Abstract:With the increase in the permeability of renewable energy and the frequency of extreme weather, the power system requires a large amount of flexible power regulation capacity. In order to realize the multi-day cooperation of reserve resources, the stochastic optimization of medium- and short-term reserve arrangement considering the typhoon uncertainty is studied in this paper. Firstly, the extreme scenario generation and reduction method considering the typhoon path -intensity prediction uncertainty is constructed. Then, considering the combined cost of preventive and emergency control for adequacy in multiple scenarios, the reserve arrangement optimization model in extreme weather is built. In this model, the pre-dispatching strategies for multiple types of reserve resources are proposed to maintain the medium- and short-term coordination. Finally, case studies on a simplified 24-node power system of Zhejiang province, China are presented based on the data of the typhoon Fireworks in July 2021, and the result shows that the proposed reserve arrangement optimization model can reduce the total cost of power systems and the risk of operation under the typhoon disaster.

Abstract:Joint chance constraints (JCCs) can ensure the consistency and correlation of stochastic variables when participating in decision-making. Sample average approximation (SAA) is the most popular method for solving JCCs in unit commitment (UC) problems. However, the typical SAA requires large Monte Carlo (MC) samples to ensure the solution accuracy, which results in large-scale mixed-integer programming (MIP) problems. To address this problem, this paper presents the partial sample average approximation (PSAA) to deal with JCCs in UC problems in multi-area power systems with wind power. PSAA partitions the stochastic variables and historical dataset, and the historical dataset is then partitioned into non-sampled and sampled sets. When approximating the expectation of stochastic variables, PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set, thus preventing binary variables from being introduced. Finally, PSAA can transform the chance constraints to deterministic constraints with only continuous variables, avoiding the large-scale MIP problem caused by SAA. Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA, SAA with improved big-M, SAA with Latin hypercube sampling (LHS), and the multi-stage robust optimization methods.

Abstract:This paper establishes a two-layer data-driven robust scheduling method to deal with the significant computational complexity and uncertainties in scheduling industrial heat loads. First, a two-layer deterministic scheduling model is proposed to address the computational burden of utilizing flexibility from a large number of bitumen tanks (BTs). The key feature of this model is the capability to reduce the number of control variables through analyzing and modeling the clustered temperature transfer of BTs. Second, to tackle the uncertainties in the scheduling problem, historical data regarding BTs are collected and analyzed, and a data-driven piecewise linear Kernel-based support vector clustering technique is employed to construct the uncertainty set with convex boundaries and adjustable conservatism, based on which robust optimization can be conducted. The case results indicate that the proposed method enables the utilization of flexibility in BTs, improving the level of onsite photovoltaic consumption and reducing the aggregated load fluctuation.

Abstract:The hydrogen energy storage system (HESS) integrated with renewable energy power generation exhibits low reliability and flexibility under source-load uncertainty. To address the above issues, a two-stage optimal scheduling model considering the operation sequences of HESSs is proposed for commercial community integrated energy systems (CIESs) with power to hydrogen and heat (P2HH) capability. It aims to optimize the energy flow of HESS and improve the flexibility of hydrogen production and the reliability of energy supply for loads. First, the refined operation model of HESS is established, and its operation model is linearized according to the operation domain of HESS, which simplifies the difficulty of solving the optimization problem under the premise of maintaining high approximate accuracy. Next, considering the flexible start-stop of alkaline electrolyzer (AEL) and the avoidance of multiple energy conversions, the operation sequences of HESS are formulated. Finally, a two-stage optimal scheduling model combining day-ahead economic optimization and intra-day rolling optimization is established, and the model is simulated and verified using the source-load prediction data of typical days in each season. The simulation results show that the two-stage optimal scheduling reduces the total load offset by about 14% while maintaining similar operating cost to the optimal day-ahead economic optimization scheduling. Furthermore, by formulating the operation sequences of HESS, the operating cost of CIES is reduced by up to about 4.4%.

Abstract:Energy equity refers to the condition in which access to the cleaner energy required by individuals is equally available to all. To relieve the energy expenditures-the key component in the concept of energy equity–of low-income communities, governments worldwide have imposed caps on soaring energy prices. However, the inherent mechanisms within the operational schedule remain undiscussed. This paper innovatively provides guidelines for operators to embed energy burden policies into the bulk power system model, by answering two critical questions. ①What is the impact on system price pattern when embedding the locational price constraints? ② How to reformulate the tie-line schedule to meet the equity thresholds? Consequently, a novel bi-level energy equity-constrained tie-line scheduling model is proposed. The conventional economic dispatch is solved at the upper level, and then a preliminary operational schedule is given to the lower level, where we propose an energy equity slackness component variable to evaluate the gap between preliminary and desired equity-satisfied operational schedules. The implicit constraints on the price are converted into explicit feasibility cuts with dual theory. Case studies on test systems demonstrate the reduced energy expenditure for underserved communities, and the optimal tie-line schedule is also validated.

