Shifting Boundary for price-based residential demand response and applications

Applied Energy 146 (2015) 353–370

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Shifting Boundary for price-based residential demand response and applications Fang Yuan Xu ⇑, Tao Zhang, Loi Lei Lai, Hao Zhou State Grid Energy Research Institute, Beijing, China

h i g h l i g h t s  A unique model on appliance level for PBP demand response behavior analysis is proposed.  Shifting Boundary is introduced for PBP effect estimation in the model.  Typical residential daily load curve under specific TOU and RTP can be estimated by Shifting Boundary within the model.  TOU optimization can be processed by Shifting Boundary analysis.  Effect of smart meter implementation can be estimated by Shifting Boundary analysis reversely.

a r t i c l e

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Article history: Received 19 May 2014 Received in revised form 5 February 2015 Accepted 5 February 2015 Available online 7 March 2015 Keywords: Demand response Price based programmes Shiftable load Shifting Boundary Pricing Smart meter

a b s t r a c t Demand Response (DR) is one of the typical methods for optimizing load characteristics in power systems. Utilities offer DR schemes to generate incentives toward consumers’ power consumption behavior for load optimization. In tariff planning, power consumption variation is an important issue which is difficult to be analyzed quantifiably. This paper develops a boundary model for analyzing consumers’ power consumption behaviors, with a particular focus on residential home appliances. Candidate tariffs are analyzed in this model for their load variation potentials. Using three case studies, this paper reflects the potential for practical applications of the model on pricing and smart meter deployment. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Demand Response (DR) in power systems is a concept defined as ‘‘changes in electric usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices when system reliability is jeopardized’’ [1]. DR entails ‘‘all intentional modifications to consumption patterns of electricity of end-use customers that are intended to alter the timing, level of instantaneous demand, or the total electricity consumption’’ [2]. Based on the behavior-driven mechanism, different DR programmes have been divided into two types: Incentive-Based Programmes (IBP) and Price-Based Programmes (PBP) [2]. IBPs rely on the operation mechanism that programme sponsors (i.e. electricity companies) pay participating electric ⇑ Corresponding author. E-mail address: [email protected] (F.Y. Xu). http://dx.doi.org/10.1016/j.apenergy.2015.02.001 0306-2619/Ó 2015 Elsevier Ltd. All rights reserved.

users to reduce their electricity loads at requested times, usually triggered by either grid reliability issues or high electricity prices [3]. IBPs are usually adopted by electricity companies to change the electricity consumption patterns of large electric users (e.g. industrial and commercial organization users). IBPs, as suggested by Albadi in [2], include classical IBP (e.g. Direct Control) and market-based IBP (e.g. Emergency Demand Response Programmes). PBPs rely on the operation mechanism that electric users are economically rational, tending to use less electricity at times when electricity prices are high, given the time-varying rates which can reflect the value and cost of electricity at different times are enabled by electricity companies via different tariffs [3]. PBPs are usually adopted by electricity companies to change the behavior of small and price-sensitive electric users (e.g. small commercial and domestic electric users). PBPs include Time of Use (TOU), Critical Peak Pricing (CPP), Extreme Day CPP (ED-CPP), Extreme Day Pricing (EDP), and Real-Time Pricing (RTP). Refs. [2,3] provide a comprehensive account of the operations on these IBPs and PBPs.

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Demand response attracts researchers as one important research domain in power systems. Effect of DR can be analyzed statistically by various measured data, which is introduced by Ueno in [4]. The impact of DR on power system operation level is also focused by multiple studies, such as the voltage control approach mentioned by Alireza in [5]. These studies focus on static DR modeling for quantifying DR effect. Most of DR effect estimation is to find out the load variation under different DR schemes. A popular method is price-elasticity-style modeling, which emphasizes on establishing a price–load elasticity matrix as the bridge between tariff and load of customer group. Some researchers use a direct proportional coefficient between price and demand to represent the relationship. Joung, Moghaddam, Ferreira, Kwag and Venkatesan have indicated their price elasticity models separately in [6–10]. The elasticity matrices in these models are summarized by large set of historical data and contain the advantages of using practical cases whose load patterns are similar to the selected historical data set. But for other cases, e.g. effect analysis of an unimplemented tariff format in tariff planning, this method will lose robustness. Unlike the static price-elasticity-style modeling, another research attention is paid to customer consuming behaviors at appliance level. Load is decoupled by different appliances and the behavior toward each appliance is modeled. The logic chain is Behavior Incentive ? Behavior Change on Appliances ? Load Change on Appliances ? Total Load Change. This method is targeting on behavior variation incentives and has more stable result than elasticity matrix as the primary cause of load variation (Behavior Incentives) is modeled as well. Various methods are implemented in relevant load model or DR analysis. Shao, Pipattanasomporn and Rahman proposed a residential load model in [11]. This model decouples the load into 4 types of appliances: Space Cooling/Heating, Water Heating, Clothes Dryer and Electric Vehicle. But for demand response research on a large group of residential customers, this model lacks a consideration of a complete set of appliances and their penetration, as well as the behavior variation. In Ghorbani’s study [12], a load model was introduced with emphasis on operational level of appliances, which is more suitable for customers’ power quality analysis than demand response. Electric Power Research Institute (EPRI) in the US has also developed a demand response model framework in [13]. The load modeling in this framework includes the analysis of both appliances and general residential life-style behaviors. However this framework lacks the details of model construction, thus can only be used as a guide for future model research. Models proposed by Walker, Capasso and Dickert in [14–16] appear to contain more suitability than the previous cases. In these studies, appliance usage is considered with home activities and penetration levels. They have high resolution of time steps, i.e. less than one hour. But these models are established at an individual consumer level so that they do not consider behavior tropism and uncertainty of a consumer population. Moreover, the behavior variation triggered by price change is not considered in these studies. Meng and Mohsenian-Rad have provided DR models with consideration of load decoupling and behavior pattern variation in [17,18]. But these two models do not cover the constraint of behavior variation, such as appliance switch-on limitation from leaving home or time limitation for dining. In this paper, a unique model for residential DR analysis was introduced. This model constructs load based on behaviors of different appliances on a multi-agent system. Behavior tropism and uncertainty of large consumer group are achieved by probabilistic modeling of consumers’ behavior. A new concept, ‘Shifting Boundary’, was implemented in this model to measure the largest load shifting potential of several Price-Based Demand Response tariffs. With ‘Shifting Boundary’, estimation of consumers’ behavior change, load variation is no longer limited by historical data set.

Effects of new tariffs can be estimated by this model even without historical data. Also, behavior alternation calculation with the constraints from life-style has been considered. Three case studies on load variation estimation, tariff optimization and smart meter deployment effect estimation were selected to reveal the practical application potential of the model. A model framework of individual consumer behavior and group power consumption is introduced in Section 2. Based on this framework, Section 3 describes the model for behavior shifting using Shifting Boundary. With Shifting Boundary, quantification of behavior transformation is achievable. To reveal the effect of Shifting Boundary, Section 4 provides a case study on the whole model. Sections 5 and 6 provide another two case studies to indicate that different PBPs (or different smart meter installation scale) can be evaluated by using Shifting Boundary.

