Identification and modelling of parameters for the information-physical-social convergence characteristics of user-side flexible resources

Abstract

The use of flexible resource information on the user side helps to increase system efficiency. Power system power variation becomes more pronounced with the access to renewable resources. Therefore, the study proposes a parameter identification and modeling method for the physical and social integration characteristics of flexible resource information on the user side. Taking the user’s air conditioning load as the object, the thermal dynamic model of the air conditioning building is constructed using equivalent thermal parameters, and the variable frequency air conditioning load is embedded in the battery model. The model parameter identification is carried out using high-dimensional model expression technology. According to the experimental data, in options 2 and 3, the system operator makes power purchases based on the storage status of the lithium battery or virtual battery, increasing the number of power purchases when the price of electricity is low and decreasing the number of power purchases when the price of electricity is high. This effectively reduces the system operator’s electricity costs. The error of multiple linear regression modelling varies widely, with relative errors up to 0.75 and an average relative error of 15.1%. The relative error of modelling based on the high-dimensional model expression technique is in the range of 0 to 0.2, with an average relative error of 5.5%. The results show that compared with multiple linear regression models, high-dimensional model representation technology has higher modeling accuracy and can accurately identify the parameters of the air conditioning load aggregation model, solving the problem of difficult parameter calculation in the practical application of the air conditioning load aggregation model, and providing technical support for power system regulation.

Keywords

User-side resources data fusion parameter identification time scale high-dimensional representation air conditioning load power dispatch

1. Introduction

Today’s non-renewable energy sources are becoming increasingly scarce and a wide range of renewable green energy sources are being developed and deployed to replace non-renewable sources such as coal, oil and gas [1]. Industrial, commercial and residential electricity consumption has increased significantly and the power system (PS) is facing many problems such as lack of capacity and a significant increase in the risk of power outages. With significant government support, wind energy, for example, is being widely used in the PS to alleviate environmental pollution and the energy crisis [2, 3]. The distribution network, which is directly connected to customers, is the last link in the PS. It has become crucial to rationally regulate demand relations, or balance supply and demand, in order to increase the operational efficiency and stability of the PS [4]. After the electricity market was changed in the United States, the notion of demand response was established. In the context of market recommendations, demand response is a new business model, which involves the use of flexible resources on the customer’s demand side and helps to achieve rational distribution dispatch [5]. In demand response, customers make changes to their electricity consumption according to market prices and adjust their electricity consumption at a certain time [6]. Air conditioning load, as a flexible and adjustable resource on the load side, has great potential for exploration and flexible scheduling methods. It is an excellent demand response resource that requires in-depth research. To improve the efficiency of PS dispatch, the study proposes a parameter identification and modelling method for the physical social integration characteristics of flexible resource information on the customer side, and takes the customer air-conditioning (AC) load as the research object, expecting to improve the accuracy of power dispatch and reduce power consumption. The study is broken down into four sections: a summary of research on data fusion and electricity demand response in the first section; the design of the parameter identification and modelling method for the physical-social fusion of flexible resource information on the user side; the validation of the results of the proposed method and model in the third section; and the conclusion of the entire paper in the fourth section.

2. Related works

Power demand response can aggregate dispersed user side resources into a tower, improving the grid’s ability to access and consume clean energy. Researchers are optimizing the distribution system based on users’ power needs to improve the rationality of power system planning. Chen et al. [7] proposed a residential electricity consumption behavior analysis and optimal control strategy, combined with the Dbscan algorithm to construct a residential electricity consumption behavior analysis model and proposed a radar matrix for judging user control attributes to achieve rational dispatch of electricity. Sultana et al. [8] proposed algorithm for power shortage and other problems to achieve the allocation of users’ unused spectrum through radio-awareness to reduce the delay to achieve the best allocation effect. The study’s findings demonstrate that the strategy performs better in terms of throughput and latency. Ferraz [9] proposed a smart residential distribution system that combines real-time residential tariffs to develop a demand response plan for the distribution company and uses IoT smart meters to accept key parameters. The findings demonstrated that the method is able to find the best possible dispatch and further reduce electricity consumption. Trovato [10] proposed a spatial variation PS scheduling model based on inertial response. The method is applied to the 2030 GB low-carbon Scenario analysis, and the results showed that the method can convert additional operating costs. Al Kez et al. [11] proposed a demand response based PS service model for Internet data centres, which enables a fast working and power supply cooperation framework through frequency response service and incorporating operational conditions and constraints to achieve central resource initiation. The simulation results showed that the strategy can reduce the need for PS rotating standby.

