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Due to the high penetration of renewable energy resources in microgrids (MGs), the grid inertia becomes low which leads to the grid to be vulnerable to large disturbances. The energy storage devices can play an important role to enhance the inertia of MGs. However, due to the high investment cost of storages or their dp/dt limitation, the installed energy storages cannot cover the challenge of high df/dt. A prominent solution to solve the problem is to use the inertia response of the wind generators. However, relatively high second frequency nadir is the main drawback of using the inertia response of the wind generators which may impose an extensive disturbance to MGs. Accordingly, a coordinated operation strategy for MGs between wind generator and hybrid energy storage (HES) system is proposed in this paper. In addition, to improve the inertia response of the MG; providing high-quality communication infrastructures with low delay and increasing the Ultracapacitor capacity have been paid attention. In this paper, the costs of the installed Ultracapacitor and quality of communication services are defined as the operation cost. Guaranteeing enough frequency damping for the MG with low operation cost are two conflict objectives. Therefore, a multi-objective optimization method is used to set the controllers’ values and reduce the operation cost. The results confirmed that the effectiveness of the proposed strategy to control hybrid power storage in coordination with the wind generator and the frequency recovery process is improved. Also, employing the optimum values guaranteed the frequency damping effectively with low operation cost. The Integral Absolute Error (IAE) value and operation cost are reduced by 13.6% and 32%, respectively. Also, the simulation results show that the maximum MG frequency deviation and maximum df/dt is well compatible with different standards in the presence of load perturbations and different wind speeds.

In this paper, we propose a simple framework for closed-loop system identification: the stabilized output error method. Traditional closed-loop system identification methods rely on the linearity of the target system, and they require the identification of noise models or prior knowledge or identifiability of the feedback controllers to obtain unbiased estimates. But in many real-world applications, the noise dynamics and feedback controllers are complex and difficult to identify, and the nonlinearity may not be ignored. The proposed framework introduces a virtual controller that stabilizes the error between model prediction and the output of the target system. This enables us to apply the output error method, which gives unbiased estimates without depending on the noise model and is applicable to a wide range of models, including nonlinear systems, to closed-loop system identification problems. The paper describes the framework and gives the theoretical support and design guidelines for virtual controllers. Through numerical examples, we show the effectiveness of the proposed framework in various situations, which include identification of (a) linear gray box models, (b) systems in the presence of disturbances having realistic complexity, and (c) a nonlinear unstable system in a human-in-the-loop environment.

The increasing number of megawatt-scale photovoltaic (PV) power plants and other large inverter-based power stations that are being added to the power system are leading to changes in the way the power grid is operated. In response to these changes, new grid code requirements establish that inverter-based power stations should not only remain connected to the grid during faulty conditions but, also provide dynamic support. This feature is referred in the literature to as momentary cessation operation. The few published studies about momentary cessation operation for PV power plants have not shed much light on the impact of these systems on the overall power system stability problem. As an attempt to address this issue, this paper proposes a control scheme for PV inverters that improves the transient stability of a synchronous generator connected to the grid. It is shown through the paper that the proposed control scheme makes the PV inverter’s dc link capacitors absorb some of the kinetic energy stored in the synchronous machine during momentary cessation. Besides that, the proposed solution is also able to improve voltage stability through the injection of reactive power. Experimental and simulation results are presented in order to demonstrate the effectiveness of the proposed control scheme.

Due to the large overshoot and poor disturbance rejection impact the control accuracy of the permanent magnet synchronous motor (PMSM) in the proportional–integral–derivative (PID) control mode. In this paper, we propose an optimal double-loop pseudo-derivative feedback (PDF) control strategy. Firstly, to obtain high-precision feedback current and minimize the influence of sampling delay, a double-feedback PDF control structure is configured based on the $\Sigma $ – $\Delta $ sampling modulation and Sinc3 filter. Secondly, we adopt an instant-sampling and instant-update (ISIU) strategy based on a field-programmable gate array (FPGA), which can reduce the update delay of the pulse-width modulation (PWM), and design the hardware timing diagram, accordingly. Then, based on the influence of the closed-loop pole position on the dynamic performance of the system and the saturation characteristics of the power device, the PDF parameters tuning method of the current loop and speed loop is proposed. Finally, the system performance under different control strategies is compared and analyzed through simulations and experiments. The results show that the optimal double-loop PDF control strategy proposed in this paper can considerably expand the bandwidth of the current loop and has better disturbance rejection.

This paper presents a bio-inspired intelligent controller to enhance the performance of a nonlinear system. The controller is designed by capturing the emotional intelligence of mammalian brain mediated by the limbic system in which certain parts are responsible for generating emotions and these can be combined together as brain affective system inspired control architecture (BASIC). This controller has been used to cope with nonlinearities present in control applications. In this paper brain inspired control architecture is proposed while incorporating the sensory cortex explicitly in the architecture and the computational equations of various modules are suitably developed. The performance of the proposed controller is analyzed on a typical nonlinear system, namely, Permanent magnet synchronous motor for speed control, harmonics in stator phase currents and ripples produced in electromagnetic torque at different operating conditions. Its performance is compared with the existing control techniques in offline simulations as well as in real-time Hardware-in-loop environment. The results establish the computational efficiency, accuracy and robustness of the proposed controller.

Due to the lack of inertial support of the physical rotor of reliable power, the problem of weak inertia of the system is prominent when large-scale grid connection. Aiming at the weak inertia problem of new energy power systems, this paper takes the photovoltaic power generation system with generalized droop control as the research object. Firstly, the paper introduces the structure of the photovoltaic power generation system and the mathematical principle of generalized droop control At the same time, the electrical torque model of the system is established in order to reveal the inertia characteristics of the grid-tied inverter under the generalized droop control, moreover, the influencing factors of the system’s inertia characteristics and the influence rules of parameters are analyzed and studied. Finally, simulation analysis verifies the correctness of the analysis. The research results show that the photovoltaic inverter system under the generalized droop control has obvious inertia characteristics, the change of inertia size is affected by the dominant zero pole of the controller, and the equivalent inertia coefficient has frequency domain characteristics.

Circuit breaker (CB) and fault current limiter (FCL) are two major fault protection devices used in mesh-type DC microgrids. This paper proposes the parameters selection method to obtain a reliable and economic configuration scheme of CBs and FCLs applied in mesh-type DC microgrid. The breaking time of CB, the nominal breaking current of CB and the inductance of FCL are selected as three optimization parameters in an evaluation model. Since the reliability of fault protection scheme depends on whether the nominal breaking current of the CB is greater than the line current at the breaking moment of CB, it is necessary to accurately calculate the post-fault line current. Based on this, an accurate transient DC microgrid model is presented in this paper. And then, an improved non-dominated sorting genetic algorithm II (NSGA-II) is used to configure the parameters of CBs and FCLs quickly. Besides, a case study on six-terminal DC microgrid test system shows that the proposed method can obtain accurate post-fault line current and can achieve the parameters selection of CBs and FCLs.