2. Residential customer behavior modeling 2.1. Multi-agent system modeling Agent based model or multi-agent system is a simulation system for reproducing the interaction between environment and a group of individuals. In this system, agent is an individual unit with intelligence and independent ability for action and decision making. Agents receive information from environment and then generate their own actions toward environments. On the other hand, environment changes its status by actions from agents and then generate new information to agents [19]. Price-Based Demand Response possesses a loop interaction structure as shown in Fig. 1. Price generator creates price information by power consumption information collected from consumers.

Price Generator Price Information

Consumption Information

Information Collection

Smart Meter Price Information

Consumption Information

Power Consumers

Fig. 1. Loop interaction structure of PBPs.

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In many cases, price generator will be a power utility. Sometimes it will be an independent governmental organization in some special areas. Power consumers receive price information through smart meters. With this information, power consumers make or update their consuming plan so as to increase their efficiency by economic incentives. Smart meter provides a platform for bi-directional information flow. It passes the price information, summary of consumption information or power utilization advices to various types of power consumers. Reversely, it collects information of consumers for price generator, including power consumption, real-time power load and power quality. In this paper, a Multi-Agent system is used to construct the loop interaction structure as shown in Fig. 1.

tariff, a detail tariff is updated in advance and is kept unchanged for a long time (such as half year). To a certain extent, TOU reflects the relationship between power demand and power supply. Eq. (2) introduces the pricing scheme of TOU tariff.

8 const1 ; i 2 ðha1 ; ha2 Þ > > > > < const2 ; i 2 ðha2 ; ha3 Þ prii ¼ .. > > . > > : constk ; i 2 ðhak1 ; hak Þ k1 X ðhajþ1  haj Þ ¼ 24

ð2Þ

j¼1

In Eq. (2), a day (24 h) is separated into k periods. Each period provides a specific price level known as constk.

2.2. Multi-agent system structure for PBP demand response Agent is an individual unit with independent ability for action and decision making. In loop interaction structure, price generator and power consumer are recognized as agents with independent decision making function, as revealed in Fig. 2. Agent of price generator is responsible for price making. Under different tariffs, the price signal is generated with various schemes. Typical PBD tariffs are listed below:  Static price tariff

 RTP price tariff Similar as TOU tariff, Real-Time Pricing tariff separates a day into several small time pieces. But each time piece is much smaller (less than 1 h), and represents a much higher changing frequency of time-varying price. This price tariff reflects the utility’s cost of generating and/or purchasing electricity at the wholesale level. In general operating state, RTP and real-time power load have a positive correlation. A typical relationship is revealed in Eq. (3).

prii ¼ a  Area Loadi Static price is the most traditional power tariff. All electricity is sold under the same price value. It contains a simple pricing scheme as given in Eq. (1).

prii ¼ const; const 2 Rþ

355

ð1Þ

where prii is the price value at the ith hour in a day.  TOU price tariff Time-of-Use pricing tariff separates a day into several periods (usually less than 5 periods). It incentivizes customers to permanently alter their energy consumption by using static price rate that are different during peak and off-peak periods [20]. Under this

ð3Þ

where Area_Loadi is the total load generated from a consumer group. a is the rate between price and load, which is usually set by utilities but limited by policies. Practically, the positive correlation mapping is much more complex than Eq. (3). Whole sale price, real-time status of operation, line losses, emergency events are all the influencing factors toward an RTP scheme. Moreover, electricity price is also limited by policies of government and other organizations (e.g. ISO). For example, electricity price for urban residential customers in China are constrained under 1 CNY/kW h by China National Development and Reform Commission. 2.3. Agent of residential consumer

Agent of Price Generator Tariff of Static Price

Tariff of TOU

Tariff of RTP

Other Tariff

Consumption & Price Information Feedback

Electricity consumption of residential consumer is one of the main components of domestic electricity consumption. Load from residential consumers are mainly generated from home appliances in residential houses. People make behavioral decisions for home area power consumption by requirements in life-style. In the loop interaction structure, each agent of consumer represents an individual family with a set of home appliances. An agent makes decision to control all home appliances and generates power load. Influencing factors for changing residential behavior are listed below:  Residential home area appliances and requirements

Agent of Consumer DR Participated

Agent of Consumer No Participation

Agent of Consumer DR Participated Agent Group of Consumers Fig. 2. Multi-agent system model for loop interaction structure.

Home appliances are used for satisfaction of residential home area requirements. Basic requirements cover food, health, comfort, entertainment and so on. Toward these requirements, typical appliances contain computers, cooking devices, fridges, air-conditioners, lights, TV sets, electric-showers and Washing Machines. While satisfying the need, residential consumers generate power load by controlling home area appliances.  Residential life-style The using of home appliances is deeply dependent on condition of life-style. For example, TV will not be switched on when people have left home or fallen asleep. So ‘At Home’ status and ‘Awake’

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status are recognized as the enabling condition for the control of certain appliances, including computers, cooking devices, air-conditioners, lights, TV sets and electric-showers. Washing Machines and Dishwashers have timing function and so are not limited by the two situations.  Residential information feedback Under demand response scheme, information availability is an important foundation for behavior modification. The potential of demand response occurs within people who can access necessary information feedback, including consumption history and price. Other consumers who cannot access information feedback will lack the information support for their decision making and so cannot take part in a demand response program. If a smart meter is the terminal for information feedback, then the consumers’ response to the price will deeply be influenced by smart meter installation scale [21].  Residential financial situation In DR loop interaction, people response to PBP by financial incentives. People will actively response to price variation if they are in a disadvantageous financial situation. In general, the change of consumer behavior will not influence much on financially rich people. Information availability of financial situation can be collected directly by surveys of DR inclination or equivalent statistics can be used instead, like Fuel Poverty rate. Considering the above impact factors, the structure of a consumer agent is represented in Fig. 3 below Fig. 3 reveals the agent structure of consumers who prefer to take part in PBPs. Definitions of the symbols are given in Table 1. Each appliance in the agent is controlled by a specified time-varying switch-on probability. Also, each agent contains an independent decision making process. Life routine, financial situation and

Table 1 Parameters of Eq. (4). Parameters

Description

LRi Swi(on/LRi)

Life routine at hour i Switch-on probability vector of all appliances given life routine at hour i Switch-on probability of appliance n at hour i Electricity price at hour i Logical parameter. ‘1’ means information feedback available. Logical parameter. ‘1’ means financial support available

swin prii IFA FS

information availability are collected for decision making. The final decision will be a rescheduled switch-on probability for each appliance. For those agents without DR participation, there is a lack of input of ‘Consumption & Price Information Feedback’ as shown in Fig. 3. Eq. (4) reveals the decision making process in Fig. 3. Revealed from Eq. (4), people will not change their behavior without information feedback or financial support. Only those people who have information feedback and do not have strong finance will have the potential of PBPs participation.