Abstract:This paper studies the problem of multi-stage robust unit commitment with discrete load shedding. In the day-ahead phase, the on-off status of thermal units is scheduled. During each period of real-time dispatch, the output of thermal units and the action of load shedding are determined, and the discrete choice of load shedding corresponds to the practice of tripping substation outlets. The entire decision-making process is formulated as a multi-stage adaptive robust optimization problem with mixed-integer recourse, whose solution takes three steps. First, we propose and apply partially affine policy, which is optimized ahead of the day and restricts intertemporal dispatch variables as affine functions of previous uncertainty realizations, leaving remaining continuous and binary dispatch variables to be optimized in real time. Second, we demonstrate that the resulting model with partially affine policy can be reformulated as a two-stage robust optimization problem with mixed-integer recourse. Third, we modify the standard nested column-and-constraint generation algorithm to accelerate the inner loops by warm start. The modified algorithm solves the two-stage problem more efficiently. Case studies on the IEEE 118-bus system verify that the proposed partially affine policy outperforms conventional affine policy in terms of optimality and robustness; the modified nested column-and-constraint generation algorithm significantly reduces the total computation time; and the proposed method balances well optimality and efficiency compared with state-of-the-art methods.

Abstract:Maintaining a continuous power balance is crucial for ensuring operational feasibility in power systems. However, due to forecasting difficulties and computational limitations, economic dispatch often relies on discrete interval horizons, which fail to guarantee feasibility within each interval. This paper introduces the concept of a continuous operating envelope for managing intra-interval fluctuations, delineating the range within which fluctuations remain manageable. We propose a parametric programming model to construct the envelope, represented as a polytope that accounts for both timescale and fluctuation dimensions. To address the computational challenges inherent in the parametric programming model, we develop a fast solution method to provide an approximated polytope. The approximated polytope, initially derived from lower-dimensional projections, represents a subset of the exact polytope that ensures operational feasibility. Additionally, we apply a polytope expansion strategy in the original dimensions to refine the approximated polytope, bringing the approximation closer to the exact polytope. Case studies on an illustrative 5-bus and a utility-scale 661-bus system demonstrate that the method effectively and stably provides a continuous operating envelope, particularly for high-dimensional problems.

Abstract:The gradual replacement of gasoline vehicles with electric vehicles (EVs) and hydrogen fuel cell vehicles (HFCVs) in recent years has provided a growing incentive for the collaborative optimization of power distribution network (PDN), urban transportation network (UTN), and hydrogen distribution network (HDN). However, an appropriate collaborative optimization framework that addresses the prevalent privacy concerns has yet to be developed, and a sufficient pool of system operators that can competently operate all three networks has yet to be obtained. This study proposes a differentiated taxation-subsidy mechanism for UTNs, utilizing congestion tolls and subsidies to guide the independent traffic flow of EVs and HFCVs. An integrated optimization model for this power-hydrogen-transportation network is established by treating these vehicles and the electrolysis equipment as coupling bridges. We then develop a learning-aided decoupling approach to determine the values of the coupling variables acting among the three networks to ensure the economic feasibility of collaborative optimization. This approach effectively decouples the network, allowing it to operate and be optimized independently. The results for a numerical simulation of a coupled system composed of a IEEE 33-node power network, 13-node Nguyen-Dupuis transportation network, and 20-node HDN demonstrate that the proposed learning-aided approach provides nearly equivalent dispatching results as those derived from direct solution of the physical models of the coupled system, while significantly improving the computational efficiency.

Abstract:The variable and unpredictable nature of renewable energy generation (REG) presents challenges to its large-scale integration and the efficient and economic operation of the electricity network, particularly at the distribution level. In this paper, an operational coordination optimization method is proposed for the electricity and natural gas networks, aiming to overcome the identified negative impacts. The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants. A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption. This method allows for the full consideration of unbalanced operational scenarios. Meanwhile, the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines. The sequential symmetrical second-order cone programming (SS-SOCP) method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process. The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network. The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost, the curtailment of installed REG, the voltage imbalance of three-phase power system, and the overall carbon emissions.