Data fusion in the information-physical society is the use of the coordination of computer resources and physical resources, combining them to improve the adaptability and security of future industrial production and information development, etc. Zhou et al. [12] suggested a reinforcement learning-based multi-sensor data fusion method, employing spline interpolation to resolve the issue of multi-far data time, to increase the robustness and reliability of detection systems. The outcomes of the simulation demonstrate the method’s viability in aerial combat. Wang et al. [13] proposed a multi-sensor data fusion based AGV navigation analysis method for differential AGV navigation problem, constructs a motion model through multi-multi-sensor based inertial guidance method, and proposes a model and algorithm for navigation and obstacle avoidance based on data fusion. The study’s findings demonstrate that the technique can raise the precision of AGV navigation. The research findings demonstrate that the method is more effective for dataset evaluation. Chen et al. [14] proposed a new approach for aspect-level sentiment classification based on multi-source data fusion, integrating resources through a unified framework, and using a pre-trained language model based on a deep bidirectional transformer. Peng et al. [15] proposed a fusion method by indexing quantum lattice nodes and classifying lattice nodes, experimental data showed that the method helps to simplify fusion results and intelligent decision making. Qi et al. [16] proposed a multimodal data fusion framework to enhance enhanced recognition of dynamic situations, designed a multi-sensor based hardware architecture that Enabling the acquisition of data from different device.

In summary, many scientific researchers have conducted many different studies and designs for user-side resource information and social data fusion, but the stability and adaptability of these methods still need to be improved. Therefore, the research proposes a parameter identification and modelling method for the physical and social fusion characteristics of flexible resource information on the user side, in the hope of improving the efficiency and accuracy of PS dispatch.

3. User-side flexible resource information-physical society convergence characteristics parameter identification and modeling method design

This chapter is a modelling design incorporating flexible resources on the user side, with the user’s AC load as the object of study. Inverter AC digital virtual battery (VB) modelling and scheduling are proposed in the first half of this chapter, and the construction of a multi-time scale fusion model for the load is covered in the second section.

3.1 Research on user-side flexible resource models based on information-physical society data fusion methods

Customer-side flexible resources are devices such as generation, consumption and storage installed on the consumer side, owned by the consumer and with the ability to interact with the grid, and are flexible resources that can participate in dispatch [17]. The study takes the AC load of the user as the target, and the different response characteristics of AC under different control methods contribute to the provision of ancillary services at different time scales. The market shares of air conditioners account for a relatively large share of inverter air conditioners. The study proposes a minute time scale digital virtual cell modelling and scheduling method for inverter air conditioners, and uses equivalent thermal parameters to construct a thermal dynamic model for air-conditioned buildings, as shown in Eq. (1).

$\displaystyle C_{a}\frac{dT_{i}(t)}{dt}=\frac{(T_{0}-T_{i}(t))}{R}-Q$ (1)

In Eq. (1), the equivalent heat capacity of the AC load is expressed by $C_{a}$ , the equivalent impedance of the AC load is expressed by $R$ , the outdoor temperature is expressed by $T_{0}$ , the indoor air temperature is expressed by $T_{i}$ , the time corresponding to indoor temperature is represented by $t$ , and the cooling capacity of the inverter air-conditioner is expressed by $Q$ in kW. The energy efficiency ratio of the compressor of the inverter air-conditioner is affected by frequency, and the relationship between the electrical power and cooling capacity of the inverter air-conditioner is shown in Eq. (2).

