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

Abstract:The oscillatory stability analysis of multi-converter-fed systems (MCFSs) with modest computational resources needs a precise parametric reduced-order impedance model (PROIM). However, the traditional Krylov subspace based parametric model order reduction (KS-PMOR) method has difficulty in building precise PROIM for MCFSs. This is because the factors related to the errors of PROIM are complicated and coupled. To fill this gap, the factors associated with the accuracy of the KS-PMOR method are estimated by defining three indicators: the convergence error, cumulative error, and rank of projection matrix. Using the three indicators, a frequency-domain adaptive parametric model order reduction (FDA-PMOR) method is developed to form the precise PROIM of MCFSs for the accurate and fast oscillatory stability analysis. The accuracy of the obtained PROIM using the proposed FDA-PMOR method and its efficiency in actual oscillatory stability analysis are validated by three MCFSs with different scales, i.e., a small-scale MCFS with four paralleled converter-based renewable energy generators (CREGs), a real-time simulation-based MCFS with eighteen paralleled CREGs, and a larger MCFS with ninety paralleled CREGs.

Abstract:Bulk power systems show increasingly significant frequency spatial distribution characteristics (FSDCs), leading to a huge difference in the frequency response between regions. Existing uniform-frequency models based on analytical methods are no longer applicable. This paper develops a reduced-order bus frequency response (BFR) model to preserve the FSDC and describe the frequency response of all buses. Its mathematical equation is proved to be isomorphic to the forced vibration of a mass-spring-damper system, and the closed-form solution (CFS) of the BFR model is derived by the modal analysis method and forced decoupling method in vibration mechanics. The correlation between its mathematical equation and the state equation for small-signal stability analysis is discussed, and related parameters in the CFS are defined by the eigen-analysis method without any additional devices or tools. Case studies show that the proposed reduced-order BFR model and its CFS can improve the solution accuracy while keeping the solution speed within milliseconds, which can preserve the significant FSDC of bulk power systems and represent a normalized mathematical description of distinct-frequency models.

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

Abstract:Short-term voltage stability (STVS) assessment is a critical monitoring technology in modern power systems. During daily operations, transmission lines may switch on or off due to scheduled maintenance or unexpected faults, which poses challenges to the STVS assessment under varying topology change conditions. To adapt the STVS assessment to the system topology changes, we propose a deep-learning-based STVS assessment model with the topology-adaptive voltage dynamic feature and the fine-tuning domain transfer for power systems with changing system topologies. The topology-adaptive voltage dynamic feature, extracted from streaming time-series data of phasor measurement units (PMUs), is used to characterize transient voltage stability. The voltage dynamic features depend on the balance of reactive power flow and system topology, effectively revealing both spatio-temporal patterns of post-disturbance system dynamics. The simulation results based on large disturbances in the New England 39-bus power system demonstrate that the proposed model achieves superior STVS assessment performance, with an accuracy of 99.65% in predicting voltage stability compared with the existing deep learning methods. The proposed model also performs well when applied to the larger IEEE 145-bus power system. The fine-tuning domain transfer of the proposed model adapts very well to system topology changes in power systems. It achieves an accuracy of 99.50% in predicting the STVS for the New England 39-bus power system with the transmission line alternation. Furthermore, the proposed model demonstrates strong robustness to noisy and missing data.

Abstract:Stray currents from DC metro systems intrude into the grounded neutrals of large power transformers, posing a major threat to the differential relay protection of transformer. In this paper, the performance of harmonic blocking based differential relay protection considering neutral stray currents (NSCs) from DC metro systems is thoroughly investigated. The findings reveal that relays may fail to clear internal faults in some scenarios because they are blocked due to NSC-induced harmonic currents. To improve the reliability of differential relay protection, a method for preventing incorrect operation is proposed using a skewness-based criterion to detect the presence of NSCs. Then, the relay is unblocked when an internal fault is simultaneously detected by the novel internal fault detection block. The proposed method is resistant to current transformer saturation and accounts for NSC fluctuations. Various time-domain simulations conducted in PSCAD/EMTDC verify the effectiveness of the proposed method.

