The tiered RDA DR is a user-level incentive program. After the RDA load aggregator receives the DR request from the main grid, it adjusts the power according to the capacity of the users’ interruptible and adjustable loads, the generation of rooftop photovoltaics, and the stored energy of the energy storage system. The compensation price is adjusted according to the grades of the users for increasing their enthusiasm in DR participation.

The framework of the tiered incentive price-based demand-side aggregated response method in the RDA is shown in Figure 2.

(1) User classification and grading

First, clustering analysis is conducted based on the characteristics of RDA users and classifies user grades based on their initial credits.

(2) Measuring RDA adjustable power

The characteristics of the RDA adjustable loads are analyzed, and the adjustable power from resources, including rooftop photovoltaics, home energy storage systems, interruptible loads, and adjustable loads, is calculated. On this basis, the overload status of the distribution transformer is monitored. When overload happens, the RDA emergency program is activated and the load is regulated to reduce the power through the transformer.

(3) RDA user demand response model

The RDA aggregator conducts load aggregation and user benefit analysis based on the DR instructions sent by the main grid and determines the baseline DR strategy. Then, the RDA aggregator determines if the RDA participates in the DR. If yes, the RDA aggregator formulates a tiered DR strategy based on the number and grades of users that participate in the DR in the RDA and organizes users to follow instructions according to grades. After demand response, compensations to users are settled and the grades of users participating in DR are adjusted for increasing their enthusiasm for future participation.

The RDA demand response program is designed to motivate RDA users to actively participate in DR, alleviate distribution line congestion, and guarantee RDA peak load supply. Different household users have different response willingness. For example, high-income household users may show lower DR willingness. Based on the characteristics shown by the daily load profiles of RDA users, Liu et al. (2020); Liu H. et al. (2022) classified them into afternoon and evening peak load, evening single peak, afternoon peak load, and evening sub-peak load and identified the degree of willingness of RDA users. In this section, RDA users are classified to explore the degrees of their willingness in participating in DR.

Since 2016, the State Grid Company has been carrying out the construction of the “Friendly Interaction between Supply and Demand” project. By upgrading the low-voltage power line high-speed carrier (HPLC) module, the energy consumption data of RDA users on a time scale of 15 min can be collected. This lays the foundation of data for RDA users interacting with the main grid (Wan and Song, 2021).

In order to improve the accuracy of RDA user classification, clustering features are selected following the typical recommendation from the Electric Power Industry Association, as shown in Table 1.

The k-means clustering method is an unsupervised iterative clustering method. This method can divide the data into k clusters. First, k users are randomly selected as initial cluster centers. Then, each remaining user is assigned to a cluster based on the distances to the cluster centers, and thereafter the cluster centers are updated. This process is repeated until convergence (Zhao et al., 2020). The k-means clustering method has a high efficiency and a relatively high accuracy, which makes it widely used. However, the k, namely the number of clusters, needs to be determined in advance, which is difficult. To this end, in this section, the traditional K-means clustering algorithm is improved so that it can dynamically adjust the number of clusters, being adaptable to the number of users in clusters. In other words, when the number of users in a cluster is less than a certain threshold, the cluster will be merged into others. When the number of users in a certain cluster is too large, the cluster will be split into two.

The steps of the improved k-means clustering algorithms are as follows:

Step 1

Randomly select k RDA users as the initial clustering centers.

Step 2

Calculate the Euclidean distance D _j (k) of each RDA user to the cluster center, as in Eq. 1, where X _j represents the values of clustering features, and assign each RDA user to the nearest cluster. d j k = ⁡ min X j − Z j k . (1)

Step 3

Based on the number of clusters after Step 2, if in any cluster, the number of users is less than the threshold Δy, the cluster is removed, and all users in it are assigned to the other clusters according to their Euclidean distances.

