Customized differential pricing for different user groups

Guo Peiyang

Supervisor: Jacqueline Lam. Co-supervisor: Victor. O.K. Li

1. Introduction

As an important type of demand response, differential pricing attempts to alter user’s consumption behavior by introducing a price signal. It promises to reduce the peak demand, therefore avoiding the expensive cost of ramping up and investment in reserve capacity. The most widely adopted differential pricing scheme in the world is Time of use (TOU), which divides a day into several peak and off-peak intervals and charges discriminative price for different time intervals. Other differential pricing schemes include critical peak pricing (CPP), which introduces a significant price hike at selected peak time with prior notice; and dynamic pricing, which requires a more frequent price signal exchange.

Depending upon the design of differential pricing programs, trial programs in various countries have received mixed results, the peak reduction ranging from 5% minimum to as 30% maximum (Newsham and Bowker, 2010). This level of peak reduction is significant in the power industry. It is estimated that a reduction of only 2–5% in system-wide demand at peak times could reduce the spot price for electricity by 50% or more (Rosenzweig et al., 2003); a 5% reduction in US demand during the highest 1% of demand hours would save the utilities $3 billion per year (Faruqui and Sergici, 2009).

Success of these trial programs does not guarantee their success in widespread real world application, especially in the residential sector. From the perspective of utilities, the heart of the problem lies in the fact that the cost avoidance from peak demand reduction could not justify the revenue loss. For differential pricing, the price for off-peak period must be kept low to keep the program attractive. This has created a trade-off between revenue loss from low off peak price and cost reduction from peak shaving. In trial studies where all users are enrolled in the program, the revenue loss are well justified by the massive peak cost reduction. However, in real application, users do not necessarily prefer to join the program. In fact, most likely, users of low usage during the peak hours tend to join the program, but they do not provide any benefits to the electricity system. Users of high usage during the peak hours, on the other hand, tend to keep away from the program in fear of bill increase (Woo, et al., 2013). This “adverse selection” of non-premium users have thwarted the utilities’ enthusiasm to introduce differential pricing.

One could not expect the challenge described above can be solved through enforcing mandatory or default program in the near term. This has to do with the low customer acceptance of differential pricing program. For example, Todd (2010) finds that a mere average of 10% recruitment rate can be expected if the U.S. citizens are solicited on differential pricing programs. As of 2015, hardly any countries or regions (except Italy and Ontario, Canada) have mandatory or default differential pricing program in place (Faruqui, 2015).

1.1 Research signficance

The adverse selection problem can be solved, if customized pricing can be offered to different types of electricity users. Electricity users are quite heterogeneous; users, with their distinctive load profile, often respond to differential pricing quite differently. They can have load profiles of morning peak, afternoon peak, dual peak, etc. For example, when a high tariff is applied to a time interval, say 7-9 pm, users corresponding to this peak interval are expected to respond to the price signal most acutely; while users whose peak does not fall within this interval are expected to respond less enthusiastically. If we can apply differential pricing to those valuable users who carry the strongest impact on system peak reduction, i.e, those who shave the most peak demand with price increase, utilities can overcome the adverse selection problem by designing programs specifically targeting at these users.

The benefits of customized design are three folds: firstly, choosing the “premium” users ensures that peak reduction is achieved in a cost-efficient way. The peak cost avoidance for utility greatly outstrip the revenue loss from lower off-peak price. Secondly, customized programs are well-suited to attract the participation of the premium users. The lower off-peak price offered to the premium users will not be spilled over to other non-premium users, thus preventing revenue loss that are largely gratuitous. Thirdly, the users stand to benefit from the lower rate at off peak time, which is bound to cut down users’ bill.

Customized tariff design is made possible by the increasing adoption of smart meters. With interval data collected from smart meter trials, researchers have been able to segment the individual load profiles of the system into several typical load profiles (TLPs). TLPs differ significantly in peak period and consumption

level. For example, Wong and Rajagopal (2012) segments over 20,000 households from a utility company into 6 TLPs; these TLPs are distinguished from each other by their respective peak periods. McLoughlin et al., (2015) clusters the Ireland smart metering data into 10 TLPs based on load profile shape and consumption level, each representing different features of peak period and total consumption. After recognizing the users’ consumption patterns, utilities could then maximize their profits by offering customized differential pricing schemes.

