Abstract
The uncertainty of user-side resource response will affect the response quality and economic benefit of load aggregator (LA). Therefore, this paper regards the flexible user-side resources as a virtual energy storage (VES), and uses the traditional narrow sense energy storage (NSES) to alleviate the uncertainty of VES. In order to further enhance the competitive advantage of LA in electricity market transactions, the operation mechanism of LA in day-ahead and real-time market is analyzed, respectively. Besides, truncated normal distribution is used to simulate the response accuracy of VES, and the response model of NSES is constructed at the same time. Then, the hierarchical market access index (HMAI) is introduced to quantify the risk of LA being eliminated in the market competition. Finally, combined with the priority response strategy of VES and HMAI, the capacity allocation model of NSES is established. As the capacity model is nonlinear, Monte Carlo simulation and adaptive particle swarm optimization algorithm are used to solve it. In order to verify the effectiveness of the model, the data from PJM market in the United States is used for testing. Simulation results show that the model established can provide the effective NSES capacity allocation strategy for LA to compensate the uncertainty of VES response, and the economic benefit of LA can be increased by 52.2% at its maximum. Through the reasonable NSES capacity allocation, LA is encouraged to improve its own resource level, thus forming a virtuous circle of market competition.
WITH the increase of renewable energy penetration, the instantaneous dynamic balance of “production-transmission-consumption” of traditional “rigid” power system is becoming more and more difficult [
Since user-side resources such as industrial, commercial, residential and other resources are mostly scattered and the controllable capacity of a single resource is uncertain, it will inevitably be difficult for grid managers to directly incorporate these resources into dispatch. In order to fully collect and utilize these scattered small- and medium-sized resources, a specialized demand response (DR) provider has emerged in developed countries, i.e., load aggregator (LA). As a new type of commercial organization, LA integrates user-side resources through technical and economic strategies and introduces them into the electricity market. In this way, small- and medium-sized resources can participate in DR projects or bid in the electricity market, which stabilizes the operation of the system and makes the market mechanism more mature. According to different types of resources, LA can be further divided into distributed power generation aggregator, electric vehicle (EV) aggregator, DR resource aggregator, intelligent housing aggregator, etc. The LA participates in electricity market transactions by integrating and controlling EVs, temperature control loads, and other flexible user-side resources.
In this context, as an emerging electricity seller that aggregates a large number of flexible user-side resources, LA has been developing rapidly [
Current researches on LA mostly focus on operational control and market competition strategies. Reference [
In addition, traditional energy storage system such as battery energy storage, flywheel energy storage, etc., is called narrow sense energy storage (NSES). Because of its advantages in separating the generation and consumption of electric energy from time and space dimensions, it has gradually become one of the key supporting technologies for future power systems. In recent years, scholars world-wide have carried out relevant research on energy storage allocation of grid side, new energy side, and user side. Reference [
To sum up, this paper proposes a generalized energy storage (GES) concept that combines VES and NSES from the perspective of power system “load-storage”. As stated in [
The main contributions of this paper are as follows.
1) This paper analyzes the operating mechanism of LA in both day-ahead and real-time markets. In day-ahead market, according to the probability distribution of GES response, the service contract is signed with independent system operator (ISO). In real-time market, the response gap caused by the uncertainty of VES response is compensated by NSES.
2) According to the response characteristics, truncated normal distribution is used to simulate the response accuracy of VES. And the response models of VES and NSES are established, respectively. On this basis, according to the strategy of VES priority response, the operation strategy of LA is analyzed.
3) The HMAI is designed to measure the risk of LA being eliminated when participating in market competition. In order to improve the market competitiveness of LA, an optimal capacity allocation model of NSES considering the HMAI is established. Through the rational allocation of NSES, both the income and response quality of LA can be significantly improved.
The rest of this paper is organized as follows. Section II is the market analysis of LA considering GES. Section III presents the model of VES and NSES response. In Section IV, the analysis of LA scheduling strategy considering VES response uncertainty is given. In Section V, an optimal capacity allocation model of NSES for LA based on HMAI is constructed. In Section VI, the numerical results based on PJM market and the corresponding explanations are given. Finally, Section VII gives the conclusions of this paper.