In this paper, a finite control set model predictive direct power control (FCS-MPDPC) method based on satisfactory optimization, for single-phase three-level PWM rectifier, is proposed to achieve global optimization that takes into account all its objectives and constraints. Satisfaction optimization aims to obtain the satisfactory solution after coordination of multiple goals, instead of the optimal solution of a single goal. By replacing “optimal” with “satisfaction”, more control degrees of freedom are acquired, so that low-priority auxiliary control objectives can participate in the optimization process. Meanwhile, in order to enhance the description accuracy of FCS-MPDPC method for the future trend of PWM rectifier, the prediction time domain is extended from the traditional single-step to multi-step, and the average switching frequency model is established to realize the low switching frequency control. The satisfactory optimized FCS-MPDPC method proposed in this paper is compared, through simulation and experimental results, with the standard FCS-MPDPC method, which verifies the effectiveness and superiority of the proposed algorithm.

In this paper, a quaternion-based adaptive dynamic surface control method is proposed for attitude tracking control for small-scale unmanned helicopters with external disturbance and uncertain dynamics. The quaternion formalism is introduced and a quaternion-based multi-input-multi-output nonlinear model is derived from the attitude dynamics of a small-scale helicopter. The low-complexity controllers are designed by the dynamic surface control method as it eliminates the problem of the explosion of items. The singularity problem is avoided by substituting Euler kinematic equations in the nonlinear model with quaternion expressions and integrating the quaternion expressions into the design process of the dynamic surface control. For improving the robustness of the control system, the radial basis function networks are applied to approximate the uncertain dynamics. The external disturbance is also compensated in the controllers’ design. This paper proves that the proposed method can guarantee the uniformly ultimate boundness of this attitude system. Simulation results are presented finally and show the effectiveness of this control approach.

By the virtue of its highly nonlinear magnetic characteristics, the Switched Reluctance Machine (SRM) poses a formidable challenge for digital current regulators operating at a fixed switching frequency. Very fast tracking performance demanded by highly dynamic reference current profiles often surpass the conventional limits on closed-loop bandwidth posed by finite sampling frequency. The non-linear nature of matched disturbance to be compensated by the controller appearing in the form of induced emf grows in significance as a function of operating speed while the varying nature of inductance profile stipulates a need for gain adaptation by the control law in order to maintain consistency in closed-loop dynamic response. In the view of these unique SRM characteristics, the paper presents a detailed theoretical analysis of the widely implemented current control techniques from literature and provides illustrations in the context of their implementation in a digital controller. The analysis presented in this paper can also serve as a foundation for more advanced versions of these control techniques as well as their combinations.

Phase-locked loop (PLL) systems play a crucial role in grid synchronization. Since variations on the grid voltage parameters are in general uncertain, the dynamics of PLLs are by nature nonlinear. This fact imposes a relevant challenge to guarantee their stability. Unfortunately, as argued in this paper, there is a remarkable lack of global stability tests even for the most common approaches, such as the synchronous reference frame (SRF). In this case, there is only available a small-signal—linearized—model-based approach to stability. The main issue of resorting to local conclusions is that synchronization is forced to operate under conservative conditions, where large-signal variations are forbidden. Needless to say, this has a detrimental impact on applications, since performance is limited by small disturbance assumptions. Motivated by this problem, in the present work, we provide global asymptotic stability tests for two fundamental PLL algorithms. Namely, the conventional SRF-PLL and the enhanced SRF-EPLL. To do so, we use a Lyapunov approach acting directly on nonlinear trajectories. Consequently, the provided stability proofs do not rely on any linearization technique, frequency-domain conversion, or small-signal model representation. The main contribution in this paper is a set of stability conditions that are valid in a global sense. Moreover, it is shown that these results have direct practical implications in the form of new robust PLL gain tuning guidelines.

In this paper, a fault-tolerant control (FTC) method for robotic manipulators is proposed to deal with the lumped uncertainties and faults in case of lacking tachometer sensors in the system. First, the third-order sliding mode (TOSM) observer is performed to approximate system velocities and the lumped uncertainties and faults. This observer provides estimation information with high precision, low chattering phenomenon, and finite-time convergence. Then, an FTC method is proposed based on a non-singular fast terminal switching function and the TOSM observer. This combination provides robust features in dealing with the lumped uncertainties and faults, increases the control performance, reduces chattering phenomenon, and guarantees fast finite-time convergence. Especially, this paper considers both two periods of time, in which before and after the convergence process takes place. The stability and the finite-time convergence of the proposed controller-observer technique is demonstrated using the Lyapunov theory. Finally, to verify the effectiveness of the proposed controller-observer technique, computer simulation on a serial two-link robotic manipulator is performed.

There is a wide application prospect of Nearest level pulse width modulation (NL-PWM) in cascaded H-bridge (CHB) converter, however, it will produce narrow- and error-pulse in the process of implementation, which has a negative impact on CHB efficiency, output voltage quality and safe operation of power devices. In this paper, the NL-PWM strategy is improved based on round function to solve the narrow pulse of traditional NL-PWM, and a step wave delay update strategy is proposed to solve the error-pulse of NL-PWM. This paper analyzes the basic principle of improved NL-PWM and its ability to avoid narrow pulse of power device, shows the harmonic characteristics of improved NL-PWM, analyzes the generation mechanism of error pulse, and calculates the error of output voltage caused by the proposed step wave delay update strategy. The correctness of theoretical analysis and the effectiveness of the proposed method are verified by simulation and experiment. The research shows that the improved NL-PWM can effectively prevent narrow pulse while maintaining good harmonic characteristics, and the proposed step wave delay update strategy can avoid error pulse and has little impact on the output of NL-PWM.