1.2 Research Gap

Not many studies have examined how customized differential pricing to users will affect utility profits. In trial studies, researchers have investigated the effect of differential pricing on users across-the-board (Herter et al., 2007; Torriti, 2012). In real world applications, studies have been done to modify the conventional differential pricing through methods such as two-part pricing (Woo et al.,1995; Oran et al., 2010), coupon pricing (Zhong et al., 2013), and stochastic optimization (Ferreira et al., 2013). However, few of these studies have attempted to increase differential pricing potency by offering customized program design.

1.3 Research Aim and Research Questions

Our research aims to study how to increase the utility’s profit and reduce users’ energy usage by offering customized program design. My research study is further divided into 3 parts:

a. Would the customized program design be any superior to uniform differential pricing design? This could be investigated from the stand point of profit increase for utilities and energy reduction for users.

b. How do we identify those users who carry the strongest impact (premium users) on cutting the peak cost comprehensively?

c. Can we identify the premium users based on a user’s demographics and external control, such as appliance ownership and dwelling type? This would allow easy implementation of customized differential pricing in places where smart metering data is not available.

2. Literature review 2.1 Review on scope of studies on differential pricing.

Differential pricing has long been a hot topic for business trials and academic studies. The first wave of study was from late 1970s to 1980s, when a myriad of trials has been undertaken to assess the plausibility of TOU tariff. The second wave of study starts with the California energy crisis in 2001, when the electricity demand largely outstripped the supply. Equipped with advanced metering technology such as AMI, differential pricing trials with more advanced design and data resolution are being conducted in places such as Ireland, California, Florida and France. Differential pricing are studied in the following ways:

The first and most researched category is the empirical study of trial programs. This category usually attempts to measure the effectiveness of the trial program with one or several parameters of elasticity. Elasticity measures the user’s response on electricity consumption due to a unit increase of electricity price. Two streams of regression are used. In one of them, we have scholars using log-linear demand equations that do not reflect completely the restrictions placed by economic theory of consumer behavior (Filippini 1995; Mountain and Lawson 1992; Baladi et al., 1998; Faruqui and Sergici 2009). In the other, we have other studies that place the peak and off-peak consumption in the context of expenditure allocation and utility maximization, which are in line with the neo-classical economical theory (Baladi, 1995; Filippini 2011; Yousefi 2011). Regardless of the streams, the products of these research efforts are a series of elasticities such as short-run and long-run elasticity (Filippini 2011) and elasticity of substitutions (Faruqui and Sergici, 2009). The advantage of elasticity-based approach is that the parameters are easy to understand and can be easily compared to other studies. However, lumping together a highly heterogeneous group of users into one or two regression equations represents a huge risk to gloss over the specific response of individual users.

The second category tries to assess the potential of differential pricing in application. Other than the simple method of using elasticities from empirical studies, two methods are particularly promising: the agent-based model and the probabilistic model. Agent-based models would include a myriad of agents that have

its own specific preference toward electricity consumption, with each agent representing one user or one type of user. After making assumptions about these users, the demand would then be derived by aggregating the individual demand. Related literature includes: Mahaligam (2013) and Liu (2013). Probabilistic model attempts to simulate the load profile using the probabilities of appliances starting up and their working duration. This often involves either constructing probability functions (Capasso 1994; Yao and Steemer, 2005; Paatero and Lund, 2006), or using Markov chain to model the users’ transitional probability from one electricity consumption behavior to another (Richardson et al., 2008, 2009, 2010, Widén et al., 2009a, 2009b, 2010, Song et al., 2014). Time use diary that records the users’ activities is usually used to specify the probability functions or transitional probability. Notably, Widén (2008) et al. and Richardson et al., (2009) construct the load profile in Sweden and UK by building a Markov model, deriving the transitional probability for every time interval, every household size and between each user’s activities. These models serve well for load construction. However, they often involve too many transition probabilities and thus is cumbersome for determining the effect of peak shaving schemes.

