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The paper introduces the concept of complex frequency. The imaginary part of the complex frequency is the variation with respect of a synchronous reference of the local bus frequency as commonly defined in power system studies. The real part is defined based on the variation of the voltage magnitude. The latter term is crucial for the correct interpretation and analysis of the variation of the frequency at each bus of the network. The paper also develops a set of differential equations that describe the link between complex powers and complex frequencies at network buses in transient conditions. No simplifications are assumed except for the usual approximations of the models utilized for the transient stability analysis of power systems. A variety of analytical and numerical examples show the applications and potentials of the proposed concept. [ABSTRACT FROM AUTHOR]

Aiming at the low-frequency oscillation (LFO) phenomenon in high-speed railways, this paper proposes a feedback linearized virtual inertia control (VIC) strategy of the traction converter based on a sliding mode observer (SMO) to improve the robustness of the system and suppress the occurrence of LFO. First, to optimize the total harmonic distortion of the traction grid-side current, the inner loop controller is designed as the feedback linearization control. Then, the voltage outer loop is designed as a combination of the VIC designed in this paper and SMO, which enhances the system inertia and reduces the impact of external interference on the system, while reducing the controller's demand for electrical power on the DC-side. Furthermore, a small-signal model is established to analyze the stability of the single-phase vehicle-grid system under the proposed control. The influence of the control parameters on stability is discussed in detail. Finally, the comparison of software simulation and hardware-in-the-loop experimental results between traditional PI control, feedback linearization control, feedback+SMO, feedback+VIC and the proposed control method shows that the proposed control has better dynamic and static characteristics, and can effectively inhibit the occurrence of LFO. [ABSTRACT FROM AUTHOR]

Power flow (PF) flexibility in the multi-terminal HVDC (MT-HVDC) grids is a thought-provoking issue. It leads to employing the active DC power flow controller (DC-PFC)s. Hence, this paper examines the static average model (AM) and power injection model (PIM) of an interline DC-PFC (IDC-PFC). It is to provide a suitable base for DC PF studies and easy embedding of the DC-PFCs into MT-HVDC grids’ PF equations. In this regard, this paper proposes a new DC PF solver (DC-PFS) for the IDC-PFC compensated MT-HVDC grids within the well-accepted Newton-Raphson (NR) framework. It requires a few modifications in the main structure of the system's Jacobin (J) matrix compared to the uncompensated MT-HVDC grid. Also, the system's admittance matrix and its symmetry are preserved. In the proposed concept, the IDC-PFC cooperates with other MT-HVDC grid's state variables to satisfy the predetermined control objective(s). Furthermore, this paper proposes a new solution procedure (SP) to handle various system's limitations during the processes of solving the DC PF problem. Meanwhile, there is no need to modify the related J matrix. The effective and accurate performance of the IDC-PFC's models, as well as presented NR-based DC-PFS and SP, are verified by performing several simulations on the 8-bus CIGRE MT-HVDC grid. [ABSTRACT FROM AUTHOR]

This paper presents a multi-stage series model predictive control (MS-MPC) for PMSM drives in order to further improve the control performance of MPC. Firstly, the basic principle of conventional MPC is introduced. Then, the multi-stage series MPC is proposed in this paper, in which the cost functions of different prediction instant are adopted to form series control structure. In this method, the current prediction trajectory of one voltage vector is extrapolated to multiple control periods, and the control performances of every voltage vector during multiple control periods are evaluated by multi-stage series cost functions. Additionally, the implementation process of the proposed method is described. Finally, the comparison experiments between the conventional MPC and the proposed method show that the proposed method can effectively reduce the switching frequency under the same control frequency. In addition, the improvement of current control performance can be achieved by the proposed method under the condition of the same switching frequency. [ABSTRACT FROM AUTHOR]

Due to the increasing penetration of distributed renewable energy generation systems, their participation in power system restoration is gaining a growing interest. For the black start of a system without synchronous generation, Wind Energy Conversion Systems (WECSs) must be able to control voltage and frequency. However, WECSs have been traditionally controlled as current sources. This paper proposes a decentralized control system for the black start of WECSs operating in parallel. In comparison with known methods for operation of distributed energy resources without synchronous generation, this paper specifically addresses the requirements of WECSs. Total wind power is regulated to match the demand during the black start process. This power is shared between WECSs according to the wind power available in each of wind turbine using a droop control characteristic between the voltage and active power. Using the so-called reactive power synchronization method, the WECSs can operate in synchronism even if wind power is significantly different in each wind turbine. Simulation results for a case study where two WECSs are connected in parallel are presented to validate the proposal. [ABSTRACT FROM AUTHOR]

Large scale renewable energy systems interfaced with voltage source converters (VSCs) experience several challenging issues when integrated to weak grids. One of the specific issue i.e. control loop interaction of vector-controlled VSC under high grid impedance leads to several instability mechanism ultimately resulting in unwanted tripping of the VSC unit. As a countermeasure, a unique nonlinear adaptive stabilizing control (NASC) technique has been proposed in this paper to enhance the dynamic stability of the VSC during such scenarios. A small-signal model is developed first to examine the instability mechanism of VSC connected to weak grids under abnormal operating conditions and varying set points of the power controller. The dominant modes are identified from the analysis and a stabilizing controller is developed based on adaptive dynamic surface control philosophy for enhancing its stability. The proposed controller has been proved to be uniformly ultimately bounded using Lyapunov analysis. Besides, the stabilizing mechanism of VSC is analyzed with the proposed controller by performing small-signal stability analysis of the entire system. The efficacy of the proposed control scheme is demonstrated by performing numerical simulations in MATLAB 2017a and conducting experimental validations in controller-hardware-in-the Loop (CHIL) platform. [ABSTRACT FROM AUTHOR]