Based on the principle of real-time power balance [

Fig. 1 Analysis of LA with GES based on real-time power balancing.
Dispatching GES through technical and economic means, LA participates in transactions as the power supply, and signs DR contracts with ISO. The main income of LA participating in services comes from policy subsidies for electricity cost savings and DR, and NSES’s profit through peak-to-valley arbitrage. With reference to the transaction process of the PJM electricity market in the United States [
1) In the day-ahead market, LA forecasts the probability distribution of “virtual electricity” that can be provided by VES resources in the next day according to the historical data. Combined with the response power provided by the NSES, the final response power of LA is reported to ISO. ISO selects one or more qualified aggregators from several LAs to sign the DR service contracts. The unified contract price mode is adopted to clear the day-ahead market.
2) In the real-time market, LA dispatches GES to complete the DR contract signed in the day-ahead market, and uses the contract price for clearing. If the actual response power of LA reaches the contractual commitment level, LA will be rewarded, including contract compensation and real-time response compensation. Otherwise, if the actual response power of LA does not reach the committed level, the real-time marginal price will be taken as the unit power penalty. The penalty price is a single form, i.e., the penalty price for over-response and under-response is the same.
The above trading processes are shown in Fig. S1 in Supplementary Material. Since electricity consumption behaviours of the users are simultaneously affected by multiple factors such as subjective factors and real-time electricity prices, the VES response is often uncertain and time-varying. Therefore, for different response requirements at different time, the probability distribution of the actual response of LA is different. In order to best satisfy the response demands at all time, the market should try to avoid using a uniform incentive price for LA. Therefore, this paper divides different response levels according to the stability of LA response, and formulates hierarchical electricity markets for different response levels. Different hierarchical electricity markets have different incentive prices. The hierarchical electricity market can stimulate the competition among LAs, thereby obtaining better response services for the power system.
The aggregation of VES resources of different scales by LA is a complex behavior with many influencing factors, so the response of VES has greater uncertainty [
(1) |
where is the volume sum in the theory of sequence operations; and K is the number of types of VES responses.
Through the analysis of historical data, the uncertainty of VES response follows normal distribution [
In order to further quantitatively describe the realized VES response in LA dispatching process, the VES response ratio is defined as the ratio between VES realized response and scheduled response during the
(2) |
where denotes the increase of load; and denotes the reduction of load.
Since the response accuracy of VES follows the truncated normal distribution, should also follow a truncated normal distribution , whose probability density function is (3):
(3) |
where and are the probability density function and cumulative distribution function of the standard normal distribution, respectively; is the expection of VES response ratio during the period; is the standard deviation of VES response riatio during the period; and and are the maximum and minimum VES response ratios of during the period, respectively. The lower limit of the probability distribution () is 0, which means that the VES will not respond.
When dispatched by LA, the random distribution of VES response depends on its resource conditions [
(4) |
With time scale , the expected value of VES response can be obtained as:
(5) |
where is the VES scheduled power.
Various types of traditional energy storage systems constitute NSES resources that can participate in LA scheduling. The NSES is regarded as a measure to deal with the uncertainty of the VES response, so the uncertainty that may exist in the NSES response is not considered. Since NSES has multi-time scales and state dependence, the response provided by NSES is related to its state of charge (SOC) and charging and discharging power. With a certain time scale , the response provided by the
(6) |
(7) |
where , and is the set of NSES; and are the quantities of charging and discharging responses for the
Taking the charging response of NSES as an example, the visualization result of (6) is shown in

Fig. 2 Response quantity of the
Then, in the case of a certain time scale , the quantity of response that all NSESs in the region can provide is:
(8) |
In order to give full play to the dominant role of VES when participating in DR, LA can firstly schedule VES. In the case of VES priority response, NSES is used to compensate for the deviation caused by VES response and to improve the response level. To quantitatively evaluate the response level of GES, the response confidence level (RCL) is introduced in this paper. RCL is the probability value of actual response in the specified response deviation range, as shown in

Fig. 3 RCL of GES.
