Abstract
Demand response (DR) has received much attention for its ability to balance the changing power supply and demand with flexibility. DR aggregators play an important role in aggregating flexible loads that are too small to participate in electricity markets. In this work, a DR operation framework is presented to enable local management of customers to participate in electricity market. A novel optimization model is proposed for the DR aggregator with multiple objectives. On one hand, it attempts to obtain the optimal design of different DR contracts as well as the portfolio management so that the DR aggregator can maximize its profit. On the other hand, the customers’ welfare should be maximized to incentivize users to enroll in DR programs which ensure the effective and flexible load control. The consumer psychology is introduced to model the consumers’ behavior during contract signing. Several simulation studies are performed to demonstrate the feasibility of the proposed model. The results illustrate that the proposed model can ensure the profit of the DR aggregator whereas the customers’ welfare is considered.
WITH the growing concern about reducing greenhouse gas emission to achieve a sustainable and environment-friendly energy system, renewable energy sources (RESs) have drawn lots of attention all over the world [
Many works have been done from different aspects to explore the operation of the DR aggregator. In [
The aforementioned studies explore the implementation of DR aggregators effectively, but neglect customers’ comfort. Considering customer preferences, an analytical method to control thermostatically controlled loads (TCLs) is proposed in [
This paper proposes a novel multi-objective optimization model for the aggregator to determine the contract details for the DR services provided by end-users as well as the optimal portfolio of DR contracts. The DR aggregator participates in the DA market with the objective of maximizing its profit and the customers’ welfare. In particular, the main contributions of this work are as follows:
1) A DR aggregator operation framework dealing with the interaction between the aggregator and customers is proposed, as well as the contract design which considers the interests from both the DR aggregator and the consumers.
2) A multi-objective model for the aggregator is formulated to maximize both the profit and the customers’ welfare, which encourages the positive enrollment of potential DR resources.
3) Consumers’ behaviors based on the consumer psychology are modeled considering customer preferences.
4) The design of three different DR contracts and the optimal portfolio of DR resources are described.
5) A comprehensive analysis for several case studies is conducted, which demonstrates the feasibility of the model and the flexibility provided by DR contracts that enables the aggregator to participate in the electricity market.
The rest of this paper is organized as follows. Section II presents the overall hierarchy of DR aggregator participation in the DA market and the details of prevailing contracts that the DR aggregator signs with customers. A mathematical model is formulated and explained in Section III. Section IV describes the problem reformulation and optimization algorithm. In Section V, case studies and simulation results are discussed. Finally, the conclusion and future work are discussed in Section VI.
In this paper, the DR aggregator provides DR services to ISO by offering customers a set of contracts in the DA market. The aggregator is considered as a price-taker entity.
The DR aggregator provides a comprehensive customer service like an integrated energy service provider, because it is hard for customers to evaluate their DR potentials. The DR aggregator can perform an overall data mining of users’ behaviors based on the technical models and the social-behavioral survey results [
In practice, DR aggregators can assemble a number of flexible customers into an aggregation to participate in the DA market with considerable weight.