Repetitive controllers (RCs) are known for their ability of controlling periodic exogenous signals, even if these signals have high harmonic content. Due to the variety of repetitive controllers proposed in the literature, which are significantly different from each other, a comparative evaluation in a collective way is analytically complex. This fact implies a greater difficulty to select the appropriate RC strategy when designing a control system, what makes most control system designers to not use this class of controllers. In order to solve this problem, the present paper develops a unified approach for representation of (real and complex) repetitive controllers, which is based on the use of multiple primitive repetitive cells in parallel. Through this approach the main characteristics of a repetitive controller, such as stability properties, dynamic response, set of harmonic components that are effectively compensated and computational burden, are easily identified. Furthermore, in order to validate the potential of the proposed unified approach, comparative studies of $nk \pm m$ RCs and $nk+m$ RCs are performed. An experimental application based on a three-phase shunt active power filter is implemented to validate the theoretical evaluation presented in this paper.

The conventional methods of observer poles placement in sensor fault detection usually adopt the trial-and-error methods. These methods cannot achieve global optimal performance because of their fixed poles placement and it leads to an observer with constant parameters, which could be reducing the system performance. Therefore, this paper proposes a fuzzy-based observer tuning method to optimize and adapt the selection of poles locations to determine the optimal gains of the observer, and it is experimentally applied to a composite sensor fault detection. Fuzzy logic is a promising method that could overcome the trial-and-error method challenges by introducing better adaptation and system robustness. The proposed observer structure includes adaptive tuning corresponding to an unknown input. Utilizing self-tuning for the observer correction stage, the gain is going to be updated online using the proposed fuzzy adaptive poles placement (FAPP) system. This paper validated the system simulation by implementing fault detection algorithms by using a real-time embedded observer-based system. The experimental results demonstrate the effectiveness of the proposed fuzzy-based observer schemes at detecting sensor faults in the Brushless DC (BLDC) motors, with significantly better performance than conventional counterparts’ methodologies. The experiments indicate that the average estimation error is 0.146, which less by 43.8% than was obtained for high levels of noise and disturbances compared with the traditional Luenberger observer approach.

By collecting the ripple current in the control coil, the self-sensing magnetic bearings can obtain rotor displacement information without a displacement sensor, which has the advantages of low cost and high integration. According to the problems of incomplete and inaccurate displacement information extraction caused by the traditional displacement estimation method using Fourier method to analyze the ripple current with non-stationary characteristics to estimate the rotor displacement with the Gibbs effect. Therefore, this paper proposes a rotor displacement estimation algorithm based on multiresolution filter bank biorthogonal spline wavelet for a magnetic bearing motor based on two-level switching power amplifier. This algorithm utilizes the biorthogonal spline wavelet with the characteristics of generalized linear phase and tight support, which can accurately demodulate the ripple current in the coil and extract the displacement information in the ripple current. Therefore, it is able to overcome the Gibbs effect in the traditional Fourier analysis estimation algorithm, to reduce the influence of ripple on rotor displacement estimation, and to improve the accuracy and stability of displacement estimation. In order to verify the correctness and effectiveness of the proposed algorithm, this paper establishes a simulation model of magnetic bearing in MATLAB Simulink and designs the proposed displacement estimator. Simulation results demonstrate that the proposed algorithm has higher accuracy and better stability than traditional displacement estimation algorithms. Experimental results show that the maximum deviation rate of the displacement estimation method proposed in this paper does not exceed 1% when the radial magnetic bearing gap is 0.5 mm, which can effectively estimate the rotor displacement.

Three-phase unbalance issue can cause adverse impacts on the power quality of the solid-state transformer (SST) based AC/DC hybrid microgrid. In this paper, an unbalanced power control strategy for cascaded dual active bridge (DAB) converter is proposed. With the strategy, the transmitted power of each DAB module in each phase is evenly distributed in terms of the three-phase unbalance degree of the three-phase AC grid. Thus, the idea of unequal power sharing in cascaded DAB can be applied to mitigate the three-phase unbalance from the perspective of power control. Moreover, this paper proposed a three-phase unbalance power mitigation algorithm based on the unbalanced power control strategy for the cascaded DAB. The proposed strategy can help the SST realize the function of mitigating three-phase unbalance when it transmits energy to the DC microgrid. Thus, the proposed control strategy can mitigate the three-phase unbalance on the premise that the power demand of the system is met. Finally, the simulations and the experiment results have verified the effectiveness and correctness of the proposed control method.

This paper addresses logarithmic vector quantizers with dynamic sensitivity design for stochastic continuous time linear system with a feedback control law. Logarithmic vector quantization is adopted so that the coarsest density of quantization and data compression efficiency are both guaranteed. In addition, the problem of quantizer saturation is treated with the mechanism of dynamic sensitivity. The dynamic of the sensitivity during “zoom-in” / “zoom-out” stages is proposed. It is shown that with the proposed algorithm, a single input continuous time linear system can be stabilized in the sense of mean square by quantized feedback control via adopting sensitivity varying algorithm. Results from theoretical analysis are verified through simulation at the end of the paper.

In this paper, an industrial grade adaptive control scheme is proposed for a micro-grid integrated dual active bridge driven battery management system (DIBMS). A benchmark industrial grade adaptive control scheme depends on two factors namely robustness and computational resource utilization when such controllers are implemented over processors. The mathematical model of DIBMS system is nonlinear, thus for desired response, non-linear controllers based on sliding mode variable structure control theory suits it well for the state regulation problem of DIBMS, however such controllers utilize high computational resources when practically implemented over processors. Keeping in view the above performance indices, this paper proposes an industrial grade computationally efficient and finite time adaptive robust convergent control for DIBMS system. A proportional integral (PI) scheme is used as central control unit and Hebbian algorithm with double integration of the state error is introduced for online tuning the gains of central control unit. The robustness and computational resource efficiency of the proposed control paradigm is validated using a laboratory scale test bench through TI Launchpad (TMS320F28379D). The superiority of the proposed AI based PI control paradigm is compared with classical PI, integer order sliding mode control (SMC), and fractional order SMC (FOSMC) in terms of computational resource utilization and robustness under all test conditions.

A fault tolerant control strategy for dual three-phase permanent magnet synchronous motor (DTP-PMSM) with 0° phase shifting between two windings is proposed in this paper. When a DTP-PMSM suffers from single- or two-phase open-circuit fault, to maintain the torque performance, current in faulty phase must be compensated by other healthy phases, which causes asymmetric self- and mutual inductances. Therefore, the 2nd harmonic component can be observed in the dq-axis currents and torque ripple also increases. To analyse this harmonic component in two types of faults, post-fault model of no-phase-shifting DTP-PMSM based on vector space decomposition (VSD) method is built in this paper. Then, proportion-integral-resonant (PIR) controller which can be used to suppress the specific periodic disturbance is applied to compensate the 2nd harmonic components. As the resonant controller is rarely dependent on motor parameters, phase and amplitude of current harmonic, the PIR controller can be applied in no-phase-shifting DTP-PMSM to suppress the harmonic caused by single- and two-phase open-circuit faults. The experimental results validate the effectiveness of the proposed fault tolerant control under single- and two-phase open-circuit faulty conditions.

