A Bi-Level Coordinated Optimization Strategy for

energies Article

A Bi-Level Coordinated Optimization Strategy for Smart Appliances Considering Online Demand Response Potential Jia Ning 1 , Yi Tang 1, *, Qian Chen 1 , Jianming Wang 2 , Jianhua Zhou 2 and Bingtuan Gao 1 1 2

*

School of Electrical Engineering, Southeast University, Nanjing 210096, Jiangsu, China; [email protected] (J.N.); [email protected] (Q.C.); [email protected] (B.G.) Jiangsu Electric Power Company Research Institute, Nanjing 211103, Jiangsu, China; [email protected] (J.W.); [email protected] (J.Z.) Correspondence: [email protected]; Tel.: +86-25-8379-0617

Academic Editor: Chunhua Liu Received: 20 March 2017; Accepted: 11 April 2017; Published: 13 April 2017

Abstract: Demand response (DR) is counted as an effective method when there is a large-capacity power shortage in the power system, which may lead to peak loads or a rapid ramp. This paper proposes a bi-level coordinated optimization strategy by quantitating the DR potential (DRP) of smart appliances to descend the steep ramp and balance the power energy. Based on dynamic characteristics of the smart appliances, the mathematic models of online DRP are presented. In the upper layer, a multi-agent coordinated distribution method is proposed to allocate the demand limit to each agent from the dispatching center considering the online DRP. In the lower layer, an optimal smart appliances-controlling strategy is presented to guarantee the total household power consumption of each agent below its demand limit considering the consumers’ comfort and response times. Simulation results indicate the feasibility of the proposed strategy. Keywords: demand response potential (DRP); bi-level strategy; smart appliance; comfort index

1. Introduction With the development of the smart grid, increasing intermittent renewable generations are connected to the power grid [1]. In contrast to the traditional peak load shifting requirements, the timing balance between peak demand and renewable energy production brings a new challenge for power system operation. Particularly in locations with a high solar electric capacity, the amount of power that must be generated from sources other than solar displays a rapid increase around sunset and peaks in the mid-evening hours, producing a graph that resembles the silhouette of a duck [2,3]. For the duck curve [4], there exist two typical line segments reflecting poor load factors: the decreasing segment for the duck abdomen and the increasing segment of the duck neck, both of which induce poor load factors by reducing average load and increasing maximum load, respectively. In power systems with a large-capacity power shortage, like the duck load curve where there is rapid growth of photovoltaic (PV) generation [5], the major concern for grid operators is, after times of high solar generation, that the power system must rapidly increase power output around the time of sunset to compensate for the loss of solar generation to keep electricity supply balance and the power system’s frequency stability. Storage can be used to fix these issues to flatten the load curve and prevent generator output fluctuation with a more well-fitting load factor. However, cost is a major limiting factor for energy storage to be utilized in a broad way. Besides strategies of generation side, demand side resources have high potential to smooth the load curve. With growing number of smart meters and smart appliances being applied on the customer

Energies 2017, 10, 525; doi:10.3390/en10040525

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side, more consumption data can be used by demand response (DR) technologies to participate in smoothing the load curve. Such growing availability of energy consumption data offers unique opportunities in understanding the dynamics on both sides including customer behaviors on the consumption side and operating requirements, planning, and optimization on the utility side. Existing DR programs usually offer identical incentives to participant consumers within the programs. However, since consumers are different in terms of life-style, electricity usage pattern [6] and response to incentives, how to calculate the concrete demand response potential (DRP) value when a DR event occurs to make the most of the DR resources of all participant consumers is a question of great significance for every DR implementer. To answer this question, a natural first step is to evaluate how much electricity usage could be reduced for each participant consumer considering the willingness and behaviors of consumers in the period of the coming DR event [7,8]. Although there are quite a few works evaluating consumers’ DRP using various methods [9–11], a method that can dynamically identify the appliances’ operation characteristics difference online is still missing, which motivates the work of this paper. In recent years, smart appliances have been extensively studied at home and abroad. Lu [12] investigated the heating, ventilation and air conditioning (HVAC) load potential for providing load balancing service. Niro et al. [13] proposed a practical strategy that can control large-scale domestic refrigerators for demand peak reduction in distribution systems. Although these studies use the DRP of the smart appliances, the method of evaluating the DRP quantitatively online is still limited. Ahmed et al. [14] the home energy management scheduling controller of the residential DR strategy is proposed to predict the optimal ON/OFF status for home appliances which can significantly reduce the peak-hour energy consumption. Bhattarai et al. [15] presents a multi-timescale control strategy to deploy electric vehicle demand flexibility to solve grid unbalancing and congestions. Shad et al. [16] presents a methodology for estimating and predicting the state of individual domestic electric water heaters (DEWHs) from models of their thermodynamics and water consumption. Authors of [14–16] did not take into account the steep ramp like in the duck curve. While in [17], the proposed DR strategy is designed in two layers (including the neighborhood area network (NAN) and the home area network (HAN)), and takes into account consumer comfort and proposes its indices, the DR strategy in HAN ignored the response times limit of all the smart appliances. An intelligent home energy management algorithm which manages household loads according to their preset priority and guarantees the total household power consumption below certain levels is presented in [18], which can benefit electric distribution utilities and DR aggregators in providing an insight into the limits and DRP available in residential markets. Half-hour-ahead rolling optimization and a real-time control strategy are combined to achieve household economic benefits and ability to deal with complex operating environments in reference [19]. Authors of [14–19] proposed different DR programs in residential household to provide the load shifting and curtailing of appliances. However, they did not consider the DRP of the smart appliances and lack the quantitative method of DRP. In this paper, we focus on a large-capacity power shortage in power system, which consists of a dispatching center, multiple agents and plenty of consumers with smart appliances including air conditioners (ACs) which are used to refrigerate, water heaters (WHs) and electric vehicles (EVs). The potential of providing load balancing services in [12] is extended to online DRP evaluation for household appliances and includes the EVs which can be interrupted for a longer time than HVAC. This study proposes a bi-level coordinated optimization strategy which includes the distribution method for allocating the demand limit to each agent in the upper method and optimization strategy for satisfying the demand limit in the lower method. The main contribution of this paper can be summarized: (1) a bi-level coordinated optimization strategy for smart appliances is proposed to not only descend the steep ramp but also reduce the peak loads; (2) a quantitative method of DRP is presented to evaluate the smart appliances’ DRP online based on their dynamic operating characteristics and comfort settings; (3) in order to satisfy the demand limit of each agent, an algorithm

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is formulated to guarantee the consumers’ comfort and response times of smart appliances within the permitted range. The rest of10,this Energies 2017, 525 paper is organized as follows. In Section 2, the bi-level DR strategy is 3proposed. of 16 Section 3 describes the appliance models and their dynamic characteristics. Section 4 presents the Thedistribution rest of this paper is organized follows. In upper Sectionlayer. 2, the In bi-level DR5,strategy is proposed. multi-agent method based onasthe DRP in Section an optimization control Section 3 describes the appliance models and their dynamic characteristics. Section 4 presents the strategy is proposed for smart appliances to guarantee the total load below demand limit. Section 6 multi-agent distribution method based on the DRP in upper layer. In Section 5, an optimization provides the simulations of different scenarios and illustrates the results. Finally, the conclusion is control strategy is proposed for smart appliances to guarantee the total load below demand limit. drawn in Section 7. Section 6 provides the simulations of different scenarios and illustrates the results. Finally, the conclusion is drawn in Section 7.