Abstract:For providing a reliable power supply in an islanded AC microgrid, it is crucial to ensure that the operating states meet the safety constraints. However, conventional distributed secondary control methods often struggle to handle voltage and frequency constraints, limiting their practical applicability. To address these limitations, this paper proposes a novel prescribed performance control (PPC) based distributed secondary coordination method for islanded AC microgrids. The proposed method introduces a systematic framework that integrates bijective transformation with distributed secondary control. In this framework, the constrained distributed voltage and frequency control problems can be transformed into unconstrained ones, enabling strict adherence to predefined performance boundaries. Additionally, Lyapunov-Krasovskii functional analysis is employed in this paper to ensure asymptotic stability and calculate the stable boundaries in the transformed error space under time-delay conditions. The effectiveness of stability recovery and prescribed performance is tested in both MATLAB/Simulink and RTLab-based hardware-in-the-loop (HIL) experimental environments.

Abstract:The dynamics of diverse synchronization control, such as grid-following (GFL) and grid-forming (GFM) control, are complicating the oscillatory behaviors in multi-converter systems. In this context, the impedance network (IN) based frequency-domain modal analysis (FMA) method is useful for diagnosing oscillations. However, since the conventional impedance model retains only electric nodes, the FMA primarily reflects the circuit-related information, e.g., node participation factor, making it less intuitive for probing the synchronous dynamics. To address this issue, this paper proposes an augmented impedance network (AIN) modeling method by explicitly characterizing synchronous control loops for stability assessment. First, a four-port augmented impedance model (AIM) with an additional synchronization port is proposed for a generic AC/DC converter, and the corresponding AIN model of a generic AC/DC multi-converter system is formulated in a scalable approach. Then, the FMA method is generalized by simultaneously incorporating the electric nodes (including AC and DC nodes) and synchronous nodes. Finally, the AIN model and its associated FMA method are comprehensively validated in a typical point-to-point high-voltage direct current (HVDC) system and a modified IEEE 9-bus system, both with GFM and GFL converters.

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: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: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.

Abstract: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..

Abstract:This paper proposes an online framework to characterize demand response (DR) over time. The proposed framework facilitates obtaining and updating the daily consumption patterns of customers. The essential concept of response profile class (RPC) is introduced for characterization and complemented by the measure of the variability in customer behavior. This paper uses a modified version of the incremental clustering by fast search and find of density peaks (CFSFDP) algorithm for daily profiles, considering the multivariate normal kernel density estimator and incremental forms of the Davies-Bouldin (iDB) and Xie-Beni (iXB) validity indices. Case studies conducted using real-world and simulated daily profiles of residential and commercial Chilean end-users have demonstrated how the proposed framework can continuously characterize DR. The proposed framework is proven to achieve realistic customer models for effective energy management by estimating the customer response to price signals at the distribution system operator (DSO) level.

Abstract:Aiming at multi-agent coordinated scheduling problems in power systems under uncertainty, a generic projection and decomposition (P&D) approach is proposed in this letter. The canonical min-max-min two-stage robust optimization (TSRO) model with coupling constraints is equivalent to a concise robust optimization (RO) model in the version of mixed-integer linear programming (MILP) via feasible region projection. The decentralized decoupling of the non-convex MILP problem is realized through a dual decomposition algorithm, which ensures the fast convergence to a high-quality solution in the distributed optimization. Numerical tests verify the superior performance of the proposed P&D approach over the existing distributed TSRO method.

Abstract:In line commutated converter based high-voltage direct current (LCC-HVDC) transmission systems, the transformer saturation can induce harmonic instability, which poses a serious threat to the safe operation of the power system. However, the nonlinear characteristics of the power grids introduced by the transformer saturation considerably limit the application of the conventional analysis methods. To address the issue, this paper derives a linear model for the transformer saturation caused by the DC current due to the converter modulation. Afterwards, the nonlinear characteristics of power grids with the transformer saturation is described by a complex valued impedance matrix. Based on the derived impedance matrix, the system harmonic stability is analyzed and the mechanism of the transformer saturation induced harmonic instability is revealed. Finally, the sensitivity analysis is conducted to find the key factors that influence the system core saturation instability. The proposed impedance model is verified by the electromagnetic transient simulation, and the simulation results corroborate the effectiveness of the proposed impedance model.