Small-signal stability problems often occur when the inverter for renewable energy generation is connected to weak grid. A small-signal transfer function integrated model reflecting the interaction of grid impedance, phase locked-loop (PLL), and current control loop is established in this paper. Based on the established model, the oscillation mechanism of the grid-connected inverter system is revealed: the inductance current flowing through the grid impedance can produce a voltage disturbance, which will eventually affect the inductance current through PLL and current control loop. Therefore, the loop composed of the grid impedance and PLL can easily lead to the oscillation of the grid-connected inverter system under weak grid condition. To suppress the oscillation, a control parameters design method of the grid-connected inverter is proposed. Without changing the control method, the proposed control parameters design method can ensure the stable operation of the grid-connected inverter system under the very weak grid condition when the short-circuit ratio (SCR) is 2. Finally, the experimental results verify the correctness of the stability analysis and the effectiveness of the control parameters design method proposed in this paper.

This paper aims to reasonably demonstrate the role of the rotor-side converter (RSC) in subsynchronous oscillation (SSO) and investigates the influence and relationships of all control parameters. Thus, the equivalent circuit of a doubly fed induction generator (DFIG) that considers the RSC is imperative. First, the pertinent equivalent model of a DFIG with RSC control is established. Compared with previous works, this paper innovatively merges the RSC and induction generator with flux and voltage, obtains a complete analytical expression for the equivalent power supply and impedance containing all parameters of both the inner and outer loops of the RSC and then constructs a reasonable equivalent model. The action of the RSC is successfully demonstrated and reflects how the control loops and parameters of the RSC affect the circuit structures and properties of the equivalent model. Then, based on this proposed model, the influence mechanism of the RSC on the SSO of the grid-connected system is carefully analyzed.

A new three phase multilevel inverter with reduced number of components count is proposed in this paper. This inverter is designed using a single DC source per phase to generate multiple level output voltage which makes it suitable for low and medium voltage applications, including ac-coupled renewables or energy storages. A generalized circuit configuration is shown in this paper following which the number of output voltage level can be increased as per expectation. Although, each element endures the voltage stress equivalent to the input DC voltage, the value of total standing voltage (TSV) is reduced by the utilization of minimized number of components with respect to the number of series connected capacitors. Further, staircase modulation scheme is used to generate the switching signals. Hence, the proposed inverter can be operated at low switching frequency with optimal output current harmonic distortion which decreases switching losses and suppresses power factor falling. In order to validate the theoretical explanations and practical performances of the proposed inverter, the hypothesis is simulated for 9, 13 and 39 output voltage level inverters for three phase with a line voltage total harmonic distortion (THD) of 6.06%, 4.16% and 2.10% respectively in MATLAB/Simulink and a 5-level single phase laboratory prototype is implemented in the laboratory.

This paper proposes a high-precision permanent magnet (PM) motor primarily used for the satellite attitude control. Considering aerospace applications, the dynamic response, weight and torque ripple are primarily concerns. To achieve the fast response and low ripple, a stator with slotless windings is designed to achieve the ripple free torque production. However, slotless windings contain visible leakage fluxes which might decrease the torque production. In this paper, several design methods are proposed to decrease leakage fluxes by concentrating the flux linkage under slotless topology. First, leakage fluxes caused by slotless windings are minimized through the radial-flux dual-rotor topology. This topology results in the flux linkage concentration in the air gap because two rotors are used separately for flux transmitter and receiver. It is concluded that the dual-rotor is well suited for a slotless windings motor to maximize the air gap flux linkage. Second, Halbach array magnets are chosen to realize the sinusoidal flux linkage distribution. Different array angles are analyzed to minimize the torque ripple. It is shown that the 22.5deg array angle results in the lowest torque ripple among three different Halbach magnets. More importantly, the average torque output is higher comparing to conventional radial magnet magnetization. Although several optimization methods have been developed on the motor geometric design, very few researches focus on the design of dual-rotor slotless windings and air gap length. This design approach further decreases leakage fluxes. In this paper, finite element analysis (FEA) is used for the satellite motor design. In addition, a motor prototype is built for experimental tests.

The concept of virtual synchronous machine (VSM) was proposed to deal with the shortcomings of low inertia and damping of traditional control strategies for power electronic converters. But what if all distributed energy resources and controllable loads in a microgrid adopt the VSM control strategy, and will it present better performance than conventional droop control-based microgrid (DMG)? In this paper, the VSM-based microgrid (VSMG) is analyzed. The small-signal modeling of the VSMG is studied at first. Then static stability and dynamic characteristics of the VSMG are analyzed and compared with the DMG in both frequency-domain and time-domain. With the growing scale of microgrids, their modeling and simulation are becoming significant computational burdens. Inspired by the participation factor analysis of the VSMG and the concept of coherency in power systems, the VSMG small-signal model is equivalent to a modified third-order synchronous generator (SG) model in this paper. The equivalencing involves gray-box system identification and is realized by estimating equivalent electrical parameters alternately and iteratively. The equivalent SG (EqSG) model is compared with three representative model order reduction methods to verify its effectiveness. Simulation results confirm the accuracy of the EqSG model substituting detailed VSMG model in time-domain simulations.

It is well-known that continuous conduction mode (CCM) operation at certain frequency yields nearly load-independent voltage gain in practical series-series compensated inductive wireless power transfer links (SS-IWPTL). Such an operation is usually referred to as “load independent voltage output” (LIVO). Residual load dependence is due to the presence of non-zero equivalent series resistances in both transmitter and receiver. On the other hand, it has been shown that voltage gain remains load-dependent at the same operating frequency in discontinuous conduction mode (DCM) irrespectively of equivalent series resistances values. Consequently, the output voltage of SS-IWPTL operated at LIVO frequency resides within a range with lower bound corresponding to rated load and upper bound corresponding to zero loading for a given input voltage. The upper bound expression (typically attained in CCM) is derived using the first harmonic approximation (FHA) based equivalent circuit and is well-established by previous works. On the contrary, derivation of the lower bound (achieved in DCM) requires differential equation (DE) based analysis and was barely treated in the literature. The paper demonstrates that lumped capacitance of receiving side coil and input capacitance of receiving side rectifier must be taken into account during DE-based analysis since they impose significant receiving side voltage oscillations, which may give rise to safety issues. In order to damp these oscillations and keep the output DC voltage below a predetermined limit, minimal loading should be applied at the SS-IWPTL output, creating an RCD-snubber equivalent. Guidelines for the minimal load sizing are derived in the paper analytically. Simulations and experiments based on a 400V, 1kW SS-IWPTL operating at LIVO frequency demonstrate excellent matching, validating the proposed analysis.