2. Bi-Level Structure Based on DRP 2. Bi-Level Structure Based on DRP Large-capacity power shortage conditions are likely to occur during critical time, when cascading

failures and large-areapower blackouts occur. DR hasare been envisioned deal critical with such Large-capacity shortage conditions likely to occur to during time,unexpected when cascading failures and blackouts occur. DR has been envisioned dealshortage with such supply-limiting events bylarge-area selectively curtailing system loads. To allocateto the power unexpected events by much selectively curtailing system loads. To allocate shortage reasonably, it is supply-limiting crucial to evaluate how electricity usage could be reduced bythe each participant power Considering reasonably, itthe is crucial to evaluate how much electricity usageproposes could be areduced each consumer. feasibility of the implementation, this paper bi-levelby coordinated participant consumer. Considering the feasibility of the implementation, this paper proposes a bioptimization strategy. level coordinated optimization strategy. To realize the proposed strategy, the technological structure is a bi-level structure, where the To realize the proposed strategy, the technological structure is a bi-level structure, where the upper layerlayer includes thethe dispatching DRagents agentsasas the curtailment service provider upper includes dispatchingcenter center and and DR the curtailment service provider (CSP)(CSP) to provide DR Service, and the lower layer consists of agents, consumers and smart appliances to provide DR Service, and the lower layer consists of agents, consumers and smart appliances including ACs, WHs and shownininFigure Figure 1. The represents uploading including ACs, WHs andEVs, EVs, as as shown 1. The greengreen arrowarrow represents uploading data and data and the redarrow arrowindicates indicates giving instructions. Consumers set parameters infor advance for all the the red giving instructions. Consumers set parameters in advance all the smart set set set , water appliances, which consist of the room temperature set point TAC , water settemperature point TWH , set smart appliances, which consist of the room temperature set pointtemperature TAC AC AC WHAC WH set AC W H W H limits oflimits AC and WHand ( Tcomfort ), travel distance L, pointtemperature TW H , temperature of AC WH_ upper (Tcom Tcom_ upper , Tcomfort , Tcomfort,_ T _ lower , T,comfort lower com f ort_upper , Tcom f ort_lower ), f ort_upper f ort_lower travel distance L, and finish time T, andcoefficient responseα time coefficient α of EV. Inofeach time interval finish time T, response time of EV. In each time interval DR period, the ACsof DR p AC to the period, the ACs upload the roomTtemperature Troompower and working power p AC the agent, upload the room temperature agent, thetoWHs upload the the WHs room and working upload thetemperature water temperature Twater and working power andupload the EVs thepower working Twater and pEV power water working power pWH and pthe theupload working , W HEVs p EV , while whilethe theagent agenttransmits transmits the DR signal (s , s , s ) to each smart appliance. Every agent sWH , sW the DR signal ( sAC ,AC ) toEV each smart appliance. Every agent has to has EVH to upload to the the dispatching dispatchingcenter center and dispatching center determines uploadthe theaggregated aggregated DRP DRP to and thethe dispatching center determines the the demand limitlimit PlimitPlimfor each agent. demand for each agent. it

Dispatching Center 1 Plim it

Agent 1 s AC

pAC Troom

sWH

pWH

… sEV

pEV

Upper Layer

N Plim it

1 DRPtotal

N DRPtotal

Agent N s AC

pAC sWH Troom

Twater

pWH

pEV

sEV Twater

Lower Layer ACs

WHs

EVs

ACs

WHs

EVs

AC AC set set WH WH Tcomfort TAC , TWH _ upper Tcomfort _ lower Tcomfort _ upper Tcomfort _ lower L , T , 

Figure 1. The structure of bi-level coordinated optimization strategy. AC: air conditioner; WH: water

Figure 1. The structure of bi-level coordinated optimization strategy. heater; EV: electric vehicle WH: water heater; EV: electric vehicle

AC: air conditioner;

The bi-level control strategy including upper and lower layers is proposed to meet the requirements load curtailment by quantitating smart response potential capacity. The bi-level ofcontrol strategy including upper andappliances’ lower layers is proposed to meet the Figure 2 depicts the flow chart of the bi-level coordinated optimization strategy. In eachpotential time interval, requirements of load curtailment by quantitating smart appliances’ response capacity. the 2proposed control strategy gathering information, which includes the status all time Figure depicts the flow chart starts of thebybi-level coordinated optimization strategy. In of each appliances, comfort range settings, water and room temperature, as well as the EV complete time. In interval, the proposed control strategy starts by gathering information, which includes the status of the upper layer, the smart appliances’ DRP of each agent is quantitated based on the dynamic

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all appliances, comfort range settings, water and room temperature, as well as the EV complete 4time. Energies 2017, 10, 525 of 16 In the upper layer, the smart appliances’ DRP of each agent is quantitated based on the dynamic operating characteristics and comfort settings of smart appliances, then the aggregated DRP of of the the operating agent is achieved. The dispatching center to the agents on the agent center allocates allocates the the total total demand demandlimit limit PPlimit to the agents on the lim it basis agent’s DRP DRP ratio ratioto tothe thetotal totalDRP. DRP.InInthe thelower lowerlayer, layer,the thecomfort comfort index proposed basis of each agent’s index is is proposed to to indicate levelofofsatisfaction satisfactionofofconsumers consumers for for the the corresponding appliance. Considering the indicate thethe level the consumers’ consumers’ comfort comfort encompassing encompassing response times, the coordination coordination optimization optimization strategy of smart smart ii appliances loads power power below below the thedemand demandlimit limit PPlimit of the ith agent. appliances is proposed to realize the total loads of the ith lim it Status of all appliances

Demand response potential of each agent

i Demand limit Plim it (kW) of each agent

Upper layer

Comfort range settings Water temperature and room temperature Comfort index of responsive appliances

EV complete time

Update appliance status

Lower layer

Figure 2. 2. The chart of of bi-level bi-level coordinated coordinated optimization optimization strategy. strategy. Figure The flow flow chart

3. Modeling and Dynamic Operating Characteristics of Residential Smart Appliances 3. Modeling and Dynamic Operating Characteristics of Residential Smart Appliances The residential appliances include heating, ventilation, ACs, WHs, clothes dryers, washing The residential appliances include heating, ventilation, ACs, WHs, clothes dryers, machines, dishwashers, ranges, refrigerators, lights, plug loads, and EVs. ACs and WHs have the washing machines, dishwashers, ranges, refrigerators, lights, plug loads, and EVs. ACs and WHs have characteristic of thermal storage whereby homeowners can defer their power consumption by the characteristic of thermal storage whereby homeowners can defer their power consumption by adjusting room/hot water temperature set points. Usage of EV can be deferred based on homeowner adjusting room/hot water temperature set points. Usage of EV can be deferred based on homeowner preference. All other loads, like cooking and TV, are not controlled. preference. All other loads, like cooking and TV, are not controlled. 3.1. AC AC Model Model 3.1. An AC AC system system with with aa thermostat thermostat works works in in an an “on–off” “on–off” manner manner and and the the AC AC will will simply simply run run at at its its An rated power when turned on. In general, a thermostat control is set that the room temperature will rated power when turned on. In general, a thermostat control is set that the room temperature will d s fluctuate around around the the thermostat thermostat set set point point TTs AC withinthe thedead deadband bandofof± TdTAC fluctuate within /2.2 . AC