Abstract:In the context of large-scale photovoltaic integration, flexibility scheduling is essential to ensure the secure and efficient operation of distribution networks (DNs). Recently, deep reinforcement learning (DRL) has been widely applied to scheduling problems. However, most methods neglect the vulnerability of DRL to state adversarial attacks such as load redistribution attacks, significantly undermining its security and reliability. To this end, a flexibility scheduling method is proposed based on robust graph DRL (RoGDRL). A flexibility gain improvement model considering temperature-dependent resistance is first proposed, which considers weather factors as additional variables to enhance the precision of flexibility analysis. Based on this, a state-adversarial two-player zero-sum Markov game (SA-TZMG) model is proposed, which converts the robust DRL scheduling problem into a Nash equilibrium problem. The proposed SA-TZMG model considers the physical constraints of state attacks that guarantee the maximal flexibility gain for the defender when confronted with the most sophisticated and stealthy attacker. A two-stage RoGDRL algorithm is proposed, which introduces the graph sample and aggregate (GraphSAGE) driven soft actor-critic to capture the complex feature about the neighbors of nodes and their properties via inductive learning, thereby solving the Nash equilibrium policies more efficiently. Simulations based on the modified IEEE 123-bus system demonstrates the efficacy of the proposed method.

Abstract:Peer-to-peer (P2P) energy trading in active distribution networks (ADNs) plays a pivotal role in promoting the efficient consumption of renewable energy sources. However, it is challenging to effectively coordinate the power dispatch of ADNs and P2P energy trading while preserving the privacy of different physical interests. Hence, this paper proposes a soft actor-critic algorithm incorporating distributed trading control (SAC-DTC) to tackle the optimal power dispatch of ADNs and the P2P energy trading considering privacy preservation among prosumers. First, the soft actor-critic (SAC) algorithm is used to optimize the control strategy of device in ADNs to minimize the operation cost, and the primary environmental information of the ADN at this point is published to prosumers. Then, a distributed generalized fast dual ascent method is used to iterate the trading process of prosumers and maximize their revenues. Subsequently, the results of trading are encrypted based on the differential privacy technique and returned to the ADN. Finally, the social welfare value consisting of ADN operation cost and P2P market revenue is utilized as a reward value to update network parameters and control strategies of the deep reinforcement learning. Simulation results show that the proposed SAC-DTC algorithm reduces the ADN operation cost, boosts the P2P market revenue, maximizes the social welfare, and exhibits high computational accuracy, demonstrating its practical application to the operation of power systems and power markets.

Abstract:The variable nature of solar power has hitherto been regarded as a major barrier preventing large-scale high-penetration solar energy into the power grid. Based on decades of research, particularly those advances made over the recent few years, it is now believed that dispatchable solar power is no longer a conception but will soon become techno-economically feasible. The policy-driven information exchange among the weather centers, grid operators, and photovoltaic plant owners is the key to realizing dispatchable solar power. In this paper, a five-step forecasting framework for enabling dispatchable solar power is introduced. Among the five steps, the first three, namely numerical weather prediction (NWP), forecast post-processing, and irradiance-to-power conversion, have long been familiar to most. The last two steps, namely hierarchical reconciliation and firm forecasting, are quite recent conceptions, which have yet to raise widespread awareness. The proposed framework is demonstrated through a case study on achieving effectively dispatchable solar power generation at plant and substation levels.

Abstract: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.

Abstract:The virtual power plant (VPP) facilitates the coordinated optimization of diverse forms of electrical energy through the aggregation and control of distributed energy resources (DERs), offering as a potential resource for frequency regulation to enhance the power system flexibility. To fully exploit the flexibility of DER and enhance the revenue of VPP, this paper proposes a multi-temporal optimization strategy of VPP in the energy-frequency regulation (EFR) market under the uncertainties of wind power (WP), photovoltaic (PV), and market price. Firstly, all schedulable electric vehicles (EVs) are aggregated into an electric vehicle cluster (EVC), and the schedulable domain evaluation model of EVC is established. A day-ahead energy bidding model based on Stackelberg game is also established for VPP and EVC. Secondly, on this basis, the multi-temporal optimization model of VPP in the EFR market is proposed. To manage risks stemming from the uncertainties of WP, PV, and market price, the concept of conditional value at risk (CVaR) is integrated into the strategy, effectively balancing the bidding benefits and associated risks. Finally, the results based on operational data from a provincial electricity market demonstrate that the proposed strategy enhances comprehensive revenue by providing frequency regulation services and encouraging EV response scheduling.

Abstract:Under-frequency load shedding (UFLS) serves as the very last resort for preventing total blackouts and cascading events. Fluctuating operating conditions and weak resilience of the future grid require UFLS adapt to various operating conditions and non-envisioned faults. This paper develops a novel data-enabled Koopman-based load shedding (KLS) to achieve the optimal one-shot load shedding for power system frequency safety. The KLS yields a network that facilitates a coordinate transformation from the delay-embedded space to a new space, wherein the dynamics can be expressed in a linear manner. The network is specifically tailored to effectively track parameter variations in the dynamic model of the power system. Linear dynamics support the development of a real-time decided load shedding strategy, while parameter tracking enables the adaptability of the KLS to non-envisioned operating conditions and faults. To address approximation inaccuracies and the discrete nature of load shedding, a safety margin tuning scheme is integrated into the KLS framework, ensuring that the system frequency trajectory remains within the safety range. Simulation results show the adaptability, prediction capability, and control effect of the proposed KLS.

