Journal of Modern Power Systems and Clean Energy

ISSN 2196-5625 CN 32-1884/TK

  • Volume 0,Issue 1,2025 Table of Contents
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    • Guest Editorial: Special Section on Dynamic Performance and Flexibility Enhancement of RES-dominated Power Systems with Gridforming Converters

      2025, 13(1):1-2. DOI: 10.35833/MPCE.2025.000013

      Abstract (9) HTML (2) PDF 212.23 K (59) Comment (0) Favorites

      Abstract:

    • >Special Section on Dynamic Performance and Flexibility Enhancement of RES-dominated Power Systems with Grid-forming Converters
    • Dynamic Analysis of Uniformity and Difference for Grid-following and Grid-forming Voltage Source Converters Using Phasor and Topological Homology Methods

      2025, 13(1):3-14. DOI: 10.35833/MPCE.2024.000722

      Abstract (10) HTML (3) PDF 3.02 M (75) Comment (0) Favorites

      Abstract:Grid-following voltage source converter (GFL-VSC) and grid-forming voltage source converter (GFM-VSC) have different dynamic characteristics for active power-frequency and reactive power-voltage supports of the power grid. This paper aims to clarify and recognize the difference between grid-following (GFL) and grid-forming (GFM) frequency-voltage support more intuitively and clearly. Firstly, the phasor model considering circuit constraints is established based on the port circuit equations of the converter. It is revealed that the voltage and active power linearly correspond to the horizontal and vertical axes in the phasor space referenced to the grid voltage phasor. Secondly, based on topological homology, GFL and GFM controls are transformed and mapped into different trajectories. The topological similarity of the characteristic curves for GFL and GFM controls is the essential cause of their uniformity. Based on the above model, it is indicated that GFL-VSC and GFM-VSC possess uniformity with regard to active power response, type of coupling, and phasor trajectory. They differ in synchronization, power coupling mechanisms, dynamics, and active power-voltage operation domain in the quasi-steady state. Case studies are undertaken on GFL-VSC and GFM-VSC integrated into a four-machine two-area system. Simulation results verify that the dynamic uniformity and difference of GFL-VSC and GFM-VSC are intuitively and comprehensively revealed.

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    • Hybrid Frequency-domain Modeling and Stability Analysis for Power Systems with Grid-following and Grid-forming Converters

      2025, 13(1):15-28. DOI: 10.35833/MPCE.2023.000842

      Abstract (8) HTML (2) PDF 3.61 M (95) Comment (0) Favorites

      Abstract:With the increase of the renewable energy generator capacity, the requirements of the power system for grid-connected converters are evolve, which leads to diverse control schemes and increased complexity of systematic stability analysis. Although various frequency-domain models are developed to identify oscillation causes, the discrepancies between them are rarely studied. This study aims to clarify these discrepancies and provide circuit insights for stability analysis by using different frequency-domain models. This study emphasizes the limitations of assuming that the transfer function of the self-stable converter does not have right half-plane (RHP) poles. To ensure that the self-stable converters are represented by a frequency-domain model without RHP poles, the applicability of this model of grid-following (GFL) and grid-forming (GFM) converters is discussed. This study recommends that the GFM converters with ideal sources should be represented in parallel with the P / Q - θ / V admittance model rather than the V - I impedance model. Two cases are conducted to illustrate the rationality of the P / Q - θ / V admittance model. Additionally, a hybrid frequency-domain modeling framework and stability criteria are proposed for the power system with several GFL and GFM converters. The stability criteria eliminates the need to check the RHP pole numbers in the non-passive subsystem when applying the Nyquist stability criterion, thereby reducing the complexity of stability analysis. Simulations are carried out to validate the correctness of the frequency-domain model and the stability criteria.

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    • Series-parallel Sequence Impedance Models of Multi-loop Grid-forming Converters

      2025, 13(1):29-41. DOI: 10.35833/MPCE.2024.000676

      Abstract (4) HTML (28) PDF 5.52 M (124) Comment (0) Favorites

      Abstract:The gradual penetration of grid-forming (GFM) converters into new power systems with renewable energy sources may result in the emergence of small-signal instability issues. These issues can be elucidated using sequence impedance models, which offer a more tangible and meaningful interpretation than dq-domain impedance models and state-space models. However, existing research has primarily focused on the impact of power loops and inner control loops in GFM converters, which has not yet elucidated the precise physical interpretation of inner voltage and current loops of GFM converters in circuits. This paper derives series-parallel sequence impedance models of multi-loop GFM converters, demonstrating that the voltage loop can be regarded as a parallel impedance and the current loop as a series impedance. Consequently, the corresponding small-signal stability characteristics can be identified through Bode diagrams of sequence impedances or by examining the physical meanings of impedances in series and in parallel. The results indicate that the GFM converter with a single power loop is a candidate suitable for application in new power systems, given its reduced number of control parameters and enhanced low-frequency performance, particularly in weak grids. The results of PLECS simulations and corresponding prototype experiments verify the accuracy of the analytical analysis under diverse grid conditions.

