimization interval, which enable the free selection of optimization interval and coordinate different time intervals of various data.

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The remainder of this paper is organized as follows: Section II introduces the TCA scheduling model. Section III introduces four typical TCA scheduling strategies, including the proposed tracking strategy. Section IV explores the impact mechanism of optimization interval. Section V proposes two time division methods. Numerical simulation and discussions are presented in Section VI. Section VII presents the conclusions and directions for future study.

II. TCA S CHEDULING M ODEL In a smart home, many smart appliances can be scheduled and controlled by HEMS to achieve specific objectives. HEMS includes many functions, one of which is energy scheduling. The scheduling makes decisions to schedule appliances before certain times, such as one day ahead, hours ahead or minutes ahead. Fig. 1 provides an illustration of home energy scheduling. The inputs for scheduling are dynamic price, outdoor temperature, and user demand information. The parameters of the appliances, available from instruction manuals, testing or onsite statistical analysis, are necessary. HEMS uses the available information to make decisions that have specific objectives and constraints. The objective function of scheduling has a big influence on the results and depends on the goals of users. Residential users primarily want to minimize total cost or improve energy efficiency. Retailers or utilities want to maximize profits, reduce peak load and maintain system stability with minimum curtailment. The government hopes to reduce carbon emission or maximize social welfare. Constraints are also very important, and include energy balance, appliance operation limits, and user comfort requirements. These results are sent to appliances for operation. Refer to [17], [19] for more details about the scheduling model. The scheduling covers a period

Fig. 1.

Illustration of home energy scheduling.

to be scheduled, which is called the scheduling horizon, as shown in Fig. 2. The scheduling horizon is divided into many time slots by optimization intervals, which indicate the interval between two commands. The optimization interval presents the duration time of a command. The smaller the interval, the more commands are to be made when the optimization horizon is fixed. This paper focuses on the TCA scheduling, because TCAs

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Scheduling horizon

Optimization interval

Fig. 2.

min f (u, T ) = u

Scheduling commands

N ∑

ck P uk

k=1

s.t. 1 UA (Tk−1 − Tamb,k )△tk + Qk △tk C C Qk = Qother,k − ηP uk

Tk = Tk−1 −

Illustration of optimization interval.

(4)

T k ≤ Tk ≤ T k usually consume the most energy, and have larger flexibility and potential benefits to be scheduled than other appliances. Moreover, TCAs cover both the electricity and cooling sector. In the scheduling, the electric dynamic is very fast and hence is usually ignored. The thermal dynamic of cooling, on the other hand, is much slower and must be considered in scheduling. Thus the thermal dynamic usually dominates in home energy dynamics. The optimization interval is an important parameter that couples electricity and heat, and is related to the thermal dynamic. To explain the main concepts of optimization interval, ACs in cooling situations are used as an example because their working principles can be usually generalized to other TCAs and heating systems. The thermal dynamic of a home can be simplified as (1) by using first-order model [7], [20]. T indicates the indoor temperature, and T amb indicates the ambient temperature. U A indicates the conductance between the indoor and ambient air masses, C indicates the heat capacity of the indoor mass. Q = QAC + Qother represents the heat flux to the mass, including the heat/cooling power of the AC (QAC , negative when cooling) and other heat power (Qother , usually positive) from outside solar sources, other appliances and people. When the AC is on, Q is usually negative, and the indoor temperature decreases. When the AC is off, Q is usually positive, and the indoor temperature increases. Thus (1) can be transformed into a different form as (2), where k indicates the time slot number and △tk is the optimization interval of time slot k. (1)

UA 1 (Tk−1 − Tamb,k )△tk + Qk △tk . C C

(2)

A. Bang Bang Control Strategy (BBCS) Bang bang control strategy (BBCS) is a very simple and widely used method to control ACs [20]. When the indoor temperature exceeds the upper bound, the AC is turned on to cool down the home until the temperature reaches the lower bound. Then the AC is turned off and the temperature goes up. This strategy is illustrated in Fig. 3 and can be modeled by using (5). This strategy has no optimization process, but simply maintains indoor temperature within the comfort zone. BBCS is applicable in the flat price range, but is not able to take advantage of the dynamic price.

Upper bound

The AC is expected to have only “on” and “off” states. This is indicated by a binary variable u . When the AC is on, u = 1 , otherwise u = 0 . The cooling power can be modeled as (3), where P is the rated electrical power of the AC and η is the coefficient of performance (COP) of the AC. QAC = −ηP u.