Swi ðon=LRi Þ ¼ ðswi1 ; swi2 ;    ; swin Þ ¼ f ðLRi ; prii ; IFA; FSÞ  const; IFA  ð1  FSÞ ¼ 0 ¼ gðLRi ; prii Þ; IFA  ð1  FSÞ ¼ 0

ð4Þ

3. Residential customer Shifting Boundary 3.1. Consumer behavior decision making By considering the information received and its own situation (life routine and financial situation), residential consumers alter their behavior decision to reduce their electricity bills. The inner structure of ‘Decision Making’ in Fig. 3 is revealed in Fig. 4. Initially when receiving the information feedback, a residential customer agent will consider its financial situation. Financial situation is an index representing the willingness of DR participation. In the survey, family willingness of DR participation, family income and the bill for basic energy usage are included. The proportion of basic energy usage bill and income is calculated. Further analysis

Life Routine

Financial Situation
Financial Situation

YES Behavior Optimization

Appliance Switch-on Prob Fig. 3. Agent structure of consumers DR participant.

Fig. 4. Inner structure of decision making.

Consumption & Price Information Feedback

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Behavioral alternation is the main influencing factor for load variation in DR. Usage reduction and usage transformation are two primary behavior rescheduling methods.  Usage reduction Reducing utilization of appliances is a straight forward consideration of bill reduction. People reduce their consumption with high electricity price and recover their consumption when price decreases. Manually consumption reduction is simple and easy to promote. It significantly decreases the bill as well as the comfort and satisfaction levels of residential customers. Price-consumption elasticity is the usual index for usage reduction quantization [22].  Usage transformation Usage transformation is another method for behavior rescheduling. People can also transform their consumptions from the time period with high price to the time period with lower price. Usage transformation does not decrease utilization of appliances and so the associated reduction of comfort and satisfaction levels is less then usage reduction. But the promotion of usage transformation and the education of usage transformation to consumers are more complex. Different educational levels or different working backgrounds will also influence the transformation. Difficulties also appear in quantifying usage transformation. To find out the quantization of usage transformation, Shifting Boundary is introduced with the following definition. ‘Under a certain PBPs participation rate and a certain consumers’ financial situation distribution, Shifting Boundary is the maximum usage transformation that a certain consumer group can achieve without usage reduction’. With the definition of Shifting Boundary, PBPs participation rate and consumers’ financial situation distribution are the premise. This premise indicates the DR participant section in a certain consumer group. Usage transformation will come from this section of people. Consumers outside this section will not reschedule their behaviors and consume electricity in their usual way. Consumers within this section are all assumed to take the most efficient usage transformation for bill reduction. Practically, not all consumers can achieve the most efficient usage transformation. Thus the definition is named boundary. A suitable promotion pattern and successful consumer education will approximate the practical usage transformation to the Shifting Boundary. Shifting Boundary indicates the maximum load-shift in a certain group of consumers. 3.3. Shifting Boundary – target function and constraints

Parameters

Description

h(Swijm(on/LRi))

Appliance working status determinations function. At hour i, this function determines the working status of the mth appliance in the jth agent. Output of this function is a Boolean number with 1 represents on-status for the appliance and 0 represents off-status Appliance working status of the mth appliance in the jth agent at hour i Working power of the mth appliance in the jth agent at hour i Power load generated from the jth agent at hour i Total daily bill for the jth agent. Number of seconds in each time interval. In this model, time interval is 1 h, so ti is 3600 seconds

On_staijm Powerijm Loadij Billj ti

8 On staijm ¼ hðSwijm ðon=LRi ÞÞ > > > > M > X > > < Loadij ¼ Power ijm  On staijm

i¼1

 Constraint from same power consumption Corresponding to definition of Shifting Boundary, utilization of each appliance is a constant. This represents that all daily requirements are satisfied as usual. This limit is set as a constraint in Eq. (6) for bill optimization. The total daily power consumption for any appliance under any agent should be kept constant.

Constr : const j ¼

24 X

Loadij  t i

ð6Þ

i¼1

 Constraint from life-style Behavioral rescheduling will be influenced by life-style (At Home status and Awake status). Fig. 5 provides typical time varying ‘At Home’ rate and ‘Awake’ rate for residential consumers. This

1

0.5

0 0

2

4

6

8

10

12

14

16

18

20

22

16

18

20

22

Daily Hour

1

0.5

0

Consumers transform their usage for bill reduction. So the target of Shifting Boundary is to make a behavioral rescheduling for bill minimization. Eq. (5) indicates the target function in Shifting Boundary. Definitions of the symbols are given in Table 2.

ð5Þ

m¼1 > > > 24 X > > > > Loadij  prii  ti : min : Billj ¼

At Home Rate

3.2. Shifting Boundary

Table 2 Parameters of Eq. (5).

Awake Rate

on relationship is taken between the proportion and the willingness locally. Threshold value of proportion for classification of willingness is a typical model in the paper. M is the threshold income value for Fuel Poverty. If a family belongs to Fuel Poverty, it will start its behavior alternation for bill reduction. The Block ‘Behavior Optimization’ helps this agent to reschedule its behaviors. Otherwise, the bill does not take a notable amount of family’s income and cannot provide a strong-enough incentive for behavior changing. In this case, this family will keep its usual behavioral habit.

0

2

4

6

8

10

12

14

Daily Hour Fig. 5. Typical time varying ‘At Home’ Rate and ‘Awake’ Rate for residential consumers.

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typical rate is derived from a survey of 4-people family and so the At Home Rate is generally over 0.5. Most of the home appliances can only be controlled when people are at home and awake. So when new behavior is rescheduled, this constraint is still in use. Eq. (7) indicates the detail of this constraint. Definitions of the symbols are given in Table 3. Some of the home appliances (Washing Machines and Dishwashers) that can be controlled when people are in sleeping status or leave-home status are not limited by this constraint.

Constr : swijm  1  At hij  Awkij

ð7Þ

 Constraint from sub-period same consumption within a day Features of appliances may limit the usage transformation. For example, breakfast will not be transformed to 21:00 in rescheduling process. The transformation of breakfast has to be limited within a daily sub-period. Table 4 reveals a typical transformation range of daily meals. In Table 4, each meal can only be shifted within the sub-period for food requirement. In other words, the consumption of Cooking Appliances within each sub-period is the same. Eq. (8) indicates this constraints. This constraint is similar to Eq. (6). But Eq. (6) is the daily consumption constraint while Eq. (8) is sub-period consumption constraint. In Eq. (8), Loadij is the same variable in Eq. (6).