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    • Resonance Characterization and Frequency-divided Compensation Strategy for Heterogeneous Inverters-paralleled System

      2025, 13(1):42-54. DOI: 10.35833/MPCE.2024.000416

      Abstract (4) HTML (24) PDF 5.72 M (83) Comment (0) Favorites

      Abstract:Currently, the dominant trend in new energy power supply systems is the heterogeneous inverters-paralleled system (HIPS), which is a combination of grid-following (GFL) and grid-forming (GFM) inverters. The dynamic characteristics of different inverters in HIPS and the differences between GFL and GFM inverters undoubtedly increase the difficulty of the stability analysis and coordinated control. This paper establishes an interactive admittance matrix model of HIPS, fully considers the interactive effects among different inverters, and explores the multi-dimensional resonance characteristics of HIPS by utilizing the modal analysis method. To achieve the coordinated control and oscillation suppression among different inverters, a frequency-divided compensation strategy is proposed, which divides the operation modes of HIPS into three categories, i.e., GFM, GFL, and hybrid modes. Specifically, the frequency division boundary is determined based on the resonance characteristics of GFL and GFM inverters, with the operation modes of HIPS being dynamically adjusted according to the harmonic power ratio. Finally, the simulation and experimental results demonstrate that the HIPS can flexibly adjust the operation modes to adapt to the complex conditions after adopting the frequency-divided compensation strategy and suppressing the oscillation frequency ratio to less than 2%, ensuring the safe and reliable operation of HIPS.

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    • Grid Strength Assessment Method for Evaluating Small-signal Synchronization Stability of Grid-following and Grid-forming Converters Integrated Systems

      2025, 13(1):55-65. DOI: 10.35833/MPCE.2024.000759

      Abstract (8) HTML (6) PDF 4.23 M (101) Comment (0) Favorites

      Abstract:Oscillations caused by small-signal instability have been widely observed in AC grids with grid-following (GFL) and grid-forming (GFM) converters. The generalized short-circuit ratio is commonly used to assess the strength of GFL converters when integrated with weak AC systems at risk of oscillation. This paper provides the grid strength assessment method to evaluate the small-signal synchronization stability of GFL and GFM converters integrated systems. First, the admittance and impedance matrices of the GFL and GFM converters are analyzed to identify the frequency bands associated with negative damping in oscillation modes dominated by heterogeneous synchronization control. Secondly, based on the interaction rules between the short-circuit ratio and the different oscillation modes, an equivalent circuit is proposed to simplify the grid strength assessment through the topological transformation of the AC grid. The risk of sub-synchronization and low-frequency oscillations, influenced by GFL and GFM converters, is then reformulated as a semi-definite programming (SDP) model, incorporating the node admittance matrix and grid-connected device capacities. The effectiveness of the proposed method is demonstrated through a case analysis.

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    • DC Voltage Control with Grid-forming Capability for Enhancing Stability of HVDC System

      2025, 13(1):66-78. DOI: 10.35833/MPCE.2024.000822

      Abstract (6) HTML (2) PDF 7.71 M (81) Comment (0) Favorites

      Abstract:Grid-forming (GFM) converters are recognized for their stabilizing effects in renewable energy systems. Integrating GFM converters into high-voltage direct current (HVDC) systems requires DC voltage control. However, there can be a conflict between GFM converter and DC voltage control when they are used in combination. This paper presents a rigorous control design for a GFM converter that connects the DC-link voltage to the power angle of the converter, thereby integrating DC voltage control with GFM capability. The proposed control is validated through small-signal and transient-stability analyses on a modular multilevel converter (MMC)-based HVDC system with a point-to-point (P2P) GFM-GFM configuration. The results demonstrate that employing a GFM-GFM configuration with the proposed control enhances the stability of the AC system to which it is connected. The system exhibits low sensitivity to grid strength and can sustain islanding conditions. The high stability limit of the system with varying grid strength using the proposed control is validated using a system with four voltage source converters.