Step 4

With the RDA users’ feature values, update the cluster centers Z _j (k) as in Eq. 2. In Eq. 2, F _j is the number of users in the jth cluster, and cRDA represents the feature values. Z j k = 1 F j ∑ j = 1 k c j RDA x j . (2)

Step 5

Determine whether a cluster needs to be split with Eq. 3, where △a represents the cluster splitting threshold. If Eq. 3 is satisfied, perform cluster splitting. In Eq. 3, △a is the splitting threshold. k < Δ a . (3)

Step 6

Determine whether clusters need to be merged with Eq. 4, where △b represents the cluster merging threshold. If Eq. 4 is satisfied, perform cluster merging. In Eq. 4, △b is the merging threshold. k > Δ b . (4)

Step 7

Calculate the squared error to check whether the convergence condition is met. The squared error of the jth cluster can be calculated as in Eq. 5. σ = 1 F j ∑ j = 1 k c j R D A − Z j k 2 . (5)

When the square error is less than the preset threshold over iterations, the algorithm is terminated, and RDA user classification is obtained.

In this paper, different DR incentive prices are adopted for users with different scores. As an example, Wang L. et al. (2022) scores positive points for users consuming electricity at load valley periods and negative points at load peak periods. We adopt a 100-point system for scoring users. The incentive area is 60–100 points, within which the RDA load aggregator is rewarded on the basis of the benchmark DR price, and the penalty area is 0–59 points, within which the RDA load aggregator is punished on the basis of the benchmark DR price.

With the user’s initial score according to the features of RDA users and typical weights from the industry association as shown in Table 1, a user’s standard score can be calculated as in Eq. 6. d STD = ∑ i = 1 n RDA d i FEA × w i n RDA . (6)

In Eq. 6, n ^RDA is the number of RDA users; dFEA i represents the feature values of RDA users; and w _j represents the weights corresponding to the features.

The initial score of a user can be calculated as in Eq. 7, where dR i is the industry typical value of the features of different types of RDA users and 60 is the passing score in the 100-point system. d INIT = ∑ i = 1 n RDA d i R × w i d STD × 60 . (7)

The RDA aggregator designs the grades, corresponding score ranges, and floating price scales referring to the standards from the Electric Power Industry Association. Clustering results based on features in Table 1 determine the types of users, and each type has the categories as shown in Table 2.

As given in Table 2, users with different scores will be assigned to different grades and have different floating prices which are designed for providing diverse incentives.

RDA controllable resources include, but are not limited to, residential loads, rooftop photovoltaics, and energy storage systems. Residential loads can be divided into two categories: non-controllable and controllable. The former includes lighting loads and televisions which will not participate in DR. Controllable loads can be further divided as interruptible and adjustable. Interruptible loads can be interrupted during operation, and adjustable loads can adjust the power consumption in a certain range. Typical controllable loads are shown in Table 3.

The interruptible power of RDA users, P ^INT(t), can be calculated as in Eq. 8. P INT t = ∑ i = 1 m INT p i UINT t . (8)

In Eq. 8, m ^INT is the number of interruptible loads participating in DR in the RDA and pUNIT i(t) is the interruptible power of different PRD interruptible loads in time interval t. The range of the interruptible power from RDA users is 0 to P ^INT(t).

The adjustable power of RDA users, P ^REG(t), can be calculated as in Eq. 9. P REG t = ∑ i = 1 m REG p i UREG t × λ i × t i REG . (9)

In Eq. 9, m ^REG is the number of adjustable loads that participate in DR; pUREG i(t) is the rated power of adjustable loads of RDA users; λ _i represents the power reduction ratios of adjustable loads of different RDA users; and tREG i represents the adjustable load power ratios of different RDA users. During time interval t, the adjustable power range of RDA users is 0 to P ^REG(t).

When the total RDA load is greater than the rated capacity of the distribution transformer, distribution transformer overload happens. A traditional dry-type transformer can only operate for 60 min, being overloaded by 20% (Liu ZH. et al., 2022). In severe cases, the distribution transformer will be burned out, resulting in a power outage. Therefore, load regulation should be conducted at the first time, when the distribution transformer is overloaded. In this paper, the overload time of the transformer is set to 1% of the typical value, namely, 0.6 min, to prevent from burning out.

When the distribution transformer is overloaded, the RDA load aggregator implements the RDA emergency load control strategy to reduce the RDA load within the normal operating range of the distribution transformer. This leads to no compensation to RDA users. During the overload period of the distribution transformer, the reduced load P ^OL(t) can be represented as in Eq. 10. P OL t = P INT t + P REG t + P PV t + P ES t . (10)

In Eq. 10, P ^PV(t) is the power generation that can be provided by the rooftop photovoltaics and P ^ES(t) is the power from energy storage discharging.

