Multi-time scale economic regulation model of virtual power plant considering multiple uncertainties of source,load and storag

Abstract

A novel multi-stage time scale economic dispatch scheme is proposed for virtual power plants, taking into account the uncertainties arising from the connection of distribution network sources. This research introduces specific scheduling schemes tailored to various time scales within distribution networks, including a fuzzy optimized day ahead scheduling scheme, an intra-day scheduling scheme combined with Deep Q Network, and an adaptive optimized real-time scheduling scheme. This plan mainly considers the impact of photovoltaic output and conducts scheduling one day in advance through fuzzy optimization. In the intraday scheduling, different strategies were adopted in the study. By combining with Deep Q Network, research on scheduling for intraday demand within the power system. The analysis is conducted through rigorous modeling. Experimental tests were conducted to evaluate the performance of the proposed schemes. The day ahead dispatching primarily considers the impact of photovoltaic output and calculates the cost associated with each link in the grid under three different meteorological conditions. In the intra-day scheduling, the total costs for Scenario 1, Scenario 2, and Scenario 3 are found to be 34,724.5 yuan, 36,296.5 yuan, and 33,275.8 yuan, respectively. Notably, strategies 1 and 2 demonstrate lower costs compared to the pre-day scheduling, with the exception of Scenario 3. In real-time scheduling, considering the matching between sources and sources, the matching rate between sources and sources can be maintained at over 95%, and the stability and cost of the power grid have significantly decreased. In summary, by proposing a multi-stage time scale economic scheduling scheme, this study fully considers the uncertainty of the power supply of the distribution network access, as well as the different needs of day, day and real-time scheduling, providing an effective solution for the power dispatching of virtual power plants and providing important technical support for the reliability and economy of the power system.

Keywords

Multi-time scale grid dispatching virtual power plant DQN fuzzy optimization adaptive optimization

1. Introduction

The growing demand for electric energy in society has outpaced the capabilities of the existing distribution network, making it challenging to meet market needs [1]. To address this issue, enhancing the resource scheduling scheme within the distribution network is crucial and can be accomplished through the implementation of virtual power plant (VPP) technology. By considering various power grid trading market forms such as day-ahead, intra-day, and real-time, advanced VPP technology can effectively mitigate the adverse impacts of diverse distributed resources on the power grid system. Furthermore, it enables energy conservation within the distribution network system, thereby improving resource utilization efficiency. Therefore, this research focuses on the current distribution network system, specifically examining the influence of uncertain pressure loads from photovoltaic, wind power, hydrogen energy, and other sources on the distribution network. Taking into account the variability of distribution network sources, a multi-time scale power grid resource scheduling scheme encompassing day-ahead, intra-day, and real-time stages is proposed. This scheme integrates fuzzy technology, deep learning, and other advanced technologies to optimally manage power grid scheduling. Through this approach, the smart grid can achieve energy savings, cost control, intelligent control, and fulfill other necessary requirements for construction purposes. The research content is mainly divided into four parts. The first part is a brief introduction to the research topic of virtual power plant scheduling by other scholars. The second part is a review of the main methods used in this study, and the third part is the model results obtained through the use of methods and an analysis of the results. The fourth part is a summary of all the above studies and prospects for future research. The innovation of this study lies in integrating fuzzy logic, deep learning, and advanced communication technologies into the framework of virtual power plants. This integration makes power grid scheduling more complex and intelligent, achieving optimal resource utilization. By considering one day in advance, on the same day, and in real-time, the study recognized and addressed the diversity of distributed energy. This comprehensive approach makes the system more adaptable and responsive, minimizing the adverse effects of uncertain pressure loads from sources such as photovoltaics, wind energy, and hydrogen.

2. Related works

VPPs are an important direction for the development of the energy field. All countries are making arrangements in this direction to seek new ways to solve energy crises, environmental pollution, and economic development. Sun et al. aimed to achieve precise control over the dispersed and massive internal demand side resource clusters of virtual power plants, and to enable virtual power plants to quickly and effectively participate in demand response. The research team used pre learning methods to enrich historical data and clustered historical data based on spectral clustering. A distributed collaborative control strategy for MEST and an alternating direction multiplier method for online transmission of historical data were proposed. Divide the hierarchical relationship of control priorities based on the results of MEST power regulation tasks. The experimental results show that the proposed algorithm and control strategy have superiority in executing distributed optimization tasks [2]. Akbary et al. proposed a framework based on virtual power plants to extract appropriate location marginal prices for each type of reserve. The proposed reserve pricing scheme compensates for the opportunity loss of energy and reserves. By applying this framework, a fair price for capacity reserves can be obtained, which allocates the same price for the same services provided at the same location. Meanwhile, considering boundary constraints, the pricing problem is decomposed into different sub problems. Through experimental analysis, this technology has good performance and is of great significance for the development of intelligent power plants [3]. Bahloul et al. conducted research on existing VPP aggregation control strategies to evaluate the performance of distributed VPP for better commercialization. At the same time, pay attention to the relationship between the network and power distribution, and optimize power grid scheduling through self-consumption strategies. Through the application, the distributed VPP mode reduces power grid load and improves customer service effectiveness. However, due to a lack of consideration for multiple energy sources, it is unable to meet the requirements of complex multi-energy scheduling [4]. Li et al. conducted an investigation on multiple VPP active power grids and proposed a data-driven fully distributed electronic control Scenario to improve power grid scheduling effectiveness. This Scenario is based on a robust regression feedback optimization algorithm, achieving feedback and corrective control for multiple VPP systems, and has excellent application results in practical applications. However, this plan does not consider the needs of different user electricity scenarios and is only suitable for small-scale scheduling systems [5]. Yi et al. conducted research on the existing power system and found that power resource scheduling still faces a large room for improvement. Therefore, based on the consideration of a large number of delayed load aggregations, a multi-time-scale scheduling Scenario was proposed based on VPP technology, and the clustering method was used to construct an economic system scheduling model. The proposed scheme is verified experimentally, and the proposed scheduling scheme can effectively reduce system energy consumption [6].