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    • Safe Reinforcement Learning for Grid-forming Inverter Based Frequency Regulation with Stability Guarantee

      2025, 13(1):79-86. DOI: 10.35833/MPCE.2023.000882

      Abstract (5) HTML (30) PDF 2.47 M (114) Comment (0) Favorites

      Abstract:This study investigates a safe reinforcement learning algorithm for grid-forming (GFM) inverter based frequency regulation. To guarantee the stability of the inverter-based resource (IBR) system under the learned control policy, a model-based reinforcement learning (MBRL) algorithm is combined with Lyapunov approach, which determines the safe region of states and actions. To obtain near optimal control policy, the control performance is safely improved by approximate dynamic programming (ADP) using data sampled from the region of attraction (ROA). Moreover, to enhance the control robustness against parameter uncertainty in the inverter, a Gaussian process (GP) model is adopted by the proposed algorithm to effectively learn system dynamics from measurements. Numerical simulations validate the effectiveness of the proposed algorithm.

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    • Proportion of Grid-forming Wind Turbines in Hybrid GFM-GFL Offshore Wind Farms Integrated with Diode Rectifier Unit Based HVDC System

      2025, 13(1):87-101. DOI: 10.35833/MPCE.2024.000432

      Abstract (6) HTML (28) PDF 6.88 M (106) Comment (0) Favorites

      Abstract:This study analyzes the stability and reactive characteristics of the hybrid offshore wind farm that includes grid-forming (GFM) and grid-following (GFL) wind turbines (WTs) integrated with a diode rectifier unit (DRU) based high-voltage direct current (HVDC) system. The determination method for the proportion of GFM WTs is proposed while considering system stability and optimal offshore reactive power constraints. First, the small-signal stability is studied based on the developed linear model, and crucial factors that affect the stability are captured by eigenvalue analysis. The reactive power-frequency compensation control of GFM WTs is then proposed to improve the reactive power and frequency dynamics. Second, the relationship between offshore reactive power imbalance and the effectiveness of GFM capability is analyzed. Offshore reactive power optimization methods are next proposed to diminish offshore reactive load. These methods include the optimal design for the reactive capacity of the AC filter and the reactive power compensation control of GFL WTs. Third, in terms of stability and optimal offshore reactive power constraints, the principle and calculation method for determining the proportion of GFM WTs are proposed, and the critical proportion of GFM WTs is determined over the full active power range. Finally, case studies using a detailed model are conducted by time-domain simulations in PSCAD/EMTDC. The simulations verify the theoretical analysis results and the effectiveness of the proposed determination method for the proportion of GFM WTs and reactive power optimization methods.

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    • A Systematic Small-signal Analysis Procedure for Improving Synchronization Stability of Grid-forming Virtual Synchronous Generators

      2025, 13(1):102-114. DOI: 10.35833/MPCE.2024.000316

      Abstract (7) HTML (1) PDF 3.37 M (79) Comment (0) Favorites

      Abstract:The integration of converter-interfaced generators (CIGs) into power systems is rapidly replacing traditional synchronous machines. To ensure the security of power supply, modern power systems require the application of grid-forming technologies. This study presents a systematic small-signal analysis procedure to assess the synchronization stability of grid-forming virtual synchronous generators (VSGs) considering the power system characteristics. Specifically, this procedure offers guidance in tuning controller gains to enhance stability. It is applied to six different grid-forming VSGs and experimentally tested to validate the theoretical analysis. This study concludes with key findings and a discussion on the suitability of the analyzed grid-forming VSGs based on the power system characteristics.

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    • Low-frequency Oscillations and Resonance Analysis of VSG-controlled PMSG-based Wind Generation Systems