AC

(1) The The mathematic mathematic model model of of AC AC (1) Controlling AC AC load load can can be be carried carried out out by by adjusting adjusting cooling cooling set set points. points. When the room room Controlling s T s+TTdd /2), temperatureincreases increasesabove abovethe thecooling coolingset setpoint pointby byhalf halfofofthe thethermostat thermostat dead band temperature dead band (T(AC AC AC 2 ), AC the the air air conditioner conditioner is ON. ON. As As the the air air conditioner conditioner drops below below the the cooling cooling set point point by half half of of the the s s − Tdd /2), the air conditioner is OFF. If the room temperature is within the thermostat dead band (T thermostat dead band ( TAC AC2 ), the air conditioner is OFF. If the room temperature is within the AC  TAC s − T d /2 ≤ T ( t ) ≤ T s + T d /2), the air conditioner will keep its previous temperature range (TAC s dAC s dAC AC air conditioner will keep its previous status. )  TAC + TAC 2 ), the temperature range ( TAC  TAC 2  TAC (tAC status. The relationship is presented in (1): The relationship is presented in (1):  s (t) + T  s d /2 d  PAC , PAC , TAC (t) ≥ TTAC (t )  TAC 2  AC (t )  TACAC s (t) − T  s d /2 d p AC (t) =p (0, (1) T ( t ) ≤ T AC t)   0, TAC (t )  TAC 2 (1) AC AC (t )  TACAC    p (t − 1), T s (st) − T dd /2 ≤ T (t) ≤ s T s ( td) + T d /2 AC

AC  TAC 2 AC 2  TAC (t )  TAC (t )AC  p AC (t  1), ACTAC (t )  TAC

AC

where thethe working power of air in time t (kW);tP(kW); power of pAC(t()t )is is PACrated where p AC working power ofconditioner air conditioner ininterval time interval is the rated AC is the ◦ F); T s ( t ) is the cooling s AC (kW); T ( t ) is the room temperature in time interval t ( set point in time AC (kW); T (t ) is the room temperature in time interval AC t (°F); TAC (t ) is the cooling set power of AC d ACis the thermostat dead band (◦ F). interval t (◦ F); and TAC d point in time interval t (°F); and TAC is the thermostat deadsband (°F). The AC is controlled by changing the cooling set point TAC (s t). Increasing the cooling set point to (t ) . Increasing ACcan is controlled byworking. changingThe thecontrolled cooling setformula point T someThe value stop the AC isACpresented in (2):the cooling set point to some value can stop the AC working. The controlled formula is presented in (2): s set TAC (t )  sAC (t )  TAC

(2)

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s set TAC (t) = s AC (t)· TAC

(2)

set is the cooling where s AC (t) is the DR control signal which is received from in-home controller; and TAC set point (◦ F).

(2)

Determination of room temperature For each time interval t, the room temperature is calculated as: TAC (t + 1) = TAC (t) − ∆t·

G (t) C p (t) + ∆t· AC · AC ∆c ∆c PAC

(3)

where ∆t is the length of time interval t (h); G (t) is heat gain rate of the house during time interval t, positive for heat gain and negative for heat loss (Bth/h); C AC is cooling capacity (Bth/h); and ∆c is energy needed to change the temperature of the air in the room by 1 ◦ F (Bth/◦ F). 3.2. WH Model The water heater model is a temperature-based model rather than energy-based one. This means that the duration of the ON period of the heating coils depends on the temperature set point and the current water temperature. When the current water temperature drops below the desired s d temperature set point by half of the thermostat dead band (TW H − TW H /2), the water heater is ON. As the water temperature goes above the desired temperature set point by half of the s d thermostat dead band (TW H + TW H /2), the water heater is OFF. If the water temperature is within the s d s d temperature range (TW H − TW H /2 ≤ TW H ( t ) ≤ TW H + TW H /2), the water heater keeps its previous status. The relationship is presented in (4):

pW H ( t ) =

   0,

s d TW H (t) ≥ TW H + TW H /2

PW H ,    p ( t − 1), WH

s d TW H (t) ≤ TW H − TW H /2

(4)

s d s d TW H − TW H /2 ≤ TW H ( t ) ≤ TW H + TW H /2

where pW H (t) is the working power of water heater in time interval t (kW); PW H is the rated power of s ( t ) is the desired temperature WH (kW); TW H (t) is the water temperature in time interval t (◦ F); TW H d set point in time interval t (◦ F); and TW is the thermostat dead band (◦ F). H s The WH is controlled by changing the water set point TW H (t). Decreasing the water set point to some value can stop the WH working. The controlled formula is presented in (5): s set TW H ( t ) = sW H ( t )· TW H

(5)

set is the water where sW H (t) is the DR control signal which is received from in-home controller; and TW H ◦ set point ( F). The water temperature in the tank is calculated as Formula (6):

TW H (t + 1) =

TW H (t)·(Vtan k − f r (t)·∆t) f r (t)·∆t + TinletV·tan k hVtan k i lgal )·3412BTU (t)− TAC (t)) + 8.34lb · pW H (tkWh − Atan k ·(TWRHtan · ∆t · 1 k 60 min Vtan k

(6)

h

where Tinlet is the temperature of inlet water (◦ F); f r (t) is the hot water flow rate in time interval t (gpm); Atan k is surface area of the tank ( f t2 ); Vtan k is the volume of the tank (gallons); Rtan k is the heat resistance of the tank (◦ F· f t2 ·h/Btu); and ∆t is the duration of each time interval (minutes) [20]. 3.3. EV Model Here, an on–off strategy is used for EV response, which means that each EV is charged by a constant and maximum power. The benefits of charging with on-off strategy instead of adjustable

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power are as follows. First of all, it was suggested that charging the EV with a constant power could prolong the battery’s service time. Secondly, smaller communication overheads are required to contact with a small subset of EVs and hence it is more practical to turn charging on or off rather than adjusting the charging rate when great amounts of EV charging are scheduled. Finally, it is expected that using on-off strategy can fully charge the EVs in shorter timeframe [21]. To model EV charging profiles, three parameters are essential: the rated charging power, the plug-in time and the battery state-of-charge (SOC). The plug-in time is related to the time of vehicle arrival at home and arrival at work. The calculation of the EV charging profile is described in (7): p EV (t) = PEV · NEV (t)·wEV (t)·s EV (t)

(7)

where p EV (t) is EV charge power in time interval t (kW); PEV is EV rated power (kW); NEV (t) is EV connectivity status in time interval t, “1” if EV is connected to the plug and “0” if EV is not connected; wEV (t) is EV charging status without control in time interval t, which depends on the battery SOC as shown in (8): “0” if EV is not being charged and “1” if EV is being charged; and s EV (t) is DR control signal for EV in time interval t, 0 = OFF, 1 = ON. ( wEV (t) =

0,

SOC (t) ≥ SOCmin

1,

SOC (t) < SOCmin

(8)

where SOC (t) is the state of charge in time interval t, and SOCmin is the minimum SOC limit of EV at the desired finish time [22]. The battery SOC after EV charging completes should fulfill customers’ demand, which is determined by: L SOC0 ≥ 1 − (9) EEV · Q EV where SOC0 is the initial SOC of EV; L is the travel distance of EV (mile); EEV is the efficiency of driving (mile/kWh); and Q EV is the full capacity of battery (kWh). The EV battery charging model is as follows: SOC (t + 1) = SOC (t) +

p EV (t)·∆t ·η Q EV

(10)

where Q EV is the full battery capacity (kWh); η is the coefficient of charging. 4. Multi-Agent Distribution Method Based on the DRP 4.1. Aggregated DRP DRP means the appliance is working and can stop working to response the DR signal without affecting the consumer’s comfort. Figure 3 shows the DRP of AC and WH in different conditions. set − T d /2 and T set + T d /2, the AC has For the AC, when the room temperature is between TAC AC AC AC DRP if the room temperature has a downward tendency and has no DRP if it has an upward tendency. In order to guarantee the comfort of consumers, the comfort range is set previously. In general, set within the dead band of ± T d /2 is between T AC the range of thermostat set point TAC AC com f ort_lower and AC Tcom f ort_upper except in the condition of AC responding. When the room temperature goes above the set + T d /2 which is below T AC TAC AC com f ort_upper , the AC has DRP until the room temperature is higher than the maximum temperature of comfort range. set − T d /2 and T set + T d /2, the AC For the WH, when the water temperature is between TW H WH WH WH has DRP if the water temperature has an upward tendency and has no DRP if it has a downward set within the dead band of ± T d /2 is tendency. In general, the range of thermostat set point TW H WH