III. TCA S CHEDULING S TRATEGIES Many strategies have been proposed to schedule TCAs, including heuristic and programming methods. Heuristic methods are simple and fast to apply in practice, but cannot obtain optimal commands. Programming methods can get optimal commands, but are usually time-intensive. Some typical scheduling strategies are introduced.

Temperature

Tk = Tk−1 −

dT = −UA (T − Tamb ) + Q dt

N is the total number of time slots. The objective in this model is to minimize the cost, where ck is the dynamic price of time slot k. This is an MILP because the states of AC denoted by uk are discrete.

Lower bound Time

Power

C

k = 1, 2 · · · , N.

(3)

A comfort zone [T, T] of the indoor temperature is given by users, where T is the upper bound temperature and T is the lower bound temperature. Both T and T can be vectors. The indoor temperature should be kept within the comfort zone by scheduling the AC. Based on this, the TCA scheduling can be modeled using (4) and only taking into consideration the AC.

Time Fig. 3.

Illustration of BBCS of ACs.

  0 uk−1 uk =  1

Tk−1 ≤ T k−1 T k−1 < Tk−1 < T k−1 Tk−1 ≥ T k−1 .

(5)


B. Optimal Bidding Strategy (OBS) Du has proposed a two-step scheduling process to schedule EWH [7]. The first step, called day-ahead scheduling, can be adopted for TCA scheduling. This strategy, known as optimal bidding strategy (OBS), uses least-price electricity while avoiding the peak price. A price threshold is calculated according to the market clearing price curve and the duration of predicted working time. If the price is lower than the price threshold, EWH is turned on, and if the temperature violates the comfort zone, then the temperature set point of the EWH can be set to the upper or lower bound. This process is repeated until the whole scheduling horizon is completed. The detailed process can be found in [7]. This method is also a heuristic method, and can benefit from the dynamic price.

C. Programming Strategy (PS) Programming strategy (PS) uses rigorous mathematical methods to solve the MILP, such as branch and bound algorithms. Now much commercial software such as CPLEX and GUROBI can solve MILP directly. PS can get optimal results, but since MILP is NP, exponent time is required to arrive at a solution. There may be hundreds or thousands of discrete variables in the scheduling, which depend on the number of appliances, number of time slots and model methods. This may result in unacceptable time costs for solving the problem by using PS.

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are very close. This step can be implemented as an algebraic manipulation and therefore is very fast. Furthermore, more complicated rules can be added to this step, such as the least operation time. { 0 Tk−1 ≤ T k−1 (6) uk = 1 Tk−1 ≥ T k−1 . E. Look-Ahead Method to Maintain Comfort Among the above four strategies, the PS can maintain the temperature within the comfort zone if it has feasible solutions. The other three strategies, however, cannot satisfy this comfort requirements because the temperature rectification (turning ACs on or off) happens after the temperature violation occurs. To deal with this problem, a look-ahead method is added. It has three steps, as follows. Step 1: At time slot k, uk is calculated by using original strategy according to Tk−1 . Step 2: Tk is calculated by using (2). This is a look-ahead step. ′ Step 3: If Tk violates comfort zone, change uk as in (7).  Tk ≤ T k  0 ′ uk = (7) uk T k < Tk < T k  1 Tk ≥ T k .

IV. I MPACT M ECHANISM OF O PTIMIZATION I NTERVAL D. Tracking Strategy (TS) A tracking strategy for TCAs is proposed in this paper that can be implemented easily and quickly. This strategy has a clear physical meaning and consists of two steps, as follows. Step 1: Relax the discrete variables of ACs and solve the relaxed problem. The binary variables indicating on/off states are relaxed into continuous variables between 0 and 1. For an AC, the implication is that the condition is ideal and the AC can generate any heat/cooling power less than the rated power in each time slot. An ideal AC has the largest flexibility and can achieve ideal effects. By solving the relaxed problem, ideal scheduling is obtained, as well as the ideal temperature curve. The relaxed problem is an LP and it can be easily and rapidly solved. Step 2: Make scheduling decisions to track the ideal temperature. Set the ideal temperature curve from step 1 as the upper bound of the comfort zone in the cooling situation (or the lower bound in the heating situation). Then schedule the AC using (6) to make scheduling commands. The tracking temperature would be always around the ideal temperature. The smaller the optimization interval is, the more similarity between the tracking temperature curve and the ideal temperature curve will be. If the optimization interval is small enough, the two curves

Optimization interval is a key parameter in home energy scheduling. It determines the time granularity of scheduling and affects the scale of the problem. From the perspective of HEMS, the optimization interval indicates scheduling ability and reaction speed. A smaller optimization interval implies that HEMS can schedule appliances more frequently, and thereby more policies can be applied. Moreover, HEMS can also react faster to variables such as intermittent renewable energy, thus avoiding unexpected incidences and achieving better performance. Furthermore, the optimization interval has more intrinsic impacts on the TCA scheduling.

