Abstract:To tackle emerging power system small-signal stability problems such as wideband oscillations induced by the large-scale integration of renewable energy and power electronics, it is crucial to review and compare existing small-signal stability analysis methods. On this basis, guidance can be provided on determining suitable analysis methods to solve relevant small-signal stability problems in power electronics-dominated power systems (PEDPSs). Various mature methods have been developed to analyze the small-signal stability of PEDPSs, including eigenvalue-based methods, Routh stability criterion, Nyquist/Bode plot based methods, passivity-based methods, positive-net-damping method, lumped impedance-based methods, bifurcation-based methods, etc. In this paper, the application conditions, advantages, and limitations of these criteria in identifying oscillation frequencies and stability margins are reviewed and compared to reveal and explain connections and discrepancies among them. Especially, efforts are devoted to mathematically proving the equivalence between these small-signal stability criteria. Finally, the performance of these criteria is demonstrated and compared in a 4-machine 2-area power system with a wind farm and an IEEE 39-bus power system with 3 wind farms.

Abstract:Renewable energy sources (RESs) are rapidly developing and their substitution for traditional power generation poses significant challenges to the frequency regulation in power systems. The load damping factor D characterizes the active power of load that changes with power system frequency, which is an important factor influencing the frequency response. However, the value of D is small, resulting in the limitation in frequency regulation of the power system. This paper proposes a parallel-type load damping factor controller to enhance load damping factor by utilizing static var generators (SVGs) in substations. Additionally, it discusses the configuration method for the relevant parameters of the controller, evaluates its frequency regulation capability, investigates the impact of large-scale application of the controller on static and dynamic loads, and conducts a comprehensive evaluation of the impact of the damping factor control process on the voltage stability of the main grid. The large-scale application of the proposed controller can significantly improve the frequency regulation capability, and almost have no influence on the working status of the load. It can also significantly improve the dynamic performance of system frequency. The proposed controller can provide technical support for the frequency regulation of new power systems with high proportion of RESs.

Abstract:In recent years, with increasing amounts of renewable energy sources connecting to power networks, sub-/super-synchronous oscillations (SSOs) have occurred more frequently. Due to the time-variant nature of SSO magnitudes and frequencies, as well as the mutual interferences among SSO modes with close frequencies, the accurate parameter estimation of SSO has become a particularly challenging topic. To solve this issue, this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision. First, by aiming at the sidelobe characteristics of the window function as evaluation criteria, a combined cosine function is optimized using a genetic algorithm (GA). Furthermore, the obtained window function is self-convolved to extend its excellent characteristics, which have better performance in reducing mutual interference from other SSO modes. Subsequently, a new form of interpolated all-phase fast Fourier transform (IpApFFT) using the optimized window function is proposed to estimate the parameters of SSO. This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience. The performance of the proposed method is demonstrated under various conditions, compared with other estimation methods. Simulation results validate the effectiveness and superiority of the proposed method.

Abstract:In recent years, with the growth of wind energy resources, the capability of wind farms to damp low-frequency oscillations (LFOs) has provided a notable advantage for the stability enhancement of the modern power grid. Meanwhile, owing to variations in the power system operating point (OP), the damping characteristics of LFOs may be affected adversely. In this respect, this paper presents a coordinated robust proportional-integral-derivative (PID) based damping control approach for permanent magnet synchronous generators (PMSGs) to effectively stabilize LFOs, while considering power system operational uncertainties in the form of a polytopic model constructed by linearizing the power system under a given set of OPs. The proposed approach works by modulating the DC-link voltage control loop of the grid-side converter (GSC) via a supplementary PID controller, which is synthesized by transforming the design problem into H-infinity static output feedback (SOF) control methodology. The solution of H-infinity SOF control problem involves satisfying linear matrix inequality (LMI) constraints based on the parameter-dependent Lyapunov function to ensure asymptotic stability such that the minimal H-infinity performance objective is simultaneously accomplished for the entire polytope. The coordinated damping controllers for the multiple wind farms are then designed sequentially by using the proposed approach. Eigenvalue analysis confirms the improved damping characteristics of the closed-loop system for several representative OPs. Afterward, the simulation results, including the performance comparison with existing approaches, validate the higher robustness of the proposed approach for a wide range of operating scenarios.