DC grid has become an important application in power transmission. However, the exist works only have the method to obtain the droop coefficient in a radial topology. Also, this droop coefficient is for V-I droop control. There is no such like method to obtain the droop coefficient for the P-V droop control. This paper proposed a new method for a complex dc grid to obtain the droop coefficients. Firstly, based on the converter control strategies, the types of converter were classified. It will help to find out which kinds of converter can be participated into the dc-side voltage control. Secondly, a virtual node was defined, and the matrix of the dc grid was reshaped to fit the new added virtual node by using the proposed simplification method. An example was shown how this method worked. After that a new method of calculating the P-V droop coefficient was proposed. Finally, a simulation model was investigated to verify if the proposed method can operate in a real system. The results showed that the simplification method can ensure the mathematical relationships of the dc system. And simulations show good performances of the droop coefficient calculation method. [ABSTRACT FROM AUTHOR]

Accurate load modeling is critical for credible power system stability analysis. Because of the increasing complexity in modern system load, establishing a more comprehensive load model and performing accurate parameter estimation are the two biggest challenges in composite load modeling. In this paper, an induction motor with variable frequency drive (IM-VFD) together with the traditional ZIP+IM model is utilized to describe the dynamic characteristics of the system load. We estimate the time-varying probabilistic distributions of all states and parameters to describe their stochastic characteristics, thereby representing the real-time varying features of an actual load. The Fokker-Planck operator is applied to linearize the updated load model in tensor format. We then use tensor decomposition to reduce the computational and storage costs for calculating load model parameters. A sensitivity indicator is used to analyze the sensitivities of the estimated parameter distributions for subsequent model reduction. Simulations demonstrate that the updated load model has better performance than the traditional ZIP+IM model. [ABSTRACT FROM AUTHOR]

This paper deals with the high accurate current set-points solution for interior permanent-magnet synchronous motors (IPMSM) in wide-speed range applications. Considering voltage and current constraints, the operating regions can be divided into maximum torque per ampere, maximum current, field weakening, and maximum torque per voltage regions, which requires solving different nonlinear functions in real time to obtain optimal current set-points. Traditional methods including curve-fitting methods and polynomial approximation (PA) methods are not easy to obtain these solutions, especially involving magnetic saturation problems. In this paper, Newton–Raphson algorithm for improving the control accuracy of the current set-points is proposed. Meanwhile, parameters influence including magnetic saturation and resistive voltage drop is fully investigated. Compared with PA method, the proposed method is able to converge to accurate solutions in few numbers of iterations with reduced execution time, which can be easily implemented on an off-the-shelf digital signal processor. Both simulation results and experimental results on an 8-kW IPMSM rig are conducted showing good agreement with the expected results. [ABSTRACT FROM AUTHOR]

This paper is concerned with control-oriented modeling of a class of wireless power transfer systems with a phase-shift-controlled inverter. Two methods are investigated: the analytical modeling method, which is based on physical laws, and the refined instrumental variable method, which is based on sampled data. It shows that the former provides physical insights into the system, and that the resulting models will be accurate if the true circuit component parameters are a priori known. Otherwise, the model accuracy may decline. By contrast, the latter provides a cheap solution for accurate modeling, based only on a set of sampled input–output data, and the resulting model can capture very well the dynamic behavior of the system within a defined operating range. In real applications, it is always hard to know the actual circuit component parameters, since they may drift from the nominal values, due to some reasons such as the aging of circuit components and the variation of coil placement, making the analytical modeling method not very accurate. Therefore, to preserve the virtues of both methods, it is suggested to use them as a combination, that is, using the analytical modeling method to determine the model structure while using the data-driven modeling method to estimate the model parameters. All results derived in this paper are verified by means of both numerical simulation and experimental validation. [ABSTRACT FROM AUTHOR]

Solid state transformer (SST) integrated hybrid dc–ac microgrid (HMG) has wide operating capabilities in presence of dc–ac loads, renewable energy resources, and energy storage. This paper proposes control strategies for localized control of zonal hybrid microgrid, enabled by the SST and centralized energy storage devices (ESD) integrated using dual active bridge (DAB) converter. The control of DAB dc–dc converter is modified for zero circulating power flow (ZCPF) operation in both SST and ESD. Power management and coordination control used in this paper ensures the power supply reliability of the zonal HMG integrated through the SST. Microgrid system, along with its proposed controllers, provides a stabilized low-voltage dc and ac network ports, in both grid feeding and forming modes. The performance of the configured HMG system is evaluated under various power management scenarios using the MATLAB software platform. Further, the SST architecture, with its proposed controller, is tested on FPGA-based hardware platform. [ABSTRACT FROM AUTHOR]

In this paper, a current controller for a parallel operation of inverters is described. When inverters operate in parallel, it is a well-known fact that the inverter current is composed of the average current (AVC) and the zero-sequence circulating current (henceforth ZSCC), which inevitably flows between inverters under the parallel operation. Considering this, previous studies concentrated on reducing ZSCC. However, in this paper, it is found that the inverter current has another component, a differential current, in addition to the two components of AVC and ZSCC. Based on these three decomposed current components, three equivalent circuits are derived from n-paralleled inverters. To minimize the differential current and improve the regulation performance of the total output phase current, a decomposed current control scheme is proposed from equivalent circuit models. The proposed algorithm is applied to a system consisting of three paralleled two-level inverters with small shared inductance whose dc links are connected in common. Additionally, synchronous pulsewidth modulation is employed as the PWM method for each inverter. The proposed current controller is compared with two conventional current controllers, one where each inverter controls its own currents and the other where only AVC is controlled. Through experiments, it is shown that these conventional controllers have limitations and the proposed current controller overcomes these limitations. The effectiveness and feasibility of the proposed control scheme are verified through experimental results. Especially, both theoretical analysis and experiment results verify that the proposed method is robust with regard to parameter errors. [ABSTRACT FROM AUTHOR]

