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To secure power system operations, practical dispatches in industries place a steady power transfer limit on critical inter-corridors, rather than high-dimensional and strong nonlinear stability constraints. However, computational complexities lead to over-conservative pre-settings of transfer limit, which further induce undesirable and non-technical congestion of power transfer. To conquer this barrier, a scenario-classification hybrid-based banding method is proposed. A cluster technique is adopted to separate similarities from historical and generated operating condition dataset. With a practical rule, transfer limits are approximated for each operating cluster. Then, toward an interpretable online transfer limit decision, costsensitive learning is applied to identify cluster affiliation to assign a transfer limit for a given operation. In this stage, critical variables that affect the transfer limit are also picked out via mean impact value. This enables us to construct low-complexity and dispatcher-friendly rules for fast determination of transfer limit. The numerical case studies on the IEEE 39-bus system and a real-world regional power system in China illustrate the effectiveness and conservativeness of the proposed method.

To provide guidance for photovoltaic (PV) system integration in net-zero distribution systems (DSs), this paper proposes an analytical method for delineating the feasible region for PV integration capacities (PVICs), where the impact of battery energy storage system (BESS) flexibility is considered. First, we introduce distributionally robust chance constraints on network security and energy/carbon net-zero requirements, which form the upper and lower bounds of the feasible region. Then, the formulation and solution of the feasible region is proposed. The resulting analytical expression is a set of linear inequalities, illustrating that the feasible region is a polyhedron in a high-dimensional space. A procedure is designed to verify and adjust the feasible region, ensuring that it satisfies network loss constraints under alternating current (AC) power flow. Case studies on the 4-bus system, the IEEE 33-bus system, and the IEEE 123-bus system verify the effectiveness of the proposed method. It is demonstrated that the proposed method fully captures the spatio-temporal coupling relationship among PVs, loads, and BESSs, while also quantifying the impact of this relationship on the boundaries of the feasible region.

Community batteries (CBs) are emerging to support and even enable energy communities and generally help consumers, especially space-constrained ones, to access potential techno-economic benefits from storage and support local grid decarbonization. However, the economic viability of CB projects is often uncertain. In this regard, typical feasibility studies assess CB value for behind-the-meter (BTM) operation or whole-sale market participation, i.e., front-of-meter (FOM). This work proposes a novel techno-economic operational framework that allows systematic assessment of the different options and introduces a two-meter architecture that co-optimizes both BTM and FOM benefits. A real CB project application in Australia is used to demonstrate the significant two-meter co-optimization opportunities that could enhance the business case of CB and energy communities by multi-service provision and value stacking.

To avoid the secondary frequency dip caused by the steep drop of the electrical power of wind turbines (WTs) at the end of frequency support stage, the torque limit-based iner-tial control (TLIC) method sets the power reference as a linear function of rotor speed, rather than the step form for the step-wise inertial control. However, the compensation effect on the frequency nadir (FN) caused by the load surge is weakened as the TLIC power is no longer in the step form. Specifically, the maximum point of the frequency response component (FRC) contributed by TLIC occurs earlier than the minimum point of FRC corresponding to the load surge, so that the FN cannot be adequately raised. Therefore, this paper first investigates the relation between the peak and nadir times of FRCs stimulated by the TLIC and load power. On this basis, with the compensation principle of matching the peak and nadir times of FRCs, the improved TLIC method based on delayed support is proposed. Finally, the effectiveness of the proposed method is validated via the experiments on the test bench of wind-integrated power system.

The offering strategy of energy storage in energy and frequency response (FR) markets needs to account for country-specific market regulations around FR products as well as FR utilization factors, which are highly uncertain. To this end, a novel optimal offering model is proposed for stand-alone price-taking storage participants, which accounts for recent FR market design developments in the UK, namely the trade of FR products in time blocks, and the mutual exclusivity among the multiple FR products. The model consists of a day-ahead stage, devising optimal offers under uncertainty, and a real-time stage, representing the storage operation after uncertainty is materialized. Furthermore, a concrete methodological framework is developed for comparing different approaches around the anticipation of uncertain FR utilization factors (determinis- one based on expected values, deterministic one based on worst-case values, stochastic one, and robust one), by providing four alternative formulations for the real-time stage of the proposed offering model, and carrying out an out-of-sample validation of the four model instances. Finally, case studies employing real data from UK energy and FR markets compare these four instances against achieved profits, FR delivery violations, and computational scalability.

The partial differential equation (PDE) solution of the telegrapher is a promising fault location method among time-domain and model-based techniques. Recent research works have shown that the leap-frog process is superior to other explicit methods for the PDE solution. However, its implementation is challenged by determining the initial conditions in time and the boundary conditions in space. This letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal decomposition. The results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme, particularly in the presence of harmonics.

Power converters and their interfacing networks are often treated as modular state-space blocks for small-signal stability studies in microgrids; they are interconnected by matching the input and output states of the network and converters. Virtual resistors have been widely used in existing models to generate a voltage for state-space models of the network that require voltage inputs. This paper accurately quantifies the adverse impacts of adding the virtual resistance and proposes an alternative method for network modelling that eliminates the requirement of the virtual resistor when interfacing converters with microgrids. The proposed nonlinear method allows initialization, time-domain simulations of the nonlinear model, and linearization and eigenvalue generation. A numerically linearized small-signal model is used to generate eigenvalues and is compared with the eigenvalues generated using the existing modelling method with virtual resistances. Deficiencies of the existing method and improvements offered by the proposed modelling method are clearly quantified. Electromagnetic transient (EMT) simulations using detailed switching models are used for validation of the proposed modelling method.

