The resource-task network (RTN) model has been widely applied to represent the technical constraints of complex industrial processes (IPs) such as steel-making, providing the basis for industrial demand response. However, the legacy RTN model contains numerous binary variables and applies different formulations for non-flexible and flexible processes, restricting its computational efficiency and applicability. To systematically improve the computational performance of IP models, we propose continuous RTN model (cRTN), a novel modeling approach that uses continuous variables to represent production tasks and progresses, which are then integrated into unified as well as computationally favorable formulations for the technical constraints in discrete IPs, including resource balance, task execution, waiting time limits, and production targets. Compared to the legacy models, cRTN features fewer binary variables, shorter solving time, and better scalability while maintaining the same accuracy. Numerical tests based on a steel plant demonstrate that cRTN is in typical cases 10 times faster than legacy models and remains tractable with increasing batch sizes, which in legacy models leads to larger problem scales and infeasible solving time. cRTN also achieves a reduction in energy costs by resolving the issue of rounding errors reported in legacy models.

The integration of distributed energy resources(DERs) has escalated the challenge of voltage magnitude regulation in distribution networks. Model-based approaches, which rely on complex sequential mathematical formulations, cannot meet the real-time demand. Deep reinforcement learning(DRL) offers an alternative by utilizing offline training with distribution network simulators and then executing online without computation. However, DRL algorithms fail to enforce voltage magnitude constraints during training and testing, potentially leading to serious operational violations. To tackle these challenges, we introduce a novel safe-guaranteed reinforcement learning algorithm, the Dist Flow safe reinforcement learning(DF-SRL), designed specifically for real-time voltage magnitude regulation in distribution networks. The DF-SRL algorithm incorporates a Dist Flow linearization to construct an expert-knowledge-based safety layer. Subsequently, the DF-SRL algorithm overlays this safety layer on top of the agent policy, recalibrating unsafe actions to safe domains through a quadratic programming formulation. Simulation results show the DF-SRL algorithm consistently ensures voltage magnitude constraints during training and real-time operation(test) phases, achieving faster convergence and higher performance, which differentiates it apart from(safe) DRL benchmark algorithms.

Peer-to-peer (P2P) trading is seen as a viable solution to handle the growing number of distributed energy resources in distribution networks. However, when dealing with large-scale consumers, there are several challenges that must be addressed. One of these challenges is limited communication capabilities. Additionally, prosumers may have specific preferences when it comes to trading. Both can result in serious asynchrony in peer-to-peer trading, potentially impacting the effectiveness of negotiations and hindering convergence before the market closes. This paper introduces a connection-aware P2P trading algorithm designed for extensive prosumer trading. The algorithm facilitates asynchronous trading while respecting prosumer's autonomy in trading peer selection, an often overlooked aspect in traditional models. In addition, to optimize the use of limited connection opportunities, a smart trading peer connection selection strategy is developed to guide consumers to communicate strategically to accelerate convergence. A theoretical convergence guarantee is provided for the connection-aware P2P trading algorithm, which further details how smart selection strategies enhance convergence efficiency. Numerical studies are carried out to validate the effectiveness of the connection-aware algorithm and the performance of smart selection strategies in reducing the overall convergence time.

To cost-effectively manage the supply-demand balance of the power system, the flexibility of industrial users could be harnessed through demand-side response. To minimize the negative impact on the production of industrial users during demand-side response, general-purpose models such as the state-task network (STN) are widely used to model the energy-consuming constraints of industrial production processes. However, the required model parameters cannot be set because the required data are privately owned by industrial users and are not directly available, hindering the accurate modeling of industrial loads. In this paper, we propose production scheduling identification (PSI), an inverse-optimization-based approach for industrial load modeling under incomplete information. In PSI, industrial users’ smart meter data are used to identify production scheduling parameters, thus addressing the problem of accurate load modeling when private data are unavailable. We implemented PSI with a modified STN and proposed a practical algorithm to obtain an effective solution. Numerical tests showed that PSI can identify the model parameters of a steel powder plant and a cement plant with acceptable accuracy, using only 21 days of hourly smart meter data. Compared with accurate models established with direct access to private data, the modeling error does not exceed 8.5% and 5.2%, respectively.