Abstract:In the existing small-signal stability constrained optimal power flow (SSSC-OPF) algorithms, only the rightmost eigenvalue or eigenvalues that do not satisfy a given threshold, e.g., damping ratio threshold and real-part threshold of eigenvalue, are considered in the small-signal stability constraints. The effect of steady-state, i.e., operating point, changes on eigenvalues is not fully taken into account. In this paper, the small-signal stability constraint that can fully reflect the eigenvalue change and system dynamic performance requirement is formed by analyzing the eigenvalue distribution on the complex plane. The small-signal stability constraint is embedded into the standard optimal power flow model for generation rescheduling. The simultaneous solution formula of the SSSC-OPF is established and solved by the quasi-Newton approach, while penalty factors corresponding to the eigenvalue constraints are determined by the stabilization degree of constrained eigenvalues. To improve the computation speed, a hybrid algorithm for eigenvalue computation in the optimization process is proposed, which includes variable selection for eigenvalue estimation and strategy selection for eigenvalue computation. The effectiveness of the proposed algorithm is tested and validated on the New England 10-machine 39-bus system and a modified practical 68-machine 2395-bus system.

Abstract:Continuous power supply of urban power networks (UPNs) is quite essential for the public security of a city because the UPN acts as the basis for other infrastructure networks. In recent years, UPN is threatened by extreme weather events. An accurate modeling of load loss risk under extreme weather is quite essential for the preventive action of UPN. Considering the forecast intensity of a typhoon disaster, this paper proposes analytical modeling of disaster-induced load loss for preventive allocation of mobile power sources (MPSs) in UPNs. First, based on the topological structure and fragility model of overhead lines and substations, we establish an analytical load loss model of multi-voltage-level UPN to quantify the spatial distribution of disaster-induced load loss at the substation level. Second, according to the projected load loss distribution, a preventive allocation method of MPS is proposed, which makes the best use of MPS and dispatches the limited power supply to most vulnerable areas in the UPN. Finally, the proposed method is validated by the case study of a practical UPN in China.

Abstract:Battery energy storage stations (BESSs) pose several challenges for both phasor-based differential protection and the newly-proposed time-domain differential protection. These challenges include low sensitivity and even rejection. Besides, the negative impact of various nonideal conditions, including current transformer (CT) saturation, errors, and outliers, on the security of differential protection remains an important problem. Motivated by the aforementioned issues, this study accounts for the trajectory distribution discrepancy on Cartesian plane under various conditions and proposes a time-domain differential protection method. In this paper, the trajectory formed by operating and restraining current samples is developed. Subsequently, after considering different operating states, the fault severity levels, and nonideal conditions, the variances in trajectory distribution between internal and external faults are extensively analyzed. On this basis, the Cartesian plane is divided into operating, uncertainty, and restraining zones. Further, the operating and restraining trajectory indices are meticulously designed and a protection criterion based on these indices is formed to accurately separate internal faults from other events, unaffected by CT saturation, errors, and outliers. The exceptional performance of the proposed protection method is extensively validated through PSCAD simulations and a hardware-in-the-loop testing platform. Regarding the dependability, sensitivity, and security, the proposed protection method outperforms three state-of-the-art differential protection methods.

Abstract:Since the scale and uncertainty of the power system have been rapidly increasing, the computation efficiency of constructing the security region boundary (SRB) has become a prominent problem. Based on the topological features of historical operation data, a sample generation method for SRB identification is proposed to generate evenly distributed samples, which cover dominant security modes. The boundary sample pair (BSP) composed of a secure sample and an unsecure sample is defined to describe the feature of SRB. The resolution, sampling, and span indices are designed to evaluate the coverage degree of existing BSPs on the SRB and generate samples closer to the SRB. Based on the feature of flat distribution of BSPs over the SRB, the principal component analysis (PCA) is adopted to calculate the tangent vectors and normal vectors of SRB. Then, the sample distribution can be expanded along the tangent vector and corrected along the normal vector to cover different security modes. Finally, a sample set is randomly generated based on the IEEE standard example and another new sample set is generated by the proposed method. The results indicate that the new sample set is closer to the SRB and covers different security modes with a small calculation time cost.

