The growing integration of distributed photovoltaics (PVs) into active distribution networks (ADNs) has exacerbated operational challenges, making it imperative to coordinate diverse equipment to mitigate voltage violations and enhance power quality. Although existing data-driven approaches have demonstrated effectiveness in the voltage control problem, they often require extensive trial-and-error exploration and struggle to incorporate heterogeneous information, such as day-ahead forecasts and semantic-based grid codes. Considering the operational scenarios and requirements in real-world ADNs, in this paper, we propose a hybrid knowledge-data-driven approach that leverages dynamic collaboration between a large language model (LLM) agent and a reinforcement learning (RL) agent to achieve two-stage voltage control. In the day-ahead stage, the LLM agent receives coarse region-level forecasts and generates scheduling strategies for on-load tap changer (OLTC) and shunt capacitors (SCs) to regulate the overall voltage profile. Then in the intra-day stage, based on accurate node-level measurements, the RL agent refines terminal voltages by deriving reactive power generation strategies for PV inverters. On top of the LLM-RL collaboration framework, we further propose a self-evolution mechanism for the LLM agent and a pretrain-finetune pipeline for the RL agent, effectively enhancing and coordinating the policies for both agents. The proposed approach not only aligns more closely with practical operational characteristics but also effectively utilizes the inherent knowledge and reasoning capabilities of the LLM agent, significantly improving training efficiency and voltage control performance. Comprehensive comparisons and ablation studies demonstrate the effectiveness of the proposed method.

The calculation of g-functions is essential for the design and simulation of geothermal boreholes. However, existing methods, such as the stacked finite line source (SFLS) model, face challenges regarding computational efficiency and accuracy, particularly with fine-grained discretization. This paper introduces a novel discretization method to address these limitations. We reformulate the g-function calculation as the solution to spatio-temporal integral equations and employ the Gauss-Legendre quadrature to approximate the spatial integrals, avoiding the assumption of a stepwise structure of heat extraction rate, thereby improving accuracy. This formulation transforms the time-consuming segment-to-segment integral calculations in SFLS model into simpler and analytical point-to-point response factors, which tackles the long-standing issue that higher discretization orders generally reduce computational error at the cost of speed. Furthermore, we identify that the governing integral equations are of the Fredholm first kind, leading to ill-conditioned linear systems that can cause g-function to diverge at high discretization orders. To address this, a regularization technique is implemented to ensure stable and convergent solutions. Numerical tests demonstrate that the proposed method is significantly more efficient, achieving comparable or improved accuracy at speeds 20 to 200 times faster than the SFLS model with optimized nonuniform discretization schemes.

This paper presents a novel and efficient approach to calculate the thermal response function (g-function) of inclined geothermal boreholes. Traditional analytical methods based on the finite line source model require computationally expensive segment-to-segment numerical integration, which becomes particularly challenging for inclined boreholes due to the complex three-dimensional geometry. We propose a semi-analytical discretized formulation that eliminates the need for complicated double integrals by directly discretizing the governing spatio-temporal integral equations using numerical quadrature rules. This approach replaces segment-to-segment response factors with efficient point-to-point coupling factors that have closed-form analytical expressions. Additionally, we develop an intuitive distance aggregation technique that exploits the symmetrical properties of borehole layouts to reduce computational complexity. The proposed method unifies the treatment of vertical and inclined boreholes within a single computational framework without introducing additional complexity for inclined configurations. Numerical validation against the reference implementation of finite line source models demonstrates excellent agreement while achieving significant computational speedups up to three orders of magnitudes times faster than state-of-the-art finite line source methods.

Although deep reinforcement learning has demonstrated significant potential in load frequency control, existing methods often exhibit insufficient robustness when facing extreme or worst-case disturbances that lie outside the standard training data. To address this issue, this article proposes an adversarial training framework based on Hamiltonian optimal control. Unlike traditional data augmentation strategies that rely on random noise, this method mathematically derives adversarial load profiles—including sustained frequency drops and oscillatory disturbances designed to induce system resonance—by designing specific Lagrangians for the objective functionals and solving the resulting Hamiltonian canonical equations. We integrate these targeted adversarial samples into the training loops of deep deterministic policy gradient (DDPG), twin delayed DDPG, and proximal policy optimization algorithms to enhance the agents’ adaptability to extreme operating conditions. Simulation results on two-area and extended three-area power system models demonstrate that the proposed method accurately identifies the system’s critical resonant frequencies. Compared to baseline controllers trained solely on random noise, the agents trained with Hamiltonian adversarial loads exhibit significantly superior frequency stability and damping characteristics when subjected to structured, time-varying extreme disturbances, effectively preventing catastrophic system instability.

