Wideband impedances of the single-phase four-quadrant converter (4QC)-based high-speed train are of great significance for small-signal stability analysis in the electric railway system. However, the conventional impedance measurement strategy relies on sweeping the desired frequencies repeatedly that extremely slows down the impedance measurement speed, which, usually, seems incapable for the actual dynamic industrial systems. Addressing this shortcoming, this article proposes a novel impedance measurement approach based on the wideband excitation to greatly enhance its rapidity. Further, to eliminate the frequency overlapping effects under the wideband excitation, the proposed alternate injection strategy realized by the multitone signal can separate the effective frequencies from the coupling frequencies in the $\alpha \beta $ frame. Afterward, the dq -frame data covering all the desired frequencies can be obtained by combining the conventional method and the proposed $\alpha \beta $ -value exchange method ( $\alpha \beta $ -VEM), which can be applied for the impedance calculation. Finally, the results of both simulation and real-time hardware-in-the-loop (HIL) tests can well verify the effectiveness of the proposed approach.

Rapid Impedance Measurement Approach Based on Wideband Excitation for Single-Phase Four-Quadrant Converter of High-Speed Train

This paper presents a ringing test for 2nd-order Sallen-Key low-pass filters. A comparison measurement is constructed, which takes into account the measurement of a self-loop function in a transfer function. Based on the phase margin at unity of the self-loop function, a general stability criterion for second-order linear systems is proposed in terms of operating regions. In case of under-damping region, the ringing occurs and makes the system unstable. The advantage of the proposed criterion lies in its simplicity than some of the existing results. The new stability criterion is applied to the network based negative feedback issues. Experimental results show that the proposed method is quite effective.

Ringing Test for Second-Order Sallen-Key Low-Pass Filters

With the growing need to support large dynamic electric loads in microgrid environments, there has been a necessary push toward highly regulated dc distribution through power electronics. Unfortunately, these systems are nonlinear by nature and provide potentially destabilizing behavior at their source interfaces. To complicate matters further, many systems are built from independently designed subcomponents with little information shared between designs. It is, therefore, necessary to have stability-driven design requirements for each subsystem to enforce stable dynamics upon system integration. Traditional techniques are currently limited to either overly conservative large signal small-gain methods or small signal transfer function approaches that are unreliable for assuring large signal stability. This article proposes a generalized passivity-based stability criterion that conservatively estimates the domain of stability for an integrated nonlinear system. Through passivity partitioning and uniquely driven domain of passivity estimation techniques, this methodology provides interface conditions that certify stability while only requiring a reduced subset of knowledge of each connected subsystem <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.

A Generalized Passivity-Based Stability Criterion for Assessing Large Signal Stability of Interconnected DC Power Systems

As a typical single-phase electric power system, high-speed railway system gradually absorbs the more single-phase electric traction vehicles (trains) with its rapid development. Traction power load (TPL) is the electrical part of the train. The incompatible interactions between traction power network (TPN) and TPL generally cause the serious wideband oscillations, fortunately, which can be readily analyzed with the identified wideband impedances. As for impedance identification, the multi-frequency harmonic generator is of great significance to rapidly excite the desired responses for impedance calculation, however which is vacant for the single-phase TPL, and needs a further study. Aiming at it, this article proposes a multi-frequency harmonic generator based on the transformer-less cascaded H-bridge (CHB) converters with floating DC capacitors. In detail, its corresponding multi-frequency harmonic control loop is derived by the internal model principle (IMP), and the inserted notch filter and repetitive controller can strengthen the multi-frequency harmonic output performance. Finally, results of simulation and corresponding down-scale physical experiment can well verify that the proposed harmonic generator can output multiple harmonics simultaneously with high purity and well-behaved tracking performance.

A Multi-Frequency Harmonic Generator Based on the Voltage Source Converter for Traction Power Load Impedance Identification

This article presents a formal mathematical correlation between the standardly used <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">port-level (terminated) single-input single-output (SISO), and the recently acknowledged <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">device-level (unterminated) multiple-input multiple-output (MIMO) impedance-based method for the stability assessment of dc-dc interlinking converters. Based on this, the conditions that must be met to ensure the correct stability assessment by the SISO method applied to a single port-pair are derived. It is shown that without prior knowledge on whether these conditions are met, the SISO method must be applied to every port-pair to account for possible <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">port-level hidden dynamics . Alternatively, the MIMO method can be used, which is revealed to inherently account for any <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">port-level hidden dynamics . It is further analyzed which method is advantageous in terms of computational complexity, intuitiveness, and simplicity for applications featuring meshed grids or multi-port interlinking converters, as well as in terms of interpreting the resulting stability margins. Finally, suitability of the MIMO method for termination-independent stability-oriented controller design and stability assessment based on measurements is highlighted. The presented methodology is illustrated for a simplified dc system with a current-controlled buck converter. Analytical stability predictions are validated using hardware-in-the-loop simulations and also experimentally, using a laboratory hardware prototype.

On the Applicability of SISO and MIMO Impedance-Based Stability Assessment of DC-DC Interlinking Converters

Advanced high-power shipboard applications such as electromagnetic rail-guns, semiconductor lasers, advanced radar, etc. create an emergent need to support large electric loads on various Navy vessels. With the necessary push towards highly regulated DC distribution through power electronics on shipboard power systems, these loads are becoming more likely to cause destabilizing behavior at their source interfaces. The stability of a system can be understood as the ability to operate as intended at a given operating point and if perturbed, the disturbance to the system will diminish over time and the system will return to its original operating behavior. Traditionally, it has been sufficient to analyze small signal stability through testing the ratio of the source impedance and load impedance with respect to the Nyquist Criterion. However, for Navy power systems with more complex circuit topologies and a trend towards higher switching frequencies, the impact of dual feed interfaces as well as previously unaccounted for common mode currents, could cause erroneous stability assessments when applying traditional techniques. This paper proposes a new method to classify the small signal stability of a complex DC interface. This is done through an expanded characterization of a system’s impedances to address the coupling between all interface connections. In this study, an example power system is defined and classified using traditional techniques in comparison to the technique proposed.

The Generalized Nyquist Criterion Applied to Complex DC Power System Networks

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The Generalized Nyquist Criterion Applied to Complex DC Power System Networks