Abstract:The increasing penetration of renewable energy resources degrades the frequency stability of power systems. The present work addresses this issue by proposing a look-ahead dispatch model of power systems based on a linear alternating current optimal power flow framework with nonlinear frequency constraints. Meanwhile, the poor efficiency for solving this formulation is addressed by introducing a physics-informed neural network (PINN) to predict key frequency-control parameter values accurately. The PINN ensures that the learned results are applicable to the original physical frequency dynamics model, and applying the predicted parameter values enables the resulting dispatch model to be solved quickly and efficiently using readily available commercial solvers. The feasibility and advantages of the proposed model are demonstrated by the results of numerical computations applied to a modified IEEE 118-bus test system.

Abstract:Building integrated energy systems (BIESs) are pivotal for enhancing energy efficiency by accounting for a significant proportion of global energy consumption. Two key barriers that reduce the BIES operational efficiency mainly lie in the renewable generation uncertainty and operational non-convexity of combined heat and power (CHP) units. To this end, this paper proposes a soft actor-critic (SAC) algorithm to solve the scheduling problem of BIES, which overcomes the model non-convexity and shows advantages in robustness and generalization. This paper also adopts a temporal fusion transformer (TFT) to enhance the optimal solution for the SAC algorithm by forecasting the renewable generation and energy demand. The TFT can effectively capture the complex temporal patterns and dependencies that span multiple steps. Furthermore, its forecasting results are interpretable due to the employment of a self-attention layer so as to assist in more trustworthy decision-making in the SAC algorithm. The proposed hybrid data-driven approach integrating TFT and SAC algorithm, i.e., TFT-SAC approach, is trained and tested on a real-world dataset to validate its superior performance in reducing the energy cost and computational time compared with the benchmark approaches. The generalization performance for the scheduling policy, as well as the sensitivity analysis, are examined in the case studies.

Abstract:Hybrid energy storage is considered as an effective means to improve the economic and environmental performance of integrated energy systems (IESs). Although the optimal scheduling of IES has been widely studied, few studies have taken into account the property that the uncertainty of the forecasting error decreases with the shortening of the forecasting time scale. Combined with hybrid energy storage, the comprehensive use of various uncertainty optimization methods under different time scales will be promising. This paper proposes a multi-time-scale optimal scheduling method for an IES with hybrid energy storage under wind and solar uncertainties. Firstly, the proposed system framework of an IES including electric-thermal-hydrogen hybrid energy storage is established. Then, an hour-level robust optimization based on budget uncertainty set is performed for the day-ahead stage. On this basis, a scenario-based stochastic optimization is carried out for intra-day and real-time stages with time intervals of 15 min and 5 min, respectively. The results show that ① the proposed method improves the economic benefits, and the intra-day and real-time scheduling costs are reduced, respectively; ② by adjusting the uncertainty budget in the model, a flexible balance between economic efficiency and robustness in day-ahead scheduling can be achieved; ③ reasonable design of the capacity of electric-thermal-hydrogen hybrid energy storage can significantly reduce the electricity curtailment rate and carbon emissions, thus reducing the cost of system scheduling.

Abstract:To address the strong thermoelectric coupling of the combined heat and power (CHP) units, the low utilization rate of energy storage, and the underexploitation of load-side resource flexibility in integrated energy systems (IESs), this paper proposes an optimal scheduling model of an IES in low-carbon communities considering flexibility of resources and the segmental control of solid oxide fuel cells (SOFCs). Firstly, by replacing the gas turbine (GT) in the CHP unit with an SOFC array to reduce carbon emissions and simultaneously weakening the thermoelectric coupling of the CHP unit, the segmental control method is used to control the SOFC array to improve the overall efficiency of the CHP unit. Secondly, coupled interactions among different types of energy storage equipments are mobilized through the integrated energy storage system to make full use of the remaining space in the heat and natural gas storage tanks. Finally, load-side flexible resources are utilized by considering transferable, substitutable, and heat loads, taking into account the thermal inertia of the building and categorizing rooms based on floors, orientations, and room area. Additionally, different user characteristics are characterized, and the flexible resources of building heating periods in northern cities in China are tapped in depth according to the actual factors. Compared with the traditional model, the optimal scheduling model proposed in this paper can reduce the wind abandonment rate and the carbon emission of community-integrated energy system (CIES) by 4.54% and 70.63%, respectively, and increase the utilization rate of heat and natural gas storage tanks by 12.34% and 30.52%, respectively, and lower the total cost by ¥2183.6 under the premise of ensuring user comfort during energy consumption, which promotes the economic and low-carbon operation of the CIES.