A. Flexibility of TCAs Optimization interval impacts the scheduling flexibility of TCAs. The TCA scheduling can be optimized because it has flexibility either to be turned on or off for a moment while maintaining the indoor temperature within the comfort zone. Flexibility is defined as the flexible temperature zone where the AC can be either turned on or off. At time slot k, to maintain indoor temperature within the comfort zone, (8) must be satisfied. T k ≤ Tk = Tk−1 − +

UA (Tk−1 − Tamb,k )△tk c

1 (Qother,k − ηP uk )△tk ≤ T k . C

(8)

Further induction gets (9) and (10), which is the intersection

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Temperature

of Tk−1 when uk = 1 and uk = 0 . If Tk−1 is in ′ ′ [T k−1 , T k−1 ], the AC can be either turned on or off at ′ time slot k . Accordingly, if Tk−1 ≤ T k−1 , the AC must ′ be turned off, and if Tk−1 ≥ T k−1 , the AC must be turned on. ′

C A

′

T k−1 ≤ Tk−1 ≤ T k−1

(9) ( )  △tk   Tk − (UA Tamb,k + Qother,k − ηP )   ′ C   ( ) T k−1 =    UA   1− △tk  C ) ( (10)  △tk   (UA Tamb,k + Qother,k ) Tk −  ′  C   ) ( . T =  k−1   UA   △tk 1− C The flexibility at time slot k is given by (11) if initial state is unknown or can be any temperature within the comfort zone. This depends on optimization interval △tk , comfort zone, and other parameters. UA /C is usually quite small compared to △tk , so the denominator changes little when △tk changes. Thus, the larger the optimization interval is, the smaller the flexibility will be. ) ( △tk Tk − Tk − ηP ′ ′ C ( ) Fk−1 = T k−1 − T k−1 = . (11) UA 1− △tk C

B. Feasibility of Scheduling The optimization interval determines the feasibility of the scheduling, which is the precondition for a scheduling problem. Take an AC for example. In Fig. 4, the red line indicates the dynamic process of indoor temperature starting from point A at time 0. The ascending temperature line corresponds to the off state, and the descending corresponds to the on state. Temperature changes are larger when the AC remains on/off for a longer time, namely, a larger optimization interval. This may cause a violation of the comfort zone, as shown at point B and C. If the optimization interval is larger than 16 min, temperature violation occurs regardless of whether the AC is on or off. When the comfort zone is considered as a hard constraint, the problem has no feasible solution. If the optimization interval is between 12 min and 16 min, the AC must be turned off, so this is feasible but not flexible. If optimization interval is smaller than 12 min, this becomes both feasible and flexible.

C. Scheduling Performance The optimization interval impacts the scheduling performance, such as the objective value and the solving time. A smaller optimization interval implies that HEMS has a greater ability to schedule appliances more frequently. This results in the ability to take advantage of cheap electricity. Moreover, a

Upper bound

10 Fig. 4.

B 12

14

16 18 Time (min)

Lower bound

Illustration of feasibility of scheduling.

smaller optimization interval leads to larger flexibility, which usually leads to a better objective value. However, smaller optimization interval causes more time slots and decision variables, which increase the scale of the problem. This costs more in solving time, especially for the PS. Note that small optimization interval can make appliances start and stop frequently, which would damage appliances and lead to additional energy loss caused by starting current [21]. The optimal solution and solving time, therefore, represent a tradeoff.