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WH WH Tcomfort Tcomfort and the condition of WH responding. When the water temperature H WH _ lowerT W _ upper except between of WH responding. When the water com f ort_lowersetand dTcom f ort_upper except the condition WH T drops below the which is above , WH ,has DRPhas until water T  T 2 set d W H _ lowerT the WH WH T temperature drops below the − T /2 which iscomfort above the WH DRPthe until the

WH

WH

com f ort_lower

temperature is lower than than the minimum temperature of the comfort range. water temperature is lower the minimum temperature of the comfort range.For Forthe theEV, EV,when when it is connected to the charging station and can charge to the minimum SOC before the desired finish time, DRP. it has DRP.

Water Heater

Air Conditioner

Tcomfort_upper DR potential Troom

None Tset+Deadband/2

Twater DR potential

No DR potential

No DR potential

DR potential

Tset

Tset-Deadband/2 None

DR potential Tcomfort_lower

Figure 3. 3. Demand response potential potential (DRP) (DRP) of of AC AC and and WH. WH. Figure Demand response

The DRP indexes of the three appliances in time interval t + 1 are obtained based on the The DRP indexes of the three appliances in time interval t + 1 are obtained based on the parameters parameters of time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which of time interval t, “1” if the appliance has DRP and “0” if the appliance has no DRP, which are described are described as following formulas (11)–(13): as following formulas (11)–(13): set d set d  (TAC (t  1)  TAC (t ) & &TAC (t  1)  (TAC  TAC 2, TAC  TAC 2))  1, set d set d /2))   ( T ( t + 1 ) < T ( t ) &&T − T /2, T + TAC set dAC ( t +AC1) ∈ ( T  AC AC AC AC DPAC(t1, 1)   || TAC (t  1)  (TAC  TAC 2, Tcomfort _ upper )AC (11)  set d AC DPAC (t + 1) = ) (11) T0, AC ( t + 1) ∈ ( TAC + TAC /2, Tcom f ort_upper others     0, others set d set d  (TWH (t  1)  TWH (t ) & &TWH (t  1)  (TWH  TWH 2, TWH  TWH 2))  1,  WH set d set d set d 1) > TH(T (tcomfort )&&T t WH + 1) T∈WH( TW DPWH (t  1)  ( TW H||(tT+ 2)H − TW H /2, TW H + TW H /2)) (12)  W H ,(T WH (t  1) W _ lower  1, W H set d  ( t + 1 ) ∈ ( T , T − T /2 ) DPW H (t + 1) = (12) T W H W H W H com f ort_lower others  0,  

0,

others

(1, N (t )  1& &SOC (t  1)  PEV P(T ·(Tt −t1) −1)  SOCmin  EV EV ·η ≥ SOCmin DP (t  1)  1, NEV (t) = 1&&SOC (t + 1) + QEVQEV DPEV (tEV+ 1) =  0, others 0, others

(13) (13)

where (t + 1), DPW H (t + 1), and DPEV (t + 1) are the DRP status of the AC, WH, and EV in time AC where DP DP AC (t  1) , DPWH (t  1) , and DPEV (t  1) are the DRP status of the AC, WH, and EV in time interval t + 1 respectively. interval t + 1 respectively. The aggregated The aggregated DRP DRP of of each each agent agent is is presented presented in in (14): (14): N1

N1

N22 N

Nk

1 jj= 1

k 1

Nk

jj j j k i Pi  DP i i (t )  k k (t ) k DRP  (t ) (t P∑  DP DRPtotal (t + =1)∑ PAC · DPAC (t) +  · DP PEV total1()t  AC AC WHW EV· DPEV ( t ) ∑ PPWHW H DP H ) + EV

i =1 i 1

(14) (14)

k =1

where DRPtotal (t  1) is the DRP of all the appliances in one agent in time interval t + 1 (kW); N1 is where DRPtotal (t + 1) is the DRP of all the appliances in one agent in time interval t + 1 (kW); N1 is the i i i is i (DP (t ) DRP the total number of ACs; the rated power ith(kW); AC (kW); is theindex DRP of index of ith PAC AC the total number of ACs; PAC theisrated power of ith of AC DPAC t) is ith AC in j j j PWH ispower AC in time interval the totalofnumber the rated of jthDP WH (kW); 2 is number time interval t; N2 is t; theNtotal WHs; Pof WHs; is the rated of jthpower WH (kW); (t) is WH

WH

j k k N 3 is the DPWH (t ) index is theofDRP index of jthinterval WH int;time totalPnumber of EVs; PEV is kth the the DRP jth WH in time N3 isinterval the totalt; number of EVs; of EV is the rated power k k EV (kW); and DP ( t ) is the DRP index of kth EV in time interval t. rated power of kth EVEV (kW); and DPEV (t ) is the DRP index of kth EV in time interval t.

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4.2. Multi-Agent Coordinated Distribution Method of Upper Layer Layer Based Based on on the the DRP DRP Figure 4 depicts the flow chart of the multi-agent coordinated distribution method in the upper layer. Based on the dynamic operating characteristics of all the smart appliances and the comfort settings given by consumers in advance, the DRP statuses of smart appliances are achieved online. online. For each agent, the aggregated DRP is obtained combining the DRP status with the rated power of smart appliances and then its corresponding corresponding DRP ratio ratio to to the the total total DRP DRP is is calculated. calculated. Each agent agent uploads the aggregated DRP to the dispatching dispatching center and the dispatching dispatching center allocates the total DR limit to the agents based based on on the the DRP DRP ratio. ratio. Dynamic operating characteristics

DRP ratio of each agent to the total DRP status of all smart appliances

Demand limit of each agent

Aggregated DRP of each agent

Comfort settings

Total demand limit

Figure 4. 4. Multi-agent coordinated distribution distribution method method flow flow chart. chart. Figure Multi-agent coordinated

The DR limit for each agent is calculated in Formula (15): The DR limit for each agent is calculated in Formula (15): DRPl  L  ! l l l l l l l l l Plim  L l total  L   pAC  pWH  pEV  pload   P lim it  it  p AC  pWH  pEV  pload DRP (15) l l l l total l  l 1 pl + pl + pl + pl  Plimit = plAC + pW · ∑ (15) EV H + p EV + pload − L  DRPtotal AC WH load − Plimit l l 1 l =1 ∑ DRP total l =1

l l where p lAC , pWH , and pEV are total working power of ACs, WHs, and EVs in the lth agent, l l l l where p AC , pW p EV is arethe total working WHs, and EVs in the lth agent, respectively respectively (kW); total powerpower of all of theACs, appliances except smart appliances in the lth H , andpload l l l l total power of all the appliances except smart appliances (kW); p is the in the lth agent (kW); is agent (kW); agent Plim it is the demand limit of the lth agent (kW); DRPtotal is the total DRP of the lthPlimit load l the demand limit of the lth agent (kW); DRPtotal is the total DRP of the lth agent (kW); L is the total (kW); L is the total number of agents; and Plim it is the total demand limit for all the agents (kW). number of agents; and Plimit is the total demand limit for all the agents (kW).