The distributed Volt/Var control solution is a promising one for active distribution networks (ADNs), but a critical issue is how to improve the distributed algorithm's convergence with less communication burden. In this paper, we propose a bi-level consensus alternation direction multiplier method-based fully distributed Volt/Var optimization algorithm (B-FADMM) for ADNs by exploiting inverter-based rapid control devices. In the first level, the Volt/Var optimal solution of subpartitions is obtained in parallel, and the second level completes the variable increment of each partition to correct the search direction of the first level. In the algorithm, firstly, an adaptive matrix $\omega $ initialization strategy is proposed to adapt to the different magnitude of variables, which avoids non-convergence or slow convergence of the algorithm. Secondly, the null-space method is used in the second level of the algorithm to obtain the null-space basis matrix on the active constraint of the subpartition, which reduces the dimensions of the problem and the computational complexity. In addition, the conjugate gradient (CG) algorithm is used to update the dual multiplier of each partition only by exchanging coupling information among partitions, which protects information privacy. Experiments showed the proposed approach attains the same result as the centralized, the computational performance of the proposed method is far superior to some popular other distributed methods in terms of accuracy, computational efficiency, and scalability. [ABSTRACT FROM AUTHOR]

This paper studies the communication time-delay issue in islanded microgrids (MGs) with the distributed secondary control architecture. Firstly, a time-delayed MG small-signal model is developed. Then, a new weight-average-prediction (WAP) controller is proposed to compensate the delayed system states. By introducing a time-delayed differential term in the proposed control law, the traditional time-delayed small-signal model is transformed into a neutral time-delayed mathematic model. Based on the developed model, the stability analysis is conducted considering both fixed time delay and time-varying delay. For the fixed time delay, a novel graphic analytical method is proposed to evaluate the time delay margin, which eliminates the conservatism compared with existing time-domain methods. For the time-varying delay, stability condition is established by a Lyapunov-Krasovskii function and linear matrix inequalities. In addition, some non-linear WAP control methods are discussed to guide the parameter tuning with a higher resolution. Lastly, the proposed method and analytical result are verified in the OPAL-RT real-time test platform. The results demonstrate the effectiveness and high performance of the proposed controller. [ABSTRACT FROM AUTHOR]

In order to realize the grid-friendly wind turbine system (WTS), applying of the virtual synchronous generator (VSG) control strategy to WTS has become a trend of research, and it is also required to analyze the grid-connected operation characteristics of the VSG controlled WTS. In this paper, the impedance modeling and impedance-based stability analysis of the VSG controlled type-IV WTS are carried out. Different from existing impedance modeling method that the WTS is modeled by a high dimensional impedance model with complex expressions, a model to describe the shaping effects of dc-link dynamics is proposed, and combined with the space vector diagram to analyze the system impedance characteristics. It is found that the impedance of the VSG controlled type-IV can be capacitive below the fundamental frequency, which is inherited from its GSC impedance and the capacitive characteristics has been weakened by the influence of dc-link dynamics. Instable risk has also been found between the VSG controlled type-IV WTS and the connected weak grid, and the instability can be avoided if the capacitive characteristics of the VSG controlled type-IV WTS are weakened by reshaping its GSC impedance or by enhancing the dc-link dynamics. Experiments are also carried out as verifications. [ABSTRACT FROM AUTHOR]

The penetration of photovoltaics (PVs) has been increasing in active distribution networks (ADN), which leads to severe voltage violation problems. PV inverters can provide fast and flexible reactive power support and are now allowed to participate in the voltage regulation process. This paper proposes a real-time combined central and local Volt/Var control (VVC) strategy to mitigate voltage violation problems while minimizing the network power loss. Based on the historical PV and load data, the load flow and optimal power flow are performed in the centralized controller (CC) to obtain multiple voltage and optimal power settings for each PV system. The local controller (LC) then generates voltage control curves with these optimal scatters. To improve the voltage control effect, a novel 3-Dimension voltage control curve is proposed considering both the measurements of node voltage and PV generation. Moreover, a data-driven deep convolution neural network is designed and trained to generate optimal local voltage control curves without prior knowledge of specific curve functions. The proposed approach is tested on the IEEE 33-bus distribution system and simulation results verify the effectiveness in voltage control compared with the optimal Q(V) and Q(P) method. [ABSTRACT FROM AUTHOR]

This paper presents a systematic investigation into the performance of a shielding wire on 10 kV overhead lines (OHLs) against indirect lightning, from the design point of view. The design parameters addressed include the grounding interval, grounding resistance, and position of the shielding wire. As a system outage is usually caused by insulator flashover at OHL poles under indirect lightning, the induced voltages there are investigated with the code developed from the Agrawal model. In the evaluation, the location of a lightning return stroke relative to a grounded or ungrounded pole is considered. It is found that the lightning channel positioned in the front of an ungrounded pole could completely wipe out the effect of the shielding wire. This occurs if the wave from the grounding point arrives later than the time to the peak of the voltage directly arising from the lightning return stroke. It is suggested providing the wire grounding at every pole even if the grounding resistance at some poles is much higher than the design value. Grounding spacing does not affect the induced voltages at the pole generally if the pole has been grounded. One critical parameter is identified, i.e., the distance between the shielding and outer phase wires. Minimizing the distance can effectively reduce the lightning-induced voltages. [ABSTRACT FROM AUTHOR]

The space charges around a HVDC transmission line may not only lead to electromagnetic environmental problems but also affect the occurrence of impulse corona and then the transient overvoltage propagation. This paper derives the equations governing the transient overvoltage propagation along a HVDC transmission line when there is either space charges surrounding the line or impulse corona. In contrast to conventional transmission line equations, the proposed equations adopted the dynamic capacitance C′ and conductance G to characterize the corona discharge in all cases, which can be obtained by a time-domain finite element method. A finite-difference time-domain method is introduced to solve the nonlinear transmission line equations. The validity of the proposed approach is verified by comparison with the lightning overvoltage waveforms measured in a literature. The transient overvoltage propagation along a long UHVDC transmission line surrounded by space charges is analyzed. [ABSTRACT FROM AUTHOR]