Due to the fact that a high share of renewable energy sources (RESs) are connected to high-voltage direct current (HVDC) sending-end AC power systems, the voltage and frequency regulation capabilities of HVDC sending-end AC power systems have diminished. This has resulted in potential system operating problems such as overvoltage and overfrequency, which occur simultaneously when block faults exist in the HVDC link. In this study, a steady-state voltage security-constrained optimal frequency control method for weak HVDC sending-end AC power systems is proposed. The integrated virtual inertia control of RESs is employed for system frequency regulation. Additional dynamic reactive power compensation devices are utilized to control the voltage of all nodes meet voltage security constraints. Then, an optimization model that simultaneously considers the frequency and steady-state voltage security constraints for weak HVDC sending-end AC power systems is established. The optimal control scheme with the minimum total cost of generation tripping and additional dynamic reactive power compensation required is obtained through the optimization solution. Simulations are conducted on a modified IEEE 9-bus test system and practical Qing-Yu line commutated converter based HVDC (LCC-HVDC) sending-end AC power system to verify the effectiveness of the proposed method.

As renewable energy continues to be integrated into the grid, energy storage has become a vital technique supporting power system development. To effectively promote the efficiency and economics of energy storage, centralized shared energy storage (SES) station with multiple energy storage batteries is developed to enable energy trading among a group of entities. In this paper, we propose the optimal operation with dynamic partitioning strategy for the centralized SES station, considering the day-ahead demands of large-scale renewable energy power plants. We implement a multi-entity cooperative optimization operation model based on Nash bargaining theory. This model is decomposed into two subproblems: the operation profit maximization problem with energy trading and the leasing payment bargaining problem. The distributed alternating direction multiplier method (ADMM) is employed to address the subproblems separately. Simulations reveal that the optimal operation with a dynamic partitioning strategy improves the tracking of planned output of renewable energy entities, enhances the actual utilization rate of energy storage, and increases the profits of each participating entity. The results confirm the practicality and effectiveness of the strategy.

There is a general concern that the increasing penetration of electric vehicles (EVs) will result in higher aging failure probability of equipment and reduced network reliability. The electricity costs may also increase, due to the exacerbation of peak load led by uncontrolled EV charging. This paper proposes a linear optimization model for the assessment of the benefits of EV smart charging on both network reliability improvement and electricity cost reduction. The objective of the proposed model is the cost minimization, including the loss of load, repair costs due to aging failures, and EV charging expenses. The proposed model incorporates a piecewise linear model representation for the failure probability distributions and utilizes a machine learning approach to represent the EV charging load. Considering two different test systems (a 5-bus network and the IEEE 33-bus network), this paper compares aging failure probabilities, service unavailability, expected energy not supplied, and total costs in various scenarios with and without the implementation of EV smart charging.

Base station (BS) backup batteries (BSBBs), with their dispatchable capacity, are potential demand-side resources for future power systems. To enhance the power supply reliability and post-contingency frequency security of power systems, we propose a two-stage stochastic unit commitment (UC) model incorporating operational reserve and post-contingency frequency support provisions from massive BSBBs in cellular networks, in which the minimum backup energy demand is considered to ensure BS power supply reliability. The energy, operational reserve, and frequency support ancillary services are co-optimized to handle the power balance and post-contingency frequency security in both forecasted and stochastic variable renewable energy (VRE) scenarios. Furthermore, we propose a dedicated and scalable distributed optimization framework to enable autonomous optimizations for both dispatching center (DC) and BSBBs. The BS model parameters are stored and processed locally, while only the values of BS decision variables are required to upload to DC under the proposed distributed optimization framework, which safeguards BS privacy effectively. Case studies on a modified IEEE 14-bus system demonstrate the effectiveness of the proposed method in promoting VRE accommodation, ensuring post-contingency frequency security, enhancing operational economics, and fully utilizing BSBBs' energy and power capacity. Besides, the proposed distributed optimization framework has been validated to converge to a feasible solution with near-optimal performance within limited iterations. Additionally, numerical results on the Guangdong 500 kV provincial power system in China verify the scalability and practicality of the proposed distributed optimization framework.

Accurate prediction of the state-of-charge (SOC) of battery energy storage system (BESS) is critical for its safety and lifespan in electric vehicles. To overcome the imbalance of existing methods between multi-scale feature fusion and global feature extraction, this paper introduces a novel multi-scale fusion (MSF) model based on gated recurrent unit (GRU), which is specifically designed for complex multi-step SOC prediction in practical BESSs. Pearson correlation analysis is first employed to identify SOC-related parameters. These parameters are then input into a multi-layer GRU for point-wise feature extraction. Concurrently, the parameters undergo patching before entering a dual-stage multi-layer GRU, thus enabling the model to capture nuanced information across varying time intervals. Ultimately, by means of adaptive weight fusion and a fully connected network, multi-step SOC predictions are rendered. Following extensive validation over multiple days, it is illustrated that the proposed model achieves an absolute error of less than 1.5% in real-time SOC prediction.

The vehicle-to-grid (V2G) technology enables the bidirectional power flow between electric vehicle (EV) batteries and the power grid, making EV-based mobile energy storage an appealing supplement to stationary energy storage systems. However, the stochastic and volatile charging behaviors pose a challenge for EV fleets to engage directly in multi-agent cooperation. To unlock the scheduling potential of EVs, this paper proposes a source-load-storage cooperative low-carbon scheduling strategy considering V2G aggregators. The uncertainty of EV charging patterns is managed through a rolling-horizon control framework, where the scheduling and control horizons are adaptively adjusted according to the availability periods of EVs. Moreover, a Minkowski-sum based aggregation method is employed to evaluate the scheduling potential of aggregated EV fleets within a given scheduling horizon. This method effectively reduces the variable dimension while preserving the charging and discharging constraints of individual EVs. Subsequently, a Nash bargaining based cooperative scheduling model involving a distribution system operator (DSO), an EV aggregator (EVA), and a load aggregator (LA) is established to maximize the social welfare and improve the low-carbon performance of the system. This model is solved by the alternating direction method of multipliers (ADMM) algorithm in a distributed manner, with privacy of participants fully preserved. The proposed strategy is proven to achieve the objective of low-carbon economic operation.