Abstract:In a high-risk sector, such as power system, transparency and interpretability are key principles for effectively deploying artificial intelligence (AI) in control rooms. Therefore, this paper proposes a novel methodology, the evolving symbolic model (ESM), which is dedicated to generating highly interpretable data-driven models for dynamic security assessment (DSA), namely in system security classification (SC) and the definition of preventive control actions. The ESM uses simulated annealing for a data-driven evolution of a symbolic model template, enabling different cooperative learning schemes between humans and AI. The Madeira Island power system is used to validate the application of the ESM for DSA. The results show that the ESM has a classification accuracy comparable to pruned decision trees (DTs) while boasting higher global interpretability. Moreover, the ESM outperforms an operator-defined expert system and an artificial neural network in defining preventive control actions.

Abstract:The significant increase in the proportion of renewable energy sources (RESs) has elevated risks of extreme ramp events and frequency instability in power systems. In recent years, frequency stability events have occurred in several countries/regions worldwide due to flexibility deficiencies. Generation flexibility has emerged as a critical factor influencing the frequency stability of power systems. This paper proposes a domain of attraction (DOA)-based quantitative method to assess the frequency stability region of power systems with a high proportion of RESs, considering generation flexibility constraints. First, ramp rate is adopted as the core indicator to characterize generation flexibility within automatic generation control (AGC) timescale, through which a nonlinear AGC model with rate saturation constraints is established. Second, the concept of DOA is introduced to define the stability region of the nonlinear AGC. Third, a quadratic Lyapunov-based estimation method is employed to quantitatively analyze the DOA of the nonlinear AGC at different generation flexibility levels. Simulation results demonstrate that increased generation flexibility expands the estimated DOA of the nonlinear AGC, whereas generation flexibility deficiency induces AGC instability. Moreover, state trajectory and time-domain simulation verify that the proposed estimation method accurately represents the stability region of the nonlinear AGC.

Abstract:With the load growth and the power grid expansion, the problem of short-circuit current (SCC) exceeding the secure limit in large-scale power grids has become more serious, which poses great challenge to the optimal secure operation. Aiming at the SCC limitations, we use multiple back-to-back voltage source converter based (B2B VSC) systems to separate a large-scale AC power grid into two asynchronous power grids. A multi-objective robust optimal secure operation model of large-scale power grid with multiple B2B VSC systems considering the SCC limitation is established based on the AC power flow equations. The decision variables include the on/off states of synchronous generators, power output， terminal voltage, transmission switching, bus sectionalization, and modulation ratios of B2B VSC systems. The influence of inner current sources of renewable energy generators on the system SCC is also considered. To improve the computational efficiency, a mixed-integer convex programming (MICP) framework based on convex relaxation methods including the inscribed N-sided approximation for the nonlinear SCC limitation constraints is proposed. Moreover, combined with the column-and-constraint generation (C&CG) algorithm, a method to directly solve the compromise optimal solution (COS) of the multi-objective robust optimal secure operation model is proposed. Finally, the effectiveness and computational efficiency of the proposed solution method is demonstrated by an actual 4407-bus provincial power grid and the modified IEEE 39-bus power grid, which can reduce the consumed CPU time of solving the COS by more than 90% and obtain a better COS.

Abstract:We propose a quasi-deterministic proxy for the network-constrained stochastic unit commitment (SUC) problem. The proposed proxy can identify very similar commitment decisions as those obtained by solving the SUC problem with a large scenario set. Its computational performance, though, is close to that of a deterministic unit commitment problem. The proposed proxy has the same formulation as the SUC problem but only includes one or two envelope scenarios, generated based on the original scenario set. The two envelope scenarios capture the maximum and minimum net-load conditions in the original scenario set. We use a systematic method to assess the quality of commitment decisions obtained by the proposed proxy. The considered case study is based on the Illinois 200-bus system.

Abstract:The increasing penetration of wind power poses challenges to the power grid operation and scheduling. Yet, if the uncertainty of wind power can be economically and effectively managed on the source side, it can drive the power grids towards renewable-dominant future. In this paper, an enhanced scheduling strategy for wind farm-flexible load joint operation system (WF-FLJOS) is proposed. The proposed strategy is designed to manage the uncertainty of wind power on the generation side when integrated into a large-scale power grid. Moreover, it can contribute to saving energy costs on the load side. Compared with the current wind farm operation rules, more stringent assessment requirements are put forward for wind power output accuracy, and the internal organization framework of WF-FLJOS is designed. For potential power violations of wind farms and flexible loads, the violation penalty mechanisms are developed to regulate the behavior of the participants. The joint operation model of the WF-FLJOS is proposed and the submission and tracking approach of the generation schedule for the wind farm is investigated. Numerical results indicate that the proposed strategy can not only improve the ability of the wind farm to track the generation schedule, but also consider the benefits of both the farm side and the load side. Meanwhile, the proposed strategy effectively reduces the schedule adjustment pressure on the main grid caused by the rolling correction mode of the intraday schedule for wind farms.