With the rapid development of industrialization, the proportion of electric arc furnaces (EAF) in distribution networks is getting higher and higher. Aiming at the problem that grid voltage is distorted by a large number of arc furnace nonlinear loads accessing to distribution networks, it is crucial to make dynamic analysis of distribution network voltage and adopt a control strategy of grid-connected converter based on the new phase-locked loop (PLL) technology. As a result, the harmonic distortion rate is reduced and the quality of grid-connected current and voltage is improved. In this paper, photovoltaic (PV) system model and the typical dynamic model of the EAF are established. By analyzing the influence of the EAF model on the PV grid-connected converter with the traditional phase-locked loop while connected to distribution network, a control strategy of the PV grid-connected converter with the self-adjusting double SOGI (MAF-SASOGI) phase-locked loop with the ideal low-pass filter is proposed. Through the simulation analysis, it is verified that precise phase locked can be realized and harmonic content of the system can be reduced by the PLL strategy proposed in this paper. Therefore, the quality of PV grid-connected voltage and current is improved.

Wind energy is one of the premier renewable energy sources that have gained popularity during the last decade. Among the currently available wind energy conversion systems (WECS), doubly fed induction generator-based technology has been widely employed due to its superior advantageous. The key features of the DFIG-based WECS include its ability to capture more wind energy and support the grid with large reactive power during short disturbance events. On the other hand, DFIG is very sensitive to grid faults which affect its fault ride through (FRT) capability. Furthermore, extreme wind gust even for short durations may lead to the violation of the low voltage ride through (LVRT) threshold limits set by worldwide transmission line operators. This situation cannot be mitigated by the turbine blades pitch controller since the response of the pitch mechanical control is much slower than the rapid dynamic change in the wind speed during short duration of wind gust events. While DFIG FRT capability has been discussed in several papers in the literature, not much attention was given to the mitigation of the effects of extreme wind gust of short duration on the DFIG performance. In this paper, the effect of various levels of wind gust on the performance of a DFIG-based wind energy conversion grid-connected system is investigated and mitigated using a new controller for superconducting magnetic energy storage (SMES) unit. A combination of hysteresis current and fuzzy logic controllers is employed to control the voltage source converter and the DC-DC chopper interfacing the SMES coil with the investigated system. Simulation results reveal the effectiveness of the proposed SMES controller that can be easily implemented within existing as well as new WECS installations.

In this paper, a new method for reducing the ripples of torque and flux is proposed for the predictive torque control (PTC) of permanent magnet synchronous motors. The conventional PTC uses equations to analyze the relationship between the electrical torque and voltage with a fixed magnitude of reference voltage. Consequently, flux and torque ripples increase significantly at low-speed operation. This paper proposes an improved PTC algorithm using a simple duty-ratio regulator. The proposed method will minimize the torque error by calculating an appropriate torque minimization function to mitigate the induced torque and flux ripple at low speed operation. This torque minimization function is synthesized into the space vector pulse-width modulation block to reduce the torque ripple induced owing to the fixed time duration. The proposed scheme considerably reduces the torque and flux ripples and establishes a fast-dynamic response of the torque in the transient state. Simulation and experimental results show that the proposed method achieves a more efficient steady-state performance and a faster step response compared with the conventional PTC.

This paper proposes an improved PWM-OFF-PWM of the brushless DC motor under braking condition which can reduce commutation torque ripple. Compared with other brake modulation methods, PWM-OFF-PWM can restrain non-commutation torque ripple attributed to non-conductive freewheeling, while incapable of suppressing commutation torque ripple at low speeds effectively. Therefore, to solve commutation torque ripple caused by the turn-off time being shorter than turn-on time, an improved PWM-OFF-PWM is proposed in this paper. Moreover, to describe the influence factors of commutation torque ripple, the formulas of the duty cycle of switching tube in the commutation period and that during non-commutation period is derived. We can conclude from mathematical analysis that when duty cycles of outgoing and incoming phases satisfy derived formula, the non-commutation current in commutation interval will be more stable, which can contribute to suppress the commutation torque ripple at low speed under PWM-OFF-PWM mode and to improve the operation stability of BLDCM. The correctness and feasibility of the proposed method can be proved by simulation and experimental results.

This work is focused on a step-down switched-inductor hybrid dc-dc converter (SIHDC) integrated in a small power wind energy conversion system (WECS). The converter has two roles, to maintain the wind turbine at the maximum power point by controlling the electric generator loading, and to charge a high power density supercapacitor, which is part of a hybrid storage unit that also contains rechargeable batteries. The paper points out the steady-state analysis of the converter in continuous and discontinuous current modes, specific for this application. The stability investigation is presented in detail, including the influence of the electrical generator. The parameterized small-signal transfer function of the control variable derived in this paper can be used to quickly obtain the information needed to evaluate the stability of any similar WECS. A current controller was designed to achieve a stable operation in continuous current mode, and afterwards the stability was checked for discontinuous current mode. A 5kW step-down SIHDC prototype was built and extensively tested, both in laboratory, by using a wind turbine emulator, and in a small power (5kW) WECS industrial platform. Experimental results obtained under real operating conditions confirm the theoretical analysis and laboratory tests, showing that SIHDC converter is a valid solution for low power wind energy conversion systems.

One of the important tasks for increasing the efficiency of photovoltaic (PV) system is the development and improvement of the maximum power point tracking algorithms (MPPT). These MPPT algorithms lead to the ability to catch efficiently the global maximum power point of the partially shaded PV array. One of these trackers is the particle swarm optimization (PSO) algorithm which is one of the Soft computing techniques. The conventional PSO based trackers have many advantages such as the simplicity of hardware implementation and independence from the installed system. The actual problem of the practical application of PSO is the determination of its parameters to ensure high effectiveness of extracting the global MPP. Analysis of scientific papers devoted to the PSO algorithm has shown that there is currently no methodology for the optimal parameters' selection of PSO algorithm based maximum power trackers for the PV system. This paper aims to create a convenient and reasonable method for choosing the optimal parameters of the PSO algorithm, taking into account the topology and parameters of the DC-DC converter and the configuration of solar panels. A new method for selecting the parameters of a buck converter connected to a battery has been presented. The optimal value of the sampling time for the digital MPP controllers, providing their maximum performance; has been determined based on a new methodology. Matlab/Simulink software package is used as the main research tool. The prominent outcomes identify that the modified PSO and its designed parameters best meet the requirements of the MPPT controller for the PV system.