$\displaystyle Q=\frac{k_{2}}{k_{1}}P_{v}+\frac{k_{1}l_{2}-l_{1}k_{2}}{k_{1}}$ (2)

In Eq. (2), the inverter air conditioner electric power is represented by $P_{v}$ , and the four constant coefficients are represented by $k_{1}$ , $k_{2}$ , $l_{1}$ and $l_{2}$ in relation to the frequency of the inverter air conditioner compressor, which can complete the continuous adjustment of the inverter air conditioner electric power. The constraints of the conventional lithium battery are shown in Eq. (3).

$\displaystyle s_{\min}\leqslant s(k+1)\leqslant s_{\max}$ (3)

In Eq. (3), the minimum and maximum values of the Li-ion battery energy storage (ES) state are represented by $s_{\min}$ and $s_{\max}$ respectively, and the Li-ion battery ES state at the $k+1$ time period is represented by $s(k+1)$ . There are other existing battery scheduling models, and the study embeds the inverter AC load into the battery model to assist the power scheduling department without modification. Equation (4) provides the formula for calculating the ES of the VB.

$\displaystyle O_{a}(k)=C_{a}(T_{\max}-T_{i}(k))$ (4)

In Eq. (4), the ES capacity of the VB at $k$ is represented by $O_{a}(k)$ , and the maximum and minimum temperatures that the AC user can withstand are represented by $T_{\max}$ and $T_{\min}$ respectively. The ES state of the VB is depicted in Eq. (5), and its definition is the same as that of the typical lithium battery.

$\displaystyle\textit{soc}(k)=\frac{O_{a}(k)}{O}=\frac{T_{\max}-T_{i}(k)}{T_{% \max}-T_{\min}}$ (5)

In Eq. (5), the ES state of VB at $k$ is represented by $\textit{soc}(k)$ , the AC room temperature at $k$ is represented by $T_{i}(k)$ and the ES of VB capacity is represented by $O$ . The conditions for the VB at any given time are shown in Eq. (6).

$\displaystyle 0\leqslant\textit{soc}(k+1)\leqslant 1$ (6)

In Eq. (6), the ES state of the VB at $k+1$ is represented by $\textit{soc}(k+1)$ . This shows that the normal lithium battery model and the VB model for a single inverter AC load can be used for typical planning, but there are some differences between the two models, as shown in Fig. 1.

Figure 1.

Differences between the two models.

In Fig. 1, the differences between the virtual battery model and the conventional lithium battery model are mainly reflected in energy storage capacity, dissipated power, and other aspects. The maximum capacity of a lithium battery is an absolute parameter, but the storage capacity of a VB is much greater than the given storage capacity, so the capacity of a VB is only a relative parameter, while the charging and discharging power is a relative parameter [18]. The AC load can be additionally dispatched in response to demand, depending on the actual situation. The dissipation power of a lithium battery is negligible, the VB has a different operating behavior to a lithium battery and its dissipation power is quite high. VB scheduling needs to take into account the impact caused by the initial temperature and update the relevant parameters of the VB in real time.

There are significant differences in control and modeling methods between variable frequency air conditioners and fixed air conditioners, and they cannot be treated equally. In order to overcome the shortcomings of existing technologies, the research provides a microscale virtual battery modeling and scheduling method for variable frequency air conditioners, which incorporates residential and small commercial variable frequency air conditioner loads into the existing scheduling model, facilitates the scheduling of relevant departments, provides energy storage services for real-time market load news aggregator, and reduces economic losses caused by factors such as power market forecasting errors.

Three layers make up the hierarchical control system created for the study. The inverter AC loads are located in the bottom layer of the hierarchical control framework, and intelligent controllers are mounted on each air conditioner separately to enable data storage, computation, and signal interaction with aggregators. The virtual cell modelling approach and the encapsulation of the model ensure user privacy and security, i.e. information such as user information, AC parameters and building structure are protected. Prior to demand response, the virtual cell parameters are transmitted from the controller to the upper layer where they are updated according to the initial temperature. The upper layer control signals are transmitted to the VB controller, among others, to adjust the operating behaviour of the AC load in combination with its own parameters and operating status. The intelligent control layer framework is shown in Fig. 2.