      2025, 13(1):115-127. DOI: 10.35833/MPCE.2024.000465

      Abstract (10) HTML (27) PDF 3.46 M (55) Comment (0) Favorites

      Abstract:With good adaptability to weak power grids, the grid-forming inverter becomes the foundation of future power grids with high-proportion renewable energy. Moreover, the virtual synchronous generator (VSG) control is recognized as the mainstream control strategy for grid-forming inverters. For permanent magnet synchronous generator (PMSG) based wind generation systems connected to power grid via VSG-controlled grid-forming inverters, some novel impacts on the low-frequency oscillations (LFOs) emerge in power grids. The first impact involves the negative/positive damping effect on LFOs. In this paper, the small-signal torque model of VSG-controlled PMSG-based wind generation systems is established based on the damping torque analysis method, revealing the influence mechanism of machine-side dynamics on LFOs and proving the necessity of the double-mass model for accurate stability analysis. The second impact is the resonance effect between torsional oscillation and LFOs. Subsequently, this paper uses the open-loop resonance analysis method to study the resonance mechanism and to predict the root trajectory. Then, a damping enhancement strategy is proposed to weaken and eliminate the negative damping effect of machine-side dynamics on LFOs and the resonance effect between torsional oscillation and LFOs. Finally, the analysis result is validated through a case study involving the connection of the VSG-controlled PMSG-based wind generation system to the IEEE 39-bus AC grid, supporting the industrial application and stable operation of VSG-controlled PMSG-based wind generation systems.

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    • Transient Stability Analysis and Improved Control Strategy of PMSG-based Grid-forming Wind Energy Conversion System Under Symmetrical Grid Fault

      2025, 13(1):128-141. DOI: 10.35833/MPCE.2024.000484

      Abstract (5) HTML (31) PDF 10.47 M (63) Comment (0) Favorites

      Abstract:The transient synchronization characteristics and instability mechanism of the permanent magnet synchronous generator (PMSG)-based grid-forming wind energy conversion system (GFM-WECS) under symmetrical grid fault have received little attention to date. In this paper, considering the dynamics of DC-link voltage, the transient stability and an improved control strategy of PMSG-based GFM-WECS are studied in detail. Firstly, considering the dynamic interactions between the machine-side converter and the grid-side converter, the large-signal equivalent model of GFM-WECS is established. Furthermore, a novel Lyapunov function is derived to evaluate the transient stability margin and instability boundary of GFM-WECS during grid voltage sag. Additionally, the impacts of current-limitation control on the transient stability of GFM-WECS are revealed. Then, a stability evaluation index is proposed to evaluate the transient stability margin of GFM-WECS. Moreover, an improved control strategy is proposed to enhance the transient response characteristics and low voltage ride-through (LVRT) capability of GFM-WECS under symmetrical grid fault. Finally, simulations and experimental results are conducted to verify the effectiveness of the proposed control strategy.

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    • Virtual Power Angle Synchronous Control for Improving Transient Stability of Grid-forming Converters

      2025, 13(1):142-153. DOI: 10.35833/MPCE.2024.000684

      Abstract (8) HTML (5) PDF 8.02 M (87) Comment (0) Favorites

      Abstract:The increasing adoption of grid-forming converters (GFMCs) stems from their capacity to furnish voltage and frequency support for power grids. Nevertheless, GFMCs employing the current reference saturation limiting method often exhibit instability during various transient disturbances including grid voltage sags, frequency variations, and phase jumps. To address this problem, this paper proposes a virtual power angle synchronous (δv-SYN) control method. The fundamental of this method is to achieve synchronization with the grid using the virtual power angle δv instead of the active power. The transient stability characteristics of the proposed method are theoretically elucidated using a novel virtual power angle-power angle (δv-δ) model. The key benefit of the proposed method is its robustness to various grid strengths and diverse forms of transient disturbances, eliminating the requirement for fault identification or control switching. Moreover, it can offer grid-forming support to the grid during grid faults. Hardware-in-the-loop experimental results validate the theoretical analysis and the performance of the proposed method.

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    • Grid-forming Control Based on Adaptive Reactive Power Allocation for Offshore Wind Farms Connected to Diode-rectifier-based HVDC System

      2025, 13(1):154-166. DOI: 10.35833/MPCE.2024.00743

      Abstract (7) HTML (30) PDF 20.75 M (99) Comment (0) Favorites

      Abstract:Diode-rectifier-based high-voltage direct current (DR-HVDC) systems are considered an attractive solution for integrating offshore wind farms (OWFs). Grid-forming (GFM) control with a rational reactive power allocation capability is crucial for the safe operation of numerous wind turbines (WTs). Most typical GFM controls aim to share surplus reactive power of the system equally among WTs, easily rendering capacity overloads for WTs that are outputting high levels of active power. In this paper, a novel GFM control for OWFs is proposed, allowing for adaptively allocating the reactive power according to the actual active power output of WTs. Firstly, the reactive power characteristics of the AC collection networks and WTs are analyzed across a wide wind power range. Then, combining the positive correlation of WT active power with the output AC voltage, a Q-θ type GFM control for WTs is presented. The adaptive reactive power allocation mechanism and the parameter design of the Q-θ based reactive power controller are elucidated, ensuring that WTs with lower active power output contribute more reactive power to the system than WTs with higher active power output. The AC impedance models of WTs under various GFM controls are established to evaluate the impact of different reactive power controllers. Finally, the feasibility of the proposed control is validated in PSCAD/EMTDC, accompanied by stability analysis.