Abstract:Improving the restoration efficiency of a distribution system is essential to enhance the ability of power systems to deal with extreme events. The distribution system restoration (DSR) depends on the interaction among the electric network (EN), cyber network (CN), and traffic network (TN). However, the coordination of these three networks and co-dispatching of multiple recovery resources have been mostly neglected. This paper proposes a novel DSR framework, which is formulated as a mixed-integer linear programming (MILP) problem. The failures in cyber lines result in cyber blind areas, which restrict the normal operation of remote-controlled switches. To accelerate the recovery process, multiple recovery resources are utilized including electric maintenance crews (EMCs), cyber maintenance crews (CMCs), and emergency communication vehicles (ECVs). Specifically, CMCs and ECVs restore the cyber function of switches in cooperation, and EMCs repair damaged electric lines. The travel time of these three dispatchable resources is determined by TN. The effectiveness and superiority of the proposed framework are verified on the modified IEEE 33-node and 123-node test systems.

Abstract:An nonlinear model predictive controller (NMPC) is proposed in this paper for compensations of single line-to-ground (SLG) faults in resonant grounded power distribution networks (RGPDNs), which reduces the likelihood of power line bushfire due to electric faults. Residual current compensation (RCC) inverters with arc suppression coils (ASCs) in RGPDNs are controlled using the proposed NMPC to provide appropriate compensations during SLG faults. The proposed NMPC is incorporated with the estimation of ASC inductance, where the estimation is carried out based on voltage and current measurements from the neutral point of the distribution network. The compensation scheme is developed in the discrete time using the equivalent circuit of RGPDNs. The proposed NMPC for RCC inverters ensures that the desired current is injected into the neutral point during SLG faults, which is verified through both simulations and control hardware-in-the-loop (CHIL) validations. Comparative results are also presented against an integral sliding mode controller (ISMC) by demonstrating the capability of power line bushfire mitigation.

Abstract:Recently, we demonstrated the success of a time-synchronized state estimator using deep neural networks (DNNs) for real-time unobservable distribution systems. In this paper, we provide analytical bounds on the performance of the state estimator as a function of perturbations in the input measurements. It has already been shown that evaluating performance based only on the test dataset might not effectively indicate the ability of a trained DNN to handle input perturbations. As such, we analytically verify the robustness and trustworthiness of DNNs to input perturbations by treating them as mixed-integer linear programming (MILP) problems. The ability of batch normalization in addressing the scalability limitations of the MILP formulation is also highlighted. The framework is validated by performing time-synchronized distribution system state estimation for a modified IEEE 34-node system and a real-world large distribution system, both of which are incompletely observed by micro-phasor measurement units.

Abstract:This paper proposes a novel fault location method for overhead feeders, which is based on the direct load flow approach. The method is developed in the phase domain to effectively deal with unbalanced network conditions, while it can also handle distributed generation (DG) units of any type without requiring equivalent models. By utilizing the line series parameters and synchronized or unsynchronized voltage and current phasor measurements taken from the sources, the method reliably identifies the most probable faulty sections. With the aid of an index, the exact faulty section among the multiple candidates is determined. Extensive simulation studies for the IEEE 123-bus test feeder demonstrate that the proposed method accurately estimates the fault position under numerous short-circuit conditions with varying pre-fault system loading conditions, fault resistances, and measurement errors. The proposed method is promising for practical applications due to the limited number of required measurement devices as well as the short computation time.