Figure 2.

Intelligent control hierarchical framework.

Figure 3.

The entire process of hierarchical control.

The intermediate layer contains the load aggregator for model fusion of the top-level AC loads and transmission of the acquired scheduling and control signals to the bottom-level virtual cells. In practical engineering control, the case-by-case control of the virtual cells is impractical, when the virtual cells need to be fused for modelling. Equation (7) displays the fused VB’s ES update.

$\displaystyle\textit{SOC}_{m}(k)=\zeta\cdot\textit{SOC}_{m}(k)+B(k)+\gamma_{m}$ (7)

In Eq. (7), the ES state of the fused virtual cell at $k+1$ is represented by $\textit{SOC}_{m}(k+1)$ , the scheduling signal is represented by $B(k)$ and the two parameters of the fused virtual cell are represented by $\zeta$ and $\gamma_{m}$ respectively. The optimized scheduling of integrated virtual batteries takes the wind power, load, and electricity price of subsequent cycles as the objective function. The optimized model of integrated virtual batteries is shown in Eq. (8).

$\displaystyle\min F_{c}=\sum\limits_{k=i}^{i+w}{[(L(k)+B(k)-G(k)p_{rt}(k))]}$ (8)

In Eq. (8), the scheduling value of the integrated virtual battery is represented by $F_{c}$ , the charging and discharging power of the energy storage equipment in the $k$ scheduling period is represented by $B(k)$ , the load, wind power generation, and electricity price in the $k$ scheduling period are represented by $L(k)$ , $G(k)$ , and $p_{rt}(k)$ , respectively, and the backward optimization period is represented by $w$ . The virtual cell fusion model is easier to use by reducing the computational difficulty of the aggregator and by generating the same control signals for transmission to lower-level devices. The fusion model combines the K-means algorithm to solve the problem of a large number of virtual cell parameters by dividing similar parameters into groups and analyzing the fusion to achieve the fusion of groups of virtual cells. The top layer of the scheduling framework is the system operator. Before optimizing the behavior of the system operator, it is assumed that bids are relatively small relative to the overall electricity market, that every bid is accepted by the market, and that load has no effect on tariff elasticity. The whole process of hierarchical control is shown in Fig. 3.

In Fig. 3, the load aggregator coordinates the bottom and top members, aggregates different virtual batteries, and generates control signals to the virtual batteries. The top-level system operator is mainly responsible for optimizing and coordinating the air conditioning load with other resources at the power system level.

3.2 Design of a multi-timescale fusion model parameter identification method for loads based on HDMR techniques

User behavior and performance in practical applications are difficult to predict accurately, and the study incorporates a high-dimensional model representation (HDMR) technique for model parameter identification. The system output expression under the HDMR technique is shown in Eq. (9).

$\displaystyle f(x)\approx f_{0}+\sum\limits_{i=1}^{nf}{f_{i}(x_{i})}+\sum% \limits_{i<j}{f_{ij}(x_{i},x_{j})}+\ldots+f_{1,2,\ldots,nf}(x)$ (9)

In Eq. (9), the zero-order component function (CF) is represented by $f_{0}$ , the system output is represented by, the second-order CF is represented by, the number of input variables is represented by $f(x)nf$ , the first-order CF is represented by $f_{i}(x_{i})$ , and the $f_{ij}(x_{i},x_{j})nf$ order CF is represented by $f_{1,2,\ldots,nf}(x)$ . The normalization of the input variables allows for simplification of the calculations by combining Monte Carlo to sample the input variables and estimate them using orthogonal polynomials, with the first and second order CF expressions shown in Eq. (10).