Constr : const jn ¼

nk X Loadij  t i

ð8Þ

i¼n1

3.4. Shifting Boundary – behavior change simulation In Fig. 2, home appliances owned by each agent are initially generated by stochastic process from group appliances owning probability. Appliances’ power and switch-on probabilities at different time intervals are also assigned to all agents before simulation. The price of corresponding inputted behaviors are initially chosen. At this level, the multi-agent system can simulate the original load of the whole agent group by the inputted behaviors. When the price is changed, agents without DR participation do not response to the price and will not change their switch-on probabilities. On the other hand, DR-participated agents will operate behavior optimization independently for their own Shifting Boundary. The target function of optimization is in Eq. (5) and the constraints are in Eqs. (6)–(8). Through optimization, each DR-participated agent will find out its new switch-on probabilities and form new load. Thus the total load is changed. Particle Swarm Optimization (PSO) is adopted as the optimization algorithm for the study. 4. Case study on residential customer load variation under different pricing scheme with Shifting Boundary 4.1. Case study description A typical Chinese resident group of 1000 people in severe winter is selected as target consumers for case study. Each family is represented by an independent agent. Altered pricing schemes are implemented on target consumers to analyze their behavior changes and load variation in weekdays.

 Home appliances in case study All target consumers are equipped with home appliances from a typical appliance set. All appliances are independently distributed on the target group with certain owning rate from a Chinese survey on a typical city residents group. Considering their utilizing feature, each appliance is with appropriate constraints from Section 3. Table 5 reveals the details of appliance set. In Table 5, Fridge is usually switched on for 24 h for food freshness purposes. So it is not controllable and its behavior will not change with different pricing scheme. Behavior changes on Electric Heater (Heater without energy storage) and Lighting are considered to cause serious problems to residential consumers. So their behaviors do not change with different pricing scheme as well. All other appliances in Table 5 are behavioral transformable and will be the main force of load variation. Behavior constraints are another influencing factor for appliance control. In the appliance set as shown in Table 5, Electric Heaters, Computers, Cooking Appliances, Lighting, Electric Showers and TV sets are only probable to be switched on when people at home. Moreover, Computers, Cooking Appliances, Lighting, Electric Showers and TV sets are controlled only by awake people. So behaviors toward these appliances are limited by life-style, which is shown with the constraint in Eq. (7). Washing Machine is an appliance with timing control. So it may operate any time during a day and will not be limited by constraint of life-style. Most of the appliances in the case study are limited by constraint of the same power as given in Eq. (6) for Shifting Boundary analysis. But this constraint is not sufficient for Cooking Appliances and TV sets as they have a ‘stronger’ limit on usage transformation. For example, breakfast can only be shifted during morning period. So for TV sets and Cooking Appliances, same power consumption should be kept during each sub-period within a day, which is the constraint given in Eq. (8).  Life-style in case study Life-Style is a critical constraint for behavior variation. All agents are operated according to their life-style rates. From our survey, agents’ time-varying at home status and sleeping status are shown in Fig. 6. In Fig. 6, families are classified with their home member quantities from 1 family member to 6 family members. Time varying at home status and sleeping status are sampled per hour in a day. In each sub-figure of at home status, curve of ‘0p’ represents the rate of family with 0 people. Curve of ‘2p’ represents the rate of family with 2 people. Other curves are with similar descriptions. In the target consumer group, distribution of family quantity is listed in Table 6.  Initial consumer behavior in case study Behavior is a basic and critical factor of each agent. Agents perform their behavior when responding to price changing. In this case study, initial behavior of each appliance is derived from residential time-varying activities from our survey in Fig. 7, as conditional switch-on probability. These initial behaviors are set as the initial point for behavior optimization. Also, it is recognized as the Table 4 Typical transformation range of daily meals.

Table 3 Parameters of Eq. (7). Parameters

Description

At_hij Awkij

‘At Home’ rate of the jth agent at hour i ‘Awake’ rate of the jth agent at hour i

Sub-period

Meals

4:00–9:59 10:00–14:59 15:00–21:59 22:00–3:00

Breakfast Lunch Dinner Supper

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set as a member object with parameters such as ‘Power’, ‘On/Off State’ and ‘Load Calculation Function’. A ‘Behavior Optimization Function (BOF)’ is integrated into each agent object. The function is triggered once every 24 h to form the new switch-on probability under the current daily price curve. The new switch-on probability will then generate new load curve. Users can select different price tariffs at any simulation time and the behavior will change when the BOF is triggered. The simulation flowchart is given in Fig. 8. Matlab is used for all simulation data pre-treatment and output analysis

Table 5 Details of home appliances in case study. Appliance

Owning rate (%)

Power (W)

Behavior change

Constraints equation enabled

Electric Heater Computer Washing Machine Cooking Appliances Fridge Lighting Electric Shower TV set

5 77 78 100 100 100 5 97

3000 290 2500 1000 80 300 3500 250

NO YES YES YES NO NO YES YES

(7) (6) (7) (6) (7) (8) NO (7) (6) (7) (7) (8)

 Initialized behavior analysis To verify the quality of our survey on consumer behavior Fig. 9 gives a comparison between the normalized load constructed from our survey and the normalized load from a China’s City. From Fig. 9, the general variation trends of both curves are the same. Practical load from a China’s city is smoother as it contains more samples.

consumer behavior under static price, to represent the general requirements without impact on daily time-varying price. Behavior for each appliance is summarized by appliance switchon probability.  Simulation environment in case study

4.2. Residential Shifting Boundary simulation under TOU Anylogic Professional 6.8.0 is used as simulation platform for this research. It provides a platform for Agent-Based modeling and Multi-Agent System simulation. Each agent is established by ‘Agent Object’ in Anylogic. Within each agent, every appliance is

When new tariff is applied on the target consumer group, the new price signals are passed to DR-participated agents and the total load is changed as the result of the behavior variation of

Family Member At-Home Percentage (1 Person Fam)

(2 People Fam)

1

1

0.5

0.5

0

0 0

6

12

18

0

6

12

18

0

0

6

(3 People Fam)

12

18

0

6

12

18

0

18

0

(4 People Fam)

1

1

0.5

0.5

0

0 0

6

12

18

0

6

12

18

0

0

6

(5 People Fam)

12

18

0

6

12

(6 People Fam)

1

1

0.5

0.5

0

0 0

6

12

18

0p

0

6

1p

12

18

0

0

2p

6

3p

12

18

0

4p

6

12

5p

1 0.8 0.6 0.4 0.2 0

6

12

18

0

6

12

18

Fig. 6. Agents’ time-varying at home status and sleeping status.

0

6p

Sleeping Family Percentage

0

18

0

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Electric Heaters will be switched on once home is not empty. Electric load of heating decreases in the morning while increases in the evening according to the life-style of the people. 90% of the lights will be applied when people are awake at home and the sky is dark. So there is the load of light in the morning and in the evening. Fridges will be switched on for 24 h, so no distinct daily variation appears in its load curve.

Table 6 Distribution of family quantity in target group. Family quantity

Quantity percentage in target group (%)

1 2 3 4 5 6

1 15 22 37 18 7

Person People People People People People

 Computers, Electric Showers and Washing Machines under TOU Shifting Boundary

DR-participated agents. This Section will firstly introduce the simulated effect on total load under TOU. Then the simulations will be conducted for behavior change in DR-participated agents due to Load Change of different appliances. Time of Use tariff is typical non-static pricing scheme that can reshape the daily load curve by changing consumer behavior. A typical TOU tariff in China as shown in Fig. 10 was selected for this case study. In target consumer group, 80% of families have installed Smart meters to receive information feedback. Considering the financial situation, 30% of families have inclinations to change their behaviors for lower bills with the same daily requirements of all home appliances. So with 80% ⁄ 30% = 24% participation rate of target group, daily load curve of Shifting Boundary is shown in Fig. 11. From Fig. 11, load of TOU peak period (8:00 to 21:00) is lower than load under static pricing as the result of consumption transformation. But TOU valley period (21:00 to 8:00) increases the load. TOU Load in the period between 7:00 and 8:00 and the period between 21:00 and 22:00 are obvious increased by concentrated consumption. Concentrated consumption represents that lots of families tend to consume electricity at a certain period.