Speed control of permanent magnet synchronous motors (PMSMs) without position sensors is preferable in some applications due to cost and mounting space concerns. For applications in which the operating speed is relatively stable, the dynamic performance and efficiency demands of PMSMs are not severe during the startup process. Under such circumstances, a sensorless controller based on back electromotive force (EMF) estimation combined with a simple startup strategy is a suitable solution. In this paper, an I-f (current-frequency) startup method and a sliding mode observer are adopted to develop a sensorless control system, and the startup process which employs the I-f method is analysed in detail. Based on the analysis, this paper proposes a simple and robust startup strategy with an adaptive compensator to realize the smooth transition from I-f control to EMF-based control. The proposed strategy allows quick startup from standstill under different load conditions without initial position estimation. Furthermore, the strategy does not introduce any additional control coefficients, and none of the original control coefficients need to be adjusted. The strategy is suitable for both surface and interior PMSMs, and a test bench based on an interior PMSM is built to validate its properties. The experimental results show that the motor can smoothly accelerate from standstill to its rated speed in less than 2 s in both loaded and non-loaded situations, and the transition between the two sensorless control methods does not cause any large speed or current fluctuations.

This paper proposes a Resistance perturbation based maximum power point tracking (MPPT) with an adaptive control limit algorithm to extract the maximum power from solar photovoltaic (PV) array. This algorithm consists of two main functions, namely 1) resistance perturbation & observation (RP&O) and 2) adaptive resistance control (ARC) limit. The RP&O operates the PV array at maximum power point (MPP), and the ARC limit continuously monitors the resistance of the PV Rpv to determine the operating limit of MPP. The ultimate aim of proposing this algorithm is to reduce the oscillations and improve MPP's tracking performance for sudden variation in temperature and irradiance conditions. Furthermore, it does not require an expensive pyranometer or temperature sensor to track the MPP of the PV array. This paper also compares the proposed and conventional MPPT algorithm's performance. Its validation results in both MATLAB/Simulink and experimental studies are presented under constant and sudden changes in irradiance conditions.

This paper investigates linear active disturbance rejection control (ADRC) for processes with time delay. In the past years several modified active disturbance rejection control methods, including Smith predictor based ADRC (SP-ADRC), predictor observer based ADRC (PO-ADRC) and delayed designed ADRC (DD-ADRC) have been proposed to tackle systems with time delay. In this paper it is shown that these modified ADRCs can be interpreted in the framework of a two-degree-of-freedom (TDOF) internal model control (IMC), so the analysis and design can all be done via the well-known IMC framework. With the aid of the TDOF-IMC framework, the three modified ADRCs are compared and some interesting conclusions are drawn. Analysis and simulation results show that PO-ADRC structure is the best delay compensation structure among the three methods. However, the overall performance of the three methods will also depend on the tuned parameters, and the robustness measure is helpful in tuning the parameters to achieve compromise in performance.

The equivalent resistance of the battery will change during charging in practical applications, so it is difficult to design a wireless power transfer (WPT) system with accurate constant current (CC) and constant voltage (CV) output characteristics. In addition, the WPT system efficiency is also affected by the change of equivalent resistance. Therefore, this paper studies the charging control and efficiency optimization strategy for the WPT system with dynamic loads. The WPT system with a structure of double-sided LCC compensation topology and containing controllable rectifier circuit at the secondary side is established, and the working process of full-bridge controllable rectifier circuit is analyzed. Then the output characteristics of the WPT system are analyzed. The expressions of the optimal transmission efficiency and the optimal equivalent impedance of the full-bridge rectifier are derived. The relationships between the equivalent impedance of the capacitor-filtered full-bridge controllable rectifier circuit and the phase shift angle, the charging current and the phase shift angle are also obtained. In this paper, the CC and CV charging strategies based on phase shift control of controllable rectifier circuit and efficiency optimization strategy based on dynamic equivalent impedance matching are proposed, which can improve the WPT system transmission efficiency while realizing CC and CV charging. Finally, the effectiveness of the proposed control strategy is verified by simulation and experiment. The WPT system realizes CC charging mode and CV charging mode in turn when the load resistance changes from $5~\Omega $ to $30~\Omega $ , and the overall efficiency is up to 90.71% at the transmission distance of 15cm.

With the construction of periodic functions relative to the meshing frequency, rotating frequency, and the faulty frequency, etc., the phenomenological model provides a simple and effective way of representing the vibration signal of the planetary gearbox. However, due to that the meshing vibration is simplified, the traditional model can only reflect the modulation characteristic of the signal, but not the impact characteristic. Therefore, an improved phenomenological model is proposed, which can satisfy these two characteristics of the vibration signal at the same time. To consider the meshing vibration correctly, two key points should be determined: occurring moment of impact signals, and their relative amplitudes. In order to calculate the occurring time, this paper proposes modifying the reference point of the meshing phase and using the modified phases to represent it. Then two experiments are designed to verify the correctness of the modified phases and the occurring moment. Fortunately, these experimental results also provide a factual basis for determining the relative amplitudes of these impact signals. Subsequently, signal model of the gearbox in the healthy state is established based on the meshing vibration characteristics. The simulation results show that the new model can satisfy the modulation and impact characteristics. In addition, combined with the time-varying meshing stiffness of the gear pair, the paper theoretically analyzes the influence of fault type, location, and size on the impact frequency in a fault meshing period. Finally, the correctness of the new phenomenological model is verified by experiments.

In recent years, T-type three-level inverter (TLI) has attracted attentions due to its advantages, such as simple structure and higher efficiency. Neutral point voltage (NPV) is very critical for its normal operation, and the necessary conditions of maintaining NPV balance respectively in a switching cycle and in a fundamental cycle are simply reviewed in this paper. With the increment of power switches, the reliability of T-type TLI becomes particularly important. When switch faults occur, fault-tolerant control strategies are usually adopted. However, in existing literatures, it is unknown whether the NPV balance can be still maintained under different fault types. Therefore, the application range of a fault-tolerant control is also unknown. In this paper, based on the necessary conditions of maintaining NPV balance, the application ranges of two representative fault-tolerant control strategies are revealed under different open-circuit (OC) fault types in inner switch. It found that the application ranges are closely related to the modulation index, load power factor (PF) and OC fault type. Finally, the correctness of the theoretical analysis is verified by the experimental results.