5. Control Control Strategy Strategy for for Smart Smart Appliances Appliances Considering Considering Consumers’ Consumers’ Comfort Comfort 5. 5.1. Flexible Comfort Index The primary difference between The primary difference betweensmart smartappliances appliancesincluding includingAC, AC,WH WHand and EV EV and and other business related with with customers’ customers’ behavior and their and industry loads is that the former are much more related using the the smart smart appliances, appliances, the the consumers’ consumers’ comfort comfort should subjective desire. In order to realize DR using be considered. The comfort index is proposed, which indicates the customer’s customer’s subjective desire of participating DR DR that that has has helped helped utilities utilities to to design design DR DR policies policies and and strategies. strategies. participating comfort index is. It means that the appliance appliance has The better the customer feels, the higher the comfort controlled when when the the comfort comfort index index is is higher. higher. The AC and WH comfort of higher priority to be controlled consumers are arerelated relatedwith withthe the room temperature water temperature, respectively. the consumers room temperature andand water temperature, respectively. WhenWhen the room room temperature is lower with the function of AC or the water temperature is higher, the consumers temperature is lower with the function of AC or the water temperature is higher, the consumers are are more satisfied the or ACWH. or WH. In order to quantify the consumers’ comfort ACWH, and more satisfied withwith the AC In order to quantify the consumers’ comfort indexindex of ACofand WH, its mathematic is proposed on the temperature comfort temperature range which is set by its mathematic model model is proposed based onbased the comfort range which is set by consumers consumers previously. The comfort index isbetween limited between andAC 1. The AC comfort decreases previously. The comfort index is limited 0 and 1. 0The comfort index index decreases with withroom the temperature room temperature increasing and comfort the WHindex comfort indexwith increases withtemperature the water the increasing and the WH increases the water temperature as formulas described(16) in formulas increasing, asincreasing, described in and (17): (16) and (17):

CAC (t ) 

AC Tcomfort _ upper  TAC (t ) AC AC Tcomfort _ upper  Tcomfort _ lower

(16)

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AC Tcom f ort_upper − TAC ( t )

C AC (t) =

AC AC Tcom f ort_upper − Tcom f ort_lower

CW H (t) =

WH TW H (t) − Tcom f ort_lower WH WH Tcom f ort_upper − Tcom f ort_lower

(16)

(17)

For the EV, the consumer cares more about whether the EV can support the distance of travel for the whole day or not, and the charging times, which can reflect the lifetime of EV battery. If the EV cannot charge to the desired SOC at the complete time, the comfort index is set as 0 which means the consumer gives the poorest rating for comfort and cannot participate the DR program. The comfort index is related with the charging times N (t) and its coefficient α. The comfort index formula of EV is as follows. ( CEV (t) =

1 − α· N (t)

SOC (t) ≥ SOCmin

0

SOC (t) < SOCmin

(18)

where C AC (t), CW H (t), and CEV (t) are the comfort index of air conditioner, water heater and electric AC WH vehicle in time interval t respectively; Tcom f ort_upper and Tcom f ort_upper are the upper limit of room AC WH temperature and water temperature respectively; Tcom f ort_lower and Tcom f ort_lower are the lower limit of room temperature and water temperature respectively; TAC (t) is the room temperature in time interval t and TW H (t) is the water temperature in time interval t; N (t) represents the total charging times during the t period; SOC (t) is the SOC of EV in time interval t; and SOCmin is the minimum SOC limit of EV at the desired finish time [12]. Based on Formula (18), the coefficient α is calculated as α = 1/N (t), then the consumers can set the value of α to limit the response times. The smart appliances are turned off starting from higher comfort index until the total load is below the demand limit, which indicates the sequence of load shedding, not the amount of load shedding. Therefore, it does not indicate more load shedding.

5.2. Control Strategy of Lower Layer As mentioned above, a higher comfort index of AC means the room temperature is closer to the comfort lower limit, which results in more power consumption. Similarly, a higher comfort index of WH/EV needs more power energy. Therefore, this section solves an electricity load scheduling problem of each agent that aims at guaranteeing the comfort index of the residence considering three kinds of appliances that are introduced in the previous section between 0 and 1. ACs and WHs are controlled on the premise of keeping the room/water temperatures limited to the comfort range, which belongs to the comfort settings permitted by consumers previously. The formulas are described as (19)–(21): AC,i AC,i i Tcom (19) f ort_lower ≤ TAC ( t ) ≤ Tcom f ort_upper , ∀i ∈ [1, N1 ] W H,i W H,i i Tcom f ort_lower ≤ TW H ( t ) ≤ Tcom f ort_upper , ∀ j ∈ [1, N2 ]

(20)

The EV SOC at the desired finish time should be below SOCmin and the charging times are limited as follows: Pk ·( T − t) L k SOC (t) + EV k ·η ≥ k k k , N k ≤ Nlimit , ∀k ∈ [1, N3 ] (21) Q EV EEV · Q EV For each agent, the total load power consumption should be below the demand limit allocated based on the DRP: N1

N2

i =1

j =1

N3

l , ∑ piAC + ∑ pW H + ∑ pkEV + plload ≤ Plimit j

k =1

∀l ∈ [1, L]

(22)

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j

k is theDR where CiACtoisprevent the ith AC theswitching jth WH comfort index; C kth time EV comfort In order thecomfort status index; of AC Cand WH frequently, the have to be EV least W H is index; and totalresponding numbers of for AC,atWH, andtlim EV respectively. 3 are the set, namely theNappliance should keep least 1 , N2 , and N it minutes once it starts to respond. In order to prevent the status of AC and WH switching frequently, the least DR time have to be When the appliances are during the tlim it period, it is uncontrolled and the remaining smart set, namely the appliance should keep responding for at least tlimit minutes once it starts to respond. appliances response to the DR event. When the appliances are during the tlimit period, it is uncontrolled and the remaining smart appliances The solution is implemented in MATLAB. Figure 5 depicts the flow chart of optimal strategy in response to the DR event. lower layer. n is the istotal number of controlledFigure smart5 depicts appliances. When the numerical The solution implemented in MATLAB. the flow chartcomparing of optimal strategy in Ptotal magnitude of total loadtotal and of demand limit , if Ptotal When is smaller than the , update the lower layer. n is the number controlled smart comparing Plimappliances. Plim numerical it it magnitude of total load P and demand limit P , if P is smaller than P , update the limit limitindexes of total in next time interval; appliances’ status and continue on thetotal contrary, the comfort smart appliances’ status and continue in next time interval; on the contrary, the comfort indexes of smart appliances except the uncontrolled ones mentioned above are calculated and ranked in descending appliances except the uncontrolled ones mentioned above are calculated and ranked in descending order which defines the largest comfort index C1 , the second largest one C2 , and so on. Next, the order which defines the largest comfort index C1 , the second largest one C2 , and so on. Next, parameters are judged as toaswhether thethe status ith smart appliance equals 1 (1 if the smart the parameters are judged to whether statusSiSof i of ith smart appliance equals 1 (1 if the smart appliance is working, 0 if0 if the not working) working)and andif if comfort index is above 0 appliance is working, thesmart smartappliance appliance is is not thethe comfort index is above 0 which meets thethe constraints ofofFormulas If so, so,the theith ithsmart smart appliance should working which meets constraints Formulas(19)–(21). (19)–(21). If appliance should stopstop working to transform Si from 1 to 0 untilthe theupdated updated total thethe demand limit. to transform thethe Si from 1 to 0 until totalload loadisisbelow below demand limit.