The last category tries to improve the effectiveness of differential pricing in real world application. Borenstein (2012) proposed an opt-in dynamic pricing plan that is equitable to both users and utilities. Ferreira et al., (2013) recognized the difficulty of TOU designing due to price-elasticity uncertainty and proposed stochastic optimization to improve it. Zhong et al., (2013) try to minimize the generation cost by proposing a voluntary coupon pricing scheme. In recognition of the adverse selection, Woo et al., (1996) proposed a two-part real time pricing plan. Similarly, Orans et al., ( 2010) and Woo et al., (1995) proposed a two-part TOU rate option, which essentially is a variant of two-part real time pricing. However, nearly all of these efforts are focused on applying differential pricing to the total user group. The only literature that comes close to customized pricing is Yang et al., (2016), where the tariff is proposed to compensate controllable load to grouped commercial and residential users. However, the aim of their study is not to maximize the utilities’ profit by balancing revenue and peak cost, and the classification does not touch upon the specific consumption pattern of residential consumers.

In sum, studies on differential pricing have so far either tried to study the effectiveness of trial program, or estimated its potential for peak shaving, or attempted to modify the conventional pricing scheme. However, all of these studies are applied on an across-the-board level. Seldom have they touched upon topic of improving differential pricing by considering users’ distinct consumption patterns and offering customized services.

2.2 Review on clustering studies

Clustering on electricity interval data was only made possible by the deployment of smart metering such as AMI. Currently, the study of clustering on electricity interval data centers around two streams:

The first stream of study focused on developing methods to cluster the interval data. Data can either be normalized beforehand to focus on load shape (Kwac 2013; Rhodes et al., 2014), or left as they are to take account of the magnitude of consumption (McLoughlin et al., 2012; McLoughlin et al., 2015). Clustering techniques can be categorized into direct clustering and indirect clustering. Direct clustering tries to directly segment the individual load profile into clusters using data mining techniques. Popular methods in this realm include k-means, hierarchical clustering, fuzzy k-means and so on. For example, Labeeuw and Deconinck (2013) used k-means to cluster over 1300 residential and SME load profile into 8 classes. Mahmoudi-Kohan et al., (2010) used fuzzy k-means to generate 4 clusters from 210 residential users. Indirect clustering refers to those whose data have been processed by dimension reduction techniques such as Principal Component Analysis and Curvilinear Component Analysis (CCA). For example, Zakaria and Lo (2009) identified 4 clusters from 300 users by first reducing the dimension from 48 to 2 and then applying Fuzzy k-means.

Instead of only focusing on clustering the interval data, the second stream of study also seeks to relate the characteristics of users to the clusters, such as socio-economic variables and appliance stock. McLoughlin et al., (2015) first segmented 4200 domestic Irish dwellings consumption over 184 days into 10 TLPs; then a multiple linear regression model is applied to relate the profile to dwelling types, socio-economic variables and appliance stock. Rhodes et al., (2014) clustered 103 households into 2 TLPs and then use the Probit model to relate the cluster and demographic variables.

As can be seen from the literature review, 1) Empirical trial studies and pricing modification have overwhelmingly focused on engaging users across-the-board. 2) Data mining techniques such as clustering

are coming out as important ways to study the heterogeneity of users. No study has so far tried to increase the potency of differential pricing program by offering customized program enabled by the data mining.

The significance of our study is that by customizing differential pricing design to users with different consumption patterns, demand peak is shaved at a cost-efficient way: that peak cost reduction are not achieved at the undue expense of revenue loss. 3. Work done during the probationary period 3.1 A qualitative study

This part of study aims to examine the effect and significance of differential pricing. Differential pricing is put in a broader picture of demand response. Extensive literature review has been done to investigate the challenges and drivers of demand response.

To advance a better understanding of the topic, it is useful to examine the challenges and drivers from the standing point of China. We have identified the challenges and drivers faced by the demand response program (Table 1).

An article has been submitted to the journal of Energy Policy.