Ammari et al. proposed a scheduling strategy based on an improved firefly algorithm for delay constrained applications in distributed green data centers and cost and energy efficient scheduling of multiple heterogeneous applications. The experimental results show that the proposed scheduling strategy model based on the improved firefly algorithm can meet the scheduling problem of distributed green data centers [7]. Freire et al. found that with the development of cloud and mobile applications, enterprises have an increasing demand for integration of applications and services in business processes. Many integration platforms use first in, first out heuristic algorithms to schedule tasks executed by computing resources. The research team has proposed a queue priority algorithm based on particle swarm optimization, which can handle large amounts of data in integrated process task scheduling. The experimental results show that the algorithm can execute the integration process and schedule data under high data volume [8]. Zhou et al. found that crowd perception can solve the problem of massive data collection faced by most data-driven applications. Therefore, the research team first proposed a workflow framework that captures the unique execution logic of perception tasks. Then, a phased approach was proposed to decouple the original scheduling problem. The experimental results show that the proposed algorithm model can perform well on scheduling problems [9].

Based on the aforementioned research, VPP technology emerges as a promising innovation in modern energy management, offering significant potential for power system management. While the mentioned research provides an analysis of the state-of-the-art features and applications of VPP, it falls short in considering multi-source storage and complex scenarios. Most studies have not fully considered the situation of multi-source energy storage, and actual power systems often face diverse scenarios and demands, such as emergencies and market changes. The current research mainly focuses on specific aspects and fails to fully cover the actual operational needs of complex multi energy and multi scenario scenarios. Some studies have not considered the electricity consumption scenarios of different users, which may lead to shortcomings in responding to actual needs. Some studies are only applicable to small-scale scheduling systems, and their feasibility and effectiveness in large-scale power grids have not been fully verified. Considering the uncertainties associated with sources, loads, and storage within the framework of VPP can greatly enhance power grid dispatching capabilities and facilitate energy conservation and emission reduction objectives. By addressing these aspects, VPP technology can provide essential support for grid dispatch operations while simultaneously promoting sustainability goals.

3. Construction of a multi-time scale economic regulation model considering multiple uncertainties of sources, loads and storages

3.1 Construction of fuzzy day-ahead scheduling model

VPP is a comprehensive intelligent power management technology that integrates computers and communication. Considering the impact of source data uncertainty on the entire power grid scheduling under virtual technology, the power grid scheduling is optimized according to different time scales of grid source response, and a multi-time scale scheduling model considering source load storage is constructed. The principle of multi-time scale scheduling is shown in Fig. 1 [10, 11].

Figure 1.

Principle of structure of time scale scheduling.

From Fig. 1, it can be seen that the scheduling and planning process of the electricity market at different time scales. Firstly, scheduling one day in advance is based on hourly timescales, and the plan is updated every 24 hours. Next, the intraday scheduling adopts a rolling time scale of one hour, with the time scale further subdivided into 15 minutes. This scheduling plan needs to be updated every 15 minutes to cope with closer real-time changes. Finally, real-time scheduling is executed on a 5-minute time scale to achieve refined management and rapid response. The uncertainty of the source includes factors such as photovoltaic power generation, electricity prices, and vehicle loads [12, 13, 14]. The prediction error of photovoltaic power generation is represented by the normal distribution. In this context, the power generation error variable is defined as $\Delta{p}^{\prime}_{\text{pv}}$ , which follows a normal distribution with parameters $\Delta{p}^{\prime}_{\text{pv}}\sim N(0,\sigma_{\text{pv}}^{\text{2}})$ , as referenced in Eq. (1).

$\displaystyle\phi(\Delta{p}^{\prime}_{\mbox{pv}})=\frac{1}{\sqrt{2\pi\sigma_{% \text{pv}}}}\int_{-\infty}^{\Delta{p}^{\prime}_{\text{pv}}}{e^{-\frac{\Delta p% _{\text{pv}}^{p^{2}}}{2\sigma_{\text{pv}}^{2}}}}d\Delta{p}^{\prime}_{\text{pv}}$ (1)

In Eq. (1), $\phi(\cdot)$ represents the probability distribution function, $d$ represents the integral symbol. Since the actual output of photovoltaics is a variable, there is Eq. (2).

$\displaystyle{p}^{\prime}_{\text{pv}}=p_{\text{pv}0}(1+\Delta{p}^{\prime}_{% \text{pv}})$ (2)

In Eq. (2), ${p}^{\prime}_{\text{pv}}$ represents the actual photovoltaic output and $p_{\text{pv}0}$ represents the predicted output. According to consumer psychology, the response load relationship of user electricity is obtained through the transfer of electricity consumption from peak to peak, flat to valley, and peak to peak. When the impact of saturation is not considered, the maximum transfer of user electricity is achieved [15, 16, 17]. The electricity load transfer rate is defined as $\tilde{\lambda}_{\text{pv}}$ , the corresponding maximum prediction error is expressed as $d_{\text{pv}}$ , the self-elasticity coefficient is expressed as $\varepsilon$ , and the peak-to-valley electricity price difference is expressed as $\Delta p_{\text{pv}}$ , as referenced in Eq. (3).