The Virtual Power Plant (VPP) has been proposed to aggregate Distributed Generations (DGs) to act like a single power plant, thus, also has functions on the frequency and voltage support. The previous models of the VPP are static and focus on the energy trading and management. For the system transient response analysis, a dynamic VPP model must be needed. The paper proposes a reduced-order yet accurate aggregated model to represent VPP transients for the stability analysis of power systems. The goal is to provide a model that is adequate for system studies and can serve to the Transmission System Operator (TSO) to evaluate the impact of VPPs on the overall grid. The proposed model can accommodate the transient response of the most relevant controllers included in the distributed generators that compose the VPP. Using a comparison with a real-time detailed Electro-Magnetic Transients (EMT) models of the VPP confirms the validity of the proposed aggregated model. The case studies based on the IEEE 39-bus system verifies the accuracy of the proposed aggregated model on the system stability analysis. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a distributed secondary voltage and frequency control scheme for an islanded ac microgrid under event-triggered communication. An integral type event-triggered mechanism is proposed by which each distributed generator (DG) periodically checks its triggering condition and determines whether to update its control inputs and broadcast its states to neighboring DGs. In contrast to existing event-triggered strategies on secondary control of microgrids, the proposed event-triggered mechanism is able to handle the consensus problem in case of asynchronous communication. Under the proposed sampled-data based event-triggered mechanism, DGs do not need to be synchronized to a common clock and each individual DG checks its triggering condition periodically, relying on its own clock. Furthermore, the proposed method efficiently reduces communication rate. We provide sufficient conditions under which microgrid's frequency and a critical bus voltage asymptotically converge to the nominal frequency and voltage, respectively. Finally, effectiveness of our proposed method is verified by testing different scenarios on an islanded ac microgrid benchmark in the MATLAB/Simulink environment as well as a hardware-in-the-loop (HIL) platform, where the physical system is modeled in the Opal-RT and the cyber system is realized in Raspberry Pis. [ABSTRACT FROM AUTHOR]

Droop control is the most common approach for controlling inverter-based micro-grids. The active power droop gain has always been considered as the main parameter for identifying the micro-grid stability margin. Increasing this margin improves the transient performance and provides robustness to the micro-grid for a wide range of operations. Previous work on droop control focused on the active power droop gain, which is required for accurate power sharing as well as for micro-grid stability assessment. This paper utilizes small-signal stability analysis to analyze the impact of the reactive power droop gain on micro-grid stability, which is ignored in previous work. Consequently, a micro-grid domain of stability chart is proposed and defined in the mpmax-nq plane, which represents the zone within which the micro-grid will maintain stable operation. The proposed domain of stability chart is utilized to assess and compare the impact of the conventional and proportional derivative (PD) reactive power droop controller on the micro-grid stability margin. The results show that there exists a reactive power droop gain at which the stability margin is minimum. Furthermore, it has been shown, through the domain of stability chart, that the PD reactive power droop controller is capable and sufficient to significantly increase the micro-grid stability margin while maintaining equal load sharing. Further, the domain of stability chart can serve as a useful tool for defining the micro-grid droop gain operational boundaries and for assessing and comparing inverter-based micro-grid control schemes. [ABSTRACT FROM AUTHOR]

In this paper, a virtual inertia and damping control (VIDC) strategy is proposed to enable bidirectional DC (bi-DC) converter to dampen the voltage oscillation, using the energy stored in energy storage system (ESS) to emulate the inertia of DC microgrid (DC-MG) without modifications of system hardware. Both inertia part and damping part are modelled in the VIDC regulator, by analogizing with DC machine. Droop control is introduced to achieve multi-parallel operation of ESS. Further, its small signal model is established and the dynamic characteristic of the DC bus voltage during power fluctuation is analyzed. A 2nd-order equivalent model is introduced to simplify the parameters design. By analyzing the control performance indices, the VIDC parameters are optimized. At last, based on the principle of equivalent machine, an inertia matching method of the multi-parallel bi-DC converters is proposed. The simulation results verify that ESS, by acting as a synthetic inertia, can improve the voltage dynamic characteristics and stability in islanded DC-MG. Compared with other control methods, it has better control effect. [ABSTRACT FROM AUTHOR]

With increasing penetration of solar PV, some distribution feeders are experiencing highly variable net-load flows and even reverse flows. To optimize distribution systems under such conditions, the scheduling of mechanical devices, such as OLTCs and capacitor banks, needs to take into account forecasted solar PV and actual grid conditions. However, these legacy switching assets are operated on a daily or hourly timescale, due to the wear and tear associated with mechanical switching, which makes them unsuitable for real-time control. Therefore, there is a natural timescale-separation between these slower mechanical assets and the responsive nature of inverter-based resources. In this paper, we present a network admissible convex formulation for holistically scheduling controllable grid assets to position voltage optimally against solar PV. An optimal hourly schedule is presented that utilizes mechanical resources to position the predicted voltages close to nominal values, while minimizing the use of inverter-based resources (i.e., DERs), making them available for control at a faster time-scale (after the uncertainty reveals itself). A convex, inner approximation of the OPF problem is adapted to a mixed-integer linear program that minimizes voltage deviations from nominal (i.e., maximizes voltage margins). The resulting OPF solution respects all the network constraints and is, hence, robust against modeling simplifications.Simulation based analysis on IEEE distribution feeders validates the approach. [ABSTRACT FROM AUTHOR]

As the output power of wind farm is fluctuating, it is one of the important ways to improve the schedule ability of wind power generation to predict the output power of wind farm. The operation mode of tracking planned output takes the planned value issued by the grid dispatching as the control basis of wind power generation. This operation mode is easy to control, which not only meets the needs of power grid dispatching, but also improves the reliability and controllability of new energy generation. This paper introduces the traditional PI control strategy of SMES and combines the advantages of SMES and the characteristics of application scenarios, and introduces sliding mode variable structure control into SMES. Through simulation and comparison of two different control modes, it is verified that SMES adopting sliding mode variable structure control have the advantages of fast response speed and strong robustness, which can make the wind farm output stable power according to the planned value. [ABSTRACT FROM AUTHOR]