$\displaystyle\left\{{\begin{array}[]{l}f_{i}(x_{i})=\sum\limits_{r=1}^{g}{% \alpha_{r}^{i}\phi_{r}(x_{i})}\\ f_{ij}(x_{i},x_{j})=\sum\limits_{p=1}^{l}{\sum\limits_{q=1}^{m}{\beta_{pq}^{ij% }}}\phi_{p}(x_{i})\phi_{q}(x_{i})\\ \end{array}}\right.$ (10)

In Eq. (10), the constant coefficients are represented by $\alpha$ and $\beta$ , the highest number of unit orthogonal polynomials are represented by $g$ , $l$ and $m$ respectively, and the orthogonal polynomials are represented by $\phi(x)$ . The objective function of the high-dimensional model is shown in Eq. (11).

$\displaystyle\min\int\limits_{X^{n}}{\left\{{f(x)-\left[f_{0}+\sum\limits_{i<j% }{f_{ij}(x_{i},x_{j})}+\ldots+\sum\limits_{i_{1}<\ldots i_{l}}{f_{i_{1},\ldots% ,i_{l}}(x,\ldots,x)}\right]}\right\}}^{2}dx$ (11)

In Eq. (11), the unit polynomials are orthogonal to each other, solved by a system of linear equations, and the estimated values of the constant coefficients can be obtained after sampling the input variables by the Monte Carlo method. At this point, the relationship between input and output is shown in Eq. (12).

$\displaystyle f(x)=f_{0}+\sum\limits_{i=1}^{n}{\sum\limits_{r=1}^{g}{\alpha_{r% }^{i}\phi_{r}(x_{i})}}+\sum\limits_{i<j}{\sum\limits_{p=1}^{l}{\sum\limits_{q=% 1}^{m}{\beta_{pq}^{ij}}}\phi_{p}(x_{i})\phi_{q}(x_{i})}$ (12)

The output variables, as shown in Eq. (12), have the property of being independent of each other after being collected by the Monte Carlo method, and the total variance of the system is shown in Eq. (13).

$\displaystyle D=\sum\limits_{i}{D_{i}}+\sum\limits_{i<j}{D_{ij}}$ (13)

In Eq. (13), the total system variance is denoted by $D$ , the second-order component variance by $D_{ij}$ and the first-order component variance by $D_{i}$ . The input to output global sensitivity is defined as shown in Eq. (14).

$\displaystyle\left\{{\begin{array}[]{l}S_{i}=\frac{D_{i}}{D}\\ \\ S_{ij}=\frac{D_{ij}}{D}\\ \end{array}}\right.$ (14)

In Eq. (14), the first-order component sensitivity is denoted by $S_{i}$ and the second-order component sensitivity is denoted by $S_{ij}$ . For multi-input, single-output systems, Monte Carlo methods are used to obtain multiple samples of the inputs and outputs and to construct HDMRs for the system inputs and outputs, with global sensitivity allowing quantification of the contribution of the input variables to the outputs. The study describes the diversity and uncertainty of the AC load parameters in terms of two indicators, type and level of diversity, and the distribution of the parameters is expressed by the AC load parameter diversity. The analysis assumes that the means and standard deviations of the parameters affecting the AC load have a constant distribution over a wide range of parameters. The modelling process of the HDMR technique is shown in Fig. 4.

Figure 4.

The entire process of hierarchical control.

The HDMR technique involves sampling prior to modelling, combining the range of values of the physical parameters of the AC load to obtain the relevant parameters, and generating the internal AC load parameters of the system according to a particular distribution law. The output quantities are calculated by merging the parameters of the model, and the sensitivity of the relevant physical parameters of the AC load is used to identify the important physical parameters [19, 20]. The Quasi Monte Carlo sampling method was used to obtain the input samples for the study [21]. Each input sample was then combined with the appropriate parameter distribution type to generate 1000 AC load parameters [22]. The values of the model parameters were then determined using independent simulation, and the output quantities of the input samples are displayed in Eq. (15).