Abstract:In practice, an equilibrium point of the power system is considered transiently secure if it can withstand a specified contingency by maintaining transient evolution of rotor angles and voltage magnitudes within set bounds. A novel sequential approach is proposed to obtain transiently stable equilibrium points through the preventive control of transient stability and transient voltage sag (TVS) problems caused by a severe disturbance. The proposed approach conducts a sequence of non-heuristic optimal active power re-dispatch of the generators to steer the system toward a transiently secure operating point by sequentially solving the transient-stability-constrained optimal power flow (TSC-OPF) problems. In the proposed approach, there are two sequential projection stages, with the first stage ensuring the rotor angle stability and the second stage removing TVS in voltage magnitudes. In both projection stages, the projection operation corresponds to the TSC-OPF, with its formulation directly derived by adding only two steady-state variable-based transient constraints to the conventional OPF problem. The effectiveness of this approach is numerically demonstrated in terms of its accuracy and computational performance by using the Western System Coordinated Council (WSCC) 3-machine 9-bus system and an equivalent model of the Mexican 46-machine 190-bus system.

Abstract:The power flow (PF) calculation for AC/DC hybrid systems based on voltage source converter (VSC) plays a crucial role in the operational analysis of the new energy system. The fast and flexible holomorphic embedding (FFHE) PF method, with its non-iterative format founded on complex analysis theory, exhibits superior numerical performance compared with traditional iterative methods. This paper aims to extend the FFHE method to the PF problem in the VSC-based AC/DC hybrid system. To form the AC/DC FFHE PF method, an AC/DC FFHE model with its solution scheme and a sequential AC/DC PF calculation framework are proposed. The AC/DC FFHE model is established with a more flexible form to incorporate multiple control strategies of VSC while preserving the constructive and deterministic properties of original FFHE to reliably obtain operable AC/DC solutions from various initializations. A solution scheme for the proposed model is provided with specific recursive solution processes and accelerated Padé approximant. To achieve the overall convergence of AC/DC PF, the AC/DC FFHE model is integrated into the sequential calculation framework with well-designed data exchange and control mode switching mechanisms. The proposed method demonstrates significant efficiency improvements, especially in handling scenarios involving control mode switching and multiple recalculations. In numerical tests, the superiority of the proposed method is confirmed through comparisons of accuracy and efficiency with existing methods, as well as the impact analyses of different initializations.

Abstract:Taking the advantage of Internet of Things (IoT) enabled measurements, this paper formulates the event detection problem as an information-plus-noise model, and detects events in power systems based on free probability theory (FPT). Using big data collected from phasor measurement units (PMUs), we construct the event detection matrix to reflect both spatial and temporal characteristics of power gird states. The event detection matrix is further described as an information matrix plus a noise matrix, and the essence of event detection is to extract event information from the event detection matrix. By associating the event detection problem with FPT, the empirical spectral distributions (ESDs) related moments of the sample covariance matrix of the information matrix is computed, to distinguish events from “noises”, including normal fluctuations, background noises, and measurement errors. Based on central limit theory (CLT), the alarm threshold is computed using measurements collected in normal states. Additionally, with the aid of sliding window, this paper builds an event detection architecture to reflect power grid state and detect events online. Case studies with simulated data from Anhui, China, and real PMU data from Guangdong, China, verify the effectiveness of the proposed method. Compared with other data-driven methods, the proposed method is more sensitive and has better adaptability to the normal fluctuations, background noises, and measurement errors in real PMU cases. In addition, it does not require large number of training samples as needed in the training-testing paradigm.

Abstract:With the rapid expansion of offshore wind farms (OWFs) in remote regions, the study of highly reliable electrical collector systems (ECSs) has become increasingly important. Post-fault network recovery is considered as an effective measure of reliability enhancement. In this paper, we propose a smart switch configuration that facilitates network recovery, making it well-suited for ECSs operating in harsh environments. To accommodate the increased complexity of ECSs, a novel reliability assessment (RA) method considering detailed switch configuration is devised. This method effectively identifies the minimum outage propagation areas and incorporates post-fault network recovery strategies. The optimal normal operating state and network reconfiguration strategies that maximize ECS reliability can be obtained after optimization. Case studies on real-life OWFs validate the effectiveness and superiority of the proposed RA method compared with the traditional sequential Monte-Carlo simulation method. Moreover, numerical tests demonstrate that the proposed switch configuration, in conjunction with proper topology and network recovery, achieves the highest benefits across a wide range of operating conditions.