Abstract: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.

Abstract:The subsynchronous oscillations (SSOs) related to renewable generation seriously affect the stability and safety of the power systems. To realize the dynamic monitoring of SSOs by utilizing the high computational efficiency and noise-resilient features of the matrix pencil method (MPM), this paper proposes an improved MPM-based parameter identification with synchrophasors. The MPM is enhanced by the angular frequency fitting equations based on the characteristic polynomial coefficients of the matrix pencil to ensure the accuracy of the identified parameters, since the existing eigenvalue solution of the MPM ignores the angular frequency conjugation constraints of the two fundamental modes and two oscillation modes. Then, the identification and recovery of bad data are proposed by utilizing the difference in temporal continuity of the synchrophasors before and after noise reduction. The proposed parameter identification is verified with synthetic, simulated, and actual measured phase measurement unit (PMU) data. Compared with the existing MPM, the improved MPM achieves better accuracy for parameter identification of each component in SSOs, better real-time performance, and significantly reduces the effect of bad data.

Abstract:This paper proposes an empirical wavelet transform (EWT) based method for identification and analysis of sub-synchronous oscillation (SSO) modes in the power system using phasor measurement unit (PMU) data. The phasors from PMUs are preprocessed to check for the presence of oscillations. If the presence is established, the signal is decomposed using EWT and the parameters of the mono-components are estimated through Yoshida algorithm. The superiority of the proposed method is tested using test signals with known parameters and simulated using actual SSO signals from the Hami Power Grid in Northwest China. Results show the effectiveness of the proposed EWT-Yoshida method in detecting the SSO and estimating its parameters.

Abstract:Electric power grids are evolving into complex cyber-physical power systems (CPPSs) that integrate advanced information and communication technologies (ICTs) but face increasing cyberspace threats and attacks. This study considers CPPS cyberspace security under distributed denial of service (DDoS) attacks and proposes a nonzero-sum game-theoretical model with incomplete information for appropriate allocation of defense resources based on the availability of limited resources. Task time delay is applied to quantify the expected utility as CPPSs have high time requirements and incur massive damage DDoS attacks. Different resource allocation strategies are adopted by attackers and defenders under the three cases of attack-free, failed attack, and successful attack, which lead to a corresponding consumption of resources. A multidimensional node value analysis is designed to introduce physical and cybersecurity indices. Simulation experiments and numerical results demonstrate the effectiveness of the proposed model for the appropriate allocation of defense resources in CPPSs under limited resource availability.

Abstract:Multi-area combined economic/emission dispatch (MACEED) problems are generally studied using analytical functions. However, as the scale of power systems increases, existing solutions become time-consuming and may not meet operational constraints. To overcome excessive computational expense in high-dimensional MACEED problems, a novel data-driven surrogate-assisted method is proposed. First, a cosine-similarity-based deep belief network combined with a back-propagation (DBN+BP) neural network is utilized to replace cost and emission functions. Second, transfer learning is applied with a pretraining and fine-tuning method to improve DBN+BP regression surrogate models, thus realizing fast construction of surrogate models between different regional power systems. Third, a multi-objective antlion optimizer with a novel general single-dimension retention bi-objective optimization policy is proposed to execute MACEED optimization to obtain scheduling decisions. The proposed method not only ensures the convergence, uniformity, and extensibility of the Pareto front, but also greatly reduces the computational time. Finally, a 4-area 40-unit test system with different constraints is employed to demonstrate the effectiveness of the proposed method.

Abstract:Wind power prediction interval (WPPI) models in the literature have predominantly been developed for and tested on specific case studies. However, wind behavior and characteristics can vary significantly across regions. Thus, a prediction model that performs well in one case might underperform in another. To address this shortcoming, this paper proposes an ensemble WPPI framework that integrates multiple WPPI models with distinct characteristics to improve robustness. Another important and often overlooked factor is the role of probabilistic wind power prediction (WPP) in quantifying wind power uncertainty, which should be handled by operating reserve. Operating reserve in WPPI frameworks enhances the efficacy of WPP. In this regard, the proposed framework employs a novel bi-layer optimization approach that takes both WPPI quality and reserve requirements into account. Comprehensive analysis with different real-world datasets and various benchmark models validates the quality of the obtained WPPIs while resulting in more optimal reserve requirements.

Abstract: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.

Abstract: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.

Abstract: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.

Abstract: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.

Abstract: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 dual-side 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.

Abstract:The increasing integration of distributed household photovoltaics (PVs) and electric vehicles (EVs) may further aggravate voltage violations and unbalance of low-voltage distribution networks (LVDNs). DC distribution networks can increase the accommodation of PVs and EVs and mitigate mutilple power quality problems by the flexible power regulation capability of voltage source converters. This paper proposes schemes to establish hybrid AC/DC LVDNs considering the conversion of the existing three-phase four-wire low-voltage AC systems to DC operation. The characteristics and DC conversion constraints of typical LVDNs are analyzed. In addition, converter configurations for typical LVDNs are proposed based on the three-phase four-wire characteristics and quantitative analysis of various DC configurations. Moreover, an optimal planning method of hybrid AC/DC LVDNs is proposed, which is modeled as a bi-level programming model considering the annual investments and three-phase unbalance. Simulations are conducted to verify the effectiveness of the proposed optimal planning method. Simulation results show that the proposed optimal planning method can increase the integration of PVs while simultaneously reducing issues related to voltage violation and unbalance.

Abstract: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 worst-case 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.

Abstract: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 cybersecurity 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.

Abstract: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.

Abstract: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.

Abstract: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 downstream 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.

Abstract: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.

Abstract: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.

Abstract: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.

Abstract: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.

Abstract: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 frequency-constrained 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.

Abstract: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.

Abstract: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.

Abstract: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 diagram 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.

Abstract: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.