In recent years, sub-synchronous oscillation accidents caused by wind power integration have received extensive attention. The recorded constant-amplitude waveforms can be induced by either linear or nonlinear oscillation mechanisms. Hence, the nonlinear behavior needs to be distinguished prior to choosing the analysis method. Since the 1960s, the higher-order statistics (HOS) theory has become a powerful tool for the detection of nonlinear behavior (DNB) in production quality control wherein it has mainly been applied to mechanical condition monitoring and fault diagnosis. This study focuses on the hard limiters of the voltage source converter (VSC) control systems in the wind farms and attempts to detect the nonlinear behavior caused by bi- or uni-Iateral saturation hard limiting using the HOS analysis. First, the conventional describing function is extended to obtain the detailed frequency domain information on the bi- and uni-Iateral saturation hard limiting. Furthermore, the bi- and tri-spectra are introduced as the HOS, which are extended into bi- and tri-coherence spectra to eliminate the effects of the linear parts on the harmonic characteristics of hard limiting in the VSC control system, respectively. The effectiveness of the HOS in the DNB and the classification of the hard-limiting types is proven, and its detailed derivation and estimation procedure is presented. Finally, the quadratic and cubic phase coupling in the signals is illustrated, and the performance of the proposed method is evaluated and discussed.

This paper introduces a distributed secondary control scheme for achieving current sharing and average voltage regulation objectives in a DC microgrid. The proposed scheme employs a dynamic diffusion algorithm (DDA) instead of the consensus algorithm to enable distributed communication among converters. To help understand DDA, the relation of DDA and other diffusion algorithms is discussed in detail and its superiority is shown by comparison with diffusion and consensus algorithms. Furthermore, considering the discrete nature and different sampling time of the digital controller and communication network, a z-domain model of the entire DC microgrid is established. The influence of communication and secondary control parameters on the system stability is investigated. Based on the established model, the tolerable communication rates are obtained. Real-time simulations conducted on the OPAL-RT platform validate the effectiveness of the proposed scheme, showcasing its advantages in terms of convergence speed and stability.

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

The concept of utilizing microgrids (MGs) to convert buildings into prosumers is gaining massive popularity because of its economic and environmental benefits. These pro-sumer buildings consist of renewable energy sources and usually install battery energy storage systems (BESSs) to deal with the uncertain nature of renewable energy sources. However, because of the high capital investment of BESS and the limitation of available energy, there is a need for an effective energy management strategy for prosumer buildings that maximizes the profit of building owner and increases the operating life span of BESS. In this regard, this paper proposes an improved energy management strategy (IEMS) for the prosumer building to minimize the operating cost of MG and degradation factor of BESS. Moreover, to estimate the practical operating life span of BESS, this paper utilizes a non-linear battery degradation model. In addition, a flexible load shifting (FLS) scheme is also developed and integrated into the proposed strategy to further improve its performance. The proposed strategy is tested for the real-time annual data of a grid-tied solar photovoltaic (PV) and BESS-powered AC-DC hybrid MG installed at a commercial building. Moreover, the scenario reduction technique is used to handle the uncertainty associated with generation and load demand. To validate the performance of the proposed strategy, the results of IEMS are compared with the well-established energy management strategies. The simulation results verify that the proposed strategy substantially increases the profit of the building owner and operating life span of BESS. Moreover, FLS enhances the performance of IEMS by further improving the financial profit of MG owner and the life span of BESS, thus making the operation of prosumer building more economical and efficient.

The increasing penetration of variable renewable energy (VRE) generation along with the decommissioning of conventional power plants in Chile, has raised several operational challenges in the Chilean National Power Grid (NPG), including transmission congestion and VRE curtailment. To mitigate these limitations, an innovative virtual transmission solution based on battery energy storage systems (BESSs), known as grid booster (GB), has been proposed to increase the capacity of the main 500 kV corridor of the NPG. This paper analyzes the dynamic performance of the GB using a wide-area electromagnetic transient (EMT) model of the NPG. The GB project, composed of two 500 MVA BESS units at each extreme of the 500 kV corridor, allows increasing the transmission capacity for 15 min during N-1 contingencies, overcoming transmission limitations under normal operation conditions while maintaining system stability during faults. The dynamic behavior of the GB is also analyzed to control power flow as well as voltage stability. The results show that the GB is an effective solution to allow greater penetration of VRE generation while maintaining system stability in the NPG.

Medium-voltage distribution systems (MVDSs) mainly consist of a feeder head, lines, distribution transformers, and the equivalent load or power supply interfaced with the distribution transformers. The information of such load or power supply can be measured via the three-wattmeter method (THM) and the two-wattmeter method (TWM). The measurements can be used to perform the control of the power supply and simulate the characteristics of the load, so the models of the load and the power supply need to consider the measurement characteristics. Existing research works on three-phase power flow (PF) just consider the measurement characteristics of THM. Hence, the PF equation of the bus measured via TWM is firstly built. Based on conventional measurements, an accurate and general model of the grounded and ungrounded slack bus is proposed. Furthermore, the influence arising from the connection type and angle shift of distribution transformers on the admittance matrix is considered, and thus a general three-phase transformer model is summarized, which is applicable for all the transformers mentioned herein. Finally, Newton's method is adopted to solve the PF calculation, and the performance of the proposed PF model is demonstrated through designed tests.

The growing integration of renewable energy generation manifests as an effective strategy for reducing carbon emissions. This paper strives to efficiently approximate the set of optimal scheduling plans (OSPs) to enhance the performance of the steady-state adaptive cruise method (SACM) of power grid, improving the ability of dealing with operational uncertainties. Initially, we provide a mathematical definition of the exact box-constrained economic operating region (EBC-EOR) for the power grid and its dispatchable components. Following this, we introduce an EBC-EOR formulation algorithm and the corresponding bi-level optimization models designed to explore the economic operating boundaries. In addition, we propose an enhanced big-M method to expedite the computation of the EBC-EOR. Finally, the effectiveness of the EBC-EOR formulation, its economic attributes, correlation with the scheduling plan underpinned by model predictive control, and the significant improvement in computational efficiency (over twelvefold) are verified through case studies conducted on two test systems..