D. User Experiences The optimization interval also influences user experiences. If optimization interval is large, HEMS cannot respond quickly to variables that vary quickly, and some experience cannot be satisfied. For example, if the optimization interval is too large, the indoor temperature fluctuates greatly, which damages the user experience. Moreover, it may cause a temperature violation. E. Accuracy of Models Since a discrete model is used, its accuracy of models depends on the optimization interval. The discretization method thus will bring errors that depend on the optimization interval. If the optimization interval is too large, the models differ greatly from the real physical characteristics and will cause large errors. Additionally, many variables have errors because the values used are usually the average values or one point in each time slot. This also results in frequent fluctuations that cannot be identified as well as quick dispatches or controls that cannot be executed. From the analysis above, optimization interval is a basic key parameter in the scheduling. On the one hand, smaller optimization interval usually leads to larger flexibility, better objective value and higher experience while larger optimization interval may make the scheduling infeasible, impair the objective value, and damage users’ experience. On the other hand, smaller optimization interval causes more time slots and decision variables, which costs in much more solving time to get the optimal objective value. Moreover, it can also damage appliances and lead to additional energy loss. V. T IME D IVISION M ETHODS In order to study the impacts of optimization interval quantitatively, different optimization intervals should be


studied. Input data such as the dynamic price usually change between every 1 hr to 5 min, namely, price interval. If optimization interval cannot divide this price interval exactly, for example, 13 min cannot divide 1 hr exactly, the remainder becomes a problem in traditional methods. The interval of different data from various systems may differ. In a scheduling problem, the different intervals should be coordinated. Two time division methods are proposed and the dynamic price is used to represent the input data.

B. Inconsistent Interval Division Method The second method is inconsistent interval division method (IIDM) shown in Fig. 6. The price period divides the scheduling horizon into several sub-horizon first; then each sub-horizon is divided again into many time slots. Optimization intervals in different sun-horizons can be different. The price of each time slot equals to the corresponding price period, but its interval is inconsistent. pi +1

pi

...

A. Consistent Interval Division Method The first method is the consistent interval division method (CIDM) as shown in Fig. 5. The interval of each time slot is consistent (=△t) across the entire scheduling horizon, and the price of time slots that cover two price periods are revised. pi +1

pi

...

... Ѭt

p sj-1 = pi Fig. 5.

a Ѭs t-a Ѭt Ѭt pj p sj+1 = pi +1 p sj+ 2 = pi +1

Illustration of consistent interval division method (CIDM).

Subscript i indicates the price period and j the time slot. If a time slot locates in only one price period, the time slot has the same price with the price period, such as psj−1 = pi , psj+1 = pi+1 and psj+2 = pi+1 . Time slot j covers two price periods (i and i + 1), and lasts a time in price period i , and △t − a in price period i + 1 . The price of time slot j is (12). It is assumed that electricity is consumed uniformly in the time slot so the price is the weighted average value of pi and pi+1 : psj =

api + (△t − a)pi+1 . △t

... Ѭt

Ѭt

a

Ѭt

p sj-1 = pi p sj = pi p sj+1 = pi +1 p sj+ 2 = pi +1 Fig. 6.

Illustration of inconsistent interval division method (IIDM).

In Fig. 6, time slot j is the last slot of price period i and its interval is a, the remainder of price period i. The price of time slot is pi . So at least two optimization intervals exist in this situation. If optimization interval can divide price interval exactly, CIDM and IIDM may remain the same if the optimization interval in different sub-horizons is the same. IIDM can be extended into more flexible time slots. For example, a smaller optimization interval can be used when the comfort zone is small to ensure feasibility and flexibility. This action is practical in HEMS because HEMS schedules appliances in single homes that do not affect other homes.

VI. N UMERICAL S IMULATION A. Simulation Setting The simulation is implemented in MATLAB and CPLEX 12.5 on a Core i5 2.50 GHz laptop with 8 GB memory. In order to explain ideas clearly, only one AC is scheduled. The scheduling horizon is 24 hr (from 7:00 to 7:00 next day). The parameter values are listed in Table I and Table II. The ambient temperature and the dynamic price are shown in Fig. 7.

(12)

Other data can be preprocessed like the dynamic price. CIDM is used to compare scheduling performance of different optimization intervals. A variable optimization interval leads to a variable scheduling horizon (=N△t) because the number of time slots N is an integer and the product is not a constant but around H. H is a constant value indicating original horizon, such as 24 hr. In order to make the results comparable, the objective value V of scheduling results is normalized by using (13). After preprocessing, CIDM is compatible with previous fixed optimization interval studies. H . Vn = V N△t

95

(13)

TABLE I PARAMETER VALUES OF N UMERICAL S IMULATION Parameter

Value

Parameter

Value

P η UA

2 kW 3.8 62.5 W−1

C T T

0.525 kWh 27◦ C 23◦ C

TABLE II OTHER H EAT P OWER Qother Time

7:00-8:00

8:00-18:00

18:00-21:00

21:00-7:00

Value (W)

1,390

1,000

1,650

1,390


Price ($)

Temperature o(C)

96

34 32 30 28

07:00

11:00

15:00

19:00 Time (a)

23:00

03:00

07:00

0.24 0.20 0.16 0.12 0.08 0.04 07:00

11:00

15:00

19:00 Time

23:00

03:00

07:00

(b)

Fig. 7.