Abstract:The main goal of distribution network (DN) expansion planning is essentially to achieve minimal investment constrained by specified reliability requirements. The reliability-constrained distribution network planning (RcDNP) problem can be cast as an instance of mixed-integer linear programming (MILP) which involves ultra-heavy computation burden especially for large-scale DNs. In this paper, we propose a parallel computing based solution method for the RcDNP problem. The RcDNP is decomposed into a backbone grid and several lateral grid problems with coordination. Then, a parallelizable augmented Lagrangian algorithm with acceleration method is developed to solve the coordination planning problems. The lateral grid problems are solved in parallel through coordinating with the backbone grid planning problem. Gauss-Seidel iteration is adopted on the subset of the convex hull of the feasible region constructed by decomposition. Under mild conditions, the optimality and convergence of the proposed method are proven. Numerical tests show that the proposed method can significantly reduce the solution time and make the RcDNP applicable for real-world problems.

Abstract:With the large-scale connection of 5G base stations (BSs) to the distribution networks (DNs), 5G BSs are utilized as flexible loads to participate in the peak load regulation, where the BSs can be divided into base station groups (BSGs) to realize inter-district energy transfer. A Stackelberg game-based optimization framework is proposed, where the distribution network operator (DNO) works as a leader with dynamic pricing for multi-BSGs; while BSGs serve as followers with the ability of demand response to adjust their charging and discharging strategies in temporal dimension and load migration strategy in spatial dimension. Subsequently, the presence and uniqueness of the Stackelberg equilibrium (SE) are provided. Moreover, differential evolution is adopted to reach the SE and the optimization problem in multi-BSGs is decomposed to solve the time-space coupling. Finally, through simulation of a practical system, the results show that the DNO operation profit is increased via cutting down the peak load and the operation costs for multi-BSGs are reduced, which reaches a win-win effect.

Abstract:With the rapid increase in the installed capacity of renewable energy in modern power systems, the stable operation of power systems with considerable power electronic equipment requires further investigation. In converter-based islanded microgrid (CIM) systems equipped with grid-following (GFL) and grid-forming (GFM) voltage-source converters (VSCs), it is challenging to maintain stability due to the mutual coupling effects between different VSCs and the loss of voltage and frequency support from the power system. In previous studies, quantitative transient stability analysis was primarily used to assess the active power loop of GFM-VSCs. However, frequency and voltage dynamics are found to be strongly coupled, which strongly affects the estimation result of stability boundary. In addition, the varying damping terms have not been fully captured. To bridge these gaps, this paper investigates the transient stability of CIM considering reactive power loop dynamics and varying damping. First, an accuracy-enhanced nonlinear model of the CIM is derived based on the effects of reactive power loop and post-disturbance frequency jump phenomena. Considering these effects will eliminates the risk of misjudgment. The reactive power loop dynamics make the model coefficients be no longer constant and thus vary with the power angle. To evaluate quantitatively the effects of reactive power loop and varying damping on the transient stability of CIM, an iterative criterion based on the equal area criterion theory is proposed. In addition, the effects of parameters on the stable boundary of power system are analyzed, and the dynamic interaction mechanisms are revealed. Simulation and experiment results verify the merits of the proposed method.

Abstract:The intermittency of renewable energy generation, variability of load demand, and stochasticity of market price bring about direct challenges to optimal energy management of microgrids. To cope with these different forms of operation uncertainties, an imitation learning based real-time decision-making solution for microgrid economic dispatch is proposed. In this solution, the optimal dispatch trajectories obtained by solving the optimal problem using historical deterministic operation patterns are demonstrated as the expert samples for imitation learning. To improve the generalization performance of imitation learning and the expressive ability of uncertain variables, a hybrid model combining the unsupervised and supervised learning is utilized. The denoising autoencoder based unsupervised learning model is adopted to enhance the feature extraction of operation patterns. Furthermore, the long short-term memory network based supervised learning model is used to efficiently characterize the mapping between the input space composed of the extracted operation patterns and system state variables and the output space composed of the optimal dispatch trajectories. The numerical simulation results demonstrate that under various operation uncertainties, the operation cost achieved by the proposed solution is close to the minimum theoretical value. Compared with the traditional model predictive control method and basic clone imitation learning method, the operation cost of the proposed solution is reduced by 6.3% and 2.8%, respectively, over a test period of three months.