For a hybrid ac/dc power system incorporating voltage source converter-based multi-terminal direct current (VSC-MTDC) grids, it is essential to solve the power flow problems efficiently for reliable operation. This paper presents an efficient ac/dc power flow algorithm considering the complementary constraints of VSC's reactive power limit and ac node voltage. It can be distinguished from the existing works in terms of both modeling and algorithm aspects. First, the VSC model is formulated, in which the interactions between the reactive power limit and the ac node voltage of VSC are viewed as complementary relations. The complementary relations are expressed using a smooth Fischer-Burmeister function. Then, power flow models of the ac grid and dc grid with a constant Jacobian matrix are formulated based on the VSC model, respectively. To efficiently solve the power flow of an ac/dc grid, the structure characteristic of the Jacobian matrix of ac/dc power flow computation is analyzed. It shows that the Jacobian matrix can be approximated as a block-upper triangular one. Based on this characteristic, a decoupled ac/dc power flow computation algorithm is provided. Test results on two hybrid ac/dc systems under different scenarios validate the correctness, convergence, and efficiency of the proposed power flow algorithm. [ABSTRACT FROM AUTHOR]

This paper tackles key industry needs in the scope of the AC Security-Constrained Optimal Power Flow (SCOPF) framework, specifically two major challenging requirements regarding generators’ post-contingency behavior: the (droop-based) frequency response and the voltage control mechanism (including PV/PQ switching). To this end, and to obtain a sufficiently accurate solution with a reasonable computational burden, we propose an approximation approach to SCOPF which extends significantly an existing algorithm with novel modelling elements: a continuous formulation to model generators’ post-contingency responses based on successive approximations, a technique to evaluate the viability of contingencies with respect to the base case set-points, and the complexity reduction of all post-contingency states through network compression and power flow piecewise linearization. All new features are validated both separately and in unison, to monitor the improvement of the solution time and the potential degradation of the solution's quality. The proposed approach is successfully applied to three power system network models, the largest of which consists of 2,000 buses and more than 3,000 contingencies. Finally, the trade-off between the limitations in terms of solution quality and the benefits in terms of computational effort are assessed for all proposed approximations. [ABSTRACT FROM AUTHOR]

Load tap changers (LTCs) are commonly used for voltage control in distribution systems. The mechanical relays on LTCs are controlled in discrete steps; hence, distribution optimal power flow (DOPF) formulations require LTCs to be modeled with integer variables. Integer variables are generally ignored or relaxed and rounded off to reduce the computational burden in DOPF models. However, in this paper, we highlight and overcome complex infeasibility issues caused by rounding methods. Moreover, recent advances in convex optimization have improved the computational tractability of the DOPF problem. In this paper, we develop and analyze numerical efficiency of different but exact formulations for incorporating LTCs as integer control assets in a relaxed second-order cone program (SOCP) version of the DOPF model. The resulting formulation becomes a mixed-integer SOCP (MISOCP), which is computationally tractable compared to mixed-integer non-linear program (MINLP). To recover the exact optimal solution in the proposed MISOCP-DOPF model, a McCormick relaxation is employed within a sequential bound-tightening algorithm. We show that solutions obtained from MISOCP-DOPF are always ac feasible. Thus, the MISOCP-DOPF yields optimal and realistic ac solutions, and is validated in large distribution feeders and is compared to MINLP counterpart. [ABSTRACT FROM AUTHOR]

This paper presents a scalable method for improving the solutions of ac optimal power flow (AC OPF) with respect to deviations in predicted power injections from wind and other uncertain generation resources. The aim of this paper is on providing solutions that are more robust to short-term deviations, and that optimize both the initial operating point and a parametrized response policy for control during fluctuations. We formulate this as a chance-constrained optimization problem. To obtain a tractable representation of the chance constraints, we introduce a number of modeling assumptions and leverage recent theoretical results to reformulate the problem as a convex, second-order cone program, which is efficiently solvable even for large instances. Our experiments demonstrate that the proposed procedure improves the feasibility and cost performance of the OPF solution, while the additional computation time is on the same magnitude as a single deterministic AC OPF calculation. [ABSTRACT FROM AUTHOR]

Compared to the AC microgrids, the advantages of DC microgrids are notable. However, the development of DC microgrids is being constrained by the lack of mature protection schemes. For the foundation of designing protection schemes, the existing fault analysis focused on the fault characteristics of voltage source converters and ignored other generators. However, in DC microgrids with high permeability of photovoltaic (PV) powers, the effects of PV powers should be paid considerable attention. In this paper, the cable fault characteristics of the PV powers are analyzed in detail, and both the pole-to-ground fault and the pole-to-pole fault are considered. The fault processes are divided into several stages, and the fault circuits and main equations are described for each stage. All of the analyses are verified by the simulation model based on the PSCAD/EMTDC, and with the help of simulation results, the two main challenges the protection system confronted with are emphasized and the impacts of fault distance are analyzed. Finally, this paper proposes to employ a more reasonable converter structure and a transverse differential protection to overcome the main challenges; the effectiveness of the methods is verified by the simulation. [ABSTRACT FROM AUTHOR]

In this paper, the model predictive current control is introduced in the semicontrolled open-winding permanent magnet synchronous motor (OW-PMSM) generation system with a common dc bus to suppress the zero-sequence current for the first time. Particularly, the basic voltage vectors of the semicontrolled OW-PMSM, which are synthesized by the three-phase full-controlled converter and the three-phase uncontrollable diode bridge, is analyzed and their influences on the zero-sequence current are investigated for the first time in this paper. Then the current-error-based cost function that includes dq-axis current error and zero-sequence current error is designed to evaluate all the voltage vectors. Moreover, to further improve the steady-state control performance of the whole generation system, a zero-sequence current suppression method based on the uncontrollable side voltage vector adjustment, which has the advantage of low computation burden, is developed. In this method, two voltage vectors of the controllable converter are applied during one control period. Based on the distribution character of the basic voltage vector in the semicontrollable OW-PMSM generation system, the first voltage vector is selected according to the three-phase current direction to adjust equivalent vector of the uncontrollable diode bridge, whereas for the second voltage vector, the selection method based deadbeat voltage vector sector is designed to reduce the range of the candidate voltage vector. In addition, the vector durations are also computed. Finally, simulation and experiment are carried out to validate the proposed control approaches. [ABSTRACT FROM PUBLISHER]