$\displaystyle\tilde{\lambda}_{\text{pv}}\left\{\begin{array}[]{l}\pm d_{\text{% pv}},\Delta p_{\text{pv}}\leqslant p_{\text{pv}1}\\ \varepsilon(\Delta p_{\text{pv}}-\Delta p_{pv1})\mp d_{\text{pv}},\Delta p_{% \text{pv1}}\leqslant p_{\text{pv}}\leqslant p_{\text{pv2}}\\ \varepsilon(\Delta p_{\text{pv2}}-\Delta p_{\text{pv1}}),p_{\text{pv}}% \geqslant p_{\text{pv2}}\\ \end{array}\right.$ (3)

In Eq. (3), $p_{1}$ and $p_{2}$ represent the inflection point of the response from the dead zone to the linear zone, and the inflection point from the linear zone to the saturation zone, respectively, and the price differences between the corresponding peak and valley points are $\Delta p_{\text{pv1}}$ and $\Delta p_{\text{pv}2}$ , respectively. When the load is consistent, the relationship between peak valley price difference and load transfer rate can be referred to in Eq. (4).

$\displaystyle d_{\text{pv}}=\left\{{\begin{array}[]{l}\lambda_{\text{pv1}},0% \leqslant\Delta p_{\text{pv}}\leqslant\Delta p_{\text{pv1}}\\ k_{1}(\Delta p_{\text{pv}}-k_{2}\Delta p_{\text{PV}}^{\text{IP}})+k_{3},\Delta p% _{\text{pv1}}\leqslant\Delta p_{\text{pv}}\leqslant\Delta p_{\text{pv2}}\\ 0,\Delta p_{\text{pv}}\geqslant p_{\text{pv2}}\\ \end{array}}\right.$ (4)

In Eq. (4), $\Delta p_{\text{PV}}^{\text{IP}}$ represents the critical electricity price difference, $\lambda_{pv1}$ is the maximum error prediction value of the load transfer rate in the dead zone, $k_{1}$ , $k_{2}$ , and $k_{3}$ are the parameters of the error change curve. $\Delta p_{\text{PV}}^{\text{IP}}$ is the main factor affecting the electricity price difference at the valley-peak inflection point, and the change relationship can be seen in Fig. 2.

Figure 2.

The relationship between peak and valley electricity price difference and load transfer rate.

The flat-valley transfer rate $\tilde{\lambda}_{fv}$ can also be derived according to the above relational formula $\tilde{\lambda}_{pf}$ , from which the day-ahead fitting relationship load expression of the time-of-use electricity price can be obtained, as referenced in Eq. (5).

$\displaystyle\tilde{L}(t,\tilde{\lambda}_{pf},\tilde{\lambda}_{pv},\tilde{% \lambda}_{fv})=\left\{{\begin{array}[]{l}L_{O}(t)-\tilde{\lambda}_{pf}L_{\text% {pav}}-\tilde{\lambda}_{pv}L_{\text{pav}},t\in T_{P}\\ L_{O}(t)-\tilde{\lambda}_{pf}L_{\text{pav}}-\tilde{\lambda}_{fv}L_{\text{fav}}% ,t\in T_{f}\\ L_{O}(t)-\tilde{\lambda}_{pv}L_{\text{pav}}-\tilde{\lambda}_{fv}L_{\text{fav}}% ,t\in T_{v}\\ \end{array}}\right.$ (5)

In Eq. (5), $L_{O}(t)$ represents the predicted load at time $t$ , $\tilde{L}$ represents the fitting load, $L_{\text{pav}}$ represents the average value of the load forecast during the peak period, and $L_{\text{fav}}$ represents the load forecast result during the normal period. $\tilde{\lambda}_{fv}$ represents the flat valley transfer rate, and $\tilde{\lambda}_{pv}$ represents the power load transfer rate. The electric load of the tram is analyzed, and the scheduling problem is resolved through predicted data, resulting in the derivation of the application electricity contract based on the scheduling outcomes [18, 19, 20]. The power load of a tram refers to the amount of electricity required for the operation of the tram system. This includes not only the energy used to drive the tram itself, but also the energy used for lighting, heating, air conditioning, and other electrical components inside the tram. Analyzing the power load of trams is crucial for understanding and managing power consumption patterns. By predicting and optimizing the electricity consumption of trams, scheduling problems can be solved. The principle of electric power dispatch for trams is illustrated in Fig. 3, encompassing the execution of contractual requirements and compensation, as well as penalties for non-compliance.

Figure 3.

Tram scheduling optimization principle.

From the information in Fig. 3, the tram load transfer situation can be obtained. Only the transfer amount is unknown in the signed contract, so the dispatch can be carried out according to the signed rules, and the expression of the car transfer amount can be referenced in Eq. (6).

$\displaystyle\Delta L_{\textit{EV}}^{pr}(t)=\left\{{\begin{array}[]{l}\Delta L% _{EV}^{\text{Peak}}(t),t\in T_{P}\\ 0,t\in T_{f}\\ \Delta L_{EV}^{\text{vally}}(t),t\in T_{v}\\ \end{array}}\right.$ (6)

In Eq. (6), $\Delta L_{\textit{EV}}^{\text{pr}}(t)$ is the time $t$ -to- moment transfer amount, $\Delta L_{\textit{EV}}^{\text{Peak}}$ is the peak transfer amount, and $\Delta L_{\textit{EV}}^{\text{vally}}$ is the valley transfer amount. $T_{P}$ . $T_{f}$ . $T_{v}$ respectively represent the peak, steady, and low periods of power grid load. The day-ahead optimal dispatching scheme is constituted by the above load model. Considering the uncertainty of the variables, the day-ahead dispatching model is constructed by using random fuzzy variables. Due to the unknown source, the net load is defined as $\tilde{\gamma}$ , as referenced in Eq. (7).

$\displaystyle\tilde{\gamma}=\tilde{L}-{p}^{\prime}_{pv}$ (7)

In Eq. (7), ${p}^{\prime}_{pv}$ is regarded as a random fuzzy variable, while $\tilde{L}$ represents a fuzzy variable. The day-ahead scheduling optimization problem is addressed by utilizing fuzzy constraints, where the minimum scheduling cost is denoted as $\min C_{\text{all}}$ , as stated in Eq. (8).

