Abstracts:The stability impacts of the internal control dynamics of the modular multilevel converters (MMCs) have been discussed recently. Yet, the impact of zero-sequence circulating-current (ZSCC) dynamics on the ac-side dynamics of the MMCs is hitherto unaddressed. This article develops the ac impedance model for the grid-connected MMCs by means of complex vectors and harmonic transfer-function matrices, which allows separately characterizing the dynamics of the ZSCC. Then, based on the complex-valued model, a single-input–single-output closed-loop equivalent impedance is derived for grid-connected MMCs, considering both the frequency-coupling dynamics of the MMCs and the interactions with the grid impedance, which enables a design-oriented analysis on the stability impact of the ZSCC. It is revealed that the resonant peaks in the ac impedance of the MMC are yielded due to the absence of the ZSCC control, which tends to destabilize the system in weak grids. A systematic parameter-tuning method of the ZSCC control loop is developed to guarantee the system stability. Case studies in time-domain simulations corroborate the theoretical analysis.

Abstracts:This article proposes a multifrequency admittance model for voltage-source converters with three-phase unbalanced grid voltages. The model is derived with multiple complex vectors and harmonic transfer functions, which is merely dependent on its own input voltage trajectory, and can accurately capture the frequency-coupling dynamics. The dynamic effects of both the basic synchronous-reference-frame phase-locked loop (PLL) and its alternative with a notch filter of the negative-sequence voltage component are compared. It is revealed that the notch-filtered PLL significantly weakens the frequency-coupling effects, which leads to a reduced order of the admittance model. The developed model is validated by a frequency scan, and the frequency-coupling effects impacted by different PLLs and voltage unbalance factors are verified by the experimental tests. Finally, a case study on stability analysis in unbalanced grids proves the significance of the model.

Abstracts:The stationary-frame complex-valued frequency-domain modeling has been applied to characterize the frequency-coupling dynamics of three-phase converters. Yet, those models are generally derived through mathematical transformations of the linearized time-invariant models in the rotating <italic>dq</italic>-frame. A step-by-step modeling method with clear physical insight in the stationary frame is still missing. This article attempts to fill in the void by introducing a general stationary (<inline-formula> <tex-math notation="LaTeX">$alpha beta$ </tex-math></inline-formula>)-frame, three-port equivalent circuit model for the converter power stage, based on the direct linearization around time-periodic trajectories. The model not only reveals the frequency-coupling effect of the ac&#x2013;dc dynamic interaction but also provides an explicit theoretical basis for incorporating the control dynamics. Moreover, the dependence of the frequency-coupling terms on the initial phase of the input voltage is pointed out. Considering the phase-dependent feature, a frequency scan method that can accurately measure the <inline-formula> <tex-math notation="LaTeX">$alpha beta $ </tex-math></inline-formula>-frame converter model is proposed. The measured frequency responses in both the nonlinear time-domain simulations and experimental tests validate the effectiveness of the frequency scan method and the theoretical analysis.

Abstracts:The properties of complex space-vector models for asymmetric three-phase systems are investigated in this article. Most importantly, three alternative methods for the stability analysis of the asymmetric closed-loop systems are presented. The end results avoid the usage of matrix manipulations. It is shown how the theory can be applied to modeling and stability analysis of a grid-connected voltage-source converter (VSC). The methods are compared using numerical examples.

Abstracts:Small-signal model impedances of grid-tied converters have recently attracted researchers&#x2019; attention and have shown great importance in stability analysis. This article proposes an impedance model in <italic>d-q</italic> frame for static synchronous compensators (STATCOMs), including dynamics from synchronization, current, voltage loops, and QV droop and reveals the significant features compared to other types of grid-tied converters that: 1) impedance matrix strongly coupled in <inline-formula> <tex-math notation="LaTeX">${d}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${q}$ </tex-math></inline-formula> channel due to nearly zero power factor; 2) different behaviors of impedances at low frequency due to inversed direction of reactive power; and 3) coupled small-signal propagation paths on the voltage at point of common coupling (PCC) from synchronization and ac voltage regulation. All these characteristics render difficulty in identifying instability patterns using existing knowledge and pinpointing the main contributor to instability among control loops, which was discussed and solved in this article. To better understand the frequency coupling effects of STATCOMs, the <italic>d-q</italic> frame impedance model was further transformed in its complex matrix form. An example of possible instability with STATCOMs was presented and analyzed using the proposed model. The impedance model was verified experimentally with a scaled-down STATCOM prototype.

Abstracts:Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a <inline-formula> <tex-math notation="LaTeX">$2times2$ </tex-math></inline-formula> system, and the current control loop of two independent power converters in parallel, a <inline-formula> <tex-math notation="LaTeX">$4times4$ </tex-math></inline-formula> system.