With the integration of massive distributed energy resources and the widespread participation of novel market entities, the operation of active distribution networks (ADNs) is progressively evolving into a complex multi-scenario, multi-objective problem. Although expert engineers have developed numerous domain specific models (DSMs) to address distinct technical problems, mastering, integrating, and orchestrating these heterogeneous DSMs still entail considerable overhead for ADN operators. Therefore, an intelligent approach is urgently required to unify these DSMs and enable efficient coordination. To address this challenge, this paper proposes the ADN-Agent architecture, which leverages a general large language model (LLM) to coordinate multiple DSMs, enabling adaptive intent recognition, task decomposition, and DSM invocation. Within the ADN-Agent, we design a novel communication mechanism that provides a unified and flexible interface for diverse heterogeneous DSMs. Finally, for some language-intensive subtasks, we propose an automated training pipeline for fine-tuning small language models, thereby effectively enhancing the overall problem-solving capability of the system. Comprehensive comparisons and ablation experiments validate the efficacy of the proposed method and demonstrate that the ADN-Agent architecture outperforms existing LLM application paradigms.

For the active distribution network (ADN) with networked microgrids (MGs), it involves both discrete devices (e.g. tap changers and capacitor banks), and continuous resources, such as inverter-based distributed energy resources (DERs) and static VAR compensators. This makes the coordinated multi-period joint active and reactive power dispatch (C-MP-ARPD) problem a bilevel mixed-integer nonlinear programming (bilevel-MINLP) one. Nevertheless, research on the bilevel coordinated optimization problems with binary variables at each level is extremely limited. To fill this research gap, this work proposes a spherical manifold-based optimization method for the C-MP-ARPD problem. Specifically, the l2-box method is employed to transform the bilevel-MINLP problem into a bilevel Riemannian nonlinear programming problem within the continuous domain. Then, a manifold-based model decomposition strategy is proposed, obtaining relaxed subproblems, box-subproblems and sphere-subproblems of both ADN and MGs, which can be efficiently coordinated by the enhanced manifold-based ADMM algorithm. Besides, a Riemannian trust-region method is employed to solve sphere-subproblems efficiently. Moreover, the bilevel relaxed subproblem of ADN and MGs is further equivalently decomposed into several small-scale subproblems by exploiting the spatio-temporal structure. Correspondingly, a hierarchical spatio-temporal decomposition method is developed to efficiently coordinate those obtained subproblems in a fully distributed and parallel manner. Finally, by integrating the aforementioned methods, a spherical manifold-based optimization approach is proposed for solving the C-MP-ARPD problem. The accuracy, computational efficiency, and convergence performance of the proposed method are verified through comparison with the commercial MIP solver Gurobi, as well as other representative distributed methods.

The increasing penetration of distributed energy resources into active distribution networks (ADNs) has made effective ADN dispatch imperative. However, the numerous newly-integrated ADN operators, such as distribution system aggregators, virtual power plant managers, and end prosumers, often lack specialized expertise in power system operation, modeling, optimization, and programming. This knowledge gap renders reliance on human experts both costly and time-intensive. To address this challenge and enable intelligent, flexible ADN dispatch, this paper proposes a large language model (LLM) powered automated modeling and optimization approach. First, the ADN dispatch problems are decomposed into sequential stages, and a multi-LLM coordination architecture is designed. This framework comprises an Information Extractor, a Problem Formulator, and a Code Programmer, tasked with information retrieval, optimization problem formulation, and code implementation, respectively. Afterwards, tailored refinement techniques are developed for each LLM agent, greatly improving the accuracy and reliability of generated content. The proposed approach features a user-centric interface that enables ADN operators to derive dispatch strategies via simple natural language queries, eliminating technical barriers and increasing efficiency. Comprehensive comparisons and end-to-end demonstrations on various test cases validate the effectiveness of the proposed architecture and methods.

This letter proposes a structure-aware automatic differentiation method to accelerate the solution of alternating current optimal power flow (ACOPF) with nonlinear programming (NLP) solvers. By exploiting the isomorphic structure of nonlinear power flow constraints in ACOPF, specialized binary code is generated to efficiently compute the Jacobian and Hessian matrix. Numerical tests show that our implementation achieves over 18% speedup in the total solution process and 40% speedup in automatic differentiation for large-scale ACOPF problems compared to state-of-the-art algebraic modeling languages of NLP.

In recent years, the rapid development of smart grid technologies and energy markets has brought massive new entities into the power system, such as virtual power plant (VPP) operators, distribution retailers, electric vehicle (EV) aggregators, and end prosumers. These entities with little knowledge of power system modeling, dispatch, and optimization require a more intelligent and flexible approach to ensure their efficient participation. Trained on a vast corpus of text data, generative pre-trained transformer (GPT) based large language models (LLMs) are embedded with massive world knowledge. With powerful comprehension and reasoning capabilities, GPT based LLMs have the potential to enable intelligent and customized dispatch. However, despite extensive experimentation, existing studies have neither addressed how LLMs should be applied in power systems nor provided a generalized framework. In this paper, we propose a generalized framework of LLMs for power system operation and discuss its implementations and limitations in detail. Comprehensive case studies and test results demonstrate the effectiveness of the proposed framework and several critical factors to ensure the performance of LLMs.