$\displaystyle\min C_{\text{all}}=C_{G}+C_{\text{ess}}+C_{\text{pex}}+C_{\text{% EV}}$ (8)

In Eq. (8), $C_{G}$ represents the total cost required for gas turbine dispatch, represents the total cost $C_{\text{ess}}$ required for energy storage dispatch, $C_{\text{pex}}$ represents the total cost required for tie line dispatch, and $C_{\text{EV}}$ represents the total cost required for electric vehicle dispatch. Then the constraint of power balance can be referenced in Eq. (3.1).

$\displaystyle\textit{Ch}\left\{{\sum\nolimits_{i=1}^{N_{G}}{P_{G}(i,t)U_{G}(i,% t)+{p}^{\prime}_{\text{pv}}(t)+\sum\nolimits_{i=1}^{N_{ess}}{p_{\text{ess}}(i,% t)+}}\sum\nolimits_{i=1}^{N_{ex}}{p_{\text{ex}}(i,t)}}\right.$ (9) $\displaystyle=\left.{\sum\nolimits_{i=1}^{N_{L}}{\tilde{L}(i,t)-}\sum\nolimits% _{i=1}^{N_{EV}}{\Delta L_{\text{EV}}(i,t)}}\right\}(\alpha_{1})\geqslant\beta_% {1}$

In Eq. (3.1), $(i,t)$ represents the shutdown situation of the $i$ device at the time moment $t$ , $\alpha_{1}$ represents the constraint confidence level under the balance power, and $\beta_{1}$ represents the confidence level of the fuzzy variable. $N_{\text{G}}$ , $N_{\text{ess}}$ , $N_{\text{ex}}$ , $N_{\text{EV}}$ represent the total number of fuel engines, energy storage devices, tie lines, and vehicles respectively, and $N_{L}$ is the total transmission power of the total equipment. $P_{G}$ indicates the gas turbine output, ${p}^{\prime}_{pv}$ indicates the actual photovoltaic output, $P_{ess}$ indicates the energy storage device output, and $p_{ex}$ indicates the tie line output. According to the above fuzzy constraints, constraint models under different states can also be established, and finally, the final target result can be obtained through target normalization.

3.2 Deeply strengthened intraday scheduling model construction

The prediction of power grid sources belongs to nonlinear problems, and applying Deep Q Network (DQN) to power grid dispatch management has outstanding advantages [21, 22]. DDQN is an improvement on DQN, introducing the concept of Double Q-Learning. In standard Q-learning, using the same neural network to select and evaluate the value of actions may lead to overly optimistic estimates of certain actions. DDQN introduces additional networks and parameters compared to DQN, which may lead to a slight increase in the computational and storage costs of the algorithm. Therefore, on some simple problems, DQN may be easier to implement and train. Therefore, the Deep Deterministic Policy Gradient (DDPG) model proposed by the Deep Mind team on the basis of DQN for continuous action problems is adopted as a form of reinforcement learning, and its principle is shown in Fig. 4 [23].

Figure 4.

Schematic diagram of DDPG principle.

In Fig. 4, $s_{t}=\left\{{s_{1},s_{2},\ldots s_{n}}\right\}$ means that the environmental state is perceived at the time moment $t$ , and $a_{t}$ means that the target chooses an action at the time moment $t$ , and the maximum value of all behaviour-weighted rewards can be referenced in Eq. (10).

$\displaystyle R_{t}=\sum\nolimits_{i=t}^{T_{s\text{tep}}}{\gamma_{\text{drl}}^% {\text{i - t}}}r_{i}(a_{i},a_{i})$ (10)

In Eq. (10), $\gamma_{\text{drl}}$ represents the penalty factor, which is set to 0.99, $T_{\text{step}}$ represents the total number of actions taken from the initial moment to the target stage, $a_{t}$ means that the target chooses an action at the time moment $t$ . Then the objective function is expressed as the total expected value with discount, as referenced in Eq. (11).

$\displaystyle J(\theta^{\mu})=E[r_{1}+\gamma_{\text{drl}}r_{2}+\gamma_{\text{% drl}}^{\text{2}}r_{3+}\cdots]$ (11)

In Eq. (11), $\gamma_{\text{drl}}$ represents the penalty factor, which is set to 0.99, $\theta^{\mu}$ is the total reward value. Using the stochastic gradient method to optimize the objective function, the gradient of the total reward value $\theta^{\mu}$ is equivalent to the Q function $\partial Q=(s,a\left|{\theta^{Q}}\right.)$ , and the expression can be referenced in Eq. (12).

$\displaystyle\frac{\partial J(\theta^{u})}{\partial\theta^{u}}=E_{s}\left[{% \frac{\partial Q(s,a\left|{\theta^{Q}}\right.)}{\partial Q^{u}}}\right]$ (12)

By the deterministic equation $a_{t}=(s_{t}\left|{\theta^{u}}\right.)$ , Eq. (13) can be obtained.

$\displaystyle\frac{\partial J(\theta^{u})}{\partial\theta^{u}}=E_{s}\left[{% \frac{\partial Q(s,a\left|{\theta^{Q}}\right.)}{\partial a}\frac{\partial\pi(s% \left|{\theta^{u}}\right.)}{\partial Q^{u}}}\right]$ (13)

According to Eq. (13), the network Scenario can be optimized through gradient updates. At the same time, it is also necessary to consider the power grid losses [24, 25]. In target scheduling, specific economic needs need to be considered, as referenced in Eq. (14).