The RCL of GES is calculated as:
(9) |
where is the response deviation interval; is the cumulative distribution function of GES response; is the actual response of GES; is the scheduled response of GES; is the dispatched response of NSES, and also the lower limit of when VES response is 0; and is the maximum response quantity of GES response.
Assume that the deviation of VES response is . With this strategy, the deviation of GES response is:
(10) |
The VES probability density curves before and after NSES response are presented in
(11) |

Fig. 4 VES probability density curve before and after NSES response.
where is the cumulative distribution function of GES response when NESE response is 0; and is the cumulative distribution function when NESE response is .
It can be seen from
(12) |
If the above relation is converted to the response ratio of GES, (11) can be rewritten as:
(13) |
where and are the upper limits of the GES response ratio before and after NSES response, respectively; is the probability density function of GES response ratio when the NSES response is 0; and is the probability density function when the NSES response is .
The expected value of GES response ratio is:
(14) |
Affected by the bonus calculation rules, this paper defines HMAI. This index is used to measure the risk of LA being eliminated when participating in market competition. According to the response fluctuation of LA, the response quality is divided into three levels. The corresponding HMAI reward rules are formulated, in order to support and cultivate high-quality LA.
(15) |
where is a variable representing the HMAI of LA. Set and as a threshold of qualified response and a threshold of high-quality response, respectively. The response levels of LA are divided as follows: ① the first level is high-quality response (HQR), ; ② the second level is qualified response (QR), ; ③ the third level is low-quality response (LQR), .
If the value of HMAI is in the LQR, the risk of LA being eliminated in the market competition is greater under such response conditions. Therefore, LA needs to choose the appropriate GES scheduling scheme and NSES allocation strategy to avoid losing market competitiveness due to the excessive HMAI value.
LA can install a certain quantity of NSES to suppress the uncertainty of VES response. The established optimal capacity allocation model of NSES for LA is shown as below.
Dividing one day into n time intervals by time interval , ISO usually issues multiple intermittent peak and valley continuous response periods. For example, assume that the “charging” response period and “discharging” response period of GES are (01:00-05:00) and (11:00-13:00; 19:00-21:00), respectively. That is, there are three continuous response periods, and there is usually a long-time interval between them. During the interval of no response demand (00:00-01:00; 05:00-11:00; 13:00-19:00; 21:00-24:00), the NSES resources in GES can be charged or idle. In view of the complex response characteristics and coupling relationship of resources in GES, it is assumed that various response resources in GES are independent each other.
As shown in Section II-B, the income of LA mainly consists of two parts: market compensation rewards including , , and and sales profit when NSES releases the electricity.
According to the realized VES response, the compensation revenue of LA can be expressed as:
(16) |
where is the
Considering response mechanism and HMAI, the market penalties that LA can circumvent after installing NSES are:
(17) |
where and are the expected response ratios before and after the addition of NSES during the
If the NSES installation reaches a certain capacity, the response level of the LA can be improved, and an additional compensation income can be obtained:
(18) |
where and are the reward multiples before and after the addition of NSES, respectively.
In addition, the sales profit (discharging) and purchasing cost (charging) of LA dispatching NSES are:
(19) |
where is the duration of the
The life cycle cost (LCC) of an NSES usually consists of the initial investment cost and the operation and maintenance cost . The initial investment cost is directly related to the rated capacity and rated power of NSES. Moreover, for convenience, in this paper is estimated as a percentage of .
(20) |
(21) |
where is the percentage of operation and maintenance cost of the
The objective function of the optimal capacity allocation model is to maximize the annual revenue of LA scheduling GES to participate in DR. With one year as the calculation period, the net revenue of LA can be calculated as:
(22) |
where is the number of days in a year for LA participating in DR.