Battery energy storage systems (BESSs) serve a crucial role in balancing energy fluctuations and reducing carbon emissions in net-zero power systems. However, the efficiency and cost performance have remained significant challenges, which hinders the widespread adoption and development of BESSs. To address these challenges, this paper proposes a real-time energy management scheme that considers the involvement of prosumers to support net-zero power systems. The scheme is based on two shared energy storage models, referred to as energy storage sale model and power line lease model. The energy storage sale model balances real-time power deviations by energy interaction with the goal of minimizing system costs while generating revenue for shared energy storage providers (ESPs). Additionally, power line lease model supports peer-to-peer (P2P) power trading among prosumers through the power lines laid by ESPs to connect each prosumer. This model allows ESP to earn profits from the use of power lines while balancing power deviations and better consuming renewable energy. Experimental results validate the effectiveness of the proposed scheme, ensuring stable power supply for net-zero power systems and providing benefits for both the ESP and prosumers.

To tackle the energy crisis and climate change, wind farms are being heavily invested in across the world. In China's coastal areas, there are abundant wind resources and numerous offshore wind farms are being constructed. The secure operation of these wind farms may suffer from typhoons, and researchers have studied power system operation and resilience enhancement in typhoon scenarios. However, the intricate movement of a typhoon makes it challenging to evaluate its spatial-temporal impacts. Most published papers only consider predefined typhoon trajectories neglecting uncertainties. To address this challenge, this study proposes a stochastic unit commitment model that incorporates high-penetration offshore wind power generation in typhoon scenarios. It adopts a data-driven method to describe the uncertainties of typhoon trajectories and considers the realistic anti-typhoon mode in offshore wind farms. A two-stage stochastic unit commitment model is designed to enhance power system resilience in typhoon scenarios. We formulate the model into a mixed-integer linear programming problem and then solve it based on the computationally-efficient progressive hedging algorithm (PHA). Finally, numerical experiments validate the effectiveness of the proposed method.

In rural territories, the communities use energy sources based on fossil fuels to supply themselves with electricity, which may address two main problems: greenhouse gas emissions and high fuel prices. Hence, there is an opportunity to include renewable resources in the energy mix. This paper develops an optimization model to determine the optimal sizing, the total annual investment cost in renewable generation, and other operating costs of the components of a hybrid microgrid. By running a k-means clustering algorithm on a meteorological dataset of the community under study, the hourly representative values become input parameters in the proposed optimization model. The method for the optimal design of hybrid microgrid is analyzed in six operating scenarios considering: (1) 24-hour continuous power supply; (2) load shedding percentage; (3) disel power generator (genset) curtailment; (4) the worst meteorological conditions; (5) the use of renewable energy sources including battery energy storage systems (BESSs); and (6) the use of genset. A mathematical programming language (AMPL) tool is used to find solutions of the proposed optimization model. Results show that the total costs of microgrid in the scenarios that cover 100% of the load demand (without considering the scenario with 100% renewables) increase by over 16% compared with the scenario with genset operation limitation. For the designs with power supply restrictions, the total cost of microgrid in the scenario with load shedding is reduced by over 27% compared with that without load shedding.

Photovoltaic (PV) and battery energy storage systems (BESSs) are key components in the energy market and crucial contributors to carbon emission reduction targets. These systems can not only provide energy but can also generate considerable revenue by providing frequency regulation services and participating in carbon trading. This study proposes a bidding strategy for PV and BESSs operating in joint energy and frequency regulation markets, with a specific focus on carbon reduction benefits. A two-stage bidding framework that optimizes the profit of PV and BESSs is presented. In the first stage, the day-ahead energy market takes into account potential real-time forecast deviations. In the second stage, the real-time balancing market uses a rolling optimization method to account for multiple uncertainties. Notably, a real-time frequency regulation control method is proposed for the participation of PV and BESSs in automatic generation control (AGC). This is particularly relevant given the uncertainty of grid frequency fluctuations in the optimization model of the real-time balancing market. This control method dynamically assigns the frequency regulation amount undertaken by the PV and BESSs according to the control interval in which the area control error (ACE) occurs. The case study results demonstrate that the proposed bidding strategy not only enables the PV and BESSs to effectively participate in the grid frequency regulation response but also yields considerable carbon emission reduction benefits and effectively improves the system operation economy.

The push for renewable energy emphasizes the need for energy storage systems (ESSs) to mitigate the unpre-dictability and variability of these sources, yet challenges such as high investment costs, sporadic utilization, and demand mismatch hinder their broader adoption. In response, shared energy storage systems (SESSs) offer a more cohesive and efficient use of ESS, providing more accessible and cost-effective energy storage solutions to overcome these obstacles. To enhance the profitability of SESSs, this paper designs a multi-time-scale resource allocation strategy based on long-term contracts and real-time rental business models. We initially construct a life cycle cost model for SESS and introduce a method to estimate the degradation costs of multiple battery groups by cycling numbers and depth of discharge within the SESS. Subsequently, we design various long-term contracts from both capacity and energy perspectives, establishing associated models and real-time rental models. Lastly, multi-time-scale resource allocation based on the decomposition of user demand is proposed. Numerical analysis validates that the business model based on long-term contracts excels over models operating solely in the real-time market in economic viability and user satisfaction, effectively reducing battery degradation, and leveraging the aggregation effect for SESS can generate an additional increase of 10.7% in net revenue.

Wind energy systems (WESs) based on doubly-fed induction generators (DFIGs) have enormous potential for meeting the future demands related to clean energy. Due to the low inertia and intermittency of power injection, a WES is equipped with a virtual inertial controller (VIC) to support the system during a frequency deviation event. The frequency deviation measured by a phase locked loop (PLL) installed on a point of common coupling (PCC) bus is the input signal to the VIC. However, a VIC with an improper inertial gain could deteriorate the damping of the power system, which may lead to instability. To address this issue, a mathematical formulation for calculating the synchronizing and damping torque coefficients of a WES-integrated single-machine infinite bus (SMIB) system while considering PLL and VIC dynamics is proposed in this paper. In addition, a power system stabilizer (PSS) is designed for wind energy integrated power systems to enhance electromechanical oscillation damping. A small-signal stability assessment is performed using the infinite bus connected to a synchronous generator of higher-order dynamics integrated with a VIC-equipped WES. Finally, the performance and robustness of the proposed PSS is demonstrated through time-domain simulation in SMIB and nine-bus test systems integrated with WES under several case studies.