$\displaystyle\min F_{\text{cost}}^{\text{h}}=\sum\nolimits_{t=1}^{T_{h}}{\left% [{\sum\nolimits_{i=1}^{N_{G}}{C_{G}^{h}(i,t)+C_{\text{ess}}^{\text{h}}(i,t)+C_% {\text{p2p}}^{\text{h}}(t)+C_{\text{buy}}^{\text{h}}(t)}}\right]}$ (14)

In Eq. (14), $C_{\text{G}}^{\text{h}}(i,t)$ and $C_{\text{ess}}^{\text{h}}(i,t)$ represent the economic cost of the gas engine and energy storage equipment at the time moment $t$ , $C_{\text{buy}}^{\text{h}}(t)$ is the power purchase cost at the time moment $t$ , and $C_{\text{p2p}}^{\text{h}}(t)$ is the network loss penalty at the time moment $t$ . If the whole system problem is considered, it is mainly in accordance with the day-ahead scheduling scheme, as referenced in Eq. (15).

$\displaystyle\min\Delta P_{\text{ex}}^{\text{h}}=\sum\nolimits_{t=1}^{T_{h}}{% \left[{\sum\nolimits_{t=1}^{N_{ex}}{\left|{p_{\text{ex}}^{\text{h}}(i,t)-p_{es% }(i,t)}\right|}}\right]}$ (15)

In Eq. (15), $p_{\text{ex}}^{\text{h}}(i,t)$ represents the power of the tie line at the time moment $t$ in the optimization stage, and $N_{es}$ represents the number of tie lines. Then in the intraday scheduling, the demand meets various conditions to meet the power balance, as referenced in Eq. (3.2) [26, 27, 28].

$\displaystyle\sum\nolimits_{i=1}^{N_{G}}{P_{\text{G}}^{\text{h}}(i,t)U_{\text{% h}}^{\text{h}}(i,t)+P_{\text{pv}}^{\text{h}}(t)+\sum\nolimits_{i=1}^{N_{ess}}{% p_{ess}^{h}}}(i,t)+\sum\nolimits_{i=1}^{N_{ex}}{p_{ex}^{h}(i,t)}$ (16) $\displaystyle=\sum\nolimits_{i=1}^{N_{L}}{L(i,t)}-\sum\nolimits_{i=1}^{N_{EV}}% {\Delta L_{\text{EV}}^{\text{h}}(i,t)}$

In Eq. (3.2), $U_{\text{h}}^{\text{h}}(i,t)$ represents the switching status of the gas turbine equipment at the time moment $t$ during optimization, $P_{\text{pv}}^{\text{h}}(t)$ is the photovoltaic output at the time moment $t$ , $\Delta L_{\text{EV}}^{\text{h}}(i,t)$ represents the transfer amount of the electric vehicle, and $p_{\text{ess}}^{\text{h}}(i,t)$ is the output of the energy storage equipment. Since the network loss of the power grid is considered at this stage, the constraint balance can be referenced in Eq. (17).

$\displaystyle\left\{{\begin{array}[]{l}P_{\text{flow}}(i)=V(i)\cdot I_{\text{% flow}}(i)\\ I_{\text{flow}}(i)=\sum\nolimits_{j=1}^{N}{(Y(i,j)\cdot V(j))}\\ \end{array}}\right.$ (17)

In Eq. (17), $P_{\text{flow}}(i)$ represents the injected power, $V(i)$ represents the voltage, $I_{\text{flow}}(i)$ represents the current, and $Y(i,j)$ represents the admittance at the node $i$ and the interval $j$ . The solution process based on deep reinforcement learning is shown in Fig. 5.

Figure 5.

Reinforcement learning intraday scheduling solution process.

3.3 Construction of real-time scheduling model

In the real-time scheduling process, it is necessary to consider the impact of source and source matching and economy on power grid scheduling, to ensure the stability and economy of power grid scheduling [29, 30, 31]. The principle of real-time scheduling is shown in Fig. 6.

Figure 6.

Schematic diagram of real-time adaptive scheduling.

Using the basic time scale scaling results for power grid optimization scheduling, when in a large fluctuation stage, a smaller scale is used, and the scheduling scaling value is set to 5 minutes, smaller scale results are used for power grid optimization scheduling. When in the stage of large fluctuations, it refers to the use of small-scale results to detect the power grid due to high load or high electricity consumption. The power matching degree of the source is referenced in Eq. (18).

$\displaystyle D=\left[{1-\frac{\sum\nolimits_{i=1}^{\text{n}^{\text{data}}}{% \left|{p_{\text{1 - eq}}^{\text{data}}(i)-\bar{p}_{\text{1 - eq}}^{\text{data}}}\right|}}{n^{\text{data}}\cdot\bar{p}_{\text{1 - eq}}^{\text{data}}}}\right]\times 100\%$ (18)

In Eq. (18), $n^{\text{data}}$ represents the number of net load forecast power points in a single scheduling stage, $p_{\text{1 - eq}}^{\text{data}}(i)$ represents the net load power prediction result of the $i$ segment, and $\bar{p}_{\text{1 - eq}}^{\text{data}}$ represents the $i$ segment average predicted net load power result. Then the net load power expression can be referenced in Eq. (19).

$\displaystyle p_{1-eq}=p_{1}-p_{g}$ (19)

In Eq. (19), $p_{g}$ represents the total distributed power supply and $p_{1}$ represents the total load. If the distributed energy is fully consumed in the area, $p_{1}>p_{g}$ . In order to deal with the power in the area well, $\eta$ is defined as the source-to-cell matching threshold, that is, the expected range of the power grid’s output capacity of the source energy is obtained through the system scheduling data. The selection of threshold value needs to take into account the fluctuating characteristics of power grid voltage and source charge, then the increasing rate of source charge in matching is shown in Eq. (20) [32, 33].

$\displaystyle M=D^{r}-D^{r-b}$ (20)

In Eq. (20), $D^{r}$ represents the scale value, and $D^{r-b}$ represents the matching degree in the basic scale value. Then the cost increase rate can be referenced in Eq. (21).