In recent years, with the development of hyper-velocity weapon, the research focus of penetration effect has switched gradually from high-velocity to hyper-velocity, with insufficient studies on penetration effect and its internal mechanism. Besides, the study on penetration effect of hyper-velocity weapon depends on the measurement of mechanical signal during penetration of projectile. In this paper, dynamic test of hyper-velocity impact penetration acceleration signal is studied in depth. Firstly, the penetration velocity and acceleration of projectile under the impact load are analyzed, the influence of the movement of the testing unit on the measured acceleration signal is studied, and the factors to be considered when measuring the hyper-velocity impact load are given. Further, this paper designs a measurement circuit and dynamic models of each measurement module, details the influence of dynamic characteristics of power delivery network on test accuracy, and provides a method to obtain dynamic characteristics of power delivery network by virtue of S parameter. Finally, to extract the real penetration overload signal, a superior noise reduction algorithm adopting Modified Ensemble Empirical Mode Decomposition (MEEMD) is proposed, taking dynamic uncertainty and degree of approximation as evaluation indicators, and the measured sensor data is analyzed and processed with the proposed superior noise reduction algorithm. The experiment results show that, this method has a better noise reduction effect, and can be adopted to effectively extract real penetration overload signal. The results have theoretical research and application value to evaluate the reasonableness and effectiveness of measurement method of hyper-velocity penetration overload signal, and seek for a superior processing method for the noisy penetration overload signal.

This paper develops a high-performance finite control set model predictive current control (FCS-MPCC) method for induction motors (IM) to ensure the system control performance over the low-switching-frequency (LSF) range, where the switching loss is low. The new controller is based on tripartite calculations in each control period and sliding mode (SM) rotor-related inductance observer. In detail, firstly, to solve the problem that the control performance of the traditional FCS-MPCC methods is low when they are used at low frequencies, tripartite calculations are employed in each control period to improve the prediction accuracy. By dividing one control period into three equal parts and executing the prediction algorithm in each subsection, the current estimation errors become lower compared to the conventional single-step Euler-discretization controller. Then, considering that the performance of an FCS-MPCC controller highly relies on the machine parameter values, but it is hard to directly obtain the accurate rotor-related inductances (mutual inductance and rotor inductance), this paper uses an online parameter observer based on the sliding mode (SM) principle to diagnose them in real time. It needs to be mentioned that when discussing the stability of the sigmoid-function-based SM observer, a new technique called estimation-error-limitation is initially adopted in this paper to simplify the analysis process. Finally, the proposed algorithms are verified by simulation, which is conducted on a three-phase IM at LSF situations.

The pre-charging control scheme of the Modular Multilevel Converters is an important research subject. At the start-up of the MMC, all capacitors in each submodule of the MMC are required to be equally charged to a certain voltage value before transferring to the normal operation, otherwise a large inrush current may occur at the instant of the start-up threatening the safe operation of the IGBTs and the capacitors. Basically, to start-up an MMC, two phases need to be considered, Uncontrollable pre-charging phase and Controllable pre-charging phase, the Uncontrollable pre-charging phase, which is our main focus has been overlooked for a while. The conventional solution for limiting the huge inrush current during the aforementioned phase was using a limiting resistor and magnetic contactor arrangement as stated in plenty of papers for the last decade. In this paper, two new methods are introduced in order to pre-charge the capacitors, at the uncontrollable pre-charging phase to their nominal voltage without using the traditional solution. Detailed design algorithms of the proposed methods are introduced. Simulation results of the proposed methods are presented to show how employing these new methods would drastically limit the surge of the circulating current during the uncontrolled start-up phase.

Paralleled DC-DC converters system normally is operated with current-sharing control to achieve equal current distribution among the converters connected in parallel. However, the added current-sharing control might make the paralleled DC-DC converters system suffer from potential degradation of stability and dynamic performances. Hence, the stability analysis of paralleled DC-DC converters system is a hot issue. In order to analyze the stability of paralleled DC-DC converters system accurately and effectively, an extended stability analysis method based on Floquet theory is proposed for paralleled DC-DC converters system in this paper with considering the periodic disturbance. And, a paralleled buck converters system with average current-mode control is taken as an analysis object. The extended stability criterion of paralleled buck converters system based on Floquet theory is derived. Finally, the simulation and experimental results verify the correctness and effectiveness of the proposed stability criterion with considering the periodic disturbance. This paper provides a new choice for the stability analysis of paralleled DC-DC converters system.

This paper presents a method for evaluating the harmonic contributions of multiple harmonic sources to voltage distortion at the point of common coupling (PCC). The proposed method quantitatively represents harmonic contributions based on the equivalent voltage models of harmonic sources. The equivalent voltage models can be estimated using the recursive least square (RLS) algorithm and measured voltage and current at the PCC. The assessment of harmonic contribution heavily depends on the accuracy of equivalent model estimation. Many existing studies have assumed that the equivalent model parameters of harmonic sources are not changed. However, because harmonic source parameters and system operating conditions are not constant in real power systems, this assumption can lead large errors in harmonic contribution assessment. In this paper, we propose a new assessment method based on variable forgetting factor RLS and parameter change detection to solve the problem. The proposed method is also effective for evaluating comprehensive harmonic contributions as well as individual harmonic contributions. The case studies show that the proposed method is superior to the previous one even under parameter changing conditions.

In this paper, an idea about the hydraulic loading device is proposed to simulate the working mechanical environment of the steam valve joystick. The simulation based on the mathematical model of active and passive loading system is utilized to reveal that the stiffness of connection components in loading system has an important influence on the control accuracy of the system. Additionally, the paper provides a design on the structure of the connecting components of valve stem. For the control strategy, a dual inertia link is used to stabilize the system. Besides, a compensation method of partial structural invariance is adopted to reduce the influence of redundant force in passive loading test. Finally, The development mode of control engineering based on xPC rapid control prototype model is used to validate the loading system. The simulation and experimental results show that the dual inertia link and compensation method are effective techniques, and the passive loading error can be controlled within the tolerance of 300N.