Table 1 Challenges faced by demand response programs

Financial and Market Issues Consumer Issues Technology issues

Improper weighting of demand response portfolio

Limited knowledge on demand response

Lack of smart infrastructure

Huge variety of electricity prices Limited potential benefits Lack of technology standardization Responsibility issue Low consumer adaptability Privacy security Revenue reduction Response fatigue

3.2 Customized pricing for Voluntary Time of Use

This part aims to demonstrate the superiority of customized tariff design over conventional uniform differential pricing from the standpoint of utility. A customized TOU pricing design is proposed to maximize the utility’s profit. Even though reducing users’ bill are not an explicit goal in this part, the design of the rate nevertheless ensures that users would stand to reduce their bill by participating in the program. A uniform TOU pricing design is provided as comparison.

3.2.1 Customized TOU design and its comparison

Design 1: Customized TOU pricing.

Under customized design, utilities first segment users’ load profile into several TLP groups; groups are then examined on how to offer the customized rate. For simplicity, a two-interval TOU structure is used, where only one continuous time interval is applied peak price.

The order in which TLP groups are given customized rate is based on the marginal profit, that is, the net system profit one unit peak price increase of one group will bring .As shown in Figure 1, raise the peak price by unit step for TLP1 will reduce the system peak cost by ∆𝐶#, but increase the revenue loss by ∆𝑅#; The resultant marginal profit for shaving TLP2 by increasing peak price is ∆𝑃#. Similarly, the marginal profit for shaving TLP1 is ∆𝑃&. If ∆𝑃& > ∆𝑃#, TLP2 will be be chosen to be offered a higher peak price. The process of choosing the TLP with most marginal profit will continue, until price increase would not yield positive profit gain on both TLP.

In order to keep the lure of program for each group, the high price at peak hour must be offset by a lower price at off-peak hour. The design of the peak and off-peak follow this rule: if the user group does not change its consumption pattern, the bill for this group under customized TOU pricing would equal to that under flat rate. This rule is in line with the argument in Borenstein (2012); it provides users with incentive to shift or shave peak demand, as any shifting or shaving would result in a bill reduction:

𝑃(∙*+,-×𝐷(∙*+,- + 𝑃(∙122*+,-×𝐷(∙122*+,- = 𝑃×(𝐷(∙*+,- + 𝐷(∙122*+,-) (Equation 1)

where: 𝑃(∙*+,-, 𝑃(∙122*+,- = the peak and off peak price for group 𝑖 𝑃 = the flat rate 𝐷(∙*+,-, 𝐷(∙122*+,- = the peak and off peak demand for group 𝑖

Figure1LoadshavingfordifferentTLPgroups

An overview of the mechanism on finding the customized pricing is described as follows:

Step 1 Segment users into N groups

Step 2 Set the peak price and off peak price for each group at the flat rate

Step 3 Calculate the marginal profit for each group at one-unit peak price rise, while the price of other groups remains unchanged. Marginal profit is the profit increment for utility after one group increase peak price by a unit (Refer to Equation 3- Equation8 for profit calculation). The off peak price of each group is given by Equation 1.

Step 4.1 If there is marginal profit greater than 0 in any group, choose the group with the maximum marginal profit. Increase peak price of the selected group by a unit and change its corresponding off peak price. Loop back to step 2.

Step 4.2 If all marginal profit is greater than 0, export the current pricing for each group as the customized pricing.

Design 2: Uniform TOU pricing

The uniform TOU pricing is designed in comparison to the customized TOU pricing. The design of the peak and off-peak follow this rule: If no users change its consumption pattern, the aggregated bill for all users under TOU pricing would equal to that under flat rate.

𝑃*+,-×𝐷*+,- + 𝑃122*+,-×𝐷122*+,- = 𝑃×(𝐷*+,- + 𝐷122*+,-) (Equation 2)

where: 𝑃*+,-, 𝑃122*+,- = the peak and off peak price for all users 𝑃 = the flat rate 𝐷*+,-, 𝐷122*+,- = the peak and off peak demand for all users. Each group of users will decide on whether to join in the program based on how their bill will change if they remain their current consumption. Therefore, given 𝑃*+,-,whether the pricing is attractive enough to group i is determined by if the offered off peak price is 𝑃122*+,- is lower than the individual off peak price 𝑃(∙122*+,-. The overview of the mechanism on finding the optimal conventional pricing is described as follows:

Step 1 Set the price for each group at the flat rate. Set an upper price limit Pmax

Step 2 Increase the system peak price and compute the system off peak price according to Equation 2, the group off peak price according to Equation 1.