The optimal dispatch of energy storage systems (ESSs) in distribution networks poses significant challenges, primarily due to uncertainties of dynamic pricing, fluctuating demand, and the variability inherent in renewable energy sources. By exploiting the generalization capabilities of deep neural networks (DNNs), the deep reinforcement learning (DRL) algorithms can learn good-quality control models that adapt to the stochastic nature of distribution networks. Nevertheless, the practical deployment of DRL algorithms is often hampered by their limited capacity for satisfying operational constraints in real time, which is a crucial requirement for ensuring the reliability and feasibility of control actions during online operations. This paper introduces an innovative framework, named mixed-integer programming based deep reinforcement learning (MIP-DRL), to overcome these limitations. The proposed MIP-DRL framework can rigorously enforce operational constraints for the optimal dispatch of ESSs during the online execution. This framework involves training a Q-function with DNNs, which is subsequently represented in a mixed-integer programming (MIP) formulation. This unique combination allows for the seamless integration of operational constraints into the decision-making process. The effectiveness of the proposed MIP-DRL framework is validated through numerical simulations, demonstrating its superior capability to enforce all operational constraints and achieve high-quality dispatch decisions and showing its advantage over existing DRL algorithms.

The growing penetration of electric vehicles (EVs) significantly changes typical load curves in smart grids. With the development of fast charging technology, the volatility of EV charging demand is increasing, which requires additional flexibility for real-time power balance. The forecasting of EV charging demand involves probabilistic modeling of high dimensional time series dynamics across diverse electric vehicle charging stations (EVCSs). This paper studies the forecasting problem of multiple EVCS in a hierarchical probabilistic manner. For each charging station, a deep learning model based on a partial input convex neural network (PICNN) is trained to predict the day-ahead charging demand's conditional distribution, preventing the common quantile crossing problem in traditional quantile regression models. Then, differentiable convex optimization layers (DCLs) are used to reconcile the scenarios sampled from the distributions to yield coherent scenarios that satisfy the hierarchical constraint. It learns a better weight matrix for adjusting the forecasting results of different targets in a machine-learning approach compared to traditional optimization-based hierarchical reconciling methods. Numerical experiments based on real-world EV charging data are conducted to demonstrate the efficacy of the proposed method.

Deep learning technology is identified as a valid tool for transient stability assessment (TSA). Moreover, the superior performance of the TSA model depends on generously labeled samples. However, the power grid is dynamic, and some topologies or operation conditions change substantially. The traditional method generates a significant quantity of samples for each specific topology. Nonetheless, generating these labeled samples and establishing TSA models is very time-consuming. This paper proposes a high-quality sample generation framework based on data-driven methods to build a high-quality offline samples database for TSA model training and updating. Firstly, the representative topologies provided by the system operator are clustered into four different categories by density-based spatial clustering of applications with noise (DBSCAN). Thus the corresponding samples are collected. Then, when a new topology is encountered in the online application, scenario matching is used to match the most similar topology category. After that, instance-based transfer learning is implemented from a database of the best-matched topology category. Finally, a deep convolutional generative adversarial network (DCGAN) is constructed to mitigate the class imbalance problem. That is, unstable scenarios occur far more rarely than stable scenarios. Consequently, a high-quality and balanced TSA model training and updating database is constructed. The comprehensive test results on the Central China Power Grid illustrate that the proposed framework can generate high-quality and balanced TSA samples. Furthermore, the sample generation time is dramatically shortened. In addition, the metrics of accuracy, reliability and adaptability of the TSA model are significantly enhanced.