$\displaystyle f(x^{(s)})=C^{(s)}(s=1,2,\ldots,N_{0})$ (15)

In Eq. (15), the output quantity is represented by $f(x^{(s)})$ , the value of the $s$ output quantity is represented by $C^{(s)}$ , and the number of groups of input samples is represented by $N_{0}$ . The normalized representation of the input quantities is shown in Eq. (16).

$\displaystyle x_{i}^{\ast}=\frac{x_{i}-x_{\min}}{x_{\max}-x_{\min}}$ (16)

In Eq. (16), the actual and standard values of the input variables and are represented by $x_{i}$ and $x_{i}^{\ast}$ , respectively, and the maximum and minimum values of the input quantities are represented by $x_{\min}$ and $x_{\max}$ , respectively. A HDMR of the technical model, encompassing primarily the pertinent parameters and the computation of the global sensitivity, is built using the values of the input-output pairs. The calculation of the first order CF yields higher order coefficients, while the second order CF yields higher order coefficients in a similar manner. The degree of influence of the physical parameters of the AC on the fusion model increases with the global sensitivity [23, 24]. After the construction of the HDMR technique model, the important AC physical parameter coefficients need to be stored to facilitate subsequent parameter identification and modulation. The constant changes in the outdoor temperature and the random adjustment of the users’ desires make the scheduling of the system loads and resources more difficult, when the HDMR technology model is required to achieve real-time updating of the parameters and to reflect the mapping relationship between the fusion model and the physical parameters. The ability to complete the real-time parameter identification of the AC load fusion model is one of the important physical parameters to be identified [25, 26]. Figure 5 shows the real-time parameter identification process for the AC load fusion model.

Figure 5.

Real time parameter identification process of AC load fusion model.

After the construction of a multi-timescale fusion model of the load based on a HDMR technique, the relationship between the physical parameters of the AC load can be obtained according to the modelling structure as shown in Eq. (17).

$\displaystyle C_{t}=22.58-4.12\phi_{1}(R_{-}\mu)+0.57\phi_{2}(R_{-}\mu)+3.66% \phi_{1}(T_{0})-1.21\phi_{1}(\eta_{-}\mu)$ (17)

In Eq. (17), the power pulse capacity is represented by $C_{t}$ and the normalized values of the three physical parameters are represented by $R_{-}\mu$ , $T_{0}$ and $\eta_{-}\mu$ respectively.

4. Analysis of the application of parameter identification and modelling methods for the information-physical-social integration characteristics of user-side flexible resources

This chapter is an analysis of the effectiveness of the methods and models proposed in Chapter 2. The first section of this chapter is an analysis of the application of the user-side flexible resource model based on the information-physical society data fusion method, and the second section of this chapter is an analysis of the application of the load multi-timescale fusion model parameter identification method based on the HDMR technique.

4.1 Analysis of user-side flexible resource model applications based on information-physical society data fusion methods

The number of variable frequency AC loads is 2000, parameters such as the equivalent heat capacity of the AC loads obey a uniform distribution within the range of values taken, the scheduling time interval is 0.5 h and the simulation test time is divided into 24 periods. In order to verify the application effect of the user side flexible resource model, three different options were set up in the experiment. In Option 1, neither type of battery is involved in the scheduling, and the system operator adjusts the purchase of electricity based on the actual market load; in Option 2, lithium batteries are not involved in the scheduling, and the system operator schedules based on the charge and discharge power of the integrated virtual battery; in Option 3, the air conditioning load is not involved in the demand response, and the system operator schedules based on the charge and discharge power of the lithium battery. The effect of outdoor temperature on the maximum charging and discharging power of the VB is shown in Fig. 6.

Figure 6.

The effect of outdoor temperature on the maximum charging and discharging power of virtual batteries.