Fig. 1 Operation framework of DR aggregator.
The DR aggregator offers multiple DR contracts, which are load curtailment (LC), load shifting (LS) and flexible charging load (FCL) to encourage residential customers to actively join in DR programs. These contracts are settled well in advance and allow the aggregator to control the customers’ loads under certain authority. Customers sign the contracts to receive incentives for their DR capacity. As a result, the customer preference can be obtained and the potential customers can be located when the DR contracts are signed. The DR aggregator participates in the DA market to submit DR bids according to customers’ DR contracts and receives penalties for false bidding if the real DR services provided by the aggregator are less than the bidding amount. In real time, customers can choose to shift a certain proportion of the contract amount and they will receive penalties for any performance failure. Basically, the DR aggregator earns profit hourly once the market is cleared. The purpose of the aggregator is to design the DR contracts and monitor customers’ actual response to maximize the total profits.
The DR aggregator can accumulate multiple customers with similar characteristics of electricity consumption into a cluster under the same DR contract. This would significantly simplify the design of DR contracts. In this work, the DR aggregator can make the best use of the flexibility of its customers by scheduling three types of DR contracts, the details of which are described below.
LC contract indicates the conventional load curtailment strategy. Customers participating in LC contracts agree to reduce a certain amount of their electricity consumptions during the scheduled time window and do not shift their loads to any other period. Suitable loads for LC contracts are lights, air-conditioners, water heaters, and non-essential applications.
Loads participating in LS contracts can be partially rescheduled during the scheduled time window and shifted to off-peak hours. Suitable loads for LS contracts are air-conditioners, washing machines, and laundry dryers.
Customers participating in FCL contracts can choose a preferred schedulable duration from the predetermined time window to reduce a certain amount of their electricity consumptions. The schedulable duration can be continuous or discrete. If the specified duration is equal to the time window set by the aggregator, the FCL contract is the same as the LC contract. For example, if the load control time window planned by the aggregator is from 08:00 a.m. to 12:00 p.m. and the preferred schedulable duration of one customer is 2 hours, this customer can be enrolled in the DR program in any 2 hours from 08:00 a.m. to 12:00 p.m.. Suitable loads for FCL contracts are pool filters, plug-in electric vehicles and high efficiency particulate air (HEPA) filters.
The operation of the DR aggregator is to design and dispatch the DR contracts, which optimize its own profit. To achieve this, the DR aggregator needs to account for the customers’ satisfaction because the more customers are enrolled in DR events, the more revenues the aggregator can gain from the DA market. This problem can be formulated as a multi-objective optimization model in which both the profit of the DR aggregator and the customers’ welfare are maximized.
The DR aggregator profits by bidding DR capacity in the DA market and paying the customers based on the DR contracts. The objective of the DR aggregator is to maximize its profit R as shown in (1), which is subjected to (2)-(4) and the contract constraints in the profit model of the DR aggregator.
(1) |
(2) |
(3) |
(4) |
where subscripts k1, k2, k3 are the customer types, , , , and , , are the total numbers of LC, LS, FCL contracts, respectively; T is the set of simulation time slots;
The objective function (1) represents the payoff of the DR aggregator. The income consists of two parts: the revenue for bidding in the DA market and the penalty to customers for their inadequate response. The expenditure is the total cost of paying the customers for their response based on the contracts and the penalty from ISO for the false bidding. The decision variables are the unit price of LC contract , the unit price of LS contract and the allowed dispatch capacity of FCL contract . According to (2), it is ensured that the bidding amount in the DA market does not exceed the total amount of load reduction capacity in the contracts. To ensure fair competition on the market, the DR aggregator will be penalized by the ISO if the real DR service provided by the aggregator is less than the bidding amount. It is assumed that the DR aggregator is equipped with interval meters recording electricity usage which must be sufficient to provide the ISO with hourly, one-minute, or real-time load data as applicable to the wholesale market [
The contract constraints in the profit model of the DR aggregator are specifically elaborated in this paper. The execution of LC, LS and FCL contracts are presented in detail as follows.
1) The LC contract can be modeled as:
(5) |
(6) |
where is the scheduling hour for the LC contract.
The cost of LC contract is determined by (5). The maximum and minimum values of the unit price of LC contract are limited by (6).
2) The LS contract can be modeled as:
(7) |
(8) |
Under LS contract, customers allow the aggregator to shift their loads from period to period .
3) The FCL contract has a fixed schedulable duration Td, which represents the total hours of load dispatch. Thus, the FCL contract can be modeled as:
(9) |
(10) |
(11) |
(12) |
where is the unit price of FCL contract, which is fixed and determined by the aggregator; and is the binary variable that indicates the status of FCL contract.
The cost of FCL contract is given by (9). The dispatch period of the FCL contract is set to be within the schedulable duration Td by (10) and (11). The maximum and minimum dispatch power provided by the customers in FCL contract is limited by (12).
The DR aggregator can obtain comprehensive information about users’ electricity consumption and DR capacity by equipping local smart meters. In the long run, the DR aggregator negotiates the details of the DR contracts with customers to encourage them to enter into the DR program. The objective of the customers is to maximize their welfare as shown in (13), which is subjected to (14)-(19) and the contract constraints in the customers’ welfare model.
(13) |
(14) |
(15) |
(16) |
(17) |
(18) |
(19) |
where Di
In this paper, the consumer psychology [