With the increasing integration of wind power into the power system, the incorporation of wind turbines into the grid's primary frequency regulation through inertia and droop control has been proven effective. However, a phenomenon known as secondary frequency dip (SFD) occurs when wind generators exit frequency regulation to restore the turbines' speeds. This paper introduces a cooperative approach to mitigate SFD. Initially, a system frequency response model is established, incorporating the combined effects of synchronous generators and wind turbines. Subsequently, a model to forecast the rotational speed of each wind turbine in response to load changes is developed. Based on these models, the droop and inertia coefficients of different turbines in a wind farm are optimized to minimize overall wind energy loss during frequency regulation, thereby alleviating SFD, while ensuring the rotational speed remains within a safe range. Additionally, a smooth transition strategy based on a low-pass filter is proposed to prevent an abrupt decrease in active power as turbines exit frequency regulation. Finally, to prevent a simultaneous drop in active power among a large number of wind turbines, a sequential exit strategy from frequency regulation is proposed. Simulation results validate the effectiveness of the proposed methods in mitigating SFD.

The high voltage direct current (HVDC) lines are required to employ supplemental control strategy to achieve mutual frequency support across asynchronous grids. Based on this, the frequencies of different sub-grids are recoupled, which poses new challenge on the automatic generation control (AGC). To address this issue, this paper proposes a model predictive control based AGC control scheme for HVDC interconnected grids considering the frequency synchronous control strategy. The state-space model is developed to accurately capture the power interactive characteristics between the interconnected grids. The numerical tests show that the proposed scheme can enhance the control performance compared with traditional methods.

As large-scale distributed energy resources are integrated into the active distribution networks (ADNs), effective energy management in ADNs becomes increasingly prominent compared to traditional distribution networks. Although advanced reinforcement learning (RL) methods, which alleviate the burden of complicated modelling and optimization, have greatly improved the efficiency of energy management in ADNs, safety becomes a critical concern for RL applications in real-world problems. Since the design and adjustment of penalty functions, which correspond to operational safety constraints, require extensive domain knowledge in RL and power system operation, the emerging ADN operators call for a more flexible and customized approach to address the penalty functions so that the operational safety and efficiency can be further enhanced. Empowered with strong comprehension, reasoning, and in-context learning capabilities, large language models (LLMs) provide a promising way to assist safe RL for energy management in ADNs. In this paper, we introduce the LLM to comprehend operational safety requirements in ADNs and generate corresponding penalty functions. In addition, we propose an RL2 mechanism to refine the generated functions iteratively and adaptively through multi-round dialogues, in which the LLM agent adjusts the functions' pattern and parameters based on training and test performance of the downstream RL agent. The proposed method significantly reduces the intervention of the ADN operators. Comprehensive test results demonstrate the effectiveness of the proposed method.

With the advanced reasoning, contextual understanding, and information synthesis capabilities of large language models (LLMs), a novel paradigm emerges for the autonomous generation of dispatch strategies in modern power systems. In this paper, we propose an LLM-based experience-driven day-ahead Volt/Var schedule solution for distribution networks, which enables the self-evolution of LLM agent's strategies through the collaboration and interaction of multiple modules, specifically, experience storage, experience retrieval, experience generation, and experience modification. The experience storage module archives historical operational records and decisions, while the retrieval module selects relevant past cases according to current forecasting conditions. The LLM agent then leverages these retrieved experiences to generate new, context-aware decisions for current situation, which are subsequently refined by the modification module to realize self-evolution of the dispatch policy. Comprehensive experimental results validate the effectiveness of the proposed method and highlight the applicability of LLMs in power system dispatch problems facing incomplete information.

With numerous distributed energy resources (DERs) integrated into the distribution networks (DNs), the coordinated economic dispatch (C-ED) is essential for the integrated transmission and distribution grids. For large scale power grids, the centralized C-ED meets high computational burden and information privacy issues. To tackle these issues, this paper proposes a spatio-temporal decomposition algorithm to solve the C-ED in a distributed and parallel manner. In the temporal dimension, the multi-period economic dispatch (ED) of transmission grid (TG) is decomposed to several subproblems by introducing auxiliary variables and overlapping time intervals to deal with the temporal coupling constraints. Besides, an accelerated alternative direction method of multipliers (A-ADMM) based temporal decomposition algorithm with a good initialization strategy, is developed to solve the ED subproblems of TG in parallel. In the spatial dimension, a multi-parametric programming projection based spatial decomposition algorithm is developed to coordinate the ED problems of TG and DNs in a distributed manner. To further improve the convergence performance of the spatial decomposition algorithm, the aggregate equivalence approach is used for determining the feasible range of boundary variables of TG and DNs. Moreover, we prove that the proposed spatio-temporal decomposition method can obtain the optimal solution for bilevel convex optimization problems with continuously differentiable objectives and constraints. Numerical tests are conducted on three systems with different scales, demonstrating the high computational efficiency and scalability of the proposed spatio-temporal decomposition method.