Parameters. (a) Ambient temperature. (b) Dynamic price.

B. Impacts of Optimization Interval Four strategies introduced in Section III are simulated with the look-ahead method to study the impacts of optimization interval. An ideal strategy (IS) is used as a baseline. The IS is Step 1 of TS, which has an ideal performance but is not applicable in practice because the binary variables are relaxed. The short names are BBCS, OBS, PS, TS, and IS. CIDM is used. The cost of five strategies with different optimization interval is presented in Fig. 8. When optimization interval is larger than 17 min, there is no feasible solution to maintain the indoor temperature within the comfort zone. Indoor temperature using five strategies is presented in Fig. 9 to Fig. 13. The optimization interval is 5 min and 10 min, respectively, in each strategy.

cost is the least cost. In this case study, when only the cost saving is considered, IS > PS > TS > OBS > BBCS. But the results of IS are just used as a baseline and they are not applicable directly. When the optimization interval is large, the difference among BBCS, OBS, TS, and PS is minimal, because there is little flexibility to find better scheduling commands. When the optimization interval is 17 min, the flexibility is zero, and there is no difference among the four strategies. When optimization interval is small, the difference among the four strategies is large because the flexibility is also large to find better scheduling commands. This makes the cost of PS and TS nearer to the ideal cost of IS. Fig. 9 presents the indoor temperature using IS, which has an ideal performance but is not applicable in practice. Optimization interval has few impacts on IS. The indoor temperature (ideal temperature) is almost the same with different optimization intervals. At most times, the ideal temperature reaches the upper bound to save energy by generating neither less nor more cooling energy because the AC is ideal. More importantly, the AC can respond to the dynamic price. When the price goes lower, the ideal temperature also goes lower, which means the AC utilizes cheaper electricity and stores it for high price periods. The ideal temperature reflects the real electricity value more than the price. When energy is stored, energy loss also happens, which is a tradeoff with the low price. So a balance between the low price and the energy loss is obtained through IS. Only when the benefits of storing energy are larger than the energy loss, the AC works to store energy. Otherwise the AC just keeps the indoor temperature at the upper bound. Therefore, the ideal temperature is also a signal of the real electricity value considering both the price and the energy loss. This is why the cost of IS is the lowest.

Temperature (ć)

28

BBCS OBS PS TS IS

1.8

26 24 22 07:00

1.4

Temperature (ć)

Infeasible

Cost ($)

1.6

11:00

15:00

28

19:00 Time

23:00

03:00

07:00

23:00

03:00

07:00

(a)

26 24 22 07:00

11:00

15:00

19:00 Time (b)

1.2 0

2

4

6

8

10

12

14

16

18

Indoor temperature

Lower bound

Upper bound

Optimization Interval (min)

Cost of five strategies with different optimization interval.

Fig. 9. Indoor temperature using IS with optimization interval of (a) 5 min (b) 10 min.

Optimization interval has big impacts on the BBCS, OBS, TS, and PS. As Fig. 8 shows, on the whole, a smaller optimization interval leads to less cost of the OBS, TS, and PS. There is little change in the cost of the IS, and the ideal

Fig. 10 presents the indoor temperature using BBCS. Since the look-ahead method is used, the indoor temperature cannot always reach the bound, which is obvious when the optimization interval is 10 min. If the AC keeps on or off

Fig. 8.


24 22 07:00

11:00

15:00

28

19:00 Time (a)

23:00

03:00

24

15:00

19:00 Time

23:00

03:00

07:00

23:00

03:00

07:00

(a)

26 24

11:00

15:00

19:00 Time (b)

Indoor temperature

26

Lower bound

Upper bound

Fig. 11. Indoor temperature using OBS with optimization interval of (a) 5 min (b) 10 min.

24 22 07:00

11:00

28

22 07:00

07:00

11:00

15:00

19:00 Time

23:00

03:00

07:00

(b)

Indoor temperature

Lower bound

Upper bound

Fig. 10. Indoor temperature using BBCS with optimization interval of (a) 5 min (b) 10 min.