Fig. 2 Relationship between allowed dispatch capacity and unit price based on consumer psychology.
Then, the relationship between the allowed dispatch capacity qi in the contract and the unit price can be described as follows.
(20) |
In addition, considering customer preferences, it is assumed that the actual dispatch load in the real-time stage can be a portion of the allowed dispatch capacity in the contract and the portion follows the normal distribution. However, the customers will be penalized for their failure of performance.
The contract constraints in the customers’ welfare model are specifically elaborated as follows.
1) The allowed dispatch capacity in LC contract is given by (21) based on the consumer psychology. According to (22), the actual dispatch load in the real-time stage is part of the allowed dispatch capacity in the contract and the portion follows the normal distribution.
(21) |
(22) |
where and are the upper limit and the lower limit of the incentive in LC contract, respectively; and is the gradient.
2) The execution of LS contract can be modeled as follows.
(23) |
(24) |
where and are the upper limit and the lower limit of the incentive in LS contract, respectively; and is the gradient. Under LS contract, customers allow the aggregator to shift their loads from period to period .
3) The allowed dispatch capacity of FCL contract is within the limitation offered by the customer, which is given by (11) and (12). Since the schedulable duration is flexible, the customers enrolled in the FCL contract give full authority to the DR aggregator to control their loads. Thus, the actual dispatched load in the real-time stage is exactly the same as the capacity in the FCL contract, which is given by (25). As the dispatch duration is relatively small and flexible, the dissatisfaction caused by the FCL contract can be ignored, as shown in (26).
(25) |
(26) |
According to the above problem formulation, it is clear that the consumer psychology will pose piecewise linear constraints, which is a common issue for most of the optimization algorithms. In this paper, the piecewise constraints are dealt with by introducing extra 0-1 integer variables. Equations (
(27) |
(28) |
(29) |
(30) |
(31) |
(32) |
(33) |
(34) |
(35) |
(36) |
where , , , , , are the new introduced binary variables which indicate each segment of the piecewise function; and M is a self-defined large number. Constraints (27), (32) ensure that and can be situated in only one segment of the piecewise function. Constraints (29), (34) confine and within ai and bi in the responsive area. These two constraints will be non-binding by the use of M in the saturation area. Constraints (30), (35) enable and to be larger than bi in the saturation area. The equivalency of (20)-(24) and (27)-(36) can be easily demonstrated by enumerating all the binary variables introduced.
After the reformulation, the proposed problem becomes a multi-objective integer optimization model. The Pareto front can present the trade-offs between each objective [
(37) |
(38) |
(39) |
(40) |
(41) |
In this section, several case studies are presented. This paper aims to show how the DR aggregator participates in the DA market based on the multi-objective optimization model while considering the customers’ welfare reflected as DR contracts. The price forecasting approach is considered out of the scope of this paper [

Fig. 3 DA expected price for DR aggregator.
For simulation purpose, customers are aggregated into several typical representative consumer types. It is assumed that customers of the same type respond to the incentives from the aggregator in the same way. The proposed multi-objective problem for the DR aggregator is implemented in MATLAB 2014 and runs in a computer with an Intel i7-3720 processor and 8 GB RAM.
The number of customer types in the three contracts k1, k2 and k3 are 3, 3, 1, respectively. The allowed dispatch capacities of LC and LS contracts of different types of customers are shown in

Fig. 4 Consumer psychology curves of different customer types in LC and LS contracts. (a) Customer response in LC contract. (b) Customer response in LS contract.