Abstract:The integrated electricity-heat-hydrogen system (IEHHS) facilitates the efficient utilization of multiple energy sources, while the operational flexibility of IEHHS is hindered by the high heat inertia of alkaline electrolyzers (AELs) and the variations of renewable energy. In this paper, we propose a robust scheduling of IEHHS considering the bidirectional heat exchange (BHE) between AELs and district heating networks (DHNs). First, we propose an IEHHS model to coordinate the operations of AELs, active distribution networks (ADNs), and DHNs. In particular, we propose a BHE that not only enables the waste heat recovery for district heating but also accelerates the thermal dynamics in AELs. Then, we formulate a two-stage robust optimization (RO) problem for the IEHHS operation to consider the variability of renewable energy in ADNs. We propose a new solution method, i.e., multi-affine decision rule (MADR), to solve the two-stage RO problem with less conservatism. The simulation results show that the operational flexibility of IEHHS with BHE is remarkably improved compared with that only with unidirectional heat exchange (UHE). Compared with the traditional affine decision rule (ADR), the MADR effectively reduces the IEHHS operating costs while guaranteeing the reliability of scheduling strategies.

Abstract:Public buildings present substantial demand response (DR) potential, which can participate in the power system operation. However, most public buildings exhibit a high degree of uncertainties due to incomplete information, varying thermal parameters, and stochastic user behaviors, which hinders incorporating the public buildings into power system operation. To address the problem, this paper proposes an interval DR potential evaluation method and a risk dispatch model to integrate public buildings with uncertainties into power system operation. Firstly, the DR evaluation is developed based on the equivalent thermal parameter (ETP) model, actual outdoor temperature data, and air conditioning (AC) consumption data. To quantify the uncertainties of public buildings, the interval evaluation is given employing the linear regression method considering the confidence bound. Utilizing the evaluation results, the risk dispatch model is proposed to allocate public building reserve based on the chance constrained programming (CCP). Finally, the proposed risk dispatch model is reformulated to a mixed-integer second-order cone programming (MISOCP) for its solution. The proposed evaluation method and the risk dispatch model are validated based on the modified IEEE 39-bus system and actual building data obtained from a southern city in China.

Abstract:The increasing integration of intermittent renewable energy sources into distribution networks has exerted significant pressure on the frequency regulation of power systems. Meanwhile, integrating small-capacity battery energy storage systems into distribution network is a growing trend in the construction of virtual power plants (VPPs), which offer great potential advantages in improving the system frequency regulation capabilities. However, the process of power dispatch for VPPs may be hindered by imperfections in the communication network, which affects their frequency control performance. Simultaneously, the economic benefits associated with their frequency control services are often overlooked. As such, we propose a co-design method of power dispatch with dynamic power regulation and communication transmission optimization for frequency control in VPPs. First, a joint design scheme of power dispatch and routing optimization under cloud-edge collaborations is proposed. This scheme encompasses a power dispatch method considering the influences of communication network and a routing optimization policy based on graph convolutional neural networks, both of which are designed to ensure the accurate and real-time frequency control service. Further, we propose a dynamic power regulation strategy under edge-edge collaborations. Specifically, according to the established correction control objective, an adaptive distributed auction algorithm (ADAA) based dynamic power regulation control method is designed to determine the optimal regulation power of VPPs, thereby improving the economic benefits of frequency control service. Finally, the simulation results validate the feasibility and superiority of the proposed co-design method for frequency control.

Abstract:Power system optimal dispatch with transient security constraints is commonly represented as transient security-constrained optimal power flow (TSC-OPF). Deep reinforcement learning (DRL)-based TSC-OPF trains efficient decision-making agents that are adaptable to various scenarios and provide solution results quickly. However, due to the high dimensionality of the state space and action spaces, as well as the non-smoothness of dynamic constraints, existing DRL-based TSC-OPF solution methods face a significant challenge of the sparse reward problem. To address this issue, a fast-converging DRL method for optimal dispatch of large-scale power systems under transient security constraints is proposed in this paper. The Markov decision process (MDP) modeling of TSC-OPF is improved by reducing the observation space and smoothing the reward design, thus facilitating agent training. An improved deep deterministic policy gradient algorithm with curriculum learning, parallel exploration, and ensemble decision-making (DDPG-CL-PE-ED) is introduced to drastically enhance the efficiency of agent training and the accuracy of decision-making. The effectiveness, efficiency, and accuracy of the proposed method are demonstrated through experiments in the IEEE 39-bus system and a practical 710-bus regional power grid. The source code of the proposed method is made public on GitHub.