Step 3 For each group, if the system off peak price is greater than the group off peak price, the group will stay in the flat rate; otherwise, the group will take the offered system peak price and system off peak price.

Step 4 Calculate the profit for the utilities. Store this value. Loop back to step 1 unless the peak price is greater than Pmax

Step 5 Choose the pricing that yields the most profit

3.2.2. Objective, assumptions and model specification

The ultimate objective of TOU design is to increase the profitability of utilities. This could be done by either boosting the revenue or cutting the cost.

Profit = Revenue − cost

The primary revenue source is the bill payment from customers. The cost consists mainly of two parts: the fuel cost and the peak cost. The peak cost includes the reserve ramping up cost, and depreciated peak capacity investment. The profit can then be expressed in the following equation.

profit = (PH∙I − CKLMN) ∙ DH∙IP&IQ#

RHQ# − CSMTU (Equation3)

where: 𝑖 = the user group; j = 1 for peak period; 2 for off peak period; n = the group number P = the price for all user groups under the flat tariff; 𝑃[ = the price at period j; 𝐷(∙[P = the demand of user 𝑖 group at period j after enforcing the TOU schemes; 𝐶2\+] = the variable operation and maintenance cost per kWh, mainly the fuel; 𝐶*+,- = the peak cost, including the spinning reserve ramping up cost, and depreciation of peak capacity

investment In order to compute the utility’s profit, the following assumptions are made:

1) In both designs, users in each TLP group will make the decision on whether to take up the TOU option, or remain in the flat rate: users in every group would first compute their new bill under the TOU designs with their current consumption pattern. If this bill amount is greater than that under flat rate, the TOU designs will not be taken up.

2) The group under the TOU would respond to the price setting by shaving or shifting peak demand. The elasticity for peak time is assumed to be 𝑒*. The relationship between peak time demand and price is expressed as: fH∙_P = fH∙_ ∙ P# P M`, t ∈ (t#,t&) (Equation4)

where: 𝑓(dP = the consumption level for group 𝑖 at t before enforcing TOU.

(𝑡#, 𝑡&) = the peak time interval.

The magnitude of 𝑒* is in negative relation with the peak price duration (Newsham and Bowker, 2010). We assume an inverse linear relationship between 𝑒* and peak price duration, and is modeled as follows:

𝑒* = 𝑒*∙f,g − 𝛽 ∙ 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 (Equation 5) where 𝑑𝑢𝑟𝑎𝑡𝑖𝑜𝑛 = the peak time duration (hour) 𝑒*∙f,g = the maximum elasticity.

The suppressed demand from peak time are either vanished (such as lighting) or shifted to off-peak period (such as cooking). A parameter α is used to measure the proportion that has been shifted to off-peak period. We assume that the shifted demand is equally distributed in off-peak hours. This assumption is not detrimental to the model, as the utilities’ profit will not be affected by how the shifted demand are distributed in off-peak period.

𝑓(∙dP = 𝑓(∙d +q(rs∙tuvwxrs∙tuvw

y )

zx(d{xd|) (Equation 6)

where:

α = the proportion of suppressed peak demand that has been shifted to off-peak period 𝑁 = the total time interval.

As demonstrated by Stern (2013), TOU does have an impact on overall energy use, indicating at least part of peak demand is shaved, not shifted (α < 1). On the other hand, however, Newsham and Bowker (2010) concludes that this effect is not quite notable. Therefore, the value of α should be just slightly lower than 1.

3) For peak demand above threshold, peak cost is incurred. Peak cost includes the reserve ramping up cost, and depreciation of peak capacity investment. Let 𝐶2 be the peak cost per kWh, the peak cost can be expressed as follows:

𝐶*+,- = 𝐶2(𝑓dP − 𝐴)(𝑓dP > 𝐴) (Equation 7)

where:

𝐶*+,- = the total peak cost, including the reserve ramping up cost, and depreciation of peak capacity investment.