Fig. 5 Distribution of real response coefficient of customer.
Using the NSGA-II, the Pareto front for the DA market model can be generated.

Fig. 6 Example of Pareto front.
The optimal schedules for the three DR contracts are shown in

Fig. 7 Optimal schedules of three DR contracts.
In the proposed model, it is assumed that the DR aggregator has full information about the DA market. It can predict the demand balance and DA prices with high accuracy to make a proper bidding strategy. The impact of the bidding strategy of DR aggregator is investigated. The other parameters such as the DA prices and the response of customers remain the same as in the base case. The data of different bidding strategies are presented in
The optimal schedules for DR contracts in cases 1 and 2 are shown in

Fig. 8 Optimal schedules of three DR contracts in case 1.

Fig. 9 Optimal schedules of three DR contracts in case 2.
The impact of the sensitivity of customer response is investigated. In case 3, customers are set to be more sensitive to the price incentives than they are in the base case, which means the slopes of the consumer psychology curves are larger; while in case 4, customers are set to be less sensitive to the price incentives than in the base case. The allowed dispatch capacities of LC and LS contracts of different customer types in case 3 and case 4 are shown in

Fig. 10 Consumer psychology curves of different customer types in LC and LS contracts of case 3 and case 4. (a) Customer response in LC contract of case 3. (b) Customer response in LS contract in case 3. (c) Customer response in LC contract of case 4. (b) Customer response in LS contract in case 4.
The optimal unit prices of the DR contracts in the base case, case 3 and case 4 are listed in Table II. In case 3, at hours 10, 17-19 and 21, the unit prices of the LC contract are lower than those in the base case since customers are more sensitive to the pricing and they respond with less incentive. Similarly, the unit prices of the LS contract at hours 7, 17-20 are smaller than those in the base case. The exceptions at the rest hours exist because the aggregator needs to reach the bidding amount as well as consider the customers’ welfare. By contrast, in case 4, at hours 7, 17 and 20, the unit prices of the LC contract are higher than those in the base case, while at hours 7, 10 and 17-19, the unit prices of the LS contract are higher than those in the base case. This is because customers are less sensitive to the pricing and they need more incentives for the DR service. The unit prices in case 4 reach the maximum value 30 $/MW several times because the limit of customer response is at 30 $/MW.
In case 3, the daily optimal profit of the DR aggregator and the customers’ welfare are $36562.23 and $51892.05, respectively, while those in case 4 are $40719.36 and $ 49916.45, respectively. The profit of the DR aggregator in case 3 increases because customers are willing to reduce their load with less incentive which is also the reason for the decrease of customers’ welfare. Similarly, the customers’ welfare increases in case 4 because there is greater incentive.
Customers respond to the price incentive with different sensitivities, thus affecting the composition of the scheduled contracts. The optimal schedules for the three DR contracts of cases 3 and case 4 are shown in

Fig. 11 Optimal schedules of three DR contracts in case 3.

Fig. 12 Optimal schedules of three DR contracts in case 4.
This paper proposes an optimization model for DR aggregators to determine the optimal contract strategy for maximizing their profit and customers’ welfare. In this model, three types of DR contracts, namely LC contracts, LS contracts and FCL contracts, are considered for customers. In terms of the responsive load, consumer behaviors are innovatively modeled through the consumer psychology in order to reveal the relationship between the incentives and the expected customer response. Besides, the actual response of customers is represented by stochastic programming. The proposed model is a multi-objective integer-programming model, which is solvable for an evolutionary algorithm after reformulating. It can be implemented to provide guidelines for the aggregators to design the DR contracts when participating in the energy markets. Several case studies are performed to investigate the feasibility and practicability of the proposed model. The results demonstrate that the proposed model is able to yield enough revenues for the DR aggregator while the customers’ welfare is also ensured.
In future study, more details of the DR contracts such as energy storage will be considered. Also, in order to broaden the application of this work, the participation in real-time markets will be introduced into the proposed model. Finally, future work might also explore other alternative ways to model consumers’ behaviors of different consumer types.
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