Fig. 11 presents the indoor temperature using OBS. The indoor temperature is also near the upper bound to save energy at most times. OBS uses the cheapest electricity to save costs when the indoor temperature goes lower. A small optimization interval can generally enhance above advantages. In this case study, OBS does not perform well in the ACs’ scheduling. Further simulation shows that OBS performs better if the parameters change, such as a larger capacity of the indoor mass, a larger comfort zone, larger other heating power (or quick consumption), which is in the case of the EWH scheduling in [7]. One reason is that the strategy in [7] always sorts the price for the entire horizon in each iteration process, and the lowest prices can reduce the price threshold. This makes for some relatively lower prices when compared to prices of neighborhood time slots that exceed the threshold; thus the appliances are turned off before violation at these time slots. While in the ACs scheduling, the ACs should be turned on and off more frequently to maintain the temperature within the comfort zone, i.e., the ACs should be turned on and off in a shorter period than the EWH. This means that the AC operating time is more short-term and the cost saving is more dependent on the neighborhood comparison. In this situation, OBS cannot be guaranteed to avoid the highest price and even use the lowest price. Fig. 12 presents the indoor temperature using PS. PS can get optimal and applicable scheduling decisions if the solving time is acceptable. The cost of PS is lowest among the four practical strategies except IS, which is not applicable. It is obvious that a small optimization interval can take more advantage of low prices and lead to less cost. The indoor

temperature with small optimization interval (5 min) is more similar to the ideal temperature in Fig. 9, i.e., it is nearer to the ideal cost. 28 Temperature (ć)

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for another optimization interval in order to make the indoor temperature reach the bound, then the comfort zone will be violated. The optimization interval has impacts on BBCS, but the relation is not apparent. BBCS is usually used with a small optimization interval; then the indoor temperature can almost reach the upper and lower bounds.

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Fig. 12. Indoor temperature using PS with optimization interval of (a) 5 min (b) 10 min.

Fig. 13 presents the indoor temperature using TS. The indoor temperature is similar to the ideal temperature in Fig. 9. The smaller the optimization interval, the more similar it is to the ideal temperature and with less cost. The indoor temperature with small optimization interval (5 min) is also similar to that in Fig. 12. This shows that the proposed TS is effective in practice. TS performs better than OBS in this case study because step 1 (same with IS) provides the real electricity value when considering both the price and the energy loss. The real electricity value can also be factored into the neighborhood comparison. Fig. 14 shows the start-stop cycle counts of BBCS, OBS, PS, and TS. BBCS has the least cycle count with little relation

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Fig. 13. Indoor temperature using TS with optimization interval of (a) 5 min (b) 10 min.

to the optimization interval while the start-stop cycle counts of OBS, PS, and TS are highly dependent on optimization interval. When the optimization interval becomes smaller, the count increases slowly on the right side, while it increases more prominently on the left side. This indicates that more flexibility comes from a smaller optimization interval. ACs can start and stop frequently to make use of low prices and save energy to reduce cost. However, frequent start-stop cycles may damage appliances and cause extra energy loss. 250

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and 10 min, the solving time of PS is unacceptable in many situations. In practice, solving time of PS depends on specific values of parameters and variables, and 11 min (or larger) cannot guarantee an acceptable solving time in other conditions. So effective strategies, such as heuristic strategies, or algorithms are needed. The numerical simulation shows that the proposed TS is an effective strategy for application in real scheduling if a suboptimal solution is acceptable. It can be used as a candidate when the PS cannot solve the TCA scheduling within a limited time. It is noteworthy that TS with a small optimization interval may achieve better results than PS with a large optimization interval. TS also can provide an approximate estimation of the PS. In addition, more complicated rules and models can be added to TS.

C. Time Division Methods Simulation The proposed CIDM and IIDM are simulated to demonstrate their applications. The CIDM is used to study the impacts of the optimization interval because the optimization interval should remain consistent when studying its impacts. In real scheduling, the IIDM can also be used. Optimization interval is 14 min in this simulation and PS is applied. The results are presented in Table III and Fig. 16.

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TABLE III C OMPARISON B ETWEEN CIDM AND IIDM U SING PS

Counts of start-stop cycle of BBCS, OBS, PS, and TS.