In recent years, high-frequency resonance (HFR) events occurred in several modular multilevel converter based high-voltage direct current (MMC-HVDC) projects. The time delay of an MMC-HVDC system is the critical factor that induces HFR. The frequency coupling affects the impedance characteristics of an MMC and further deteriorates system stability. Therefore, in this paper, a multi-input multi-output admittance model of an MMC-HVDC system is developed to analyze its frequency characteristics. The effects of current loop, power loop, phase-locked loop, and operating point on the MMC frequency coupling degree are analyzed in detail. Meanwhile, to further suppress HFR in the MMC-HVDC system, an enhanced impedance reshaping control strategy based on the equivalent single-input single-output impedance model is proposed. Finally, the accuracy of the enhanced impedance model and the effectiveness of the impedance reshaping control are verified by electromagnetic transient simulations in PSCAD.

The nuclear event risk (NER) is an important and disputed factor that should be reasonably considered when planning the pathway of nuclear power development (NPD) to assess the benefits and risks of developing nuclear power more objectively. This paper aims to explore the impact of nuclear events on NPD pathway planning. The influence of nuclear events is quantified as a monetary risk component, and an optimization model that incorporates the NER in the objective function is proposed. To optimize the pathway of NPD in the lowcarbon transition course of power supply structure evolution, a simulation model is built to deduce alternative NPD pathways and corresponding power supply evolution scenarios under the constraint of an exogenously assigned carbon emission pathway (CEP); moreover, a method is proposed to describe the CEP by superimposing the maximum carbon emission space and each carbon emission reduction (CER) component, and various CER components are clustered considering the emission reduction characteristics and resource endowments of different power generation technologies. A case study is conducted to explore the impact of NER and its risk valuation uncertainty on NPD pathway planning. The method presented in this paper allows the impact of nuclear events on NPD pathway planning to be quantified and improves the level of coordinated optimization of benefits and risks.

We consider a power system whose electric demand pertaining to freshwater production is high (high freshwater electric demand), as in the Middle East, and investigate the tradeoff of storing freshwater in tanks versus storing electricity in batteries at the day-ahead operation stage. Both storing freshwater and storing electricity increase the actual electric demand at valley hours and decrease it at peak hours, which is generally beneficial in term of cost and reliability. But, to what extent? We analyze this question considering three power systems with different generation-mix configurations, i. e., a thermal-dominated mix, a renewable-dominated one, and a fully renewable one. These generation-mix configurations are inspired by how power systems may evolve in different countries in the Middle East. Renewable production uncertainty is compactly modeled using chance constraints. We draw conclusions on how both storage facilities (freshwater and electricity) complement each other to render an optimal operation of the power system.

To reduce the difficulty and enhance the enthusiasm of private-owned electric vehicles (EVs) to participate in frequency regulation ancillary service market (FRASM), a decision aid model (DAM) is proposed. This paper presents three options for EV participating in FRASM, i. e., the base mode (BM), unidirectional charging mode (UCM), and bidirectional charging/discharging mode (BCDM), based on a reasonable simplification of users' participating willingness. In BM, individual EVs will not be involved in FRASM, and DAM will assist users to set the optimal charging schemes based on travel plans under the time-of-use (TOU) price. UCM and BCDM are two modes in which EVs can take part in FRASM. DAM can assist EV users to create their quotation plan, which includes hourly upper and lower reserve capabilities and regulation market mileage prices. In UCM and BCDM, the difference is that only the charging rate can be adjusted in the UCM, and the EVs in BCDM can not only charge but also discharge if necessary. DAM can estimate the expected revenue of all three modes, and EV users can make the final decision based on their preferences. Simulation results indicate that all the three modes of DAM can reduce the cost, while BCDM can get the maximum expected revenue.

This paper proposes a new method for service restoration of distribution network with the support of transportable power sources (TPSs) and repair crews (RCs). Firstly, a coupling model of distribution networks and vehicle routing of TPSs and RCs is proposed, where the TPSs serve as emergency power supply sources, and the RCs are used to repair the faulted lines. Considering the uncertainty of traffic congestion, the probability distribution of the travel time spent on each road is derived based on the Nesterov user equilibrium model, and a two-stage stochastic program is formulated to determine the optimal routings of TPSs and RCs. To efficiently solve the proposed stochastic mixed-integer linear program (MILP), a two-phase scenario reduction method is then developed to scale down the problem size, and an adaptive progressive hedging algorithm is used for an efficient solution. The effectiveness of the proposed methods and algorithms has been illustrated in a modified IEEE 33-bus system.

Line commutated converter based high-voltage direct-current (LCC-HVDC) transmissions are prone to harmonic oscillation under weak grids. Impedance modeling is an effective method for assessing interaction stability. Firstly, this paper proposes an improved calculation method for the DC voltage and AC currents of commutation stations to address the complex linearization of the commutation process and constructs an overall harmonic state-space (HSS) model of an LCC-HVDC. Based on the HSS model, the closed-loop AC impedances on the LCC-HVDC sending and receiving ends are then derived and verified. The impedance characteristics of the LCC-HVDC are then analyzed to provide a physical explanation for the harmonic oscillation of the system. The effects of the grid strength and control parameters on system stability are also analyzed. To improve the impedance characteristics and operating stability of the LCC-HVDC system, a virtual impedance based stability enhancement control is proposed, and a parameter design method is considered to ensure satisfactory phase margins at both the sending and receiving ends. Finally, simulation results are presented to verify the validity of the impedance model and virtual impedance based stability enhancement control.