Abstract:In an autonomous droop-based microgrid, the system voltage and frequency (VaF) are subject to deviations as load changes. Despite the existence of various control methods aimed at correcting system frequency deviations at the secondary control level without any communication network, the challenges associated with these methods and their abilities to simultaneously restore microgrid VaF have not been fully investigated. In this paper, a multi-input multi-output (MIMO) model reference adaptive controller (MRAC) is proposed to achieve VaF restoration while accurate power sharing among distributed generators (DGs) is maintained. The proposed MRAC, without any communication network, is designed based on two methods: droop-based and inertia-based methods. For the microgrid, the suggested design procedure is started by defining a model reference in which the control objectives, such as the desired settling time, the maximum tolerable overshoot, and steady-state error, are considered. Then, a feedback-feedforward controller is established, of which the gains are adaptively tuned by some rules derived from the Lyapunov stability theory. Through some simulations in MATLAB/SimPowerSystem Toolbox, the proposed MRAC demonstrates satisfactory performance.

Abstract:The unbalanced state of charge (SOC) of distributed energy storage systems (DESSs) in autonomous DC microgrid causes energy storage units (ESUs) to terminate operation due to overcharge or overdischarge, which severely affects the power quality. In this paper, a fuzzy droop control for SOC balance and stability analysis of DC microgrid with DESSs is proposed to achieve SOC balance in ESUs while maintaining a stable DC bus voltage. First, the charge and discharge modes of ESUs are determined based on the power supply requirements of the DC microgrid. One-dimensional fuzzy logic is then applied to establish the relationship between SOC and the droop coefficient R_d in the aforementioned two modes. In addition, when integrated with voltage-current double closed-loop control, SOC balance in different ESUs is realized. To improve the balance speed and precision, an exponential acceleration factor is added to the input variable of the fuzzy controller. Finally, based on the average model of converter, the system-level stability of microgrid is analyzed. MATLAB/Simulink simulation results verify the effectiveness and rationality of the proposed method.

Abstract:Networked microgrids (NMGs) are critical in the accommodation of distributed renewable energy. However, the existing centralized state estimation (SE) cannot meet the demands of NMGs in distributed energy management. The current estimator is also not robust against bad data. This study introduces the concepts of relative error to construct an improved robust SE (IRSE) optimization model with mixed-integer nonlinear programming (MINLP) that overcomes the disadvantage of inaccurate results derived from different measurements when the same tolerance range is considered in the robust SE (RSE). To improve the computation efficiency of the IRSE optimization model, the number of binary variables is reduced based on the projection statistics and normalized residual methods, which effectively avoid the problem of slow convergence or divergence of the algorithm caused by too many integer variables. Finally, an embedded consensus alternating direction of multiplier method (ADMM) distribution algorithm based on outer approximation (OA) is proposed to solve the IRSE optimization model. This algorithm can accurately detect bad data and obtain SE results that communicate only the boundary coupling information with neighbors. Numerical tests show that the proposed algorithm effectively detects bad data, obtains more accurate SE results, and ensures the protection of private information in all microgrids.

Abstract:Adopting high penetration levels of electric vehicles (EVs) necessitates the implementation of appropriate charging management systems to mitigate their negative impacts on power distribution networks. Currently, most of the proposed EV charging management techniques rely on the availability of high-bandwidth communication links. Such techniques are far from realization due to ① the lack of utility-grade communication systems in many cases such as secondary (low-voltage) power distribution systems to which EVs are connected, rural areas, remote communities, and islands, and ② existing fears and concerns about the data privacy of EV users and cyber-physical security. For these cases, appropriate local control schemes are needed to ensure the adequate management of EV charging without violating the grid operation requirements. Accordingly, this paper introduces a new communication-less management strategy for EV charging in droop-controlled islanded microgrids. The proposed strategy is autonomous, as it is based on the measurement of system frequency and local bus voltages. The proposed strategy implements a social charging fairness policy during periods when the microgrid distributed generators (DGs) are in short supply by allocating more system capacity to the EVs with less charging in the past. Furthermore, a novel communication-less EV load shedding scheme is incorporated into the management strategy to provide relief to the microgrid during events of severe undervoltage or underfrequency occurrences due to factors such as high loading or DG outages. Numerical simulations demonstrate the superiority of the proposed strategy over the state-of-the-art controllers in modulating the EV charging demand to counteract microgrid instability.