The batch and online workload of Internet data centers (IDCs) offer temporal and spatial scheduling flexibility. Given that power generation costs vary over time and location, harnessing the flexibility of IDCs’ energy consumption through workload regulation can optimize the power flow within the system. This paper focuses on multi-geographically distributed IDCs managed by an Internet service company (ISC), which are aggregated as a controllable load. The load flexibility resulting from spatial load regulation of online workload is taken into account. A two-step workload scheduling mechanism is adopted, and a computation-power coupling model of ISC is established to facilitate collaborative optimization in active distribution networks (ADNs). To address the model-solving problem based on the assumption of scheduling homogeneity, a model reconstruction method is proposed. An efficient iterative algorithm is designed to solve the reconstructed model. Furthermore, the Nash bargaining solution is employed to coordinate the different optimization objectives of ISC and power system operators, thereby avoiding subjective arbitrariness. Experimental cases based on a 33-node distribution system are designed to verify the effectiveness of the model and algorithm in optimizing ISC’s energy consumption and power flow within the system.

Over the past decade, bidding in power markets has attracted widespread attention. Reinforcement Learning (RL) has been widely used for power market bidding as a powerful AI tool to make decisions under real-world uncertainties. However, current RL methods mostly employ low dimensional bids, which significantly diverge from the N price-power pairs commonly used in the current power markets. The N-pair bidding format is denoted as High Dimensional Bids (HDBs), which has not been fully integrated into the existing RL-based bidding methods. The loss of flexibility in current RL bidding methods could greatly limit the bidding profits and make it difficult to tackle the rising uncertainties brought by renewable energy generations. In this paper, we intend to propose a framework to fully utilize HDBs for RL-based bidding methods. First, we employ a special type of neural network called Neural Network Supply Functions (NNSFs) to generate HDBs in the form of N price-power pairs. Second, we embed the NNSF into a Markov Decision Process (MDP) to make it compatible with most existing RL methods. Finally, experiments on Energy Storage Systems (ESSs) in the PJM Real-Time (RT) power market show that the proposed bidding method with HDBs can significantly improve bidding flexibility, thereby improving the profit of the state-of-the-art RL bidding methods.

The scale of distributed energy resources is increasing, but imperfect business models and value transmission mechanisms lead to low utilization ratio and poor responsiveness. To address this issue, the concept of cleanness value of distributed energy storage (DES) is proposed, and the spatiotemporal distribution mechanism is discussed from the perspectives of electrical energy and cleanness. Based on this, an evaluation system for the environmental benefits of DES is constructed to balance the interests between the aggregator and the power system operator. Then, an optimal low-carbon dispatching for a virtual power plant (VPP) with aggregated DES is constructed, where-in energy value and cleanness value are both considered. To achieve the goal, a green attribute labeling method is used to establish a correlation constraint between the nodal carbon potential of the distribution network (DN) and DES behavior, but as a cost, it brings multiple nonlinear relationships. Subsequently, a solution method based on the convex envelope (CE) linear re-construction method is proposed for the multivariate nonlinear programming problem, thereby improving solution efficiency and feasibility. Finally, the simulation verification based on the IEEE 33-bus DN is conducted. The simulation results show that the multidimensional value recognition of DES motivates the willingness of resource users to respond. Meanwhile, resolving the impact of DES on the nodal carbon potential can effectively alleviate overcompensation of the cleanness value.

Virtual power plants (VPPs) have become an important technological means for large-scale distributed energy resources to participate in the operation of power systems and electricity markets. However, the operation of VPPs is challenged by stochastic resource characteristics, complex control features, heterogeneous information structures, and strategic game behaviors among stakeholders. To clarify the key problems and solutions to these challenges, this article describes the resource coordination problems and multidimensional interaction mechanism, and it elaborates the overall decision-making process of VPPs. It also discusses different specific operational stages that VPPs should attach importance to from three separate perspectives: energy, information and the market. From each perspective, every section first analyzes the motivation of decision-making, then analyzes the complexity of the problem models, and summarizes the different modeling methods and solving techniques, thus completing a comprehensive review of VPP operation. Furthermore, the article adopts an interdisciplinary approach, utilizing a literature review and technical statistics to capture the multifaceted contributions of decision-making to VPP operations. It delves into the evolving trends of decision-making technology, analyzed from the coupling cyber-physical-social perspective. Finally, the future trajectory of research issues is deliberated.