𝐶*+,- = the peak cost per kWh 𝑓dP =the system consumption profile after TOU application. 𝐴 =the system peak threshold determined by utilities

The unit peak cost 𝐶2 is far from being a constant as the unit peak cost varies according to the peak level. The greater the peak demand, the higher the peak cost per kWh. Before applying TOU, the unit peak demand is approximately 0 at the time immediate within the peak period; it increases to a maximum level 𝐶f,g at the system peak. As illustrated in Figure 2, at the start of peak period, the unit peak cost is about 0; as the demand approach the maximum level, the unit peak cost increases to 𝐶f,g.

Figure2peakcostperkWh

We assume a linear relation between the peak demand and 𝐶2:

𝐶2 =��v�2�v�x�

(𝑓d − 𝐴) (Equation 8) where:

𝐶f,g = the maximum peak cost per kWh 𝑓f,g = the maximum peak demand level before TOU application 𝑓d = the system consumption profile before TOU application

After applying TOU, the relationship between 𝐶2 and peak demand stay the same (the slope in the previous equation stays the same). 3.3 A numerical study

The dataset used in this study is 15-minute residential electric usage interval data in summer of 2011 from 6,662 residential users of the utility company PG&E. The 6 users’ TLPs are clustered based on Smith et al., (2012). Figure 3 is the system load profile. Figure 4 is the resultant 6 TLP groups entitled respectively “afternoon”, “daytime”, “dual”, “evening”, “morning” and “night”, each representing the time at which the peaks occur.

Figure3systemloadprofileFigure4Typicalloadprofiles

The parameters are listed as below: Table2numericalstudyparameters

Parameters Value Note and references P 0.20 Dollar/kWh The flat tariff rate (based on PG&E E1 rate, 2016)

α 0.9 The proportion of suppressed peak demand that has been shifted to off-peak period. It is estimated based on Stern (2013), Newsham and

Bowker (2010) 𝐶f,g 4 Dollar/kWh This is the maximum per kWh cost of peak demand. It includes the

ramping up cost, and the peak capacity cost depreciated with every kWh generation. This parameter is selected based on the California ISO real time price and system profile.

F 0.12 Dollar/kWh The variable operation and maintenance cost per kWh, mainly the fuel. It is estimated based on the levelized cost of electricity (EIA, 2013) of gas-fired conventional station and profit margin of PG&E

𝑒*∙f,g 0.8 Those two together are used to compute the peak elasticity. The basis for the selection are: King and Chatterjee (2003), Reiss and White (2005), Fan and Hyndman(2011)

𝛽 0.05

A 900 KW, 950KW,1000KW

A is the threshold demand level above which the utilities consider as peak demand. It is determined by system load profile and utilities capacity stock

Gross profit is defined as the revenue from electricity bill minus the fuel cost. The operation profit is defined as the gross profit minus peak cost. The results are as follows:

1) Threshold=3600 kW Peak period (15:30, 23:00)

Table3profitwhenthreshold=3600kW

Gross profit Peak cost Operation profit Design 1 5625 1168 4457 Design 2 3789 1770 2019

Table4pricingfortwodesignwhenthreshold=3600kW

afternoon daytime dual evening morning night Design1 (0.18,0.22) 0.2

(Flat rate) 0.2 (Flat rate)

(0.18,0.22) 0.2 (Flat rate)

(0.1,0.4)

Design2 0.2 (Opt out)

(0.02,0.48) 0.2 (Opt out)

0.2 (Opt out)

(0.02,0.48) (0.02,0.48)

For the customized design (design1), the TLP users group of afternoon, evening and night are offered the customized TOU design, while the other two groups remains on flat rate as they are not the target of customized design. For uniform design (design2), all users are offered a TOU rate of (0.02,0.48). However, only the TLP users of dual, morning and night have taken up the offer, while the rest opt to stay in flat rate. The off peak price is very low in the case, reflecting the fact that the benefit from shaving peak is so great that utilities is willing to offer very low price to induce peak shaving.

The profit of customized design it larger than uniform design by almost 2,438 dollar/day. This profit increase is significant enough considering the daily revenue of about 15,700 dollar for the studied 6,662 users and a net profit margin of about 9% for a utility company in the U.S.1.