Abstract:Driven by increasing penetration of intermittent renewable energy generation, modern power systems are promoting the integration of energy storage (ES) and advocating high-resolution dynamic security constrained optimal power flow (DSCOPF) models to exploit ES time-shifting flexibility against contingencies and respond promptly to more frequent variations in the system operating status. While pioneering research works explore different methods to solve security constrained optimal power flow (SCOPF) problems at individual time steps, real-time implementation of DSCOPF still faces challenges associated with uncertainty adaptation, complex constraint satisfaction， and computational efficiency. This paper proposes a physics-guided safe policy learning method, featuring an analytical evaluation model to provide both accurate safety and cost-efficiency evaluations. A primal-dual-based learning procedure is developed to guide policy learning, fostering prompt convergence. A spatial-temporal graph neural network is constructed to enhance perception on the spatial-temporal uncertainties and leverage policy generalization. Case studies validate the effectiveness and scalability of the proposed method in safety, cost-efficiency, and computational performance and highlight the value of enhanced perception on IEEE 39-bus and 118-bus test systems.

Abstract:The widespread penetration of wind power has introduced challenges in managing the rotor angle stability characteristics of the power system, affecting both small- and large-disturbance rotor angle stabilities due to its uncertain steady-state power output and inverter-based grid interfacing. Traditionally, the two stability criteria are separately analyzed and improved via preventive control, e.g., generation rescheduling. However, they may have conflicting relationship during the preventive control optimization. Therefore, this paper firstly integrates both small- and large-disturbance rotor angle stabilities and proposes an optimization model for preventive generation rescheduling to simultaneously improve them while considering wind power uncertainty. The stability constraints are linearized using trajectory sensitivity analysis, while the wind power fluctuation is represented by employing a scenario-based Taguchi’s orthogonal array testing (TOAT) method. An iterative solution method is proposed to efficiently solve the optimization model. The proposed optimization model is established on the New England 10-machine 39-bus system and a large Nordic system, demonstrating its robustness and effectiveness in addressing wind power fluctuations.

Abstract:As power systems scale up and uncertainties deepen, traditional centralized optimization approaches impose significant computation burdens on large-scale optimization problems, introducing new challenges for power system scheduling. To address these challenges, this study formulates a distributionally robust optimization (DRO) scheduling model that considers source-load uncertainty and is solved using a novel distributed approach that considers the distribution of tie-line endpoints. The proposed model includes a constraint related to the transmission interface, which consists of several tie-lines between two subsystems and is specifically designed to ensure technical operation security. In addition, we find that tie-line endpoints enhance the speed of distributed computation, leading to the development of a power system partitioning approach that considers the distribution of these endpoints. Further, this study proposes a distributed approach that employs an integrated algorithm of column-and-constraint generation (C&CG) and sub-gradient descent (IACS) to address the proposed model across multiple subsystems. A case study of two IEEE test systems and a practical provincial power system demonstrates that the proposed model effectively ensures system security. Finally, the scalability and effectiveness of the distributed approach in accelerating problem-solving are confirmed.

Abstract:Variable renewable energy (VRE) integrated via non-synchronous inverters exhibits low inertia and fluctuating output, posing substantial frequency security challenges for future power systems. When frequency security constraints are omitted from generation planning, the resulting low-inertia generation portfolios often fail to meet critical frequency requirements. To address this issue, this paper proposes a novel frequency security constrained generation planning (FSCGP) model that leverages the frequency support potential of diverse power sources, including conventional thermal generators (CTGs), VRE units, concentrating solar power (CSP) units, and energy storage systems (ESSs). A physics-data hybrid-driven method is introduced to formulate frequency security constraints, enabling accurate representation of diverse frequency regulation characteristics, particularly the fast frequency support capabilities of inverter-based generators (IBGs). To further enhance the computational efficiency, several acceleration techniques are incorporated into the proposed FSCGP model. Case studies based on a modified IEEE RTS-79 system validate the effectiveness of the proposed FSCGP model. The numerical results identify the primary contributors to frequency security under different renewable energy penetration (REP) levels and demonstrate the cost-effectiveness of coordinating various frequency support sources, especially CSP units and IBGs, in mitigating challenges in low-inertia grids.

Abstract:In this paper, policy-assisted graph reinforcement learning (PAGRL) is proposed for real-time economic dispatch (RTED). RTED is presented as a sequential decision problem formulated by Markov decision process (MDP). PAGRL employs a graph convolutional network to extract grid operation features containing topological information and then an agent that performs power dispatch is trained through proximal policy optimization. Moreover, the adaptiveness of agent to more hard-to-learn scenarios is enhanced by difficulty sampling, and policy-assisted action post-processing mechanism is designed to reduce search space and improve decision quality, which provides a general performance enhancement scheme for reinforcement learning in power system applications. Comparative studies on modified IEEE 118-bus system and real-world provincial grid demonstrate the flexible and reliable performance of the proposed PAGRL for RTED.