Start

Calculate the comfort indexes and rank C1, C2, …, Cn in descending order

No

Ptotal>Plimit? Yes i=1

No

Si=1&&Ci>0?

Ptotal=Ptotal-Pi

Yes Si=0

i=i+1

i=n?

No

Yes End

Figure 5.5.Flow strategyininlower lower layer. Figure Flowchart chartof of optimal optimal strategy layer.

6. Case Study 6. Case Study 6.1. Simulation Settings 6.1. Simulation Settings This section demonstrates the feasibility of the proposed bi-level DR strategy and analyzes the This section demonstrates the feasibility of the proposed bi-level DR strategy and analyzes the DRP of all the smart appliances and its impact factors. We evaluate the proposed bi-level DR strategy DRP of all the smart appliances and its impact factors. We evaluate the proposed bi-level DR strategy in Section 2 in a community with 10 agents including 1000 residential houses and 3.3 MW PV. The rated

in Section 2 in a community with 10 agents including 1000 residential houses and 3.3 MW PV. The rated power of AC, WH, and EV are 3 kW, 4 kW and 3.3 kW, respectively. For the comfort range setting, the room temperature should be between 19 and 24 °C; the water temperature should be between 44 and 50 °C; the EV should finish charging by 6 a.m. and its SOC should be above 0.95 at the desired finish time; the capacity of EV is 33 kWh.

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power of AC, WH, and EV are 3 kW, 4 kW and 3.3 kW, respectively. For the comfort range setting, the room temperature should be between 19 and 24 ◦ C; the water temperature should be between 44 and 50 ◦ C; the EV should finish charging by 6 a.m. and its SOC should be above 0.95 at the desired finish time; the capacity of EV is 33 kWh. In this paper, it is assumed that the PV starts dropping off and the utility power plants need to ramp up quickly at 6 p.m., and that a demand limit is imposed on this agent during the quickly increased ramp and evening peak period (between 6 p.m. and 11 a.m.). Note that the demand limit level can vary every 15 min or every hour depending on system requirements, but for the purpose of this study, a demand limit of the dispatching center includes a ramp limit assumed to vary every 1 min and peak demand limit assumed to be fixed. Also, 11 a.m. is assumed to be the end of the DR event. For DR control, we set the control interval ∆t as one minute, which is short enough that the customers’ load demand and the renewable energy supply are assumed static. For the DRP of lower layer, the time interval is 15 min. In order to analyze the DRP of all the smart appliances and its impact factors, there are different parameters for each agent shown in Table 1. Some houses expand the comfort range of AC, WH and EV in agents 2 and 3; some have different DR times limit in agents 4 and 5; some have diverse composition of each kind of smart appliances in agents 6 and 7; and the others have different responsive appliances ratio to the smart appliances in agents 8–10. Table 1. The simulation parameters of all the agents. No.

Quantity (AC-WH-EV)

1 Responsive (AC-WH-EV)

1 2 3 4 5 6 7 8 9 10

100-100-100 100-100-100 100-100-100 100-100-100 100-100-100 90-50-100 50-80-100 100-100-100 100-100-100 100-100-100

100-100-100 100-100-100 100-100-100 100-100-100 100-100-100 90-50-100 50-80-100 70-70-70 50-50-50 30-30-30

Comfort Range TAC TAC TAC TAC TAC TAC TAC TAC TAC TAC

∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C, ∈ [19 ◦ C,

24 ◦ C ] TW H 26 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H 24 ◦ C ] TW H

∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [42.5 ◦ C, 50◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCmin = 0.5 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95 ∈ [44 ◦ C, 50 ◦ C ] SOCW = 0.95

2 α

3 T

0.1 0.1 0.1 0.4 0.1 0.1 0.1 0.1 0.1 0.1

10 10 10 10 0 10 10 10 10 10

1:

2 : the response the quantity of responsive appliances which are permitted to respond for the smart appliances; 3 : the least response time of AC and WH (min). times coefficient of EV;

6.2. Simulation Results 6.2.1. Upper Layer Simulation Results Figure 6 illustrates the performance of the proposed bi-level coordinated optimal strategy in keeping the total household consumption below demand limit level and reducing the ramp. Figure 6 displays household consumption between 4 p.m. and 8 a.m. with improved ramp limit and peak demand limit. Table 2 presents the results of multi-agent coordinated distribution method in upper layer. In order to show the variation tendency of DRP during the DR event, the sampling time is set simply as 1 h. It can be seen from Table 2 that the DRP of distinct agent is different and varies with the time going. The ratios of DR to DRP (β) are the same for all the agents. The actual response power of smart appliances is 0, since the total load equals the demand limit at 18:00 when the DRP of agents 1–5 are equivalent because of the same compositions and operating parameters of smart appliances except the comfort settings.

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Figure 6. The total powerconsumption consumption before before after the DRDR signal. Figure 6.6.The total power and after the signal. Figure The total power consumption beforeand and after the DR signal. Table 2. Simulation results of upper layer. Table Table2.2.Simulation Simulationresults resultsof ofupper upperlayer. layer. 19:00 (β = 23.89%) 20:00 (β = 35.45%) 18:00 (β ⑤ = 0%) 19:00 (β = 23.89%) 20:00 (β = 35.45%) No. 18:00 (β ⑤ = 0%) 5

④ DP (β DRP = 23.89%) DP 20:00DRP (β = 35.45%) 18:00 (β DRP = 0%) DP19:00

21:00 (β = 33.19%)

22:00 (β = 19.83%)

21:00 (β = 33.19%) 22:00 (β = 19.83%) DRP(β = 33.19%) DP DRP 21:00 22:00 (β =DP 19.83%) ④ DRP 344.4 DP 0 DRP DP DRP DP DRP DP DRP 100.5 DP 1 421.4 100.7 529 187.5 494 163.9 506.7 4