In Fig. 6, the maximum charge power (MCP) and maximum discharge point power are 6.6 MW and $-$ 2.1 MW respectively at an outdoor temperature of 26 ${}^{\circ}$ C in time period 1, 2.1 MW and $-$ 6.3 MW respectively at an outdoor temperature of 37 ${}^{\circ}$ C in time period 15, and 6.8 MW and $-$ 1.9 MW respectively at an outdoor temperature of 27 ${}^{\circ}$ C in time period 24. Trend analysis shows that the MCP of the VB decreases as the outdoor temperature increases, indicating that the MCP of the VB changes in the opposite direction to the outdoor temperature. As the MCP of the VB decreases, the maximum discharge power increases. It is well known that the activation of lithium ions decreases at the lower temperature, impairing the charge/discharge power. The actual electricity purchased by the system operator under the three schemes is shown in Fig. 7.

Figure 7.

Actual purchase of electricity by system operators under three different scheduling strategies.

In Fig. 7, under three different schemes, the peak daily electricity consumption of operators is $220, $260, and $310, respectively. In options 2 and 3, the system operator makes power purchases based on the ES state of the lithium battery or VB, increasing these purchases when the price of electricity is low and decreasing these purchases when the price of electricity is high. This effectively reduces the system operator’s electricity costs and also demonstrates the similarity between the operating behavior of lithium batteries and VBs, both of which can be used in systems. The variation of maximum charge and discharge power under different VB storage states is shown in Fig. 8.

Figure 8.

Change in maximum charging and discharging power under different VB ES states.

In Fig. 8, the power with positive value is the MCP and the power with negative value is the maximum discharging power. It can be seen that the MCP remains unchanged after increasing the scheduling period to a certain extent, indicating that longer scheduling periods are not conducive to the regulation ability of the VB, and that the MCP does not change much when the scheduling period is less than 1 hour and there is a tendency for the remaining change, so the scheduling period should be set to at least 1 hour but not more than 3 hours. The overall trend of the MCP is that it decreases as the scheduling period increases and then stabilises.

4.2 Analysis of the application of load multi-timescale fusion model parameter identification methods based on HDMR techniques

To test the effectiveness of the multi-time-scale fusion model parameter identification method for loads based on HDMR technology, 10,000 units each of fixed-frequency and inverter air conditioners were selected as experimental objects and five experimental scenarios were set up. Scenario 1 is an independent simulation of 100 groups of air conditioners; Scenario 2 is an independent simulation of 10 air conditioners with random values of physical parameters and 100 samples; Scenario 3 is an independent simulation of only $R_{-}\mu$ with random values and the remaining parameters unchanged; Scenario 4 is an independent simulation of only $T_{0}$ with random values and the remaining parameters unchanged; Scenario 5 is an independent simulation of only $\eta_{-}\mu$ with random values and the remaining parameters unchanged. Scenario 5 is a stand-alone simulation with only random values and the remaining parameters unchanged. The relationship between the physical parameters of the AC load in each scenario is shown in Fig. 9.

Figure 9.

The relationship between physical parameters of AC load in various scenarios.

Figure 9a shows the change in AC power pulse capacity under scenario 1 and scenario 2. It can be seen that the change in AC power pulse for the 100 samples in scenario 1 is not significant and the difference in power between scenario 2 and scenario 1 is small, indicating that the impact of the physical parameters of the AC load on power is quite small. In Fig. 9b it can be seen that $R_{-}\mu$ has a large effect on the power pulse capacity, showing a quadratic trend. In Fig. 9c it can be seen that $T_{0}$ has a significant effect on the power pulse capacity, showing a linear trend. In Fig. 9d, it can be seen that $\eta_{-}\mu$ has a smaller effect on the power pulse capacity, showing a slight linear trend. The experimental results show that the three input physical parameters $R_{-}\mu$ , $T_{0}$ and $\eta_{-}\mu$ have a large variation on the power capacity of the AC load. A comparison of the independent simulations and the power pulse capacity based on the HDMR technique (labelled Hdmr) is shown in Fig. 10.

Figure 10.

Comparison of power pulse capacity between independent simulation and HDMR technology.