Computers, Dishwashers, Electric Showers and Washing Machines are usage transformable appliances. Their daily consumptions are kept the same while behavior is changing. Fig. 13 reveals the load curve variation of these 4 appliances. From Table 5, Washing Machines are only constrained by their daily total consumption without condition of sleep or at home. People’s life-style does not have any effect on the control of these two appliances for their timing function. So in Fig. 13, load of pricepeak period can be shifted to any time of price-valley period. Thus the load between 21:00 and 8:00 of the next morning increases. Computers and Electric Showers are not only covered by constraints of same daily consumption but also the constraint of lifestyle. People can only switch on these two appliances when they are at home and awake. So for these two appliances, load of price-peak period are mainly shifted to the periods between 21:00 and 22:00, 22:00 and 23:00 and 7:00 and 8:00, because these 3 hours have the highest at home rate and lowest sleeping rate of price-valley period. Load is seldom shifted to period between 23:00 and 7:00 as most of people are sleeping. In other words, the load for Computers and Electric Showers have formed a morning peak and a new evening peak under TOU Shifting Boundary, and this represents a risk of concentrated consumption.

 Heater, Lighting and Fridge under TOU Shifting Boundary In Table 5, consumer behavior toward Electric Heaters, Lighting and Fridges will not change under different pricing scheme. A same price variation appears under TOU and static pricing. From Fig. 12, daily load variation under static pricing and TOU are almost the same. Small differences still exist as a result of randomness from behavior generation on switch-on probability.

 Cooking and TV under TOU Shifting Boundary Cooking and TV sets are also usage transformable appliances. Not only their daily consumptions, but also consumptions of subperiod in Table 4 should be kept the same while behavior is changing. Fig. 14 shows the load curve variation of cooking and TV.

Computer

Cooking 0.2

Switch on Prob

Switch on Prob

0.25 0.2 0.15 0.1 0.05 0

0

5

10

15

0.15 0.1 0.05 0

20

0

5

Hour

Washing Machine

0.1 0.05

10

Hour

15

20

0.04

Switch on Prob

Switch on Prob

Switch on Prob

0.15

5

20

TV 0.8

0

15

Hour

Electric Shower 0.2

0

10

0.6 0.4 0.2 0

0

5

10

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20

0.03 0.02 0.01 0

Hour Fig. 7. Initial consumer behavior on home appliances before optimization.

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Normalized Winter Daily Load Curve

1

Typ Load From A China's City Model Load under Static P 0.8

0.6

0.4

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18

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24

Hour Fig. 9. normalized load comparison between the load constructed from Survey and Load of a China’s City.

 Load variation comparison under TOU Shifting Boundary

For cooking, the first sub-period is from 4:00 to 9:59, in which 4:00 to 7:59 belongs to price-valley period. So the load of cooking will be transformed from the period between 8:00 and 9:59 to the period between 4:00 and 7:59. Also, Cooking Appliances can only be switched on when people are at home and awake. So the period between 7:00 and 7:59 suffers most transformed load with the highest product between at home probability and awake probability. Thus, there is a new morning peak of cooking load in the period between 7:00 and 7:59. The second sub-period is from 10:00 to 14:59. The whole subperiod belongs to price-peak period. So electricity price during this sub-period remains the same. No incentive for load shifting appears. The third sub-period is from 15:00 to 21:59. Within this sub-period, only 1 h (21:00 to 21:59) belongs to price-valley period. So load of other hours will be shifted to this hour, forming a concentrated cooking consumption. The last sub-period is from 22:00 to 3:59. The whole sub-period belongs to price-valley period. So electricity price during this subperiod remains the same. No incentive for load shifting appears. TV is suffering the same sub-period as cooking. So the period between 7:00 and 7:59 and the period between 21:00 and 21:59 are suffering most of the load transformation.

0.7 0.65 Price (kWh / 1 CNY)

Fig. 8. Simulation flowchart.

Load shifting of target consumer group is a comprehensive combination of all appliances’ utilization shifting. Residents shift their daily using time of appliances to reduce consumption in peak-price period so as to reduce the bill. Table 7 shows the feature variation of appliances’ load curve between static pricing and TOU. In Table 7, ‘Ori Peak’ represents the average load variation between TOU and static pricing in the period between 18:00 and 20:00; ‘Ori Valley’ represents the average load variation in the period between 3:00 and 5:00; ‘Evening Concentration’ represents the average load variation in the period between 21:00 and 21:59; ‘Morning Concentration’ represents the average load variation in the period between 7:00 to 7:59. Negative value in Table 7 means load of static price is lower than that in TOU and vice versa. In Table 7, TOU is selected in this case study and there is 30.3 kW potential (about 6.1% of original daily peak) of original peak reduction. This potential is mainly contributed by consumption shifting of cooking, TV sets and Computers. On the other hand, valley of daily load curve has an increased potential of 9.2 kW (about 1.8% of original daily peak). This potential is mainly contributed by Dish Washers and Washing Machines as they can be switched on without constraints from life-style. Due to cooking and TV watching have extra limits on their consumption shifting (Eq. (8)), they cause risk of concentrated consumption in the period between 21:00 and 21:59 and the period between 7:00 and 7:59. This risk may generate a new daily peak.

0.6 0.55 0.5 0.45 0.4 0.35 0

2

4

6

8

10

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18

20

Hour Fig. 10. A typical 2-period TOU tariff for Chinese Residents.

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 Daily bill under TOU Shifting Boundary

5

x 10 7

Static P

6

Winter Typical Daily Load Curve (W)

Other than load characteristics, TOU in the case study can save a resident’s bill from 3.44 CNY/Day to 3.27 CNY/Day, which is 4.9% reduction. In the Shifting Boundary analysis, daily power consumption under static pricing is 6.98 kW h/Day, which is the same as that under TOU.

TOU 5

4.3. Residential Shifting Boundary simulation under RTP 4

3

2

1 0

2

4

6

8

10

12

14

16

18

20

22

24

Hour Fig. 11. Daily load curve comparison between static pricing and TOU Shifting Boundary.