DRP DRP DP DRP DP DRP DP DRP DP DP 1 0 0 421.4 100.7 529 187.5 494 163.9 504.3506.7 100.0 100.5 2 344.4 344.4 455.4 108.8 577 204.6 522 173.2 12 344.4 0 421.4 100.7 529 187.5 494 163.9 506.7 100.5 3 344.4 344.4 421.4 100.7 529 187.5 494 163.9 508504.3 100.7 100.0 0 0 455.4 108.8 577 204.6 522 173.2 23 344.4 0 0 0455.4421.4 204.6 522 173.2 4 344.4 344.4 361.4108.8 86.3 577529 115.7 41.0 54.9 18.2 41504.3 100.7 187.5 494 163.9 508 8.1 100.0 100.7 34 344.4 0 0 0421.4361.4 187.5 494 163.9 508 5 344.4 344.4 421.4100.786.3 100.7 529 531 188.3 362 120.1 115.7 41.0 54.9 18.2 359.7 41 71.3 100.7 8.1 4 344.4 0 361.4 401.4 86.3 95.9 115.7462 41.0 54.9 18.2 41 8.1 6 163.8 453 150.3 5 344.4 295.4 0 0 421.4 100.7 531 188.3 362 120.1 460.7359.7 91.4 71.3 5 344.4 0 188.3 362 120.1 359.7 85.1 71.3 7 262.4 0421.4 334.4100.7 79.9 531 431 152.8 432 143.4 429.3 6 295.4 0 401.4 95.9 462 163.8 453 150.3 460.7 91.4 6 295.4 0 163.8 453 150.3 460.7 73.4 91.4 8 229.5 0401.4 317.8 95.9 75.9 462 429 152.1 376 124.8 370.2 262.4 165.4 79.9 431 152.8 432 143.4 429.3 3.4 85.1 85.1 77 262.4 0 0 0334.4334.4 152.8 432 143.4 9 192.3 79.9 45.9 431 276 97.9 135.8 45.1 17429.3 8 229.5 0 317.8 75.9 429 152.1 376 124.8 370.2 73.4 8 229.5 152.1 376 124.8 370.2 30.3 73.4 10 81.40 0317.8 106.8 75.9 25.5 429 156 55.3 142 47.1 152.8 165.42756.1 276 97.9 135.8 1150.2 45.1 3349.7 3.4 99 Total 165.4 0 0 0192.3192.3 97.9 135.8 45.1 1717 664.2 3.4 3433.745.945.9 820.2 2764035.7 1430.8 3465.7 10 106.8 25.525.5 55.3 ⑤ 142 142 47.1 152.8 30.3 10 81.481.4 ④0: the0actual 106.8 156156 55.3 47.1 30.3 response power of smart appliances (kW); : the ratio of DP to DRP.152.8 Total 2756.1 1150.2 3349.7 664.2 Total 2756.1 0 0 3433.7 3433.7 820.2 820.2 4035.7 4035.7 1430.8 1430.8 3465.7 3465.7 1150.2 3349.7 664.2 No. No.

4 : the 5⑤

(1) Comfort range: To simulate the scenarios about comfort it is assumed that the room ④: the actual response power smartappliances appliances (kW); :range, of of DPDP to DRP. actual response power of of smart (kW); :the theratio ratio to DRP. temperature range is expanded to be between 19 °C and 26 °C and the water temperature range is (1) range: simulate scenarios range, itSOC is assumed that the room alsoComfort expanded to be To between 42.5 the °C and 50 °C inabout agentcomfort 2. The minimum limit at the desired (1) Comfort range: To simulate the scenarios about comfort range, it is assumed that the room finish time is 0.5isinexpanded agent 3. The results forand comparing agents 1–3 are shown in Figure 7. is temperature range to simulation be between 19◦ °C 26 °C and the water temperature range temperature range is expanded to be between 19 C and 26 ◦ C and the water temperature range is also Both the room temperature range and the water temperature range in agent 2 are expanded, which also expanded to be between 42.5 °C and 50 °C in agent 2. The minimum SOC limit at the desired expanded to be between 42.5 ◦ C appliance and 50 ◦ Ccan in respond agent 2.inThe minimum limit at Therefore, the desired that larger range of SOC temperature. thefinish finishmeans time is 0.5the in corresponding agent 3. The simulation results for comparing agents 1–3 are shown in Figure 7. time variation is 0.5 in agent for comparing agents range 3. of The DRP simulation in agent 2 isresults larger than the one in agent 1. 1–3 are shown in Figure 7. Both the

Both the room temperature range and the water temperature range in agent 2 are expanded, which room temperature range and the water temperature range in agent 2 are expanded, which means means that the corresponding appliance can respond in larger range of temperature. Therefore, the that the corresponding appliance can respond in larger range of temperature. Therefore, the variation variation range of DRP in agent 2 is larger than the one in agent 1. range of DRP in agent 2 is larger than the one in agent 1.

Figure 7. DRP with different comfort ranges.

Figure Figure7.7.DRP DRPwith withdifferent differentcomfort comfortranges. ranges.

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In the agent 3, the minimum SOC the EVs should charge to at the desired finish time reduces In the agent 3, the minimum SOC the EVs should charge to at the desired finish time reduces from 0.95 to 0.5. This means that the EVs charge to prospective SOC using less time and have more fromIn 0.95 0.5. This that SOC the EVs charge to prospective using less time and have more theto agent 3, themeans minimum the EVs should charge to atSOC the desired finish time reduces from time to respond to the DR signal. As shown in Figure 7, the DRP in agent 3 is larger than the one in time to0.5. respond to the DR shown Figure 7, the DRP in agent 3 isand larger than thetime one in 0.95 to This means thatsignal. the EVsAscharge toin prospective SOC using less time have more to agent 1. agent 1. to the DR signal. As shown in Figure 7, the DRP in agent 3 is larger than the one in agent 1. respond (2) Response times limit: Figure 8 depicts the impact of DR times for DRP by changing the (2) Response times limit: Figure Figure 88 depicts depicts the the impact impact of of DR times for DRP by changing the coefficient α of the EVs and the least DR time for AC and WH, respectively. The coefficient α in agent coefficient α of the EVs and the least DR time for AC and and WH, WH, respectively. respectively. The coefficient α in agent 4 is 0.4, which means the EVs response times are limited to be less. Figure 8 illustrates that the DRP 4 is 0.4, which which means meansthe theEVs EVsresponse responsetimes timesare arelimited limitedtotobebeless. less.Figure Figure 8 illustrates that DRP 8 illustrates that thethe DRP in in agent 1 is larger than the one in agent 4 and varies later on account of the potential used during in agent is larger than in agent 4 and varies later on account of the potential used during agent 1 is1 larger than thethe oneone in agent 4 and varies later on account of the potential used during the the DR event. In Figure 9, the EV mean response times reduce much more in agent 4 compared with the event. In Figure 9, the EV mean response times reduce much more in agent 4 compared DR DR event. In Figure 9, the EV mean response times reduce much more in agent 4 compared withwith the the agent 1 and the AC and WH mean response times definitely increase much more. the agent 1 and the AC mean response times definitely increase much more. agent 1 and the AC andand WHWH mean response times definitely increase much more. In agent 5, the least DR times of AC and WH are set as 0, not 10 min like in agent 1. It is definite In agent 5, the least DR times of AC and WH are set as 0, not 10 min like in agent 1. It is definite that the variation range of DRP in agent 1 is less than the in agent 5 as a result of the restriction on that the variation variation range rangeof ofDRP DRPininagent agent1 1isisless lessthan than the agent 5 as a result of the restriction on the in in agent 5 as a result of the restriction on the the DR behavior of the AC and WH. When the limit time of DR changes from 10 min to 0, the AC and the behavior of AC the AC When the limit ofchanges DR changes 10 to min theand AC WH and DR DR behavior of the and and WH.WH. When the limit timetime of DR fromfrom 10 min 0, to the0,AC WH mean response times increase, which leads to the variation of EVs shown in Figure 9. WH response increase, which the variation of shown EVs shown in Figure 9. meanmean response timestimes increase, which leadsleads to thetovariation of EVs in Figure 9.

Figure limits. Figure8.8. 8.DRP DRPwith withdifferent differentresponse responsetimes times Figure DRP with different response times limits. limits.