Chance-constrained real-time dispatch (CCRTD), which coordinates hour-ahead schedules and automatic generation control (AGC) to jointly optimize the generation and affine policies of units, is crucial for handling uncertainties. However, the chance constraints in CCTRD are essentially intractable due to the affine coupling of random and decision variables. To address this issue, we recursively decompose the quantiles with non-Gaussian uncertainties into difference of convex (DC) functions, which are implicitly piecewise but second-order continuous to ensure computational reliability. Then, CCRTD is reformulated as a DC programming and is efficiently solved utilizing the penalty convex-concave procedure (CCP). The effectiveness of the approach is verified by numerical tests.

The need to transition toward low-carbon energy systems has never been more urgent [...]

As a part of the integrated energy system (IES), gas pipeline networks can provide additional flexibility to power systems through coordinated optimal dispatch. An accurate pipeline network model is critical for the optimal operation and control of IESs. However, inaccuracies or unavailability of accurate pipeline parameters often introduce errors in the state-space models of such networks. This paper proposes a physics-informed recurrent network (PIRN) to identify the state-space model of gas pipelines. It fuses sparse measurement data with fluid-dynamic behavior expressed by partial differential equations. By embedding the physical state-space model within the recurrent network, parameter identification becomes an end-to-end PIRN training task. The model can be realized in PyTorch through modifications to a standard RNN backbone. Case studies demonstrate that our proposed PIRN can accurately estimate gas pipeline models from sparse terminal node measurements, providing robust performance and significantly higher parameter efficiency. Furthermore, the identified state-space model of the pipeline network can be seamlessly integrated into optimization frameworks.

Wind farm layout and yaw control both play key roles in maximizing energy yield. However, these two factors are often optimized separately, which can lead to less effective designs. This article proposes a new biobjective optimization method for wind farm layout that includes yaw control. The two main goals are to maximize annual energy production (AEP) and minimize land use. To efficiently solve the lower-level yaw control problem, a hierarchical search method (HSM) is proposed. This method can quickly provide nearly optimal yaw settings for any specific layout. In the upper-level layout optimization, the epsilon-constraint method is used alongside sequential quadratic programming (SQP). The proposed method is tested with simulations on the FLORIS platform, using NREL 5 MW reference turbines. Compared to traditional layout optimization method, the integrated layout and yaw optimization achieves the highest AEP across all tested land area limits. Compared to the gradient-based method, our proposed HSM can avoid getting trapped in local optima and has a much faster computation time in the power optimization problem.

The high voltage DC links are required to provide frequency regulation support to alleviate frequency concerns of multi-area asynchronous power systems. However, the inter-area DC frequency support capabilities lack coordination with the intra-area frequency regulation resources of sub-grids under the existing scheduling mode, which may lead to frequency safety issues after power disturbance. To address this issue, this paper proposes a collaborative scheduling optimisation model, where the DC droop factors are set as scheduling variables and periodically allocated in coordination with the frequency regulation capabilities and power scheduling plan of each sub-area. Several types of power disturbances, including the intra-area disturbances as well as the inter-area DC blocking disturbances, are considered. The RoCoF and frequency deviation of all sub-networks under these disturbance scenarios are constrained in the proposed model. Case studies show that the frequency safety can be guaranteed and the asynchronous power system would benefit from the improved operational flexibility.

With the increasing number of distributed energy resources in active distribution networks (ADNs), the complexity of dispatch modeling and optimization has led to extremely heavy burdens for distribution system operators. The natural language dispatch, which integrates Large Language Models (LLMs), can reduce the operators' heavy burden and thereby reduce the probability of making mistakes. However, traditional LLM application methods suffer from issues such as low accuracy. This paper proposes an LLM-based dispatch framework for ADNs. The framework constructs a sequential-agent architecture with four stages-problem identification, problem analysis, problem solving, and instruction translation-using LLMs to solve dispatch problems described in natural language and generate dispatch instructions. By encapsulating common constraints and objective functions and leveraging the enhanced Retrieval-Augmented Generation (RAG) technique, LLMs can successfully master the PyOptInterface mathematical modeling language and effectively handle complex ADN dispatch problems. Experimental results show that the proposed framework achieves accuracy rates of 100% and 90% in two different dispatch problems, significantly outperforming other comparative baselines. The generated dispatch instructions are trustworthy, highlighting the potential of the framework for application in power system dispatch optimization.