Real-Time Price (RTP) is a dynamic pricing scheme that reflects the real-time pressure suffered on a power system. In this study, hourly price is proportional to the real-time power load of target group of consumers, which is shown in Eq. (3). The proportional rate between group load and price is 11.5/8,000,000. Same as the study of TOU, 80% of families have installed Smart meters to receive information feedback, and 30% of the families have inclinations to change their behaviors for lower bills with the same daily requirements for all home appliances. So, considering 80% ⁄ 30% = 24% participation rate of target group, daily load curve of Shifting Boundary under RTP is shown in Fig. 15 below. From Fig. 15, RTP has more potential for a smooth daily load curve than TOU and static pricing scheme. Load shifting is more averagely distributed and with less concentrated consumption appears.  Concentrated consumption under RTP Shifting Boundary

By analyzing the load boundary, the trend and risk of variation in daily load curve are revealed. Practically, the effect of load shifting will not exceed this boundary because not all of consumer group can find out the best transformation methods and some consumers may have their own special constraints.

Consuming shifting in boundary is promoted by financial incentives. So power consumption can only be moved from periods of high price levels to periods with low price levels. In previous TOU analysis, large time segment of low price levels is sleeping time. For those appliances with constraints of life-style, time zones

4

5

x 10

x 10

7

3

Lighting Load (W)

Heating Load (W)

Static P

6

5

4 Static P

TOU

2

1

TOU

3

0 0 2 4 6 8 10 12 14 16 18 20 22 24

0 2 4

6 8 10 12 14 16 18 20 22 24

Hour

Hour 4

x 10

Fridge Load (W)

8.05 8 7.95 7.9

Static P TOU

7.85 7.8 0 2 4 6 8 10 12 14 16 18 20 22 24

Hour Fig. 12. Load curve comparison between static pricing and TOU Shifting Boundary for Heaters, Lighting and Fridges.

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Computer

x 10

x 10

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4

Electric Shower

3

5

Static P

2.5

Static P

TOU

TOU 2

(W)

(W)

4 3

1.5

2

1

1

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0 0 2 4 6 8 10 12 14 16 18 20 22 24

0 2 4 6 8 10 12 14 16 18 20 22 24

Hour

Hour 4

x 10

Washing Machine

5

Static P TOU

4

(W)

3 2 1 0 0 2 4 6 8 10 12 14 16 18 20 22 24

Hour Fig. 13. Load curve comparison between static pricing and TOU Shifting Boundary for Computer, Electric Shower and Washing Machine.

4

14 12

x 10

4

Cooking 12

Static P TOU

10

x 10

TV Static P TOU

10 8

(W)

(W)

8 6

6 4 4 2

2 0

0 0 2 4 6 8 10 12 14 16 18 20 22 24

Hour

0 2 4 6 8 10 12 14 16 18 20 22 24

Hour

Fig. 14. Load curve comparison between static price and TOU Shifting Boundary for Cooking and TV.

that can accommodate their shifting consumption are small. Thus concentrated consumption occurs. In previous analysis, Cooking Appliances, Computers and TV sets are concentrated used under TOU, which generate new peak in load curve. On the other hand, RTP provides a much more dynamic price curve and generates more diversity among price for each hour. So consumers obtain more zones to accommodate their shifting consumption. The

concentrated consumptions are decreased. Fig. 16 shows the daily load curve of appliances under RTP. Under TOU tariff, an obvious peak of concentrated consumption appears in load curves of Computers, Electric Showers and cooking. RTP provides more time zones for low price levels so that consumers have more time selections for shifting. Thus less concentrated consumption occurs and load curve of RTP Boundary

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Table 7 Load variation between TOU and static price. App

Ori Peak (kW)

Ori Valley (kW)

Evening Concen (kW)

Morning Concen (kW)

Comp Cook Fridge Heater Electric Shower Light TV Washm Total

5.6 15.1 0 0.3 0.3 0.3 7.4 1.9 30.3

0.6 0.5 0 0 0.1 0.1 0.3 7.7 9.2

10.1 73.6 0.1 0 4.8 1.3 32.0 4.1 126.0

9.9 8.4 0 0.5 3.0 1.3 9.2 7.4 36.1

 Shifting boundary comparison between TOU and RTP

becomes much smoother than TOU case, which implies that load curve under RTP has less risk of generating a new peak.  Price variation under RTP Shifting Boundary The price from RTP program aims to reflect the real-time load pressure of a power utility. Practically load is a time-varying variable with certain varying tendency and uncertainty. Price varying tendency reflects the actual tendency of general power requirement and is predictable. Price varying uncertainty reflects the small change of requirement by random factors and is unpredictable. In our model, varying tendency is represented by switch on probability of appliances. Appliances states are decided by random number generated on the probability. Varying uncertainty is generated during random number generation. Mapping to RTP program, varying tendency and uncertainty is passed to daily price curve. Fig. 17 provides a 5-day price curve variation of RTP from simulation. Unlike the stable change in TOU tariff, every daily price curve under RTP tariff has a similar varying tendency but with slightly uncertain differences. If Standard Deviation (STD) is used to analyze the daily differences on hourly price, the average STD of RTP price curve is 0.023 CNY/kW h, representing 6% of price uncertainty. Price uncertainty decreases the satisfaction of consumers and increases the complexity of behavior changing. This impact 5

x 10 Daily Load Curve (W)

8

Static P 6

reduces initiative of demand response participation. So the implementation of RTP may require more education for promotion. Also, functions to support automatic consumption scheduling will contribute to the result.

TOU RTP

4 2

TOU and RTP are both dynamic pricing schemes that intend to optimize consumer behaviors so as to optimize daily load curve. Fig. 18 shows the statistic result of boundary load curve under TOU and RTP. In Fig. 18, daily peak of load curve, Daily Valley of load curve, Peak-Valley Differences and Load between 18:00 and 20:00 are selected for comparison. Under static price, daily peak of load curve appears between 18:00 and 20:00. In simulation of TOU and RTP, a higher price level is given to this time period to promote consumers to shift consumption out. So if the load between 18:00 and 20:00 is recognized as 100%, the load will reduce to 93.5% under TOU or 94.0% under RTP. But TOU has an effect of concentrated consumption, so a new daily peak is generated between 21:00 and 21:59. This peak is 123.4% of daily peak under static pricing. In other words, daily peak under TOU in this case study increases instead of an obvious reduction. RTP does not have serious concentrated consumption. So its daily peak can be reduced by about 6%. Daily Valley is another feature of power load. Price level at time zone of Daily Valley are set to lower level so that consumers can shift their consumption into this period. All Daily Valleys of the 3 pricing occur during the period between 2:00 and 4:00 in the morning. If Daily Valley of static pricing is recognized as 100%, it will increase to 104.8% under TOU or 110.5% under RTP from the simulation. From Fig. 17, TOU and RTP can alter daily peak and increase Daily Valley. If Peak-Valley Difference of static pricing is recognized as 100%, it will change to 130.6% under TOU or 87.5% under RTP. The reduction of daily peak and Peak-Valley Difference may decrease the requirement of generation capacity and spinning reserve, which increase the energy efficiency of power system operations. Dynamic pricing may change power bills for consumers. Fig. 19 shows variation of daily bill resulting from those DR-participated consumers. Daily bill of target consumer group in this case study under static pricing is 3.44 CNY/Day. By shifting consumer behaviors, residents can achieve 3.27 CNY/Day under TOU Boundary with the same power consumption. Under RTP Boundary, residents can achieve 2.89 CNY/Day with the same power consumption. From Fig. 19, TOU and RTP in this case study can both reduce the daily bills and RTP has a stronger reduction effect. In this case, TOU has reduced the bill into 95.1% while RTP has reduced the bill into 84.2% under the same power consumption.