Figure 9. Mean response times of all appliances with different response times limit. Figure response times times limit. limit. Figure 9. 9. Mean Mean response response times times of of all all appliances appliances with with different different response

(3) Composition of each kind of smart appliance: Different smart appliance composition can (3) Composition of each kind of smart appliance: Different smart appliance composition can of 90 each kind of smart appliance: Different smart appliance composition can affect(3) theComposition DRP. There are ACs (3 kW), 50 WHs (4 kW) and 100 EVs (3.3 kW) in agent 6 and 50 ACs, affect the DRP. There are 90 ACs (3 kW), 50 WHs (4 kW) and 100 EVs (3.3 kW) in agent 6 and 50 ACs, affect the DRP. 90 ACs (3 kW), 50 WHsconsumption (4 kW) and 100 EVs (3.3 kW) in 6 andin50agent ACs, 80 WHs and 100There EVs inare agent 7. The total power in agent 6 equals to agent the power 80 WHs and 100 EVs in agent 7. The total power consumption in agent 6 equals to the power in agent WHs and 100 EVs in the agent 7. The total 6power consumption in agent 6 equals to the the ACs power in agent 7.80Figure 10 shows that DRP in agent is larger than the one in agent 7, since work more7. 7. Figure 10 shows that the DRP in agent 6 is larger than the one in agent 7, since the ACs work more Figure 10 shows that the DRP in agent 6 is larger than the one in agent 7, since the ACs work more frequently than the WHs. frequently than the WHs. frequently than the WHs.

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Figure 10. DRP with different composition of each kind of smart appliances.

(4) The ratio of responsive loads to the smart appliances: At last, we evaluate the impact of different ratios of responsive loads to the smart appliances. Agents 8–10 have the same number of smart appliances as withDRP agent 1, different but not all the smart appliances are permitted to respond. The Figure Figure 10. 10. DRPwith with different composition composition of of each each kind kind of of smart smart appliances. appliances. percentage of responsive loads in agent 8, agent 9 and agent 10 are 70%, 50% and 30%, respectively. Figure shows of agent 1 and 8–10.appliances: The DRP isAthigh the percentage is high (4)11The ratiothe of DRP responsive loads toagents the smart last,when we evaluate the impact of (4)the The ratio of responsive loads to the tendency smart appliances: At last, we evaluate theare impact of except time of red circle and the variation of DRP in agent 1 and agents 8–10 almost different ratios of responsive loads to the smart appliances. Agents 8–10 have the same number of different ratios of responsive loads to the smart appliances. Agents 8–10 have the same number the same. At the end of the DR 1, event, there no smart positive correlation DRP and the ratio smart appliances as with agent but not allisthe appliances arebetween permitted to respond. The of smart appliances as with agent 1, but not all the smart appliances are permitted to respond. owning to the DR actions loads before. percentage of responsive in agent 8, agent 9 and agent 10 are 70%, 50% and 30%, respectively. The percentage of responsive loads in agenthigher 8, agent 9 and agent 10 areloads 70%, 50% and 30%, In 11 general, ratio of responsive is higher thanrespectively. the is one in Figure showsthe theDRP DRPin of agent agent 91 with and agents 8–10. The DRP is high when the percentage high Figure 11 shows the DRP of agent 1 and agents 8–10. The DRP is high when the percentage is high agent depicted invariation Figure 11, the redofcycle DRP in agent is almost lower except10. the However, time of redas circle and the tendency DRP shows in agentthe 1 and agents 8–10 9are except the with time the of red circle and the variation tendency of DRP in agentin1 agent and agents 8–10 are almost compared agent 10. The reason is that more smart appliances 9 respond to the DR the same. At the end of the DR event, there is no positive correlation between DRP and the ratio the same. At the end of the DR21:00. event, there is no positive correlation between DRP and the ratio signal and use more DRP before owning to the DR actions before. owning to the DR actions before. In general, the DRP in agent 9 with higher ratio of responsive loads is higher than the one in agent 10. However, as depicted in Figure 11, the red cycle shows the DRP in agent 9 is lower compared with the agent 10. The reason is that more smart appliances in agent 9 respond to the DR signal and use more DRP before 21:00.

Figure Figure11. 11.DRP DRPwith withdifferent differentratio ratio of of responsive responsive loads. loads.

6.2.2. In Lower Layer Results general, theSimulation DRP in agent 9 with higher ratio of responsive loads is higher than the one in agentFor 10. each However, as the depicted in Figure 11, the red cycle shows the DRP in 9 isthe lower compared agent, statuses of smart appliances are controlled toagent realize total power Figureis11. DRP with different ratio of the responsive with the agent 10. The that more smart in results agent 9loads. to the DR signal and consumption below thereason demand limit. In order to appliances illustrate ofrespond lower layer strategy, Figure use more DRP before 21:00. 12 shows the power consumption of each kind of smart appliances in agent 1. 6.2.2.In Lower Layer Results depicts the AC power from 16:00 to 08:00, in which the Figure 12, Simulation the first subfigure 6.2.2. Lower Layer Simulation nonperiodic curve indicates theResults ACsofresponse to the DR signal. The second shows WH For each agent, the statuses smart appliances are controlled to subfigure realize the totalthe power For eachbelow agent,thethe statuses of In smart to realize total Figure power consumption demand limit. orderappliances to illustrateare thecontrolled results of lower layer the strategy, consumption below the demand limit. In order to illustrate the results of lower layer strategy, Figure 12 12 shows the power consumption of each kind of smart appliances in agent 1. shows power of each kind of smart appliances in agent 1. to 08:00, in which the In the Figure 12,consumption the first subfigure depicts the AC power from 16:00 nonperiodic curve indicates the ACs response to the DR signal. The second subfigure shows the WH

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power the12, third depicts the EV which start to charge at in 17:00 andthe finish at 06:00. In and Figure thesubfigure first subfigure depicts thepower AC power from 16:00 to 08:00, which nonperiodic The blue area, the green area and yellow are the WH, AC subfigure and EV energy 16:00 to 08:00 curve indicates ACs response to the area DR signal. The second shows from the WH power and respectively. the third subfigure depicts the EV power which start to charge at 17:00 and finish at 06:00. The blue area, green area and yellow area are the WH, AC and EV energy from 16:00 to 08:00 respectively.

Figure Power consumption consumption of of each Figure 12. 12. Power each kind kind of of smart smart appliances. appliances.

7. Conclusions This paper presents a novel bi-level coordinated optimal strategy for smart appliances to balance a large-capacity power shortage, which which can can not only only descend descend the the ramp ramp and and reduce reduce the the peak peak loads. loads. The strategy layers. In In thethe upper layer, the demand limitlimit is allocated to each strategyconsists consistsofoftwo two layers. upper layer, the demand is allocated toagent each based agent on the on aggregated demand response potential of the smart In the lower online based the aggregated demand response potential of the appliances. smart appliances. In the layer, lowerthe layer, the DRP is DRP calculated and each agent their smart to guarantee the total load power online is calculated and eachschedules agent schedules theirappliances smart appliances to guarantee the total load below demanddemand limit considering the consumers’ comfortcomfort and response times. times. power required below required limit considering the consumers’ and response Acknowledgments: This National Natural Science Foundation of China (Grant No. Acknowledgments: This work workisissupported supportedbybythe the National Natural Science Foundation of China (Grant 51577030) and the Science and technology project of Jiangsu Electric Power Company Research Institute (Grant No. 51577030) and the Science and technology project of Jiangsu Electric Power Company Research Institute (Grant No. 5210EF150028). No. 5210EF150028). Ning, Yi Yi Tang Tang and contributed in in developing developing the the ideas ideas of of this this research. research. Author Author Contributions: Contributions: Jia Jia Ning, and Bingtuan Bingtuan Gao Gao contributed Jia Ning, Qian Chen, Jianming Wang and Jianhua Zhou performed this research. All the authors read and Jia Ning, Qian Chen, Jianming Wang and Jianhua Zhou performed this research. All the authors read and approved the final manuscript. approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.

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