The rapid development of renewable distributed generation in active distribution networks (ADNs) imposes an increasing burden on the transfer capability of the ADNs, bringing new challenges to the distribution network expansion planning (DNEP) problem. Dynamic thermal rating (DTR), which evaluates the equipment rating based on the actual weather conditions and equipment thermal states, can enhance the equipment transfer capability to support the integration of renewable distributed generation. In this paper, we propose a DNEP model of ADNs incorporating the DTR of cables and transformers, given that underground cable feeder is preferred in the rapid urbanization trends. Then, we derive a linear reformulation of the original DNEP model and propose a modified Benders decomposition (MBD) algorithm to solve the DNEP model. To select more effective representative day scenarios, we propose a cost-based clustering method for representative day selection applicable to solving the DNEP model. Case studies based on the IEEE 33-node system and the PG&E 69-node system show that the implementation of DTR saves 14.7% and 15.1% of the investment costs of the two systems respectively. The effectiveness of the MBD algorithm and the cost-based clustering method is also verified by the case studies.

The output fluctuation of renewable energies poses challenges to the power system and can reduce the profits of the energy resources in power markets with imbalance settlement. Virtual power plants (VPPs) can aggregate renewable energies to smooth the overall output fluctuations, thereby enhancing their market profits. In addition, incorporating air conditioning loads, whose energy-consuming flexibility brought by the thermal inertia of buildings is considerable, can further enhance the energy management capabilities and market profits of the VPP. To achieve this, a profit allocation model that considers the operational characteristics of air conditioning is needed, which has been seldom studied in the existing literature. This paper proposes a novel profit allocation method inspired by the bargaining game theory, which takes into account the characteristics and contributions of air conditioning to the VPP’s profit. Simulation results validate that our method is not only incentive-compatible but also properly considers the contributions of each member within the VPP.

With the increasing uncertainty caused by the complexity of the world’s energy environment and the increasing penetration rate of renewable energy, it is significant to estimate the future operation of power markets in advance. Forecasting individual bids in spot electricity markets is a promising new method for achieving so, but it has not been fully studied due to the difficulty of forecasting a bid function. The idealization of existing optimization-based models decreases their practical effects in real markets. Thus, we propose a scalable forecasting framework that incorporates several customized state-of-art machine learning methods according to the characteristics of the bidding data. First, several low-rank approximation algorithms are customized to encode the high-dimensional bidding curves into low-dimensional feature spaces and reconstruct them from the predicted feature space. Second, a transformer-based multidimensional time series prediction algorithm is proposed to predict the bidding feature based on both related factors and historical bidding records. To appropriately evaluate the performances of the forecasting methods, we introduce a dynamic criterion based on the economic implications of bids. The comprehensive framework is tested based on actual market data from the Australian national electricity market, and in the empirical example, the feasibility and effectiveness of the proposed framework are demonstrated.

Fast and accurate electricity price prediction can effectively reflect the operational status of the electricity market. In addition, it is the basis for decision-making in the electricity market. To solve the difficulties in input feature selection and model construction in data-driven electricity price prediction, a method for predicting electricity market prices based on combined input features is proposed. Firstly, historical information as the original information database is collected; Secondly, select the maximum information coefficient (MIC) for feature extraction, the ReliefF feature extraction method, and the stacked denoising autoencoder (SDAE) for feature extraction as inputs; Finally, by integrating the probability outputs of multiple LSTM models, the output result of the combined feature prediction is obtained. The analysis of numerical examples shows that combining input features can effectively improve the accuracy of electricity price prediction, and the proposed combined prediction model has high accuracy.