To maximize conversion efficiency, photovoltaic (PV) systems generally operate in the maximum power point tracking (MPPT) mode. However, due to the increasing penetration level of PV systems, there is a need for more developed control functions in terms of frequency support services and voltage control to maintain the reliability and stability of the power grid. Therefore, flexible active power control is a mandatory task for grid-connected PV systems to meet part of the grid requirements. Hence, a significant number of flexible power point tracking (FPPT) algorithms have been introduced in the existing literature. The purpose of such algorithms is to realize a cost-effective method to provide grid support functionalities while minimizing the reliance on energy storage systems. This paper provides a comprehensive overview of grid support functionalities that can be obtained with the FPPT control of PV systems such as frequency support and volt-var control. Each of these grid support functionalities necessitates PV systems to operate under one of the three control strategies, which can be provided with FPPT algorithms. The three control strategies are classified as: ① constant power generation control (CPGC), ② power reserve control (PRC), and ③ power ramp rate control (PRRC). A detailed discussion on available FPPT algorithms for each control strategy is also provided. This paper can serve as a comprehensive review of the state-of-the-art FPPT algorithms that can equip PV systems with various grid support functionalities.

With the increasing proportion of renewable energy sources (RESs) in power grid, the reserve resource (RR) scarcity for correcting power deviation of RESs has become a potential issue. Consequently, the power curve of RES needs to be more rigorously assessed. The RR scarcity varies during different time periods, so the values of assessment indicators should be dynamically adjusted. The assessment indicators in this paper include two aspects, i. e., deviation exemption ratio and penalty price. Firstly, this paper proposes a method for dynamically calculating the supply capacity and RR cost, primarily taking into account the operating status of thermal units, forecast information of RES, and load curve. Secondly, after clarifying the logical relationship between the degree of RR scarcity and the values of assessment indicators, this paper establishes a mapping function between them. Based on this mapping function, a dynamic setting method for assessment indicators is proposed. In the future, RES will generally be equipped with battery energy storage systems (BESSs). Reasonably utilizing BESSs to reduce the power deviation of RESs can increase the expected income of RESs. Therefore, this paper proposes a power curve optimization strategy for RESs considering self-owned BESSs. The case study demonstrates that the dynamic setting method of assessment indicators can increase the revenue of RESs while ensuring that the penalty fees paid by RESs to the grid are sufficient to cover the RR costs. Additionally, the power curve optimization strategy can help RESs further increase income and fully utilize BESSs to reduce power deviation.

In the competitive energy market, energy retailers are facing the uncertainties of both energy price and demand, which requires them to formulate reasonable energy purchasing and selling strategies for improving their competitiveness in this market. Particularly, the attractive multi-energy retail packages are the key for retailers to increase their benefit. Therefore, combined with incentive means and price signals, five types of multi-energy retail packages such as peak-valley time-of-use (TOU) price package and day-night bundled price package are designed in this paper for retailers. The iterative interactions between retailers and end-users are modeled using a bi-level model of stochastic optimization based on multi-leader multi-follower (MLMF) Stackelberg game, in which retailers are leaders and end-users are followers. Retailers make decisions to maximize the profit considering the conditional value at risk (CVaR) while end-users optimize the satisfaction of both energy comfort and economy. Besides, a distributed algorithm is proposed to obtain the Nash equilibrium of above MLMF Stackelberg game model while the particle swarm optimization (PSO) algorithm and CPLEX solver are applied to solve the optimization model for each participant (retailer or end-user). Numeral results show that the designed retail packages can increase the overall profit of retailers, and the overall satisfaction of industrial users is the highest while that of residential users is the lowest after game interaction.

Interval state estimation (ISE) can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements, thereby analyzing the impact of uncertain pseudo-measurements on states. However, predicted pseudo-measurements have prediction errors, and their confidence intervals do not necessarily contain the truth values, leading to estimation biases of the ISE. To solve this problem, this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression (GPR) model, thereby improving the prediction accuracy of pseudo-measurement confidence intervals. Besides, a weight assignment strategy for improving the robustness of weighted least squares (WLS) ISE is proposed. This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudo-measurement intervals with larger deviations, thereby improving the estimation accuracy and robustness of the ISE. This paper adopts the data from the supervisory control and data acquisition (SCADA) system of the New York Independent System Operator (NYISO). It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods. In addition, this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case. Finally, the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.

Active distribution network (ADN), as a typically cyber-physical system, develops with the evolution of Internet of Things (IoTs), which makes the network vulnerable to cyber-security threats. In this paper, the eavesdropping attacks that lead to privacy breaches are addressed for the IoT-enabled ADN. A privacy-preserving energy management system (EMS) is proposed and empowered by secure data exchange protocols based on the homomorphic cryptosystem. During the information transmission among distributed generators and load customers in the EMS, private information including power usage and electricity bidding price can be effectively protected against eavesdropping attacks. The correctness of the final solutions, e.g., optimal market clearing price and unified power utilization ratio, can be deterministically guaranteed. The simulation results demonstrate the effectiveness and the computational efficiency of the proposed homomorphically encrypted EMS.

Frequency regulation of voltage source converter-based multi-terminal high-voltage direct current (VSC-MTDC) system with offshore wind farms enhances the frequency stability by compensating the power for a disturbed AC system. However, it is difficult to reasonably allocate frequency-regulation resources due to a lack of coordination mechanisms between wind farms and the MTDC system. Moreover, it is difficult for the frequency control of the wind farms to manage changes in wind speed; and the risk of wind-turbine stalls is high. Thus, based on the kinetic energy of wind turbines and the power margin of the converters, the frequency-regulation capability of wind turbines is evaluated, and a dynamic frequency-support scheme considering the real-time frequency-support capability of the wind turbines and system frequency evolution is proposed to improve the frequency-support performance. A power adaptation technique at variable wind speeds is developed; the active power in the frequency-support stage and restoration stage is switched according to the wind speed. A hierarchical zoning frequency-regulation scheme is designed to use the frequency-regulation resources of different links in the MTDC system with wind farms. The simulation results show that the novel frequency-regulation strategy maintains frequency stability with wind-speed changes and avoids multiple frequency dips.