This paper presents a direct voltage control method for interior permanent magnet synchronous motors (IPMSMs) with a single speed regulator. The method achieves maximum torque per ampere (MTPA) operation by controlling the magnitude and the angle of the voltage vector. For that, the mathematical model for the MTPA trajectory of the IPMSM is derived in the voltage plane. As such, no current sensor is needed, which makes the proposed strategy tolerant to current sensors failure unlike cascaded control loop based methodologies. Although no current sensor is used, the control strategy tracks MTPA trajectory by taking into account both voltage and current limits of the machine. The complete MTPA derivation in the voltage plane is presented in this paper; but, only the final solution is needed for real-time implementation. Henceforth, the simplicity of the control scheme combined with its current sensor dependence free characteristics make it a good candidate for real-time implementation in vehicular applications. The concept is developed and evaluated experimentally on a 10-HP IPMSM. [ABSTRACT FROM AUTHOR]

The three-phase dual active bridge (3p-DAB) converter is widely addressed in emerging power systems applications such as solid-state transformer and dc microgrids. Its successful integration requires accurate modeling of its small-signal characteristics. Due to its dc–ac–dc structure, the DAB converter brings many challenges to small-signal modeling. The state-space averaging (SSA) has been the first proposed methodology to approximate the control-to-output and line-to-output transfer functions of the 3p-DAB. However, as shown in this paper, SSA is not precise for the stability analysis of 3p-DAB converters. A generalized state-space averaging (GSSA) model based on the dynamic phasor concept is developed in this paper for the Y-Δ 3p-DAB. A hybrid SSA and GSSA model representation is then proposed for the evaluation of all the converter transfer functions. The developed models are validated with detailed time-domain switch-level simulations in an electromagnetic transient-type (EMT-type) program. They are also used for the accelerated stability prediction in an EMT-type program. [ABSTRACT FROM PUBLISHER]

Conventional finite control set-model predictive control (FCS-MPC) applies single voltage vector within each control period. This leads to relatively high steady-state ripples and requires fast sampling rate. Additionally, enumeration-based optimal vector selection is computationally intensive. Recently, double-vector-based schemes have been proposed to improve the steady-state performance of FCS-MPC. However, they are usually complicated in vector selection and duty ratio calculation. In this paper, a universal multiple-vector-based MPC (UMV-MPC) is proposed, which achieves the same performance as the state-of-the-art double-vector-based MPC, but executes in a much more efficient and universal way. Unlike conventional FCS-MPC, enumerating process and state predictions for candidate voltage vectors are not required in the proposed UMV-MPC to select the best voltage vectors. In UMV-MPC, the optimal vectors and duty ratios are directly constructed from deadbeat control (DBC) based on space vector modulation (SVM), which is easy to follow and quick to use. The proposed UMV-MPC is not only more efficient than prior methods, but also reveals the inherent relationship between double-vector-based MPC and DBC with SVM. A comparative study of UMV-MPC and prior double-vector-based MPC is carried out in this paper. The theoretical analysis as well as simulation and experimental tests on a 2.2-kW induction motor drive are demonstrated to validate the effectiveness of the proposed UMV-MPC. [ABSTRACT FROM AUTHOR]

In virtual synchronous generator (VSG)-related discussions, the inner voltage and current controls are always omitted due to their fast dynamics. However, converters require a lower switching frequency as their power rating increases, which constrains the cascaded controls’ bandwidths. Hence, the interactions between the controls at different time-scales should be analyzed. Specifically, the aim is to reveal the effects of inner control loops on the VSG system from the torque perspective. First, this paper derives a linearized model of the internal voltage phase and amplitude, which accurately depicts the VSG system characteristics. Subsequently, based on this linearized model, we derive an equivalent single-input single-output motion-equation- based model. The proposed model can be used to investigate the change in damping and synchronizing torque components under low control bandwidths and weak grid conditions. Finally, simulation results are presented to validate the proposed modeling and effects analysis. Our model is general and can be used for any power ratings, and the study also provides a guide to designing control parameters for VSG systems. [ABSTRACT FROM AUTHOR]

This paper introduces a new nonlinear voltage-mode controller for a PWM dc-dc buck converter operating in continuous conduction mode. The sliding-mode control technique is used to derive a simplified equivalent control law based on the averaged dc-dc buck converter dynamics. As opposed to the reported design approaches, the proposed control scheme only requires the output voltage in the feedback loop without the need to the capacitor current. Thus, the analogue implementation cost is reduced and the drawback of adding a capacitor current sensor to the power converter is eliminated. The control equation is realized in a simple analogue circuit using few op-amps and resistors, which is suitable for industrial applications. The system modeling and control design procedure along with the derivation of the existence and stability conditions are presented. The control system performance is analyzed using MATLAB and SaberRD simulations. Furthermore, a simple analogue prototype of the simplified nonlinear voltage-mode controlled dc-dc buck converter is developed on a PCB. The simulation and experimental results show that the controller maintains a constant switching frequency, exhibits fast transient response, and provides good tracking performance under large disturbances. [ABSTRACT FROM AUTHOR]

The steady-state performance of modular multilevel converter (MMC) can be optimized by the following methods: circulating current injection, third-harmonic signal injection, and average capacitor voltage control. However, most of the papers, due to the deficiencies of their MMC models, are limited to the study of adopting just one method and only optimizing a single-aspect of the performance. Thus, this article proposes a general MMC model for the comprehensive study of the steady-state performance optimization. The general model is built based on an equilibrium equation between the internal quantities and the external quantities of the MMC. This general model is capable of analyzing the optimization where the optimizing methods are combined and used to improve the multiaspect performance of the MMC. In addition, more influence factors are taken into account; hence, the calculation error can be smaller than 1% and even the minor effect of each optimizing method can be reflected. The proposed model is compared with traditional models; and it is found that both dc and fundamental components in modulation signals will be affected by the injected circulating current, rather than the constant values in the traditional models. Finally, the proposed MMC model is verified by both simulation and experiment. [ABSTRACT FROM AUTHOR]