The constraints are:
(23) |
(24) |
(25) |
(26) |
(27) |
(28) |
where is the HMAI threshold; is the duration of the response period; and are the boolean variables representing the charging and discharging flag bits of the
After the establishment of the proposed model, in the MATLAB software environment, this paper firstly simulates the expected response ratio of GES by Monte Carlo method. Then the adaptive particle swarm optimization algorithm is used to solve the above optimization problem, and the capacity allocation strategy of the LA installed NSES is obtained [
Based on the data from PJM market in the United States [
Due to the various NSES resources on the user side, a unified scheduling reward and punishment system has not yet been formed. Therefore, this paper assumes that the NSES installed in LA only includes lithium batteries for large-scale applications. And during the response process, the charging and discharging power of the NSES and VES are constant. The capacity cost and power cost parameters of NSES are and , respectively. Its capacity and the maximum charging and discharging power meet a certain proportion, i.e., . Life cycle of NSES is . The charging and discharging efficiencies of the battery are . The annual operation and maintenance cost ratios are . The discount ratio is .
Finally, the parameters of the algorithm are set as follows. The individual learning factor and population learning factor of adaptive particle swarm optimization are 2 and 1.5, respectively, and the population size is 50. The value of inertia weight ranges from 0.5 to 0.9, and its evolution coefficient is 1.12. The maximum number of iterations is 200. The number of Monte Carlo simulation is 5000, i.e., 5000 sampling points. The above optimization model is implemented on a computer with an Intel i7-10710U processor and 16 GB RAM.
For reasonably setting the standard deviations, the with different standard deviations is observed for 5000 times. of truncated normal distribution with different standard deviations is shown in

Fig. 5 of truncated normal distribution with different standard deviations. (a) . (b) . (c) . (d) .
The simulation results show that when the standard deviation is less than 0.1, the VES response ratio is concentrated in a small range. In this case, there is basically no possibility of user default, which is not in line with realistic logic. That is, this scenario does not reflect the advantages of configuring NSES. When the standard deviation of normal distribution exceeds 0.5, the distribution of sampling points is almost uniform. In this situation, the probability of user default is too high. That is, the resource response level of LA is so low that it cannot compete in the market. When the standard deviation of truncated normal distribution is 0.2, the distribution of sampling points not only reflects the response positivity of users, but also reflects the uncertainty of the VES response. Therefore, the standard deviation of the truncated normal distribution obeyed by is set to be 0.2.
Taking the promotion of LA response level to QR in Section VI-C as an example,

Fig. 6 Calculation convergence process.
Firstly, this paper analyzes the impact of HMAI classification standard on upgrading the resource quality of LA. Assume that the market is divided into the following three specific categories of response quality: HQR, whose HMAI is less than 10%; QR, whose HMAI is between 10% and 20%; and LQR, whose HMAI is greater than 20%. The thresholds of the above conditions are and .
The HMAI of LA without participation of NSES can be observed in
1) The HMAI threshold is set to be 20%, i.e., the LA response quality is upgraded to QR after the allocation of NSES. The NSES capacity to be installed at this time is . And the cost of avoiding punishment for LA is $5.5×1
2) is set to be 10%, i.e., the LA response quality is upgraded to HQR after the allocation of NSES. The NSES capacity to be installed at this time is 3.23 MW/6.46 MWh. Due to the level promotion, the cost of avoiding punishment for LA is $14.7×1
From

Fig. 7 Revenue of LA and penalty under different targets of response level.
As can be seen from
Limited by the technology, the investment and construction costs of lithium battery energy storage and other battery energy storage are still high. Therefore, LA should be guided to actively improve its own response quality level by formulating reasonable compensation rules. Three different scenarios of compensation rules are set to analyze the net income of LA and the SIPP of NSES in each scenario.
Scenario 1: the compensation price of QR and that of HQR are both equal to spot market prices.
Scenario 2: the compensation price of QR is equal to the spot market price, and the compensation price of HQR is 0.5% higher than the spot market price.
Scenario 3: the compensation price of QR is 0.5% higher than the spot market price, and the compensation price of HQR is 1.0% higher than the spot market price.