0

Daily Price (CNY/kWh)

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0.6

5. Case study on residential customer TOU time zone planning support with Shifting Boundary 5.1. Case study description

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0.3

RTP 0.2 0

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20

22

Hour Fig. 15. Daily load curve and price comparison among 3 PBPs.

24

From previous case study, Shifting Boundary of a TOU tariff has demonstrated the load shifting trend by generating a typical daily load curve of target consumer group as well as typical daily load curves of all appliances. In other words, TOU tariff can be evaluated by its Shifting Boundary. This case study intends to use Shifting Boundary to evaluate different TOU tariffs for supporting tariff planning. TOU distributes different price levels into different time zone in a day. For example, TOU in Fig. 8 contains 2 time zones. The one of

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4

Computer (W)

x 10

Cooking (W)

x 10

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2.5

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Static P TOU RTP

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Hour Fig. 16. Daily load curve of appliances under different PBPs.

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PriceVariation

Static Price

TOU

1 95.10%

TOU RTP

RTP 100% 100%

100%

CNY / kWh

0.8

95% 0.6

90%

84.20%

85% 0.4

80% 0.2

1

2

3

4

5

6

75%

Daily Bill

Day Fig. 17. 5-days (weekdays) price curve variation comparison between RTP and TOU.

higher price is from 8:00 to 21:00 in the day time, called price peak period. The other with lower price is from 21:00 to 8:00 in the night time, called price valley period. Time points for period substitution are 8:00 and 21:00. In fact, time zone of TOU may have other selections. The substitution time point in the morning can be 6:00, 7:00 or 9:00. Some selections are shown in Table 8 below. Shifting Boundary is computed from each selection in Table 8 for a time zone planning with the best daily load curve. Target consumer group is the same as that in previous case study. Peak Period Starting Time is varying from 6:00 to 10:00 and Peak Period Ending Time is varying from 19:00 to 23:00. 5.2. Simulation result and analysis As the load variation under different TOU scenarios can be simulated by the model, the best scenario can be found out. In this case study, each scenario is constructed by a Peak Period Starting Time and a Peak Period Ending Time. Simulations are implemented on different combination of these 2 parameters. Features of load under different scenarios are criteria for scenario selection Simulations are implemented for each selection. Table 9 provides the indices of load curves under different TOU time zone planning. In Table 9, ‘Load between 7:00 and 8:00’ measures the consuming level between 7:00 and 8:00, where morning peak occurs within this period. ‘Load between 18:00 and 20:00’ measure power load between 18:00 and 20:00, where daily peak under static price occurs within this period. ‘Load between 21:00 and 22:00’ measures the new peak of load generated by concentrated consumption.  Daily morning peak

Static Price 140% 120%

TOU

RTP

130.60%

123.40% 93.10%

110.50% 104.80%

93.50% 87.50%

100%

94.00%

80% 60% 40%

Daily Power Consumption

Fig. 19. Variation of daily bill and daily consumption under different pricing schemes.

Table 8 Some TOU tariffs selections of time zone planning. TOU time zone selection

Peak Period Starting Time

Peak Period Ending Time

Selection Selection Selection Selection Selection Selection Selection Selection Selection

6:00 6:00 6:00 7:00 7:00 7:00 8:00 8:00 8:00

20:00 21:00 22:00 20:00 21:00 22:00 20:00 21:00 22:00

1 2 3 4 5 6 7 8 9

Under static price, morning load peak appears between 7:00 and 8:00. Fig. 20 shows morning peak variation from Table 9. From Fig. 20, Daily Morning Peak is mainly influenced by Peak Period Start Time. When Peak Period Start Time changes from 6:00 to 8:00, the morning peak will increase. If it changes from 8:00 to 10:00, the morning peak decreases instead. When Peak Period Start Time is set at 6:00 or 7:00, the period between 7:00 and 8:00 is with high price level. Consumption is shifted out from this time period. Thus the morning peak is comparatively low. When Peak Period Start Time is set at 8:00, the period between 7:00 and 8:00 becomes an hour with low price level. Power from other periods with high price is shifted into this period. For those appliances (Cooking and TV) constrained by Eq. (8), hours with low price level in morning sub-period are 4:00–5:00, 5:00–6:00, 6:00–7:00 and 7:00–8:00. Except 7:00–8:00, all other hours in morning sub-period are with high sleeping rate. As cooking and TV should be switched on while awake, 7:00–8:00 become the only time to suffer most of shifting load from morning sub-period. Thus a concentrated consumption occurs in this hour, pushing up the morning peak. When Peak Period Start Time is set at 9:00 or 10:00, more hours in morning sub-period are with low price level while people awake. Thus more time space is available to distribute the shifting load and consumption into more hours. So the morning power peak is not as high as 8:00. Fig. 21 provides a Daily Morning Peak comparison among different Peak Period Start Time.

20% 0% Daily Peak

Daily Valley

Peak-Valley Difference

Load Between 18:00 to 20:00

Fig. 18. Boundary comparison between static pricing, TOU and RTP.

 Daily Evening Peak Under static pricing, Daily Evening Peak appears between 18:00 and 19:00. By analyzing previous case study, concentrated

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Fang Yuan Xu et al. / Applied Energy 146 (2015) 353–370 Table 9 Load curves under different TOU time zone planning. 19:00 Load between 7:00 and 8:00 (kW)

Load between 18:00 and 19:00 (kW)

Load between 21:00 and 22:00 (kW)

New evening peak appear hour

Peak Period Start Time

Load between 7:00 and 8:00 (kW)

Load between 18:00 and 19:00 (kW)

Load between 21:00 and 22:00 (kW)

New evening peak appear hour

6:00 7:00 8:00 9:00 10:00 Peak Period End Time 6:00 7:00 8:00 9:00 10:00 Peak Period End Time 6:00 7:00 8:00 9:00 10:00

260.7 290.1 300.8 286.3 280.4 21:00 262.9 266.3 296.3 278.5 270.7 23:00 253.4 272.1 313.6 293.7 283.1

466.7 483.9 466.7 463.7 471.0

534.2 553.4 532.7 533.5 529.4

19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00

274.3 266.5 292.1 288.4 269.9

445.9 436.1 429.0 438.3 428.4

582.7 568.3 539.4 542.4 534.7

20:00–21:00 20:00–21:00 20:00–21:00 20:00–21:00 20:00–21:00

450.9 444.5 436.0 436.1 440.3

580.9 571.0 566.9 552.2 549.4

21:00–22:00 21:00–22:00 21:00–22:00 21:00–22:00 21:00–22:00

6:00 7:00 8:00 9:00 10:00 22:00 6:00 7:00 8:00 9:00 10:00

267.0 270.8 303.6 298.9 286.0

468.1 462.0 457.7 475.3 469.6

465.1 459.9 451.3 473.9 468.4

19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00

466.1 464.5 454.8 460.0 463.2

462.1 458.3 448.9 456.8 462.5

19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00 19:00–21:00

Load Between 7:00 to 8:00 (kW)

Peak Period End Time Peak Period Start Time

20:00

320 300 280 260 240 10

23 22

9 21

8 20

7 6

Peak Period Start Time

Peak Period End Time

19

Fig. 20. Daily morning peak variation.