The essence of RDA demand response is that after the RDA load aggregator receives the instructions from the main grid, it estimates the capacity of available DR and determines whether participating in DR can be profitable. If yes, it will organize users in the RDA to participate in DR. The compensation prices will be adjusted according to the user grades to increase the enthusiasm of RDA users to participate in DR.

In this paper, the load aggregators are of two levels: the transformer distribution area level and regional level. The transformer distribution area level load aggregators are responsible for integrating RDA resources within the scope of a single distribution transformer, and the regional load aggregators are responsible for further integrating the load aggregators of transformer distribution areas. Controllable loads are aggregated by aggregators to participate in DR, and RDA users of different types are incentivized as in Table 2. RDA users’ photovoltaic and energy storage systems can sell electricity to load aggregators for profit.

The comprehensive income function of a regional level load aggregator, f ^AREA, can be formulated as in Eq. 11, where m ^RDA is the number of residential distribution areas of distribution area level load aggregator and fRDA i represents the incomes of transformer distribution area level load aggregators. f AREA = ⁡ max ∑ i = 1 m RDA f i RDA . (11)

The income function of a distribution area level load aggregator can be formulated as in Eq. 12. f E = ⁡ max f GET − f BUYU − f BUYPE , (12) f BUYU = ∑ i = 1 m INT + m REG p i USER t × v i USER , (13) f BUYPE = ∑ i = 1 m PE p i PE t × v i PE . (14)

In Eq. 12 to Eq. 14, f ^GET is the profit of the load aggregator obtained from the main grid operator for participating in DR; f ^BUYU is the compensation to users in the RDA for participating in the DR; f ^BUYPE is the compensation from the load aggregator to the RDA users for using the rooftop photovoltaics and energy storage in participating in DR; pUSER i(t) is the power of different RDA users during the DR period; vUSER represent the prices for different RDA users to participate in DR; m ^PE is the number of rooftop photovoltaics and energy storage systems in the RDA; pPE i(t) represents the power from the rooftop photovoltaics and the energy storage system in the DR period; and vPE i represents the price for the rooftop photovoltaic and the energy storage system for exporting power to the main grid.

The constraint of the adjustable load can be formulated as in Eq. 15, where pRPL i(t) is the rated power of the RDA transformer. p i RPL t ≥ p i USER t − p i PE t . (15)

RDA DR pricing is to set the benchmark price for RDA users in DR. When the RDA load aggregator benefits from participating in DR, it obtains the price from the equilibrium of the game considering the DR price from the main grid, energy export prices to rooftop photovoltaic generation, and energy export prices to energy storage discharging. The equilibrium will be used to derive the DR base price.

The leader–follower game is a static game model with complete information. The leader takes the lead in making decisions, and the followers make decisions based on the leader’s decisions. The above process is repeated until a Nash equilibrium is reached (Huang et al., 2023) to maximize the benefits of participants. The leader–follower game is a classic game model with the advantages of high efficiency, flexibility, and reliability and has been widely used in the field of power systems. Based on the user classification results, this section uses the leader–follower game to implement the demand response pricing game between the RDA load aggregator and RDA users of different types. In the game, the RDA load aggregator is considered the leader, and different types of RDA users who participate in DR through load adjustment, rooftop photovoltaic power generation, and energy storage system discharging are considered followers. After several iterations, the game is terminated when reaching the Nash equilibrium, achieving optimal benefits for the leader and the followers.

The objective of the RDA demand response pricing game, z ^SG, can be formulated as in Eq. 16. z SG = l RA ∪ l USER ∪ l PV ∪ l ES , r RA v INIT , v RAP , r USER p i USER t r PV p i PV t r ES p i ES t Q RA , Q USER , Q PV , Q ES , (16) l USER = l 1 USER , l 2 USER , … , l m USER l PV = l 1 PV , l 2 PV , … , l m PV l ES = l 1 ES , l 2 ES , … , l m ES . (17)