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    • Frequency Deadband Control of Grid-forming Energy Storage Inverter in Primary Frequency Regulation

      2025, 13(1):167-178. DOI: 10.35833/MPCE.2024.000757

      Abstract (8) HTML (29) PDF 8.96 M (77) Comment (0) Favorites

      Abstract:With the increased penetration of renewable energy sources, the grid-forming (GFM) energy storage (ES) has been considered to engage in primary frequency regulation (PFR), often necessitating the use of a frequency deadband (FDB) to prevent excessive battery charging cycling and mitigate frequency oscillations. Implementing the FDB is relatively straightforward in grid-following (GFL) control. However, implementing the FDB in GFM control presents a significant challenge since the inverter must abstain from providing active power at any frequency within the FDB. Therefore, in this paper, the performance of PFR control in the GFM-ES inverter is analyzed in detail first. Then, the FDB is implemented for GFM inverters with various types of synchronization methods, and the need for inertia response is also considered. Moreover, given the risk of oscillations near the FDB boundary, different FDB setting methods are proposed and examined, where an improved triangular hysteresis method is proposed to realize the fast response and enhanced stability. Finally, the simulation and experiment results are provided to verify the effectiveness of the above methods.

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    • Matching Synchronous Machine Control for Improving Active Support of Grid-forming PV Systems with Enhanced DC Voltage Dynamics

      2025, 13(1):179-189. DOI: 10.35833/MPCE.2023.000624

      Abstract (6) HTML (27) PDF 3.67 M (102) Comment (0) Favorites

      Abstract:With photovoltaic (PV) sources becoming more prevalent in the energy generation mix, transitioning grid-connected PV systems from grid-following (GFL) mode to grid-forming (GFM) mode becomes essential for offering self-synchronization and active support services. Although numerous GFM methods have been proposed, the potential of DC voltage control malfunction during the provision of the primary and inertia support in a GFM PV system remains insufficiently researched. To fill the gap, some main GFM methods have been integrated into PV systems featuring detailed DC source dynamics. We conduct a comparative analysis of their performance in active support and DC voltage regulation. AC GFM methods such as virtual synchronous machine (VSM) face a significant risk of DC voltage failure in situations like alterations in solar radiation, leading to PV system tripping and jeopardizing local system operation. In the case of DC GFM methods such as matching control (MC), the active support falls short due to the absence of an accurate and dispatchable droop response. To address the issue, a matching synchronous machine (MSM) control method is developed to provide dispatchable active support and enhance the DC voltage dynamics by integrating the MC and VSM control loops. The active support capability of the PV systems with the proposed method is quantified analytically and verified by numerical simulations and field tests.

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    • >Original Paper
    • Stochastic Optimization of Medium- and Short-term Reserve Arrangement for Preventive and Emergency Control Under Typhoon Disaster

      2025, 13(1):190-201. DOI: 10.35833/MPCE.2024.000353

      Abstract (7) HTML (2) PDF 2.44 M (59) Comment (0) Favorites

      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.

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    • Power System Reliability Evaluation Based on Sequential Monte Carlo Simulation Considering Multiple Failure Modes of Components

      2025, 13(1):202-214. DOI: 10.35833/MPCE.2023.000939

      Abstract (6) HTML (30) PDF 2.63 M (57) Comment (0) Favorites

      Abstract:The component aging has become a significant concern worldwide, and the frequent failures pose a serious threat to the reliability of modern power systems. In light of this issue, this paper presents a power system reliability evaluation method based on sequential Monte Carlo simulation (SMCS) to quantify system reliability considering multiple failure modes of components. First, a three-state component reliability model is established to explicitly describe the state transition process of the component subject to both aging failure and random failure modes. In this model, the impact of each failure mode is decoupled and characterized as the combination of two state duration variables, which are separately modeled using specific probability distributions. Subsequently, SMCS is used to integrate the three-state component reliability model for state transition sequence generation and system reliability evaluation. Therefore, various reliability metrics, including the probability of load curtailment (PLC), expected frequency of load curtailment (EFLC), and expected energy not supplied (EENS), can be estimated. To ensure the applicability of the proposed method, Hash table grouping and the maximum feasible load level judgment techniques are jointly adopted to enhance its computational performance. Case studies are conducted on different aging scenarios to illustrate and validate the effectiveness and practicality of the proposed method.