From Fig. 22, Peak Period End Time mainly influences Daily Evening Peak and Load between 21:00 and 22:00. Comparing to use 19:00 as Peak Period End Time, using 20:00 or 21:00 may achieve a lower daily peak. This is because the whole period between 18:00 and 20:00 will be fully covered with high electricity price. Also, appliances constrained by Eq. (8) still have time space with low price in evening sub-period to suffer the load shift. So consumption is shifted out from 18:00 to 20:00 when using 20:00 or 21:00 as Peak Period End Time. The shifted consumption generates a new peak at different hour. So shifting load under TOU will lead to risk of concentration consumption. When using 22:00 or 23:00 as Peak Period End Time, the whole evening sub-period is covered by high price level. Time zones after 23:00 are associated with high sleeping rate and cannot suffer shifted load. Thus, load at Daily Evening Peak has limited transformation to other time zone and the daily peak appears at the same period as original peak. Fig. 23 provides a Daily Evening Peak comparison among different Peak Period Start Time.

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Daily Load Curve (W)

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Time 6am Time 7am Time 8am Time 9am Time 10am

6. Case study on residential customer smart meter installation scale analysis with Shifting Boundary 6.1. Case study description

Daily Morning Peak

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Hour Fig. 21. Daily Morning Peak comparison among different Peak Period Start Time (Peak Period End Time is 21:00).

consumption may occur and generate new peak load. Fig. 22 shows the variation of original Daily Evening Peak and new evening peak generated by concentration consumption.

In case study one, participation rate of a tariff is constructed by smart meter installation scale and consumers scale who have inclinations for lower bills. Usually, the proportion of consumers who contain willingness for lower bills cannot be changed within a short time. So the smart meter installation scale becomes the main impact factor of PBP consumer participation. This case study intends to use Shifting Boundary to evaluate the impact from smart meter installation scale. As deployment of smart meter increases, more agents become DR-participated agents and the total load variation becomes more significant. In simulation, each scenario has a diverse consumer participation rate and a same price tariff. The effect of smart meter scale can be studied with comparisons between total load features of different scenarios. Assume that 30% consumers have inclinations for lower bills in target group, Table 10 provides relations between scales of smart meter installation and consumer participation rate.

Fang Yuan Xu et al. / Applied Energy 146 (2015) 353–370

5

x 10 7

500

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400 10 9 8 7 6

Peak Period Start Time Load Between 21:00 to 22:00

0% 10% 30% 50% 70% 90% 100%

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Daily Load Curve (W)

Load Between 18:00 to 19:00

368

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24

Hour

Fig. 22. Variation of original Daily Evening Peak and new peak generated by concentrated consumption (Peak Period Start Time is 8:00).

Fig. 24. daily load curve comparison among multiple smart meter installation scales under TOU.

5

x 10

700 Static P End Time 19pm End Time 20pm End Time 21pm End Time 22pm End Time 23pm

6

5

New Peak Original Daily Evening Peak

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Load Curve Parameters of Shifting Boundary (kW)

Daily Load Curve Compare (W)

7

600

500

400

300

200

100

Hour Fig. 23. Daily Morning Peak comparison among different Peak Period End Time (Peak Period Start Time is 8:00).

Morning Peak Daily Peak Daily Valley

0

20

40

60

80

100

Smart Meter Installation Scale (%) Fig. 25. Comparison between morning peak, daily peak and Daily Valley among multiple smart meter installation scales under TOU.

Table 10 Relation between smart meter scale and consumer participation rate. Scenario

Smart meter scale (%)

Consumer participation willing (%)

Consumer participation rate (%)

1 2 3 4 5 6 7 8 9 10

10 20 30 40 50 60 70 80 90 100

30 30 30 30 30 30 30 30 30 30

3 6 9 12 15 18 21 24 27 30

6.2. Analysis on multiple smart meter installation scales under TOU and RTP Daily load curve is influenced by smart meter installation scale under various PBP. Only those whose pricing information is easily available can take part in behavior changing. To evaluate the load curve variation trend, Shifting Boundary is computed under each scenario of Table 10. Target consumer group is the same as that in case study one. TOU tariff in Fig. 9 is selected for simulation. Figs. 24 and 25 show the Shifting Boundary for various scenarios. From Figs. 24 and 25, more consumers decide to change their behaviors while smart meter installation scale increases. So load

Fang Yuan Xu et al. / Applied Energy 146 (2015) 353–370 5

x 10 5.5

0% 10% 30% 50% 70% 90% 100%

5

Daily Load Curve (W)

4.5 4 3.5 3 2.5 2 1.5 1 0

2

4

6

8

10

12

14

16

18

20

22

24

Hour Fig. 26. Daily load curve comparison among multiple smart meter installation scales under RTP.

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relationship between individual consumer behaviors and group daily load. A new concept, ‘Shifting Boundary’, was proposed and implemented in the model to measure the largest load shifting potential under several Price-Based Demand Response tariffs. Three case studies were implemented to indicate the model utilization in load analysis, PBPs evaluation and optimization, and evaluation of the effect due to smart meter installation scale. By comparing simulations based on survey data and practical results, it demonstrated that this new model has a high confidence level to produce results close to practical situations. The model developed could be used for strategic planning and design analysis. However, further work is anticipated. This paper only provides a quantification method of usage transformation. Practically, DR effect is the combination between usage reduction and usage transformation. So the combination effect will be a point for future work. In the development of Smart Grid, distributed generation will include new types of appliances covered in home area. So consideration of distributed generation will be a point for future work too. Other than just residential consumers, behavior of industrial and commercial consumers contains different impacts. So an extension of the model framework which covers industrial and commercial consumers is necessary. With the framework extension, the impact of PBPs toward a complete consumer group can be better described. Acknowledgments Financial support from State Grid Corporation of China is very much appreciated.

Load Curve Parameter of Shifting Boundary (kW)

550 500

References 450

Morning Peak Daily Peak Daily Valley

400 350 300 250 200 150 100 0

20

40

60

80

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Smart Meter Installation Scale (%) Fig. 27. Comparison between morning peak, daily peak and Daily Valley among multiple smart meter installation scales under RTP.

shifting within daily load curve tends to be more obvious. The concentrated consumption becomes more obvious as well. But limited by financial participation willingness, when all consumers have installed smart meters, only 30% will join TOU in this case study. In other words, the ultimate effect of smart meter under TOU in this case study is the black curve in Fig. 24. Similar result is shown by RTP simulation in Figs. 26 and 27.

7. Conclusion and future work This paper introduces a model framework for consumer behavior PBPs analysis. This framework illustrates the close-loop

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