Abstracts:The synchronization between the power grid and distributed power sources is a crucial issue in the concept of smart grids. For tracking the real-time frequency and phase of three-phase grids, phase-locked loop (PLL) technology is commonly used. Many existing PLLs with enhanced disturbance/harmonic rejection capabilities, either fail to maintain fast response or are not adaptive to grid frequency variations or have high computational complexity. This article, therefore, proposes a low computational burden repetitive controller (RC) assisted PLL (RCA-PLL) that is not only effective on harmonic rejection but also has remarkable steady-state performance while maintaining fast dynamic. Moreover, the proposed PLL is adaptive to variable frequency conditions and can self-learn the harmonics to be canceled. The disturbance/harmonic rejection capabilities together with dynamic and steady-state performances of the RCA-PLL have been highlighted in this article. The proposed approach is also experimentally compared to the synchronous rotation frame PLL (SRF-PLL) and the steady-state linear Kalman filter PLL (SSLKF-PLL), considering the effect of harmonics from the grid-connected converters, unbalances, sensor scaling errors, dc offsets, grid frequency variations, and phase jumps. The computational burden of the RCA-PLL is also minimized, achieving an experimental execution time of only <inline-formula> <tex-math notation="LaTeX">$12~mu text{s}$ </tex-math></inline-formula>.

Abstracts:This article considers the control problem for a motor/generator set, where a prime mover drives a generator and the electrical power produced drives a motor. Both the generator and the motor are assumed to be doubly fed induction machines with direct ac connection between their stators. The rotors are controlled by three-phase converters, so that operation is possible with motor and generator speeds that are different from each other, and not synchronized with the electrical frequency of the stator voltages. The strong couplings between the two machines motivate the design of an integrated controller. This article proposes a general framework for such a design based on a joint model of the two machines. A specific method is also developed for the control of the stator voltages and the motor velocity. In its simplest form, the proposed algorithm does not rely on current sensors. A current command option is also developed that ensures closer tracking and limiting of the rotor currents. The algorithm is relatively simple and all its parameters can be computed based on the estimates of the machine parameters. Practical implementation and testing can be performed rapidly. Experiments performed on a small-scale laboratory testbed show very good tracking performance of a speed reference profile.

Abstracts:Advances in electrostatic machine design have enhanced the torque density of macroscale electrostatic machines toward practical use. A recently developed fractional horsepower three-phase separately excited synchronous electrostatic machine (SEM) demonstrates torque densities comparable to those of air-cooled permanent-magnet-based electromagnetic machines (1.5 Nm/kg) when excited with a medium voltage (5 kV). SEMs develop torque from voltage, not from current, and therefore incur nearly zero losses at low speeds or stall. However, there is no off-the-shelf medium-voltage drive at this power level, and the appropriate control framework for these machines has yet to be established. This article presents a complex vector voltage regulator control approach as a means for modulating torque in an SEM. Ampere-second (charge) is sourced from a current source inverter (CSI) serving as the drive electronics for voltage regulation. Together, the control approach and the CSI hardware form the first high-performance electrostatic drive. Key research outcomes include the theoretical development and experimental verification of charge-oriented control via voltage regulation. Experimental results are presented for rotational and stall conditions, which are reflective of the &#x201C;position and hold&#x201D; applications suited to electrostatic machines. The dynamic performance of the voltage regulator is verified by measuring the controller frequency response function, dynamic stiffness, and command tracking on a separately excited SEM.

Abstracts:Rotary&#x2013;linear electric machines can perform coupled rotary and linear motion. In addition, they can have magnetic bearings (MBs) integrated and magnetically coupled with the rotary, linear, or rotary&#x2013;linear machine operation. Since rotary&#x2013;linear machines with MBs have not been thoroughly analyzed in the literature, the models that provide understanding of their operation and give basis for the control system implementation are not entirely covered. Hence, in this article, an enhanced complex space vector-based model of the rotary&#x2013;linear machine with MBs is derived and expressions for the torque, thrust force, and MB force are given. The rotary&#x2013;linear machine complex space vector of the voltage, current, or flux linkage is defined using the proposed transformation with two complex frames: one related to the rotation and MBs and another to the linear motion. This results in complex space vectors with two complex units; however, the techniques used for a conventional complex space vector calculation can also be applied to the proposed complex space vector description. This is also experimentally validated on a hardware prototype of a magnetically levitated linear tubular actuator (MALTA), whose position control system is designed and implemented based on the enhanced space vector modeling approach, with the dynamic operation of the MALTA, including linear motor operation with an axial stroke of 10mm and a mechanical frequency of 17Hz.