The smart distribution network (SDN) is integrating increasing distributed generation (DG) and energy storage (ES). Hosting capacity evaluation is important for SDN planning with DG. DG and ES are usually invested by users or a third party, and they may form friendly microgrids (MGs) and operate independently. Traditional centralized dispatching method no longer suits for hosting capacity evaluation of SDN. A quick hosting capacity evaluation method based on distributed optimal dispatching is proposed. Firstly, a multi-objective DG hosting capacity evaluation model is established, and the hosting capacity for DG is determined by the optimal DG planning schemes. The steady-state security region method is applied to speed up the solving process of the DG hosting capacity evaluation model. Then, the optimal dispatching models are established for MG and SDN respectively to realize the operating simulation. Under the distributed dispatching strategy, the dualside optimal operation of SDN-MGs can be realized by several iterations of power exchange requirement. Finally, an SDN with four MGs is conducted considering multiple flexible resources. It shows that the DG hosting capacity of SDN oversteps the sum of the maximum active power demand and the rated branch capacity. Besides, the annual DG electricity oversteps the maximum active power demand value.

Moving away from fossil fuels towards renewable sources requires system operators to determine the capacity of distribution systems to safely accommodate green and distributed generation (DG). However, the DG capacity of a distribution system is often underestimated due to either overly conservative electrical demand and DG output uncertainty modelling or neglecting the recourse capability of the available components. To improve the accuracy of DG capacity assessment, this paper proposes a distributionally adjustable robust chance-constrained approach that utilises uncertainty information to reduce the conservativeness of conventional robust approaches. The proposed approach also enables fast-acting devices such as inverters to adjust to the real-time realisation of uncertainty using the adjustable robust counterpart methodology. To achieve a tractable formulation, we first define uncertain chance constraints through distributionally robust conditional value-at-risk (CVaR), which is then reformulated into convex quadratic constraints. We subsequently solve the resulting large-scale, yet convex, model in a distributed fashion using the alternating direction method of multipliers (ADMM). Through numerical simulations, we demonstrate that the proposed approach outperforms the adjustable robust and conventional distributionally robust approaches by up to 15% and 40%, respectively, in terms of total installed DG capacity.

Given large-scale modern power systems with power electronic converters, the numerical simulation with subsynchronous oscillation (SSO) faces great challenges in engineering practice due to sharply enlarged modeling scale and high computational burden. To reduce the modeling scale, network partition and equivalent becomes a vital technique in numerical simulations. Although several methods have been developed for network equivalent, a generally accepted rule for network partition is still required. This paper proposes that the system can be partitioned into three parts, i. e., the internal, the middle, and the external subsystems, in which the internal subsystem consists of all power electronic components, the middle subsystem includes those selected AC dynamic components with detailed models, and the remaining components and buses constitute the external subsystem. The external subsystem is further represented by an equivalent RLC network determined by the frequency dependent network equivalent (FDNE) method. In the proposed method, the observability index and the electrical distance index are used to identify the interface between the middle and the external subsystems. Case studies based on a modified Hydro-Quebec system are used to verify the effectiveness of the proposed method.

The setting work of backup protection using steady-state current is tedious, and mismatches occasionally occur due to the increased proportion of distributed generations (DGs) connected to the power grid. Thus, there is a practical need to study a backup protection technology that does not require step-by-step setting and can be adaptively coordinated. This paper proposes an action sequence adaptive to fault positions that uses only positive sequence fault component (PSFC) voltage. Considering the influence of DGs, the unified time dial setting can be obtained by selecting specific points. The protection performance is improved by using the adjacent upstream and down-stream protections to meet the coordination time interval in the case of metallic faults at the near- and far-ends of the line. Finally, the expression and implementation scheme for inverse-time backup protection (ITBP) based on the unified characteristic equation is given. Simulation results show that this scheme can adapt to DG penetration scenarios and can realize the adaptive coordination of multi-level relays.

With the development of advanced metering infrastructure (AMI), large amounts of electricity consumption data can be collected for electricity theft detection. However, the imbalance of electricity consumption data is violent, which makes the training of detection model challenging. In this case, this paper proposes an electricity theft detection method based on ensemble learning and prototype learning, which has great performance on imbalanced dataset and abnormal data with different abnormal level. In this paper, convolutional neural network (CNN) and long short-term memory (LSTM) are employed to obtain abstract feature from electricity consumption data. After calculating the means of the abstract feature, the prototype per class is obtained, which is used to predict the labels of unknown samples. In the meanwhile, through training the network by different balanced subsets of training set, the prototype is representative. Compared with some mainstream methods including CNN, random forest (RF) and so on, the proposed method has been proved to effectively deal with the electricity theft detection when abnormal data only account for 2.5% and 1.25% of normal data. The results show that the proposed method outperforms other state-of-the-art methods.

With the rapid development of renewable energy, wind-thermal-bundled power transmission by line-commutated converter based high-voltage direct current (LCC-HVDC) systems has been widely developed. The dynamic interaction mechanisms among permanent magnet synchronous generators (PMSGs), synchronous generators (SGs), and LCC-HVDC system become complex. To deal with this issue, a path analysis method (PAM) is proposed to study the dynamic interaction mechanism, and the damping reconstruction is used to analyze the damping characteristic of the system. First, based on the modular modeling, linearized models for the PMSG subsystem, the LCC-HVDC subsystem, and the SG subsystem are established. Second, based on the closed-loop transfer function dia-gram of the system, the disturbance transfer path and coupling relationship among subsystems are analyzed by the PAM, and the damping characteristic analysis of the SG-dominated oscillation mode is studied based on the damping reconstruction. Compared with the PAM, the small-signal model of the system is obtained and eigenvalue analysis results are presented. Then, the effect of the control parameters on the damping characteristic is analyzed and the conclusions are verified by time-domain simulations. Finally, the penalty functions of the oscillation modes and decay modes are taken as the objective function, and an optimization strategy based on the Monte Carlo method is proposed to solve the parameter optimization problem. Numerical simulation results are presented to validate the effectiveness of the proposed strategy.