$\displaystyle N=\frac{C^{r}-C^{r-b}}{C^{r-b}}$ (21)

In Eq. (21), $C^{r}$ represents the index value after switching, and $C^{r-b}$ represents the scheduling cost in the basic index value. Since it is necessary to ensure the effective docking of scheduling in this scheduling, $T^{R}$ is defined as the real-time basic time scale, $T^{r-b}$ is the corresponding division value, and $T^{r}$ is the adaptive time division value, then the relevant constraints need to be satisfied as seen in Eq. (22) [34, 35, 36].

$\displaystyle\left\{{\begin{array}[]{l}T^{R}=m\cdot T^{r-b},m\in N^{*}\\ T^{r-b}=n^{r}\cdot T^{r},n^{r}\in N^{*}\\ \end{array}}\right.$ (22)

The principle of real-time adaptive scheduling can be seen in Fig. 7.

Figure 7.

Principle of real-time adaptive scheduling.

The scheduling basis is mainly obtained from optimization data such as day-ahead scheduling and intraday scheduling [37, 38, 39]. The minimum operating cost of the objective function at this stage is shown in Eq. (23).

$\displaystyle\min F_{\text{cost}}^{\text{r}}=C_{\text{buy}}^{\text{r}}+C_{% \text{p2p}}^{\text{r}}+\sum\nolimits_{i=1}^{N_{ess}}{C_{\text{ess}}^{\text{r}}% (i)}$ (23)

In Eq. (23), $C_{\text{ess}}^{\text{r}}(i)$ represents the scheduling cost of energy storage equipment in the $i$ segment, $C_{\text{buy}}^{\text{r}}$ represents the real-time dispatch purchase cost, and $C_{\text{p2p}}^{\text{r}}$ represents the network loss penalty cost. Furthermore, the optimal outcome of the tie line power is also taken into consideration to enhance the matching effectiveness between power sources. The objective of minimizing the difference is represented by Eq. (24).

$\displaystyle\min F_{\text{ex}}^{\text{r}}=\sum\nolimits_{t=1}^{T_{r}}{\left[{% \sum\nolimits_{i=1}^{N_{ex}}{\left|{p_{\text{ex}}^{\text{r}}(i,t)-p_{\text{ex}% }^{\text{h}}(i,t)}\right|}}\right]}$ (24)

In Eq. (24), $p_{\text{ex}}^{\text{r}}(i,t)$ represents the $i$ tie line power at the time scale $t$ , $T_{r}$ represents the number of dispatching segments, and $p_{\text{ex}}^{\text{h}}(i,t)$ represents the net load value after ideal optimization. Assuming that the total amount of electricity transmission is $E$ , the allocation loss of the power grid is as shown in Eq. (25) [40].

$\displaystyle p_{\textit{loss}}=p_{k}\cdot E-\sum\limits_{i=1}^{n}{x_{i}}$ (25)

In Eq. (25), $X_{i}$ represents the economic load reduction component, and the total loss ratio of electricity transmission during normal operation of the power grid is $p_{k}$ . By calculating the allocation losses of the power grid, targeted scheduling of the power grid can be carried out. Through the analysis of day ahead scheduling and day in scheduling, it provides a scheme for the power dispatching of virtual power plants.

4. Performance analysis of the example model

4.1 Introduction to experimental background

Taking a certain VPP project as the research object, the low voltage of the power grid is $\pm$ 375 V, and the medium voltage is $\pm$ 10 kV. At the same time, the maximum upper limit power of the inverter in the power grid is 5 MW, the power and storage capacity are 3000 MW, the storage capacity of the power plant is 800 MW, the load capacity is 2400 MW, and the common coupling point (PCC) reactive power rate of the power grid is 0.9. At the same time, in photovoltaic prediction, the normal distribution requirement is met, with less than 50% of the electric capacity of the tram that needs to be charged. The unit price of vehicle charging subsidy in the contract is 0.32 yuan/kW $\cdot$ h, while the penalty price is 0.02 yuan/kW $\cdot$ h. Through the proposed method, three stages of real-time coordination and optimization of the distribution network day and night have been gradually achieved, and the specific parameter information is shown in Table 1.

Table 1
Partial experimental parameter information

Parameter information	Value
Peak hour electricity price	1.136 yuan/kW $\cdot$ h
The electricity price at ordinary times is	0.66 yuan/kW $\cdot$ h
Hourly electricity price	0.35 yuan/kW $\cdot$ h
Tie line transmission power dispatching cost	0.485 yuan/kW h
Converted energy storage virtual dispatching cost	0.5 yuan/kW $\cdot$ h

The scheduling of three-time scales, namely pre-day, intra-day, and real-time, is a progressive relationship. Scenario 1: without considering the impact on the source and not guiding the tram; Scenario 2: without considering and guiding the tram; Scenario 3: without considering and guiding the tram; Scenario 4: without considering and guiding the tram. The results are shown in Table 2.

Table 2

Grid dispatching cost of different photovoltaic output

Meteorological conditions	$C_{G}$ cost/yuan	$C_{ess}$ cost/yuan	$C_{pex}$ cost/yuan	$C_{EV}$ cost/yuan	$C_{all}$ cost/yuan
Condition 1	7876	93	21786	2729	32448
Condition 2	7931	108	32731	2901	43649
Condition 3	7449	101	22435	2779	33249

In Table 2, Meteorological conditions 1, 2, and 3 respectively refer to conditions with strong light, weak light, and moderate light. Considering the influence of photovoltaic output, the total cost of weather conditions 1 and 3 is similar. The main reason is that the dispatch model optimizes the smoothness of the total power of the tie line to improve the stability of the power grid. The overall high cost of meteorological condition 2 is due to the increase in scheduling costs when the overall output is low. The corresponding tie line power change can be seen in Fig. 8.

