Abstract-The analysis and design of current regulators for multiphase ac loads is presented using complex vector notation. The use of complex vector notation provides a way of comparing the performance of controller topologies through their complex vector root locus and complex vector frequency-response functions. Limitations in the performance of the synchronous frame proportional plus integral current regulator are outlined and several ways of improving its performance are suggested and investigated.Index Terms-Complex vector controls analysis, complex vector frequency response, complex vector root locus, current regulators, synchronous frame regulators.

Islanding detection is of great importance for reliable operation of smart grids. Islanding-detection methods can be classified into three different groups, i.e., active, passive, and communication-based methods. Active methods inject a disturbing signal (typically a voltage) and analyze the system response (typically in the current). These techniques have a low nondetection zone (NDZ) but present the inconvenience inherent to injecting a disturbing signal. Passive methods monitor the grid condition from the grid variables. These techniques are easy to implement but present a large NDZ. Communication methods have the inconvenience of relying on communications, currently being of limited use. This paper proposes a new active islanding-detection method, based on the measurement of the grid high-frequency impedance by means of the injection of a high-frequency voltage. The advantages of the method are almost negligible adverse effects due to the injected high-frequency voltage and accurate and fast islanding detection, i.e., in the range of a few milliseconds. Furthermore, the estimated high-frequency impedance can be used for the adaptive control of the power converter.Index Terms-Active islanding detection, grid impedance measurement, high-frequency signal injection, power system monitoring.

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This paper deals with discrete-time models and current control methods for synchronous motors with a magnetically salient rotor structure, such as interior permanent-magnet synchronous motors and synchronous reluctance motors (SyRMs). The dynamic performance of current controllers based on the continuous-time motor model is limited, particularly if the ratio of the sampling frequency to the fundamental frequency is low. An exact closed-form hold-equivalent discrete motor model is derived. The zero-order hold of the stator-voltage input is modeled in stationary coordinates, where it physically is. An analytical discretetime pole-placement design method for two-degrees-of-freedom proportional-integral current control is proposed. The proposed method is easy to apply: only the desired closed-loop bandwidth and the three motor parameters (R s , L d , L q ) are required. The robustness of the proposed current control design against parameter errors is analyzed. The controller is experimentally verified using a 6.7-kW SyRM drive. Index Terms-Current control, delay, discrete-time model, interior permanent-magnet synchronous motor (IPM), saliency, synchronous reluctance motor (SyRM), zero-order hold (ZOH). I. INTRODUCTIONS YNCHRONOUS motors with a magnetically salient rotor-such as interior permanent-magnet synchronous motors (IPMs), synchronous reluctance motors (SyRMs), and permanent-magnet (PM)-assisted SyRMs-are more and more applied in hybrid (or electric) vehicles, heavy-duty working machines, and industrial applications. In these applications, the maximum speeds and, consequently, the maximum operating frequencies can be very high (e.g., 12 000 r/min corresponding to the frequency of 1000 Hz for a ten-pole machine). Since the switching frequency of the converter feeding the motor Manuscript

Abstract-The analysis and design of current regulators for polyphase ac loads is presented using complex vector notation. The ac motor current regulation problem is analyzed by studying both the command tracking and disturbance rejection capability of the current regulator. The use of complex vector notation and the generalization of classical control tools like root locus, frequency-response functions, and dynamic stiffness functions to complex vectors provide a way of comparing the performance of different controller topologies. Limitations in the performance of the synchronous frame proportional and integral current regulator are outlined, and several ways of improving its performance are suggested and investigated.Index Terms-AC current regulators, complex vector analysis, complex vector controls design.