This paper presents voltage regulation and current tracking control strategies for three phase two-level grid-connected power converters. By using power-invariant Park’s transformation, an averaged mathematical model of power converters is obtained in dq synchronous reference frame. Then a novel control strategy using adaptive control and ${H}_{\infty }$ technique is proposed to regulate the dc-link output voltage as well as track a desired current reference for three-phase power rectifiers. More specifically, an efficient adaptive controller is established in the external loop for regulating dc-link output voltage in the presence of external disturbances. A set of ${H}_{\infty }$ controllers are designed in the internal loop to force the input currents track their desired values. Finally, simulation results obtained from the proposed control method are presented, analyzed, and compared with that of sliding mode control, and the superiority of the proposed control laws is verified. [ABSTRACT FROM AUTHOR]

This paper presents an augmented design method for the dc/dc modular multilevel converter considering the control (e.g., the phase difference between arms ac voltages) and hardware aspects (e.g., type and number of submodules (SMs)) of the converter simultaneously. The proposed augmented design determines the number of SMs and their types (e.g., half- or full-bridge) in each arm and phase difference between arms ac voltages that minimize the total converter losses. Computationally-efficient analytical and semi-analytical methods are proposed to estimate the conduction and switching losses. To verify the effectiveness of the proposed method, the losses obtained from the proposed analytical and semi-analytical methods are compared with the results of the detailed converter switching model implemented in the Simulink environment. The performance of the converter designed by the augmented approach is compared with the conventional topology in terms of total losses and the number of SMs. The comparative study showed that the proposed design method yields a converter with lower total losses and number of SMs. Moreover, the proposed design method extends the operation regime of the converter, especially when the dc links voltage levels are close; this extension is not possible in the conventional modular dc/dc converter. [ABSTRACT FROM AUTHOR]

Different from voltage-source converter (VSC), reactive power absorption of line-commutated converters (LCCs) changes depending on DC voltage level. Therefore, the amount of AC voltage fluctuations at inverter side are different according to I – V droop constants in hybrid multi-terminal high-voltage direct current (MT-HVDC) system. This paper proposes a method for calculating the I – V droop constants in a hybrid MT-HVDC system to suppress these AC voltage fluctuations, based on the sensitivity of AC and DC networks. Simulations performed using PSCAD demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper discusses the implementation of a transient stability model of Compressed Air Energy Storage (CAES) systems in a power system analysis package. A block-diagram based model of a two-machine CAES system is proposed, including specific controls for active power, reactive power, and State of Charge (SoC), which consider limits associated with the cavern pressure. As an application, the model is implemented in Powertech's TSAT software connected to the 9-bus WSCC benchmark power system, which is then used to study the impact of a CAES facility in the transient and frequency stability of the system. Several contingencies are simulated comparing the CAES performance to a gas turbine and a base-case without storage, demonstrating that the CAES system improves the system transient stability due to its charging stage, controls, and additional inertia. Finally, the CAES model is used to study the effects of cavern sizes in the frequency of the system. It is shown that CAES systems have certain special characteristics that make them attractive as a storage technology to provide stability and regulation services, besides their energy arbitrage capabilities. [ABSTRACT FROM AUTHOR]

The existing three-phase imbalanced power flow calculation models for isolated micro-grid do not consider the non-smooth constraints such as voltage control limits and dead zone characteristics, which makes the power flow calculation results cannot meet the actual model constraints. In this paper, a more robust projected Levenberg-Marquardt (PLM) method is used to solve the problem after the non-smooth constraints are converted into smooth functions, which can reduce the model dependence on the initial values and solve the convergence problem caused by non-smooth constraints. The numerical experiments of micro-grid show that considering the non-smooth constraints can effectively improve the accuracy of power flow calculation. In addition, the PLM method has better convergence dealing with non-smooth constraints even poor initial value settings. [ABSTRACT FROM AUTHOR]

This paper presents the design, implementation, and performance testing of integral sliding mode control (ISMC) for a permanent magnet synchronous generator based wind turbine. More specifically, ISMC is combined with a feedback linearization (FBL) technique to recover its transient performance under model uncertainty and external disturbances. In this paper, we simplified the integral sliding surface structure to make it more convenient for real-time implementation. It turns out that the resulting integral sliding surface has a PI-like structure plus an additional part that has the role of preserving the nominal transient performance of the FBL. This key feature of the proposed PI-type sliding surface (PI-type SS) cannot be achieved under the conventional PI-type SS. Simulation and experimental tests are carried out to show the effectiveness of the proposed approach. The results revealed that the proposed PI-type SS is able to remove the steady-state error and retain the nominal transient performance of the FBL despite the presence of model uncertainty. [ABSTRACT FROM AUTHOR]

An analytical steady-state model of the modular multilevel converter (MMC) can be used for component sizing and assessment of the impact of different parameters on the MMC performance. Thus, this paper proposes an enhanced steady-state model for the MMC, which enables one to calculate the amplitudes of the harmonic components of MMC arm currents, submodule capacitor voltages, and arm voltages. In addition, the proposed model allows for the calculation of the amplitude and phase angle of the modulating signal, and it also presents a criterion for resonance of the arm currents. This is achieved by means of a polynomial function of the modulation index, and through checking the stability criteria established by the proposed model. The capability of formulating the modulating signal enables a more accurate calculation of the steady-state amplitudes of the variables, as compared to the previously published models. This paper also presents an accurate method of submodule capacitor sizing, based on the proposed steady-state model. The proposed method gives the exact value of the submodule capacitance (i.e., the capacitance that results in dc voltage fluctuations within a desired range) for a prespecified submodule capacitor voltage variation and a given circulating current amplitude. The stability criterion given by the proposed steady-state model, used for sizing the arm inductance, and the submodule capacitor voltage variation given by the proposed capacitor sizing method, used for sizing the submodule capacitor, allows for the determining of the operating limits of the MMC in terms of its parameters. Extensive simulation results are presented to demonstrate the efficacy of the proposed steady-state model and the capacitor sizing method. Further, the results obtained from the proposed capacitor sizing method are compared with experimental results from the literature. [ABSTRACT FROM AUTHOR]