Recently, small-signal stability of the modular multilevel converter (MMC) based high-voltage direct current (HVDC) transmission for wind farm integration has attracted great attentions. The impedance-based frequency-domain method is an effective tool for such studies, in which the accuracy of the impedance model is of significant importance. Currently, the decoupled single-input single-output (SISO) sequence impedance of the MMC-HVDC system with wind farm is commonly used due to the simplicity in stability analysis. However, since both the MMC and wind farm exhibit frequency coupling behaviors, the decoupled SISO sequence impedance model may lead to inaccurate stability conclusion under certain conditions. In order to improve the model accuracy, based on the harmonic state-space (HSS) modeling approach, this paper proposes a generalized multi-input multi-output (MIMO) sequence impedance model of the MMC-wind farm system. The proposed MIMO impedance model can effectively capture the frequency couplings in the interconnected system, based on which the coupling mechanism of multi-frequency components within the MMC is then revealed. To facilitate the interconnection analysis, the model truncation criteria is proposed and validated by comparing the accuracy of the MIMO model with different truncated dimensions. In addition, this paper considers the internal impedance network of the wind farm when developing the aggregated wind farm impedance model for interaction stability analysis. Finally, the proposed MIMO sequence impedance model is applied to accurately predict the instability of the MMC-HVDC connected wind farm system.

This paper proposes an extension to the established loop-shaping method, where the loop-shaping method is modeled mathematically and solved as a mathematical optimization program. In this process, a novel cost function is proposed and employed as the objective of optimization in the controller tuning problem. This cost function evaluates different characteristics of the system in the frequency domain, such as the stability margins and the operability bandwidth. These characteristics reflect the quality of load disturbance rejection, set-point tracking, and operability bandwidth of the control system. Consequently, the proposed technique circumvents running a time-domain simulation completely. More importantly, the proposed technique can be used with any controller structure. The generic cost function can be customized to fit any control objective and application. This is conducted in the second half of this paper, with the aim of obtaining a system with near-optimum time-domain performance with respect to the integral of time times absolute error (ITAE) criterion. At the same time, the control system obtained with the customized cost function has better operability bandwidth than that of a system optimized in the time-domain for the ITAE criterion. The proposed optimization model is analyzed for two plant models: first order and second order plus dead-time (FOPDT), (SOPDT), respectively.

This paper presents a rotating restart method for $v/f$ scalar controlled Synchronous Reluctance Machines (SynRMs) using a single DC -link current sensor. In such a case, the initial rotor position and speed are required to restart the machine due to the absence of a position sensor. The method proposes to inject three active voltage vectors in the stationary reference frame to induce the phase currents required for estimating the rotor position and speed. In addition, the phase current reconstruction method is proposed to reduce the distortion of the measured phase currents caused by adopting a single DC -link current sensor and to consequently enhance the rotor position estimation accuracy. With the proposed method, the appropriate voltage vector can be applied to the machine, thus minimizing the inrush current during the restart. Furthermore, the proposed method only requires the machine parameters on the nameplate, and it does not require any additional machine-specific tuning processes. This paper proposes a simple restart method suitable for scalar-controlled SynRM drives with a single DC -link current sensor. The effectiveness of the proposed restart scheme is validated through the simulation and experimental results.

In order to meet the needs of bus electrification and intellectualization, a controller for the steering power system of an intelligent electric bus is studied in this paper. The contents mainly include: based on the structural principle and control strategy of the EHPS system, Luenberger observer is designed, which is applied to the sensorless control system of PMSM. Then, a controller with STM32F103zet6 chip as its core is designed and manufactured. The hardware design of the controller includes the minimum system circuit, power supply circuit, signal acquisition circuit, integrated driver module circuit, CAN communication circuit, fault and high temperature alarm circuit of the single chip computer; combining the design of each hardware part, the controller of EHPS system is made. In the aspect of software implementation, the control decision-making part, a motor drive control part, fault diagnosis, and transmission part are mainly designed. Finally, the bench test and vehicle test of the controller are carried out. The purpose of the bench test is to test the control effect of the controller on the motor. The bench test results show that the target speed response of the motor is fast and the output is stable. The controller developed in this paper realizes the control of PMSM. The purpose of the real vehicle test is to test whether the controller meets the actual application requirements of the steering power system of the vehicle. The actual vehicle test results show that the steering wheel's torque decreases obviously, and the steering power system has good power-assisting performance when the EHPS system controller works. With the increase of vehicle speed, the power-assisting torque decreases accordingly. EHPS system realizes the dynamic change of power-assisting and meets the requirements of the conventional power-assisting mode of the car. In addition, the controller can realize the active steering control by controlling the electric power assistant device, which provides a platform for the realization of lane auxiliary maintenance, automatic parking, unmanned driving, and other functions.

High-speed solid-rotor induction machines (IMs) suffer from higher rotor eddy-current losses (as a result of the air-gap flux density harmonics) more than any other type of high-speed machines because of the solid-rotor steel. A double-layer short-pitch asymmetric winding arrangement with prefabricated coils is proposed in this paper to mitigate the solid-rotor losses and enable easier assembly. However, the asymmetric winding also brings some current unbalance because of three-phase asymmetric stator inductances, especially the winding leakage inductances. Current unbalance can cause harmful effects for both the machine and supply, e.g., torque ripples, unbalanced magnetic pulls, and unbalanced thermal loads of the supply network and supply power electronics. Additionally, a three-phase unbalanced current can cause an extra source of electromagnetic emission to the environment, which can be harmful to surrounding electronics and can cause extra eddy-current losses in surrounding solid surfaces (e.g., a metal terminal box). To mitigate the current unbalance, two methods are compared in this paper. The first method is a slight increase of the stator slot height and placing of the coil sides at the top or bottom within the slot height for different phases. The stator slot height is optimized based on the 2-D finite-element method (FEM) to achieve the best solution for mitigation of the current unbalance. The other method is based on the results of the first method, and the coil side position for a specific phase is further adjusted. Unlike conventional methods of mitigating the current unbalance by power electronics, the proposed method suppresses the current unbalance solely by adjusting the machine design, which avoids extra investments for power electronics devices. In addition, the machine control strategy remains unchanged compared with the traditional one.

The constant extinction angle control and constant DC voltage control are widely used for the inverter station of Line Commutated Converter based High Voltage Direct Current (LCC-HVDC) system in practical engineering. Under different control strategies, the control system parameters would have totally different effects on the stability of the LCC-HVDC system. In this paper, the small-signal models of the LCC-HVDC system with constant extinction angle control and LCC-HVDC system with constant DC voltage control are developed, respectively. Based on the eigenvalue analysis, this paper conducts a comprehensive comparison of the effects of a phase-locked loop (PLL) and LCC controller on the small-signal stability of LCC-HVDC system with different control strategies at the inverter station under weak AC grid condition. Then, the coupling effect between the PLL and LCC controller parameters is investigated when LCC-HVDC system adopts different control strategies. This paper can provide useful guidance for the systematic design and control parameter selection of LCC-HVDC projects.