Fig. 15 shows the solving time of BBCS, OBS, PS, and TS. Maximum solving time is set 3600 seconds in CPLEX to solve PS, so the result is not exactly optimal when the solving time reaches 3600 s. It can be seen that PS costs more time while the three other strategies are very fast. In a practical TCA scheduling, if PS is used, the solving time must be taken into consideration, especially when the scale of scheduling is large and the solving time is limited. In Fig. 15, when optimization interval is between 3 min

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14 min cannot divide 1 hr (60 min) exactly, having a remainder of 4 min. The CIDM only has one optimization interval (14 min), while the IIDM has two optimization intervals (14 min and 4 min). So the number of time slots with the IIDM is bigger than the number with the CIDM.

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this paper includes the influence of uncertainty, approaches to deal with infeasible problems, more effective algorithms and an adaptive optimization interval that considers various parameters and different energy dynamics.

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Indoor temperature using PS with (a) CIDM, (b) IIDM.

This leads to larger flexibility, making the payment with IIDM less. In the lower figure (IIDM) in Fig. 16, many short temperature reductions exit. This shows that the AC is often turned on at the time slots of 4 min. The reason is that the price of the next time slot is higher, and 4 min provides opportunities to store minor cheaper energy. While the corresponding time slot with CIDM covers both lower and higher price periods, it is not cost-effective to turn on the AC to use both lower and higher prices. It can be inferred that a small optimization interval just before the start of price periods can help create the advantages of dynamic prices.

VII. C ONCLUSION HEMS has become an important research area, but little attention has been paid to optimization interval. This paper studies the impacts of optimization interval on home energy scheduling when considering TCAs. A TCA scheduling model and four scheduling strategies are introduced. A tracking strategy is developed to get suboptimal scheduling commands quickly. Impact mechanism of optimization interval is analyzed. Optimization interval, which reflects the scheduling ability of HEMS, has great impacts on the flexibility of TCAs, the feasibility of scheduling, scheduling performance, user experience, and model accuracy. The flexibility of TCAs is defined and modeled by using the flexible temperature zone. Smaller optimization interval leads to larger flexibility, more feasibility, better objective value, higher user experience and more accurate model. Two time division methods are proposed to cope with variable optimization interval and to coordinate different time intervals of different data. A numerical simulation verifies the analysis and the proposed methods. This research highlights the importance and impacts of the optimization interval. It is a preliminary step to the study of optimization interval in scheduling, and more work is needed to study further problems. Future work related to