Abstract:In recent years, the expansion of the power grid has led to a continuous increase in the number of consumers within the distribution network. However, due to the scarcity of historical data for these new consumers, it has become a complex challenge to accurately forecast their electricity demands through traditional forecasting methods. This paper proposes an innovative short-term residential load forecasting method that harnesses advanced clustering, deep learning, and transfer learning technologies to address this issue. To begin, this paper leverages the domain adversarial transfer network. It employs limited data as target domain data and more abundant data as source domain data, thus enabling the utilization of source domain insights for the forecasting task of the target domain. Moreover, a K-shape clustering method is proposed, which effectively identifies source domain data that align optimally with the target domain, and enhances the forecasting accuracy. Subsequently, a composite architecture is devised, amalgamating attention mechanism, long short-term memory network, and seq2seq network. This composite structure is integrated into the domain adversarial transfer network, bolstering the performance of feature extractor and refining the forecasting capabilities. An illustrative analysis is conducted using the residential load dataset of the Independent System Operator to validate the proposed method empirically. In the case study, the relative mean square error of the proposed method is within 30 MW, and the mean absolute percentage error is within 2%. A significant improvement in accuracy, compared with other comparative experimental results, underscores the reliability of the proposed method. The findings unequivocally demonstrate that the proposed method advocated in this paper yields superior forecasting results compared with prevailing mainstream forecasting methods.

Abstract:Electrical water heaters (EWHs) are important candidates to provide demand-response services. The traditional optimization method for EWHs focuses on the optimization of the electricity consumption, without considering the shifting potential of the water-use activities. This paper proposes an optimization method for EWHs considering the shifting potentials of both the electricity consumption and water-use activities. Considering that the water-use activities could be monolithically shifted, the shifting model of the water-use activities was developed. In addition to the thermodynamic model of the EWH, the optimal scheduling model of the EWH was developed and solved using mixed-integer linear programming. Case studies were performed on a single EWH and aggregate EWHs, demonstrating that the proposed method can shift the water-use activities and therefore increase the load-shifting potential of the EWHs.

Abstract:Demand response transactions between electric consumers, load aggregators, and the distribution network manager based on the “combination of price and incentive” are feasible and efficient. However, the incentive payment of demand response is quantified based on private information, which gives the electric consumers and load aggregators the possibility of defrauding illegitimate interests by declaring false information. This paper proposes a method based on Vickrey-Clark-Groves (VCG) theory to prevent electric consumers and load aggregators from taking illegitimate interests through deceptive declaration in the demand response transactions. Firstly, a demand response transaction framework with the price-and-incentive combined mode is established to illustrate the deceptive behavior in the demand response transaction. Then, the idea for eradicating deceptive declarations based on VCG theory is given, and a detailed VCG-based mathematical model is constructed following the demand response transaction framework. Further, the proofs of incentive compatibility, individual rationality, cost minimization, and budget balance of the proposed VCG-based method are given. Finally, a modified IEEE 33-node system and a modified IEEE 123-node system are used to illustrate and validate the proposed method.

Abstract:The accurate identification of smart meter (SM) fault types is crucial for enhancing the efficiency of operation and maintenance (O&M) and the reliability of power collection systems. However, the intelligent classification of SM fault types faces significant challenges owing to the complexity of features and the imbalance between fault categories. To address these issues, this study presents a fault diagnosis method for SM incorporating three distinct modules. The first module employs a combination of standardization, data imputation, and feature extraction to enhance the data quality, thereby facilitating improved training and learning by the classifiers. To enhance the classification performance, the data imputation method considers feature correlation measurement and sequential imputation, and the feature extractor utilizes the discriminative enhanced sparse autoencoder. To tackle the interclass imbalance of data with discrete and continuous features, the second module introduces an assisted classifier generative adversarial network, which includes a discrete feature generation module. Finally, a novel Stacking ensemble classifier for SM fault diagnosis is developed. In contrast to previous studies, we construct a two-layer heuristic optimization framework to address the synchronous dynamic optimization problem of the combinations and hyperparameters of the Stacking ensemble classifier, enabling better handling of complex classification tasks using SM data. The proposed fault diagnosis method for SM via two-layer stacking ensemble optimization and data augmentation is trained and validated using SM fault data collected from 2010 to 2018 in Zhejiang Province, China. Experimental results demonstrate the effectiveness of the proposed method in improving the accuracy of SM fault diagnosis, particularly for minority classes.