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    • Graph Attention Network Based Deep Reinforcement Learning for Voltage/var Control of Topologically Variable Power System

      2025, 13(1):215-227. DOI: 10.35833/MPCE.2023.000712

      Abstract (8) HTML (2) PDF 3.34 M (84) Comment (0) Favorites

      Abstract:The high proportion of renewable energy integration and the dynamic changes in grid topology necessitate the enhancement of voltage/var control (VVC) to manage voltage fluctuations more rapidly. Traditional model-based control algorithms are becoming increasingly incompetent for VVC due to their high model dependence and slow online computation speed. To alleviate these issues, this paper introduces a graph attention network (GAT) based deep reinforcement learning for VVC of topologically variable power system. Firstly, combining the physical information of the actual power grid, a physics-informed GAT is proposed and embedded into the proximal policy optimization (PPO) algorithm. The GAT-PPO algorithm can capture topological and spatial correlations among the node features to tackle topology changes. To address the slow training, the ReliefF-S algorithm identifies critical state variables, significantly reducing the dimensionality of state space. Then, the training samples retained in the experience buffer are designed to mitigate the sparse reward issue. Finally, the validation on the modified IEEE 39-bus system and an actual power grid demonstrates superior performance of the proposed algorithm compared with state-of-the-art algorithms, including PPO algorithm and twin delayed deep deterministic policy gradient (TD3) algorithm. The proposed algorithm exhibits enhanced convergence during training, faster solution speed, and improved VVC performance, even in scenarios involving grid topology changes and increased renewable energy integration. Meanwhile, in the adopted cases, the network loss is reduced by 6.9%, 10.8%, and 7.7%, respectively, demonstrating favorable economic outcomes.

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    • Voltage Sag Monitor Placement for Fault Location Detection Based on Precise Determination of Areas of Vulnerability

      2025, 13(1):228-240. DOI: 10.35833/MPCE.2023.001022

      Abstract (6) HTML (8) PDF 1.92 M (77) Comment (0) Favorites

      Abstract:The increase in the number of sensitive loads in power systems has made power quality, particularly voltage sag, a prominent problem due to its effects on consumers from both the utility and customer perspectives. Thus, to evaluate the effects of voltage sag caused by short circuits, it is necessary to determine the areas of vulnerability (AOVs). In this paper, a new method is proposed for the AOV determination that is applicable to large-scale networks. The false position method (FPM) is proposed for the precise calculation of the critical points of the system lines. Furthermore, a new method is proposed for the voltage sag monitor (VSM) placement to detect the fault locations. A systematic placement scheme is used to provide the highest fault location detection (FLD) index at buses and lines for various short-circuit fault types. To assess the efficiency of the proposed methods for AOV determination and VSM placement, simulations are conducted in IEEE standard systems. The results demonstrate the accuracy of the proposed method for AOV determination. In addition, through VSM placement, the fault locations at buses and lines are detected.

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    • Unit Commitment with Joint Chance Constraints in Multi-area Power Systems with Wind Power Based on Partial Sample Average Approximation

      2025, 13(1):241-252. DOI: 10.35833/MPCE.2023.001038

      Abstract (6) HTML (3) PDF 3.11 M (49) Comment (0) Favorites

      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.

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    • Harmonic Resonance Analysis and Suppression for Suburban Railway Continuous Power Supply Systems

      2025, 13(1):253-264. DOI: 10.35833/MPCE.2024.000348

      Abstract (7) HTML (34) PDF 5.49 M (78) Comment (0) Favorites

      Abstract:The continuous power supply system, which eliminates the neutral section and realizes safe and reliable operation, shows a development trend in suburban railways. However, the access of a power quality compensator (PQC) may alter the impedance characteristics of the system and introduce additional harmonics with a broader frequency band, potentially increasing the risk of resonance. Accordingly, in this paper, an analytical method is first adopted in conjunction with a field test to construct a simplified harmonic model for an actual continuous suburban line. A modal scanning algorithm is then used to analyze the effects of the controller and filter in the PQC on the harmonic resonance of the suburban railway continuous power supply system. Based on the improved particle swarm optimization algorithm, a multi-objective optimization design for PQC is proposed that can suppress harmonic resonance, filter the harmonics, and reduce the cost while preserving the stability of the control system. Finally, a real case study based on the field test demonstrates the effectiveness of the proposed design.