2) Threshold=3800kW Peak period (16:45, 22:45)

Table5profitwhenthreshold=3800kW

Gross profit Peak cost Operation profit Design 1 6015 440 5575 Design 2 5202 489 4713

1 The daily revenue is computed based on the 78,000 kWh consumption by the 6662 users at the flat rate of $0.2 per kWh. the In 2014, average net profit margin in the utilities sector typically ranged from 8-10% in U.S. based on statistics from Yahoo Business.

Table6pricingfortwodesignwhenthreshold=3800kW

afternoon daytime dual evening morning night Design1 (0.19,0.22) 0.2

(Flat rate) 0.2 (Flat rate)

(0.19,0.22) 0.2 (Flat rate)

(0.14,0.34)

Design2 0.2 (Opt out)

(0.11,0.38) 0.2 (Opt out)

0.2 (Opt out)

(0.11,0.38) (0.11,0.38)

For the customized design, the TLP users of afternoon, evening and night are selected for customized design. For uniform design,users of daytime, dual and night choose to join in the TOU program of (0.11, 0.38), while the other three group opt out because of the high peak price.The profit in design 1 is greater than design 2 by over 863 dollar/day.

3) Threshold=4000 kW Peak period (18:00, 22:15)

Table7profitwhenthreshold=4000kW

Gross profit Peak cost Operation profit

Design 1 6314 137 6176 Design 2 6073 153 5920

Table8pricingfortwodesignwhenthreshold=4000kW

afternoon daytime dual evening morning night Design1 (0.19,0.22) 0.2

(Flat rate) (0.19,0.24) (Flat rate)

(0.19,0.22) 0.2 (Flat rate)

(0.18,0.26)

Design2 (0.18,0.26)

(0.18,0.26)

0.2 (Opt out)

0.2 (Opt out)

(0.18,0.26)

(0.18,0.26)

For the customized design (design1), the TLP users of afternoon, dual, evening, and night are chosen to offer the customized price. The other user groups are offered flat rate, indicating that the revenue loss from this group outstrips the peak cost avoidance. For uniform design (design2), users of afternoon, daytime, morning and night choose to join the uniform TOU program, while the rest opt out and stay with the flat rate. The profit gain from customized pricing still has an edge over uniform design by 256 dollar/day.

Figure5sensitivitytest

4. Future work 4.1 Customized differential pricing to reduce energy usage

So far we have focused on customized differential pricing to maximize the profits of utilities. As future work, we would also study how to design customized differential pricing to reduce customer usage. We can also study a two-objective function problem of maximizing the utility’s profits while also minimizing customer usage.

4.2 Other indicators that would influence customized design

In this part, the order by which the user groups are offered customized design are further examined. In the customized TOU demonstration, the order is decided by the peak time demand proportion. Other indicators such as the price responsiveness of each user group may be studied. It has been proved that distribution of electricity price elasticities in users are quite skewed (Reiss and White (2005)). Examining the price responsiveness for each user group would help to identify the premium users with more certainty.

4.3 Identifying the optimal number of segments

In this part, customized differential pricing will be tested by changing the number of clusters. As the cluster size gets bigger, we expect the benefit of customization would increase first, and finally decrease as the cost for clustering is too much. In the end, the optimal cluster number will be found.

4.4 Mapping of the relationship between load profile and household characteristics

This part would relate the clustering results to socio-economic variables, appliance stock and dwelling type. It corresponds to question 3. 5. Conclusion Differential pricing is a promising tool to increase the profit of utilities without incurring adverse effect on users’ bill. The argument for differential pricing is that its peak cost avoidance effect outweighs the associated revenue loss. This holds true in trial studies where all recruited users participate in the program by default. However, when applying it to the real world where mandatory or default program is not possible, it usually suffers from the problem of “adverse selection” where only users with low usage at peak time opt in the program. My study investigate how utilities stand to benefit and overcome the problem by customizing rate to users after examining their consumption pattern. During the probationary period, I have finished a review article on the benefit of differential pricing. A preliminary study has also been done to demonstrate the superiority of customized TOU over conventional uniform TOU design. For future study, focus will be shifted to developing comprehensive methodology for the customization process. Other indicators such as price responsiveness will be added to more accurately identify the premium users. I also plan to relate the premium users to external manifestation such as demographics and appliance stock. In this way, the customization can be applied to places where smart meter data is not available.

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