The comparison of net revenue and SIPP of LA in different market scenarios is shown in

Fig. 8 Comparison of net revenue and SIPP of LA in different market scenarios.
For the sake of reliable and stable operation of electricity market, ISO will encourage LA to improve its response quality. Therefore, it is necessary to provide additional economic compensation for LA at the HQR level. Under the incentive effect of additional compensation, i.e., scenario 2 and scenario 3, the net revenue of LA at the HQR level increases by 35.4% and 82.3% compared with scenario 1, i.e., $1.3×1
The SIPPs of NSES in the three scenarios are shown by the red line in
Sections VI-C and VI-D discuss the impact of HMAI classification standard and compensation rules on the investment of LA in NSES, respectively. Since different types of markets have different requirements for the response quality of LA, there are also differences in the design of the above two in the market rules.
Through the adjustment of HMAI classification standard and compensation rules, this paper analyzes the change of SIPP when LA reaches HQR level. The HQR thresholds are set to be 10%, 5%, and 1%, respectively. Compensation coefficients, i.e., the ratios of compensation price to spot market price, are set to be 1.00, 1.01, 1.05, and 1.10, respectively. The SIPP values of NSES in different permutations are observed, as shown in
The numerical results show that the stricter the HQR threshold is set, the more NSES the LA needs to allocate. As a result, the SIPP of NSES becomes larger. When the HQR threshold is set to be 1%, even if the compensation coefficient is as high as 1.1, i.e., the compensation price is 10% higher than the spot market price, the SIPP of NSES still has 10.6 years. At present, the life of lithium battery is mostly 10 years, so it can be roughly judged that the threshold setting is not economical. In addition, a reasonable compensation price is also crucial. According to the results in
Finally, it analyzes the influence of the NSES allocation capacity on the economic benefits of LA. The threshold value of QR and HQR levels adopts the parameters of Section VI-C, and the compensation price adopts the parameters in scenario 3 of Section VI-D.
The market profit of LA can be significantly improved by scheduling NSES to suppress the response uncertainty of VES. However, as the installed capacity of NSES increases, there will be a redundancy in capacity. And the redundant capacity cannot further improve the economic benefits of LA. In addition, the high cost of NSES makes the net income of unit energy storage increase first and then decrease. The results show that the net income per NSES increases to a maximum of 242315.1 $/MWh when the installed capacity is 3.611 MW/7.222 MWh. At this time, the SIPP of NSES is 4 years. To sum up, LA can obtain better investment return and shorter SIPP by reasonably allocating the capacity of NSES.
When LA participates in electricity market transactions to obtain profits, it will face the problem of default due to the influence of VES response uncertainty. In order to ensure the stability of LA participating in the market, this paper takes the NSES as a means to reduce default risk. Based on this, a capacity allocation model of NSES with HMAI is established. Finally, in order to verify the effectiveness of the model, four examples are analyzed from HMAI classification standard, compensation rules, market rules (combining the above two), and NSES allocation capacity. The main conclusions are as follows.
1) By limiting different HMAI, LA will allocate NSES to improve its response level, so as to improve its own economic benefits. In the given case study, when the response level reaches HQR, the total revenue of LA increases from $9×1
2) By setting reasonable compensation rules, LA can allocate NSES more actively and improve its response quality level. In the given case study, the net income of LA at the HQR level will increase from $9.6×1
3) By establishing reasonable market rules, it can not only promote the upgrading of LA to HQR level, but also ensure the reliability of electricity market operation. In the case study, the SIPP of NSES can be reduced to 3.8 years at most.
4) By allocating appropriate NSES allocation capacity on the user side, the redundancy of energy storage capacity and waste of resources can be avoided. And LA can obtain better return to investment and shorten the SIPP. In the case study, the optimal installed capacity of NSES is 3.611 MW/7.222 MWh, and the SIPP of NSES is 4 years.
This paper aims to provide a model for emerging electricity sellers to avoid default response, without consideration of the benefits of other electricity sellers. Therefore, it is worth further study on the profit of other market players and their competitive game with other players in the market.
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