In Fig. 8, at 10:00 in the morning, the total power consumption of the unoptimized weather state 2 is higher, 5.3 MW, and the optimized power consumption is 2.0 MW.

Table 3

Results of time-of-use electricity price under different photovoltaic output

PV output type	Peak time	Peacetime period	Valley time
Condition 1	–	0 to 4	4 to 5
	16 to 24	5 to 6	6 to 8
	–	8 to 11	11 to 16
Condition 2	9 to 12	12 to 17	0 to 8
	17 to 21	21 to 24
Condition 3	–	0 to 3	–
	10 to11	5 to 6	3 to 5
	16 to 23	8 to 10	6 to 8
	–	11 to 12	12 to 16
	–	23 to 24	–

Figure 8.

The results of the total power of the tie line under different photovoltaic outputs.s

4.2 Simulation experiment results

Comparing the performance of various algorithm models, the results are shown in Fig. 9.

Figure 9.

Comparison of recall rates and F1 values of four algorithms.

Figure 9(a) shows the accuracy of the four algorithms on different datasets, while Fig. 9(b) shows the F1 values of the four algorithms on different datasets. As shown in Fig. 9(a), as the training set increases, the accuracy of all four models increases. Among them, the proposed DQN algorithm model performs well among the four methods. When the dataset size is around 500, the recall rates of the four algorithm models are 0.96, 0.83, 0.79, and 0.63, respectively. As shown in Fig. 9(b), as the training set increases, the F1 values of the four algorithm models continue to increase. When the dataset size is 500, the F1 values of the four algorithm models are 0.97, 0.90, 0.76, and 0.65, respectively. The experimental results show that the proposed DQN algorithm model exhibits good performance in terms of recall and F1 value among the four models.

According to the electricity price measurement period of the Japanese Electricity Dispatcher in Table 3, the peak period is mainly concentrated after 16:00 p.m., and the valley period is mainly from 0 p.m. to 5 p.m. A deep reinforcement scheduling model is then used to train the results of three scheduling strategies for intraday scheduling. In Scenario 1, the meteorological condition is 1, and the signing rate of the tram contract is 0.5. Under Scenario 1, the daily scheduling results are shown in Fig. 10.

Figure 10.

Optimization results of Scenario scheduling within 1 day.

In Fig. 10(a), network loss in Scenario 1 is to use day-ahead scheduling to obtain the final tie line power consumption through power flow calculation. The overall power consumption is 5% higher than day-ahead optimization and intra-day rolling optimization, and the absolute value difference between intra-day rolling scheduling and day-ahead scheduling is 0.8354 MW, which can be said that scheduling can improve the stability of the connecting line. Figure 10(b) shows the response results of the dispatching unit, the total output of the gas turbine is higher at 0–5 minutes, 35–45 minutes and 75–90 minutes, and the output of energy storage equipment is generally lower.

In Scenario 2, the weather condition is 1, and the tram contract signing rate is 0.2. The intraday scheduling results under Scenario 2 scheduling are shown in Fig. 11.

Figure 11.

Optimization results of Scenario scheduling within 2 days.

In Fig. 11(a), considering that the tram contract is relatively low in this Scenario, the peak-shaving and valley-filling power of the tie line is not as good as Scenario 1. At the same time, the absolute value difference between the intraday rolling scheduling and the day-ahead scheduling is 0.8142 MW, still at a relatively good track result. Figure 11(b) corresponds to the response results of the dispatching unit. Compared with Scenario1, the overall output has effectively decreased, mainly due to the lower rate of tram contract signing.

In Scenario 3, the weather condition is 2, and the tram contract signing rate is 0.5. The intraday scheduling results under Scenario 3 scheduling are shown in Fig. 12.

Figure 12.

Optimization results of Scenario scheduling within 3 days.

Figure 12(a) shows the Scenario 3 scheduling, due to the constraints of cost factors, the absolute value difference between intraday rolling scheduling and day-ahead scheduling is 2.1087 MW, which is better than Scenario 1 and Scenario 2. But in the rolling optimization, the power of the tie line can still approach the advance scheduling, so the optimization still meets the requirements. Figure 12(b) corresponds to the response result of the dispatching unit, and the output of the gas turbine decreases compared with Scenario 2. The results of the three intraday rolling scheduling optimizations are counted, as shown in Table 4.

In Table 4, compared with the day ahead dispatching, the cost of energy storage and fuel engines in Scenario 1 and Scenario 2 has increased, but the cost of power purchase and network loss has decreased, and the total cost has decreased significantly. Compared with the day ahead scheduling, the cost of energy storage and fuel engines in Scenario 3 has slightly decreased, but the cost of network loss has expanded, and the total cost has significantly increased compared with the day ahead scheduling, reaching 33275.8 yuan.

In real-time scheduling performance testing, the CIP protocol is used to monitor and record data on energy production, consumption, and demand energy consumption during each time period through a real-time energy monitoring system. On the basis of daily scheduling, energy storage units 1 and 2 will be used as optimization scheduling units. The matching rate of internal monitoring exceeds the set threshold of 95% within 15 minutes, and the real-time scheduling index value will be set to 5 minutes. The scheduling time will be set to 4–6 p.m., as shown in Fig. 13.

Table 4

Results of intraday scheduling cost

Policy type	Energy storage cost/yuan	Fuel engine cost/yuan	Network loss cost/yuan	Power purchase cost/yuan	Total cost/yuan
Scenario 1	Day ahead scheduling	91	7845.4	183.5	27466.5	35586.4
	Intraday dispatching	98	7887.5	176.5	26562.5	34724.5
Scenario 2	Day ahead scheduling	145	7886.5	206.5	29028.6	37266.6
	Intraday dispatching	151	7883.5	198.6	28063.4	36296.5
Scenario 3	Day ahead scheduling	108	7843.6	166.5	24885.6	33003.7
	Intraday dispatching	106	7834.6	169.6	25165.6	33275.8

Figure 13.