[1] N. Lu and S.Katipamula, “Control strategies of thermostatically controlled appliances in a competitive electricity market,” in Power Engineering Society General Meeting, 2005, pp. 202–207. [2] M. Begovic, “Smart homes: energy and technology fuse together,” Power and Energy Magazine, IEEE, vol. 11, no. 5, pp. 10–16, 2013. [3] P. Siano, “Demand response and smart grids—a survey,” Renewable and Sustainable Energy Reviews, vol. 30, no. 5, pp. 461–478, 2013. [4] B. Asare-Bediako, W. L. Kling, and P. F. Ribeiro, “Home energy management systems: evolution, trends and frameworks,” in Proc. 47th International Universities Power Engineering Conference (UPEC), 2012, pp. 1–5. [5] Y. Ozturk, D. Senthilkumar, S. Kumar, and G. Lee, “An intelligent home energy management system to improve demand response,” IEEE Transactions on Smart Grid, vol. 4, no. 2, pp. 694–701, 2013. [6] A. Anvari-Moghaddam, H. Monsef, and A. Rahimi-Kian, “Optimal smart home energy management considering energy saving and a comfortable lifestyle,” IEEE Transactions on Smart Grid, vol. 6, no. 1, pp. 324–332, 2015. [7] P. Du and N. Lu, “Appliance commitment for household load scheduling,” IEEE Transactions on Smart Grid, vol. 2, no. 2, pp. 411–419, 2011. [8] Z. Xu, R. Diao, S. Lu, J. Lian, and Y. Zhang, “Modeling of electric water heaters for demand response: A baseline pde model,” IEEE Transactions on Smart Grid, vol. 5, no. 5, pp. 2203–2210, 2014. [9] N. Lu and Y. Zhang, “Design considerations of a centralized load controller using thermostatically controlled appliances for continuous regulation reserves,” IEEE Transactions on Smart Grid, vol. 4, no. 2, pp. 914–921, 2013. [10] N. Lu, “An evaluation of the hvac load potential for providing load balancing service,” IEEE Transactions on Smart Grid, vol. 3, no. 3, pp. 1263–1270, 2012. [11] H. Hao, Y. Lin, A. S. Kowli, P. Barooah, and S. Meyn, “Ancillary service to the grid through control of fans in commercial building hvac systems,” IEEE Transactions on Smart Grid, vol. 5, no. 4, pp. 2066–2074, 2014. [12] H. Tischer and G. Verbic, “Towards a smart home energy management system - a dynamic programming approach,” in Innovative Smart Grid Technologies Asia (ISGT), 2011 IEEE PES, Nov 2011, pp. 1–7. [13] M. A. A. Pedrasa, T. D. Spooner, and I. F. MacGill, “Coordinated scheduling of residential distributed energy resources to optimize smart home energy services,” IEEE Transactions on Smart Grid, vol. 1, no. 2, pp. 134–143, 2010. [14] A. H. M. Rad and A. L. Garcia, “Optimal residential load control with price prediction in real-time electricity pricing environments,” IEEE Transactions on Smart Grid, vol. 1, no. 2, pp. 120–133, 2010. [15] H. T. Nguyen, D. T. Nguyen, and L. B. Le, “Energy management for households with solar assisted thermal load considering renewable energy and price uncertainty,” IEEE Transactions on Smart Grid, vol. 6, no. 1, pp. 301–314, 2015. [16] Z. Chen, L. Wu, and Y. Fu, “Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization,” IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 1822–1831, 2012. [17] M. C. Bozchalui, S. A. Hashmi, H. Hassen, C. A. Canizares, and K. Bhattacharya, “Optimal operation of residential energy hubs in smart grids,” IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 1755–1766, 2012. [18] K. M. Tsui and S. C. Chan, “Demand response optimization for smart home scheduling under real-time pricing,” IEEE Transactions on Smart Grid, vol. 3, no. 4, pp. 1812–1821, 2012. [19] Z. Pan, H. Sun, and Q. Guo, “Tou-based optimal energy management for smart home,” in Innovative Smart Grid Technologies Europe (ISGT EUROPE), 2013 4th IEEE/PES, Oct 2013, pp. 1–5. [20] Z. Yu, L. Jia, M. C. Murphy-Hoye, A. Pratt, and L. Tong, “Modeling and stochastic control for home energy management,” in Power and Energy Society General Meeting, 2012 IEEE, July 2012, pp. 1–9.

100


[21] A. Aswani, N. Master, J. Taneja, D. Culler, and C. Tomlin, “Reducing transient and steady state electricity consumption in hvac using learningbased model-predictive control,” Proceedings of the IEEE, vol. 100, no. 1, pp. 240–253, Jan 2012.

Zhaoguang Pan (S’13) was born in Zhejiang Province, China, on April 9, 1991. He received the B.S. degree in 2013 from the Department of Electrical Engineering, Tsinghua University, Beijing, China. He is currently a Ph.D. candidate with the Department of Electrical Engineering, Tsinghua University, Beijing, China. His research interests include demand side energy management, flexible demands, and integrated energy system.

Qinglai Guo (SM’14) was born in Jilin City, China, on March 6, 1979. He received the B.S. degree in 2000, and the Ph.D. degree in 2005 from the Department of Electrical Engineering, Tsinghua University, Beijing, China. He is currently an Associate Professor with Tsinghua University. His current research interests include smart grids, cyber-physical systems, and electrical power control center applications. Dr. Guo is a member of the CIGRE C2.13 Task Force on Voltage/Var Support in System Operations.

Hongbin Sun (SM’12) received the double B.S. degrees in 1992, and the Ph.D. in 1997 from the Department of Electrical Engineering, Tsinghua University, Beijing, China. He is currently a Changjiang Scholar of Education, Ministry of China; a Full Professor of electrical engineering with Tsinghua University; and an Assistant Director of the State Key Laboratory of Power Systems, Tsinghua University. From 2007 to 2008, he was a Visiting Professor with the School of Electronics Engineering and Computer Science. He has published over 300 academic papers. His current research interests include smart grids, renewable generation integration, and electrical power control center applications. Prof. Sun is a Fellow of the Institution of Engineering and Technology (IET), and a member of IEEE PES CAMS Cascading Failure Task Force and CIGRE C2.13 Task Force on Voltage/Var Support in System Operations. He won the China National Technology Innovation Award in 2008, the National Distinguished Teacher Award in China in 2009, and the National Science Fund for Distinguished Young Scholars of China in 2010.