Air conditioning load clusters, as a significant source of demand-side flexibility, can provide auxiliary services such as secondary frequency regulation for the power system. Due to the requirement of following accuracy for frequency regulation, the power consumption of air conditioners needs to be precisely controlled, which in existing research is usually assumed to be achieved by switching compressors or changing operating frequencies. However, these control methods are likely difficult to implement in practice, as under protocol restrictions, most users can only indirectly change the operating status of the air conditioner through temperature set points. In this paper, we propose a control framework that leverages temperature set point adjustments, a protocol-supported approach, to coordinate air conditioning loads for frequency regulation. The framework involves obtaining a set point-power change mapping relationship based on simulation or experiment, approximated by piecewise linearization. The temperature set points are then adjusted to optimize the total power of the air conditioning cluster to follow the frequency regulation signal, formulated as a mixed-integer optimization problem. Our method, validated by case studies, offers a practical solution for frequency regulation in the face of non-uniform and non-open air conditioning control protocols, thus promoting the broad application of demand response.

The grid-connected electric vehicles (EVs) serve as a promising regulating resource in the distribution grid with Vehicle-to-Grid (V2G) facilities. In the day-ahead stage, electric vehicle batteries (EVBs) need to be precisely dispatched and controlled to ensure high efficiency and prevent degradation. This article focuses on considering a refined battery model, i.e., the electrochemical model (EM), in the optimal dispatch of the local energy system with high penetration of EVs which replenish energy through V2G-equipped charge station and battery swapping station (BSS). In this paper, to utilize the EM efficiently, recursive EVB constraints and a corresponding matrix-based state update method are proposed based on EM power characterization. The charging EV state distribution is profiled and a multi-layer BSS model along with binary aggregation is proposed, in order to overcome the computation complexity of combining the refined battery constraints with the mixed integer optimization. Finally, a local energy system scenario is investigated for evaluation. The efficiency and effectiveness of EM consideration are assessed from the perspective of both the system and battery.

The increasing prevalence of renewable energies has led to greater volatility in electricity prices, posing a greater challenge for Energy Storage (ES) to arbitrage effectively in the fluctuating spot markets. To better cope with price uncertainties using large amounts of hidden experiences from global electricity markets, we propose an approach called Transformer-DDRL to enhance the performance of Day-Ahead (DA) ES bidding. Initially, based on the Transformer network, we develop an expressive deep neural network that is capable of encoding large amounts of bidding experiences and generating 24-hour DA bidding curves. Subsequently, we train the proposed Transformer network based on Deep Differentiable Reinforcement Learning (DDRL). Using DDRL, we directly optimize the network parameters of the Transformer with respect to the bidding objective to achieve effective learning. Finally, we train the proposed bidder on a global price dataset and achieve state-of-the-art returns in multiple markets, demonstrating its promise as a versatile market bidding model.

Under high renewable penetration, the declining energy prices cannot reflect capacity costs of generators. To deal with the missing money problem, several markets around the world have introduced capacity remuneration mechanisms. These mechanisms act well for the generation side by compensating investment costs, but the cost allocation methods among the demand side are non-differentiated or lagging, thus failing to effectively guide consumption patterns. This research proposes a novel two-step cost allocation framework to formulate real-time cost obligations. In replacement of load levels, net load levels (load minus renewable output) are used to measure adequacy conditions under high renewable penetration. The capacity costs are pre-allocated by Shapley value to obtain a mapping function from net load levels to cost obligations. In the real-time, the mapping function is incorporated into the spot market clearing model to generate obligations endogenously. Numerical analyses are conducted on the IEEE test system and an empirical case with California real data. Compared with the lagging obligations formulated by the current mechanism, the proposed framework can reduce peak net load by incentivizing demand responses and storage participation. The profile of real-time capacity cost obligations is illustrated for the California market to show the practicability of the method on a real-market.

System operators can allow virtual power plants (VPPs) to submit their feasible region (FR) for market clearing and dispatch. A VPP as a whole must determine its FR to submit based on the individual operation model of its internal distributed energy resources (DERs), which is an FR aggregation problem. Existing FR aggregation approaches rely on analytical methods, which have issues with generality and adaptability. In this paper, we propose a data-driven approach to approximate the energy-regulation FR of VPPs. We adopt the virtual battery model to approximate the aggregate FR of a VPP, and we determine the model parameters through inverse optimization based on generated multiscenario operation data by using the original operation model. Numerical tests verify the accuracy of the proposed method. We believe that our work helps to better leverage the flexibility of DERs.