Real-time scheduling optimization results.

In Fig. 13(a), it is observed that after optimizing the scheduling of the interconnection line, it shows a tendency towards the ideal fluctuation curve and demonstrates a commendable power performance. However, in Fig. 13(b), there is significant fluctuation from 4:5 to 4:30, yet the source-to-source matching rate remains above 95%. The experiment is conducted during the time intervals of 7:30–7:45 and 11:00–11:15. During these intervals, the matching rates between sources are measured at 93.15% and 94.25%, respectively. The reason for this situation is the use of advanced scheduling optimization algorithms, which enable the system to better adapt to the matching relationship between power demand and sources, reduce power fluctuations, and make the overall performance of the system more stable. By conducting real-time scheduling during critical periods, the system can more flexibly respond to changes in electricity demand. The adjustment of scheduling values takes into account the measurement results of the matching rate between sources, further improving the adaptability of the system. To ensure system stability and comprehensive considerations, a scheduling value of 2.5 is selected for the interval of 7:30–7:45, while a scheduling value of 1.25 is chosen for the interval of 11:00–11:15. By implementing the aforementioned real-time scheduling approach, the scheduling effect of the power grid is improved.

5. Conclusion

A daily real-time scheduling model is developed by leveraging virtual power plant technology and accounting for the uncertainty of distribution network sources. Due to the unpredictable nature of power supply and load in day-ahead dispatching, a fuzzy function is utilized to construct a dispatching model that accommodates uncertain sources and loads. The model takes into account power grid losses and incorporates deep reinforcement technology to optimize daily scheduling. Considering the fluctuation of sources and loads, a real-time scheduling model is constructed using a time scale switching Scenario. In the day-ahead dispatching test, three different meteorological conditions affecting photovoltaic output are analyzed, and the cost impact of each grid link is determined. Based on the day-ahead scheduling, further tests are conducted, optimizing three different scheduling strategies. As a result, Scenario 1 and Scenario 2 exhibit respective reductions in total cost by 34,724.5 yuan and 36,296.5 yuan compared to the initial day-ahead scheduling. Moving to real-time scheduling, appropriate scheduling values for each time period are selected based on changes in energy storage equipment data, achieving a source-to-source matching rate exceeding 95%. The model proposed in this study still has shortcomings. The small size of the trained dataset results in suboptimal performance of the model, and the proposed method may also have certain limitations when dealing with complex scheduling. In future research, it is possible to consider improving the algorithm to achieve better performance even in smaller datasets. For complex case designs, multiple assumptions can be added to make the model’s performance more superior. In future research, it is possible to consider improving the algorithm to achieve better performance even in smaller datasets. For complex case designs, multiple assumptions can be added to make the model’s performance more superior. In future work, the consideration of grid losses can be enhanced in later periods to improve the accuracy of grid dispatching, even though it is currently not factored into the day-ahead dispatching process.

Formulas

$\Delta{p}^{\prime}_{pv}$	Power generation error variable	$\phi(\cdot)$	Probability distribution function	${p}^{\prime}_{pv}$	Actual PHOTOVOLTAIC output
$p_{pv0}$	Predicted output	$\tilde{\lambda}_{pv}$	Power load transfer rate	$d_{pv}$	Maximum prediction error
$\varepsilon$	Self-elasticity coefficient	$\Delta p_{pv}$	Peak and valley electricity price difference	$\Delta p_{PV}^{IP}$	Critical electricity price difference
$\lambda_{pv1}$	Dead-zone load transfer rate	$k$	Error variation curve parameters	$\tilde{\lambda}_{fv}$	Predicted load
$L$	Fit the load	$\Delta L_{EV}^{Peak}$	Peak transfer amount	$\Delta L_{EV}^{vally}$	Valley value transfer
${p}^{\prime}_{pv}$	Random fuzzy variables	$C$	Total costs required for scheduling	$\alpha_{1}$	Constraint confidence
$P_{ess}$	Output power of the energy storage device	$p_{ex}$	Pull line output power	$\gamma_{drl}$	Penalty coefficient

$T_{step}$	Total number of actions	$\theta^{\mu}$	Total reward value	$C_{G}^{h}(i,t)$	Economic cost of a gas engine
$p_{ex}^{h}(i,t)$	Cable power	$N_{es}$	Number of connecting lines	$U_{h}^{h}(i,t)$	Gas turbine equipment switching status
$P_{pv}^{h}(t)$	Photovoltaic output	$p_{ess}^{h}(i,t)$	Output of the energy storage devices	$I_{flow}(i)$	Current

Abbreviations

Deep Q network	DQN	Virtual power plant	VPP	Double Q-Learning	DDQN
Deep Deterministic Policy Gradient	DDPG	Common coupling point	PCC	Policy Gradient	PG
Predict Earliest Finish Time	PEFT	Common Industrial Protocol	CIP	/	/

Footnotes

Acknowledgments

The work was financially supported by Science and Technology Projects from State Grid Shanghai Municipal Electric Power Company (Research and Application of Key Technologies for Safe and Efficient Operation of Hydrogen-electricity Coupled Micro-energy Grid for Safety Visualization, 52091123000C).

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Multi-time scale economic regulation model of virtual power plant considering multiple uncertainties of source,load and storag

Abstract

Keywords

1. Introduction

2. Related works

3. Construction of a multi-time scale economic regulation model considering multiple uncertainties of sources, loads and storages

3.1 Construction of fuzzy day-ahead scheduling model

4.1 Introduction to experimental background

Table 1 Partial experimental parameter information

Formulas

Abbreviations

Footnotes

Acknowledgments

References

Table 1
Partial experimental parameter information