Abstract:The oscillation phenomena associated with the control of voltage source converters (VSCs) are concerning, making it crucial to locate the sources of such oscillations and suppress the oscillations. Therefore, this paper presents a location scheme based on the energy structure and nonlinearity detection. The energy structure, which conforms to the principle of the energy-based method and dissipativity theory, is developed to describe the transient energy flow for VSCs, based on which a defined characteristic quantity is implemented to narrow the scope for locating the sources of oscillations. Moreover, based on the self-sustained oscillation characteristics of VSCs, an index for nonlinearity detection is applied to locate the VSCs that produce the oscillation energy. The combination of the energy structure and nonlinearity detection distinguishes the contributions of different VSCs to the oscillation. The results of a case study implemented by the PSCAD/EMTDC simulation validate the proposed scheme.

Abstract:Previous studies have demonstrated that disharmony among voltage-source-controlled units (VSCUs) may occur on an alternating current (AC) transmission or distribution line under steady-state operating conditions (SSOCs) or quasi-static operating conditions (QSSOCs). As the studies on frequency disharmony have been expanded to multiple disharmonized VSCUs in the local power grid, its adverse effects on AC lines and equivalent load (EL) at the bus without active voltage control ability (non-active bus) need to be investigated further. Considering the locality of disharmony and common topological connections among VSCUs, this paper adopts a Y-type three-terminal local power grid (LPG) as the research object. The disharmony among the three VSCUs is discussed. Firstly, for the load at non-active bus, the formulas for single-phase instantaneous voltage, load current, load power, as well as average power under disharmony operating conditions (DOCs) are derived. The characteristic indicators of the above electrical quantities are defined, which can measure the amplification and reduction degrees of the above electrical quantities before and after disharmony. Secondly, for the line directly connected to VSCUs, the formulas for single-phase instantaneous line current and power and the average power under DOCs are derived. The characteristic indicators of power flow are defined, which can be used to quantify the peak amplification impact of oscillation before and after disharmony. Finally, the case study on the Y-type three-terminal LPG under the single-disharmony and the multi-disharmony switching scenarios indicates that the long-period power oscillation caused by disharmony may occur in the load flow at the non-active bus and the line flow. The oscillation causes a serious decrease in load capability and a significant amplification of the peak of line power oscillation.

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:Dynamic operating envelopes (DOEs), as a key enabler to facilitate distributed energy resource (DER) integration, have attracted increasing attention in the past years. However, uncertainties, which may come from load forecasting errors or inaccurate network parameters, have been rarely discussed in DOE calculation, leading to compromised quality of the hosting capacity allocation strategy. This letter studies how to calculate DOEs that are immune to such uncertainties based on a linearised unbalanced three-phase optimal power flow (UTOPF) model. With uncertain parameters constrained by norm balls, formulations for calculating robust DOEs (RDOEs) are presented along with discussions on their tractability. Two cases, including a 2-bus illustrative network and a representative Australian network, are tested to demonstrate the effectiveness and efficiency of the proposed approach.

Abstract:This study presents a harmonic transfer function (HTF) based single-input single-output (SISO) impedance modeling method. The method converts an HTF from phase domain to sequence domain and then transforms it into an SISO impedance while preserving the frequency coupling information of different sequences and different harmonics. Applications of this method to a line-commutated converter based high-voltage direct current (LCC-HVDC) system are presented. The results demonstrate the accuracy of the derived SISO impedance, and a truncation-order selection is suggested. The case study shows that the proposed method facilitates simpler impedance measurements and associated stability analysis.