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    • Two-layer Data-driven Robust Scheduling for Industrial Heat Loads

      2025, 13(1):265-275. DOI: 10.35833/MPCE.2024.000105

      Abstract (4) HTML (5) PDF 3.02 M (128) Comment (0) Favorites

      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.

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    • Two-stage Optimal Scheduling of Community Integrated Energy System Considering Operation Sequences of Hydrogen Energy Storage Systems

      2025, 13(1):276-288. DOI: 10.35833/MPCE.2023.001027

      Abstract (5) HTML (1) PDF 3.35 M (85) Comment (0) Favorites

      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%.

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    • Resonance Assessment of Large-scale Wind Park Connected to Primary Distribution Network

      2025, 13(1):289-299. DOI: 10.35833/MPCE.2024.000127

      Abstract (8) HTML (4) PDF 3.89 M (80) Comment (0) Favorites

      Abstract:On-shore wind parks are typically connected to the high-voltage (HV) transmission system through a bulk transformer. However, wind generators may be connected directly at a medium-voltage (MV) level, such as a utility-owned primary distribution network, if the network is capable of sustaining the power flow and ensuring adequate power quality for its users. This paper presents the findings of a comprehensive study on the management of resonance in a utility-owned wind park in Costa Rica. The wind park is connected directly to the MV primary distribution network and has no shunt capacitor for power factor correction. The results demonstrate that such configuration has a higher immunity to resonances, as the total grid equivalent impedance perceived by the wind park is typically dominated by the absent HV/MV transformer and shunt capacitor bank. Moreover, the capacitance provided by the underground feeders of the wind park did not result in natural oscillation frequencies in the range of typical harmonic distortions observed in MV distribution networks that violated power quality standards.

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    • DistFlow Safe Reinforcement Learning Algorithm for Voltage Magnitude Regulation in Distribution Networks

      2025, 13(1):300-311. DOI: 10.35833/MPCE.2024.000253

      Abstract (2) HTML (27) PDF 2.10 M (27) Comment (0) Favorites

      Abstract: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 DistFlow safe reinforcement learning (DF-SRL), designed specifically for real-time voltage magnitude regulation in distribution networks. The DF-SRL algorithm incorporates a DistFlow 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.

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    • Security Risk Assessment and Risk-oriented Defense Resource Allocation for Cyber-physical Distribution Networks Against Coordinated Cyber Attacks

      2025, 13(1):312-324. DOI: 10.35833/MPCE.2024.000288

      Abstract (7) HTML (3) PDF 2.75 M (50) Comment (0) Favorites

      Abstract:With the proliferation of advanced communication technologies and the deepening interdependence between cyber and physical components, power distribution networks are subject to miscellaneous security risks induced by malicious attackers. To address the issue, this paper proposes a security risk assessment method and a risk-oriented defense resource allocation strategy for cyber-physical distribution networks (CPDNs) against coordinated cyber attacks. First, an attack graph-based CPDN architecture is constructed, and representative cyber-attack paths are drawn considering the CPDN topology and the risk propagation process. The probability of a successful coordinated cyber attack and incurred security risks are quantitatively assessed based on the absorbing Markov chain model and National Institute of Standards and Technology (NIST) standard. Next, a risk-oriented defense resource allocation strategy is proposed for CPDNs in different attack scenarios. The trade-off between security risk and limited resource budget is formulated as a multi-objective optimization (MOO) problem, which is solved by an efficient optimal Pareto solution generation approach. By employing a generational distance metric, the optimal solution is prioritized from the optimal Pareto set of the MOO and leveraged for subsequent atomic allocation of defense resources. Several case studies on a modified IEEE 123-node test feeder substantiate the efficacy of the proposed security risk assessment method and risk-oriented defense resource allocation strategy.