In Eq. 16 to Eq. 17, l ^RA, l ^USER, l ^PV, and l ^ES represent the RDA load aggregator, RDA users participating in DR load reduction, rooftop photovoltaic power generation, and energy storage discharging, respectively. Different types of RDA users have different capacities on load reduction, rooftop photovoltaic power generation, and energy storage discharging. {lUSER 1, lUSER 2, …, lUSER m} represent the m categories of RDA users who participate in DR load reduction; {lPV 1, lPV 2, …, lPV m} represent the m categories of RDA users who participate in rooftop photovoltaic power generation; and {lES 1, lES 2, …, lES m} represent the m categories of RDA users participating in energy storage discharging. r ^RA, r ^USER, r ^PV, and r ^ES are the price bidding strategies of the above four game participants, respectively. v ^INIT and v ^RAP are the DR basic price and reward/penalty incentive price for the RDA load aggregator, respectively. In addition, pUSER i(t) represents the power consumption of RDA users participating in DR load reduction; pPV i(t) is the power consumption of RDA users participating in rooftop photovoltaic power generation; pEV i(t) is the power consumption of RDA users participating in energy storage discharging. Q ^RA, Q ^USER, Q ^PV, and Q ^ES are the utility functions of the RDA load aggregator, RDA users participating in DR load reduction, RDA users participating in rooftop photovoltaic power generation, and RDA users participating in energy storage discharging, respectively.

In the leader–follower game, the RDA load aggregator, RDA user rooftop photovoltaics, and RDA user energy storage systems take maximizing the utility as the objective. RDA users participate in the game, taking minimizing the utility as the objective. The iterative process is repeated until the Nash equilibrium is reached and game participants stop updating their strategies. The basic price v ^BASIC from the Nash equilibrium can be written as in Eq. 18. v BASIC = argmax Q RA v INIT , v RAP , p i LUSER t , p i LPV t , p i LES t . (18)

In Eq. 18, pLUSER i(t) is the power consumption of RDA users in the Nash equilibrium solution; pLPV i(t) is the rooftop photovoltaic power generation in the Nash equilibrium solution; and pLES i(t) is the energy storage discharging power in the Nash equilibrium solution.

The power consumption of RDA users in the Nash equilibrium solution should satisfy Eq. 19. p i LUSER t = argmin Q USER v INIT , v RAP , p i USER t . (19)

The rooftop photovoltaic power generation pLPV should satisfy Eq. 20. p i LPV t = argmax Q PV v INIT , v RAP , p i PV t . (20)

The energy storage discharging power pLES i should satisfy Eq. 21. p i LES t = argmax Q ES v INIT , v RAP , p i ES t . (21)

With the Nash equilibrium, the RDA load aggregator, RDA users, RDA rooftop photovoltaics, and RDA energy storage systems cannot gain more profit by unilaterally changing their strategy. The solving process of the game can be referred to Huang et al. (2020), and due to the space limitation, it is not repeated in this paper.

(1) Power constraint

In Eq. 22, pDR i(t) is the integrated power from the RDA load aggregator.

The power from rooftop photovoltaics and energy storage discharging should satisfy Eq. 23. p i PV t + p i EV t ≤ p i RPL t . (23)

(2) Price constraint

The highest compensation price paid by the RDA load aggregator to RDA users, v ^MAX, should satisfy Eq. 24. v MAX ≤ v GRID . (24)

In Eq. 24, v ^GRID is the price sent by the main grid to the RDA load aggregator.

In order to avoid the fact that an RDA user’s willingness to participate in DR decreases after it already has a high score, the RDA demand response model proposed in this paper deducts scores after users enjoyed the DR incentives for realizing sustainable incentives to RDA users. The score adjustment rules, as shown in Table 4, are based on the typical settings of the power industry.

In the settlement, the RDA load aggregator updates the scores of RDA users according to Table 4 and adjusts the corresponding tiers. The adjusted scores, V _e, for RDA users can be calculated as in Eq. 25. v e = v b + w a × Δ s 1 − w b × Δ s 2 − w c × Δ s 3 − w d × Δ s 4 − w e × Δ s 5 . (25)

In Eq. 25, V _b represents the initial scores of RDA users; w _a is the provided demand response; w _b is the load growth default during DR time; w _c is the score deduction after having increased prices; w _d is the number of abnormal disconnections of rooftop photovoltaics and energy storage systems; w _e represents the power quality deviation of rooftop photovoltaic power generation and energy storage discharging. In addition, △s₁, △s₂, △s₃, △s₄, and △s₅ are the score adjustments, as shown in Table 4.