As the proportion of renewable energy (RE) increases, the inertia and the primary frequency regulation (FR) capability of the power system decrease. Thus, ensuring frequency security in the scheduling model has become a new technical requirement in power systems with a high share of RE. Due to a shortage of conventional synchronous generators, the frequency support of multi-source converters has become an indispensable part of the system frequency resources, especially variable-speed wind turbine generation (WTG) and battery energy storage (BES). Quantitative expression of the FR capability of multi-source converters is necessary to construct frequen-cyconstrained scheduling model. However, the frequency support performance of these converter-interfaced devices is related to their working states, operation modes, and parameters, and the complex coupling of these factors has not been fully exploited in existing models. In this study, we propose an integrated frequency-constrained scheduling model considering the coordination of FR capabilities from multi-source converters. Switchable FR control strategies and variable FR parameters for WTG with or without reserved power are modeled, and multi-target allocation of BES capacity between tracking dispatch instruction and emergency FR is analyzed. Then, the variable FR capabilities of WTG and BES are embedded into the integrated frequency-constrained scheduling model. The nonlinear constraints for frequency security are precisely linearized through an improved iteration-based strategy. The effectiveness of the proposed model is verified in a modified IEEE 24-bus standard system. The results suggest that the coordinated participation of BES and WTG in FR can effectively reduce the cost of the scheduling model while meeting frequency security constraints.

The uncertainties of the power load, wind power, and photovoltaic power lead to errors between point prediction values and real values, which challenges the safe operation of distribution networks. In this paper, a robust reactive power scheduling (RRPS) model based on a modified bootstrap technique is proposed to consider the uncertainties of power loads and renewable energy sources. Firstly, a deterministic reactive power scheduling (DRPS) model and an RRPS model are formulated. Secondly, a modified bootstrap technique is proposed to estimate prediction errors of power loads and renewable energy sources without artificially assuming the probability density function of prediction errors. To represent all possible scenarios, point prediction values and prediction errors are combined to construct two worst-case scenarios in the RRPS model. Finally, the RRPS model is solved to find a scheduling scheme, which ensures the security of distribution networks for all possible scenarios in theory. Simulation results show that the worstcase scenarios constructed by the modified bootstrap technique outperform popular baselines. Besides, the RRPS model based on the modified bootstrap technique balances economics and security well.

The equivalent impedance parameters of loads have been widely used to identify and locate the harmonic sources. However, the existing calculation methods suffer from outliers caused by the zero-crossing of the denominator. These outliers can result in inaccuracy and unreliability of harmonic source location. To address this issue, this paper proposes an innovative method of equivalent impedance parameter calculation of three-phase symmetrical loads that avoid outliers. The correctness and effectiveness of the proposed method are verified by simulations on Simulink using actual monitoring data. The results show that the proposed method is not only simple and easy to implement but also highly accurate.

In response to the increasing penetration of volatile and uncertain renewable energy, the regional transmission organizations (RTOs) have been recently focusing on enhancing the models of pump storage hydropower (PSH) plants, which are one of the key flexibility assets in the day-ahead (DA) and real-time (RT) markets, to further boost their flexibility provision potentials. Inspired by the recent research works that explored the potential benefits of excluding PSHs' cost-related terms from the objective functions of the DA market clearing model, this paper completes a rolling RT market scheme that is compatible with the DA market. Then, with the vision that PSHs could be permitted to submit state-of-charge (SOC) headrooms in the DA market and to release them in the RT market, this paper uncovers that PSHs could increase the total revenues from the two markets by optimizing their SOC headrooms, assisted by the proposed tri-level optimal SOC headroom model. Specifically, in the proposed tri-level model, the middle and lower levels respectively mimic the DA and RT scheduling processes of PSHs, and the upper level determines the optimal headrooms to be submitted to the RTO for maximizing the total revenue from the two markets. Numerical case studies quantify the profitability of the optimal SOC headroom submissions as well as the associated financial risks.

The operation of integrated energy systems (IESs) is confronted with great challenges for increasing penetration rate of renewable energy and growing complexity of energy forms. Scenario generation is one of ordinary methods to alleviate the system uncertainties by extracting several typical scenarios to represent the original high-dimensional data. This paper proposes a novel representative scenario generation method based on the feature extraction of panel data. The original high-dimensional data are represented by an aggregated indicator matrix using principal component analysis to preserve temporal variation. Then, the aggregated indicator matrix is clustered by an algorithm combining density canopy and K-medoids. Together with the proposed scenario generation method, an optimal operation model of IES is established, where the objective is to minimize the annual operation costs considering carbon trading cost. Finally, case studies based on the data of Aachen, Germany in 2019 are performed. The results indicate that the adjusted rand index (ARI) and silhouette coefficient (SC) of the proposed method are 0.6153 and 0.6770, respectively, both higher than the traditional methods, namely K-medoids, K-means++, and density-based spatial clustering of applications with noise (DBSCAN), which means the proposed method has better accuracy. The error between optimal operation results of the IES obtained by the proposed method and all-year time series benchmark value is 0.1%, while the calculation time is reduced from 11029 s to 188 s, which verifies that the proposed method can be used to optimize operation strategy of IES with high efficiency without loss of accuracy.

This study proposes a hybrid network model based on data enhancement to address the problem of low accuracy in photovoltaic (PV) power prediction that arises due to insufficient data samples for new PV plants. First, a time-series generative adversarial network (TimeGAN) is used to learn the distribution law of the original PV data samples and the temporal correlations between their features, and these are then used to generate new samples to enhance the training set. Subsequently, a hybrid network model that fuses bi-directional long-short term memory (BiLSTM) network with attention mechanism (AM) in the framework of deep & cross network (DCN) is constructed to effectively extract deep information from the original features while enhancing the impact of important information on the prediction results. Finally, the hyperparameters in the hybrid network model are optimized using the whale optimization algorithm (WOA), which prevents the network model from falling into a local optimum and gives the best prediction results. The simulation results show that after data enhancement by TimeGAN, the hybrid prediction model proposed in this paper can effectively improve the accuracy of short-term PV power prediction and has wide applicability.