In Fig. 10, it can be seen that the difference in AC capacity between the two methods is small, with an average error of 4.3% based on the HDMR technique, indicating that the mapping relationship between power capacity and physical parameters can be constructed with high accuracy based on the HDMR technique. The errors in the calculation of the AC load power pulse capacity for the three parameter distribution types are shown in Fig. 11.

Figure 11.

Calculation error of AC load power pulse capacity under three parameter distribution types.

Figure 12.

Comparison of modeling results based on HDMR technology and multiple regression modeling.

Figure 11 shows that there is little difference in the error of the multi-timescale fusion model of the load based on the HDMR technique under the three distributions, with an average relative error of 4.65% under the log-normal distribution, 4.5% under the uniform distribution and 4.3% under the normal distribution. This indicates that the type of AC load does not have a significant effect on performance. The results based on high dimensional model expression technique modelling (labelled Hdmr) compared to multiple regression modelling are shown in Fig. 12.

In Fig. 12, it can be seen that the error in the multiple linear regression modelling is highly variable, with a relative error of up to 0.75 and an average relative error of 15.1%, while the relative error in the modelling based on the HDMR technique is in the range of 0 to 0.2, with an average relative error of 5.5%, and the results show that the modelling accuracy based on the HDMR technique is much higher. Multiple linear regression can only describe the independent effect of input variables on output, and the relationship between input and output is linear. Therefore, the coupling effect between input variables and the nonlinear relationship between input and output cannot be quantified using multiple linear regression methods. On the contrary, modelling based on high-dimensional model representation technology can not only determine the effect of coupling between input variables on output, but also describe the nonlinear relationship between input and output. This makes modelling based on high-dimensional model representation technology more widely applicable than multiple linear regression methods. The accuracy comparison of parameter identification between the load multi time scale fusion model (labeled A) based on high-dimensional model representation technology and the traditional physical resource model (labeled B) based on current and voltage is shown in Fig. 13.

Figure 13.

Sensitivity and accuracy comparison of model parameter identification.

As shown in Fig. 13, the parameter identification accuracy of the traditional physical resource model based on current and voltage is in the range of 0.5 to 0.8, and the parameter identification accuracy is lower when the demand for users is high during the day and user behavior increases. The accuracy of the load multi time scale fusion model based on high-dimensional model expression technology is maintained in the range of 0.9 to 1.0, and the accuracy does not change significantly over time, indicating that the high-dimensional model expression technology has better performance in identifying the parameters of the load multi time scale fusion model.

5. Conclusion

Demand-side data is abundant in user-side flexible resources, and this data has a significant influence on PS scheduling. The study proposes a parameter identification and modelling method for the information-physical-social fusion characteristics of the user-side flexible resources, and proposes an inverter AC minute-scale time-scale digital VB modelling and dispatching method combined with HDMR techniques for model parameter identification, taking the user AC load as the object. The experimental data showed that under three different schemes, the operator spent approximately $7500, $5900, and $6100 respectively. In Scheme 2 and Scheme 3, the system operator purchases electricity based on the energy storage status of virtual batteries or lithium batteries, increasing the quantity of electricity purchased when the electricity price is low, and reducing the quantity of electricity purchased when the electricity price is high, which can effectively reduce the power consumption of the system operator. When the VB dispatching period is less than 1 hour, the MCP does not change much and there is a tendency of residual change, so at least set the dispatching period to 1 hour, but should not exceed 3 hour. The error variation of multiple linear regression modelling is very obvious, the relative error is up to 0.75, the average relative error is 15.1%, the relative error of modelling based on HDMR technique was less than 0.2, with an average relative error of 5.5%. The results showed that the HDMR-based technique had higher modelling accuracy and was useful for parameter identification in AC load fusion models. The limitation of this study is that the sample size is limited, and the number of air conditioning loads in centrally controlled projects may be larger. Future research can be carried out to optimize the scheduling of resources for other systems such as wind power and further improve the rationality of energy distribution.

Footnotes

Funding

The work was financially supported by Science and Technology Projects of State Grid Corporation of China (5400-202317213A-1-1-ZN).

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