This paper presents a single-stage nonisolated switched capacitor ac–dc converter for power-factor correction (PFC). This converter features reduced passive components, single switch, transformerless high voltage gain, and improves the power factor, reduces total harmonic distortion, and voltage stress across the switch. The peak current mode with a dynamic resonant perturbation scheme compensates the subharmonics that exist at zero crossing of the source current is implemented for PFC. In this paper, the principle of operation, large signal modeling of the circuit, and control method for the proposed PFC converter are provided. [ABSTRACT FROM PUBLISHER]

The neutral-point voltage-balancing control is a critical issue of a neutral-point-clamped converter. The conventional control strategy is to inject the specific zero-sequence voltage to regulate the redundant vector, but it is unacceptable to the three-phase four-wire system. This paper provides a neutral-point voltage-balancing control by the dipolar modulation, and the control freedom of the zero-sequence voltage is flexible. Therefore, the proposed method is suitable for both three-phase three-wire and three-phase four-wire systems. Besides, the proposed method improves the control dynamic in a reactive power system. The proposed neutral-point voltage-balancing control is verified by the mathematical analysis and experimental results. The control dynamic, power loss estimation, and the output current performance are analyzed in this paper. [ABSTRACT FROM PUBLISHER]

This paper proposes an optimized mathematical model of the voltage-source inverter parallel-operation system (VSIPS) and proposes an improved droop control method based on this model, which can realize accurate power sharing in VSIPS. First, this paper analyzes VSIPS as a multi-input and multioutput system and proposes a precise definition of circulating current. The circulating-current model, the steady-state model, and the small-signal model are proposed subsequently based on the optimum design of wire impedance, which constitute the optimized mathematical model of VSIPS in s-domain. The circulating-current phasor model and the circulating-current power phasor model (CCPPM) are also proposed. Second, the mathematical model of traditional droop control is built and analyzed based on CCPPM, which elaborates the tradeoff of droop control between the steady-state voltage bias and the load-sharing accuracy, and proves that the $V- Q$ droop control cannot realize accurate reactive-power sharing. Third, an improved droop control method ( $\omega - P_{{\text{cir}}}$ and $V- Q_{{\text{cir}}}$ control) is proposed, which can realize the accurate active- and reactive-power sharing and eliminate the steady-state voltage bias simultaneously. Finally, simulation and experimental results are presented, which validate the proposed mathematical model of VSIPS, the analysis of droop control, and the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents a methodology to perform small-signal analysis of an offshore ac network, which is formed by interconnecting several offshore wind power plants. The offshore ac network is connected with different onshore ac grids using point-to-point voltage-source-converter high-voltage direct current (VSC-HVDC) transmission links. In such a network, each offshore VSC-HVDC converter operates in grid-forming mode. In this paper, the offshore VSC grid-forming control is enhanced by using a frequency and voltage droop scheme in order to establish a coordinated grid control among the offshore converters. A small-signal model of the offshore ac network is developed that includes the high-voltage alternating current cables' model, the converters' current, and voltage-control model, the frequency droop scheme, and the voltage droop scheme. Based on this model, an eigenvalue analysis is performed in order to study the influence of the frequency and voltage droop gains on overall offshore ac network stability. Finally, theoretical analysis is validated by performing nonlinear dynamic simulation. [ABSTRACT FROM PUBLISHER]

This paper proposes a current sensorless control strategy for the dual active bridge (DAB) converter with nonlinear disturbance observer (NDO)-based load current feedforward. The proposed method can regulate both the dc-bus voltage and the current of the DAB converter without current sensors. Several performance indexes are established for the parameter design and a detailed design method is presented in this paper. When a single-phase H-bridge inverter is connected, the double-frequency oscillation from the feedback path is suppressed by proper parameter design, while the transient response of dc-bus voltage can be further improved by the NDO-based load current feedforward with a notch filter in the feedforward path. The performance of the proposed control method and the effectiveness of the parameter design are verified in a prototype by experimental results. [ABSTRACT FROM PUBLISHER]

Load modelling plays a key role in assessing peak load reduction and has attracted renewed interest recently due to increasing diversity and uncertainty in load characteristic resulted by emergence of new types of loads and more penetrations of distributed renewable generations onto electricity networks. This paper presents a methodology for the development of a static load model based load characteristic profile in medium voltage distribution networks from year-long field measurements. High-resolution load monitoring devices with the 1 s sampling rate installed at 60 primary substations in the U.K. distribution network are used to collect the data for the purpose of load modelling. Load models at these 60 substations comprising domestic, commercial/industrial, and mixed-type load demand are presented in the paper together with relevant model parameters. Field trials (which involve triggering transformer taps to initiate voltage changes) were performed throughout the year on 15 selected substations aimed at load profile validation. The developed load profiles take into account seasonal, weekly, and daily variations of P–V and Q–V characteristics. Representative 24 h (0.5 h) load matrices are developed for all 60 substations and provide an insight into the operational flexibility and network resilience to voltage variations. [ABSTRACT FROM AUTHOR]

This paper examines distribution systems that have a high integration level of distributed energy resources (DERs), and addresses the design of local control methods for real-time voltage regulation. Particularly, the paper focuses on proportional control strategies wherein the active and reactive power output of DERs are adjusted in response to (and proportionally to) local changes in voltage levels. The design of the voltage-active power and voltage-reactive power characteristics leverages suitable linear approximations of the ac power flow equations and is network-cognizant; that is, the coefficients of the controllers embed information on the location of the DERs and forecasted noncontrollable loads/injections and, consequently, on the effect of DERs power adjustments on the overall voltage profile. A robust approach is pursued to cope with uncertainty in the forecasted noncontrollable loads/power injections. The stability of the proposed local controllers is analytically assessed and numerically corroborated. [ABSTRACT FROM AUTHOR]