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    • A Robust Short-circuit Calculation Method for Islanded, Grid-connected, and Utility Microgrids

      2025, 13(1):325-337. DOI: 10.35833/MPCE.2023.001041

      Abstract (4) HTML (2) PDF 4.37 M (78) Comment (0) Favorites

      Abstract:In this paper, a robust method for quantifying the impact of short-circuit faults on microgrids is proposed. Microgrids can operate in both islanded (grid-forming) and grid-connected (grid-following) modes, and the ownership and responsibility for the microgrid operation can vary significantly from distribution system operators (DSOs) to third-party microgrid operators. This necessitates the development of a robust short-circuit calculation (SCC) method that can provide accurate results for all the possible microgrid topologies, operational modes, and ownership models. Unlike previously developed SCC methods for microgrids, the SCC method proposed in this paper provides highly accurate results for all possible microgrid topologies: islanded microgrid, grid-connected microgrid, and utility microgrid as a part of a larger distribution grid. In addition, the proposed SCC method solves the short-circuit faults of any complexity, with the same simplicity. The proposed SCC method is tested on a complete model of a real-life microgrid on the Case Western Reserve University campus, operating in both islanded and grid-connected modes. The computational results show the advantages of the proposed SCC method in comparison to the previous ones for microgrids, regarding the robustness (ability to solve complex short-circuit faults with an arbitrary number of faulted buses and phases that affect a microgrid of any topology), as well as the accuracy of the results.

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    • Price-based Demand Response Supported Three-stage Hierarchically Coordinated Voltage Control for Microgrids

      2025, 13(1):338-350. DOI: 10.35833/MPCE.2024.000263

      Abstract (7) HTML (27) PDF 3.83 M (91) Comment (0) Favorites

      Abstract:Photovoltaic (PV) inverter, as a promising voltage/var control (VVC) resource, can supply flexible reactive power to reduce microgrid power loss and regulate bus voltage. Meanwhile, active power plays a significant role in microgrid voltage profile. Price-based demand response (PBDR) can shift load demand via determining time-varying prices, which can be regarded as an effective means for active power shifting. However, due to the different characteristics, PBDR and inverter-based VVC lack systematic coordination. Thus, this paper proposes a PBDR-supported three-stage hierarchically coordinated voltage control method, including day-ahead PBDR price scheduling, hour-ahead reactive power dispatch of PV inverters, and real-time local droop control of PV inverters. Considering their mutual influence, a stochastic optimization method is utilized to centrally or hierarchically coordinate adjacent two stages. To solve the bilinear constraints of droop control function, the problem is reformulated into a second-order cone programming relaxation model. Then, the concave constraints are convexified, forming a penalty convex-concave model for feasible solution recovery. Lastly, a convex-concave procedure-based solution algorithm is proposed to iteratively solve the penalty model. The proposed method is tested on 33-bus and IEEE 123-bus distribution networks and compared with other methods. The results verify the high efficiency of the proposed method to achieve power loss reduction and voltage regulation.

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    • Bi-level Robust Clearing Framework of Integrated Electricity and Gas Market Considering Robust Bidding of Smart Energy Hubs

      2025, 13(1):351-364. DOI: 10.35833/MPCE.2024.000093

      Abstract (4) HTML (1) PDF 2.44 M (105) Comment (0) Favorites

      Abstract:With the implementation of the integrated electricity and gas market (IEGM), the smart energy hubs (SEHs) tend to participate in the market clearing for the optimization of the energy purchase portfolio. Meanwhile, the renewable energy is mushrooming at different scales of energy systems, which can introduce utility-level and distribution-level uncertainties to the operation of the IEGM and SEHs, respectively. Considering the impacts of divergent uncertainties, there exist complicated interactions between the IEGM clearing and the robust bidding of SEHs. The lack of consideration of such interactions may lead to inaccurate modeling of the IEGM clearing and cause potential market inefficiency. To handle this, a bi-level robust clearing framework of the IEGM considering the robust bidding of SEHs is proposed, which simultaneously considers the impacts of utility-level and distribution-level uncertainties. The proposed framework is partitioned into two levels. The upper level is the robust clearing mechanism of the IEGM. At this level, the uncertainty locational marginal electricity and gas prices are derived considering the utility-level uncertainties and the uncertainty-based bidding of SEHs. Given the price signals deduced in the upper level, the lower-level robust bidding of the SEH seeks the optimal bidding strategies while hedging against distribution-level uncertainties. To address the proposed framework, an effective algorithm combining column-and-constraint generation (C&CG) algorithm with the best-response decomposition (BRD) algorithm is formulated. The devised algorithm can efficiently solve the individual robust optimization model and coordinate the interaction of two levels. Numerical experiments are carried out to verify the effectiveness of the proposed framework. Moreover, the impacts of uncertainties on the market clearing results along with the optimal biddings of SEHs are further demonstrated within the proposed framework.

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