Abstract:As the share of renewable generations (RGs) in power systems grows, the demand for peak regulation has increased, leading to higher associated costs. In this paper, we propose a mechanism for allocating peak regulation cost among RGs and distributing compensation among peak regulation resources (PRRs). This mechanism is integrated into a coordinated generation scheduling model to enhance the economic efficiency of independent system operators (ISOs) and incentivize PRRs. First, we propose a model for peak regulation cost of diverse PRRs. Next, we develop a method for constructing an RG output curve that facilitates peak regulation. The waveform difference between this constructed curve and the RG forecasted output curve is then calculated. In addition, we create a mechanism for peak regulation cost allocation and compensation distribution that incorporates the waveform difference, the peak regulation contribution of PRRs, and participant satisfaction as key indicators. We then establish a coordinated generation scheduling model using this mechanism, which is solved through the column-and-cut generation algorithm and rolling optimization. Finally, we conduct case studies based on an improved IEEE 30-bus test system and perform several comparative analyses to validate the effectiveness of the proposed mechanism and coordinated generation scheduling model.

Abstract:To maintain the frequency stability of power systems integrated with large-scale renewable energy sources (RESs), a frequency-constrained unit commitment (FCUC) model is proposed, which incorporates a coordinated frequency control strategy of wind turbines and energy storage system (WT-ESS), a vital component for enhancing frequency regulation capacity of wind farms. Analytical formulations for the maximum rate of change of frequency (RoCoF) and steady-state frequency deviation are derived for both serial control and parallel control, accounting for the output-limited state of energy storage under serial control. To address the problem of solution slowness caused by the strong nonlinear frequency nadir constraints, a model-based multi-directional bilayer solution method is proposed. This method employs the simulation model to detect whether the frequency nadir constraint is active and generates parallel optimized cuts in three directions. Simulation results on the IEEE 39-bus test system demonstrate that the proposed FCUC model and solution method could accurately reflect the primary frequency regulation (PFR) characteristics of WT-ESS. Furthermore, the coordinated frequency control strategy effectively reduces overall operating costs while ensuring frequency security.

Abstract:Power transfer limit (PTL) calculation plays an important role in assessing power network capability under certain constraints of system security and stability. However, the impact of ambient factors, which is different due to variations in time and space, is ignored in traditional methods to obtain PTL, thus inducing errors. Furthermore, system operation based on traditional PTL results may increase system security risks, particularly in the case of power flow congestion under heavy loads. Therefore, this paper proposes a decentralized PTL calculation method with improved optimal power flow model, which allows for the effect of the ambient factors characterized by the balance of heat absorption and dissipation for overhead conductors. The ambient factors of overhead transmission lines and the temperature of overhead conductors are involved as independent variables and state variables, respectively. Moreover, the sequential optimization problem is decomposed into several subproblems by the optimal conditional decomposition to deal with the temporal coupling constraints, and a parallel decomposition framework is used to solve multiple subproblems in parallel. Finally, the proposed method is implemented on two test systems under varying ambient factors, demonstrating the efficiency of the proposed method and the significant impacts of spatial and seasonal differences on PTL results.

Abstract:The high share of intermittent wind power jeopardizes system frequency security in isolated offshore field microgrids (IOFMs). Existing scheduling strategies, mainly focusing on stable energy supply and demand, fail to ensure frequency security due to the limited flexible and dispatchable resources in the IOFM. Thus, this paper proposes an optimal scheduling model of wind power generators with unified frequency response and spinning reserve constraints to assist operators in efficiently managing turbine generators. Frequency security indices are introduced to quantify the impact of both sudden wind power shortages and continuous wind power fluctuations on the frequency dynamics under different control modes. Based on these indices, unified frequency response and spinning reserve constraints are analytically derived to support the optimization of the control mode and on/off status of wind power generators. These highly nonlinear unified constraints are then reformulated as mixed-integer linear constraints, which are integrated into the scheduling model with operating costs as the objective. The proposed model is tested using a modified real-world IOFM. The results demonstrate that the proposed model not only ensures system frequency security but also reduces operating costs and carbon emissions.

Abstract:The integrated energy cyber-physical system (IECPS), a typical cyber-physical system (CPS), demonstrates tight interaction between cyber and physical spaces across time and space, exhibiting inherent spatial-temporal properties. Effective IECPS modeling requires the simultaneous consideration of both temporal and spatial properties, which remains a significant challenge. This paper proposes a hierarchical spatial-temporal event modeling method for IECPS based on hybrid automata (HA). Different event model layers are defined, representing events as functions of attributes, time, and space, with attributes characterized by system states. An integration method for multi-layer events is introduced, enabling accurate reflection of the system spatial-temporal characteristics and the current operating state of energy units. The modeling is applied to the optimal regulation of IECPS. Numerical simulations demonstrate that the proposed HA-based modeling method achieves precise regulation of IECPS while reducing system operating costs.