Impedance-Based Analysis of Interconnected Power Electronics Systems: Impedance Network Modeling and Comparative Studies of Stability Criteria

Abstract

Impedance is an intuitive and efficient way for dynamic representation of power electronics devices. One of the evident strengths, when compared to other small-signal methods, is the natural association with circuit theory. This makes them possible to be connected through basic circuit laws. However, careful attention should be paid when making this association since the impedances obtained through linearization are local variables, often referred to locally defined reference frames. To allow the operations of these impedances using basic circuit laws, a unified/global reference has to be defined. Though this issue was properly addressed on the state-space models, a thorough analysis and a clarification regarding the unified impedances and stability effects are still missing. This paper aims to bridge this gap by introducing the Impedance Operator (IO) and associated properties to the development of impedance networks. First, the IO for both the AC coupled and AC/DC coupled systems are presented and verified through impedance measurements in PSCAD/EMTDC. Then, three types of impedance network-based stability criterions are presented along with a clarification on the consistency of stability conclusions. Finally, the Nyquist-based analysis is explored, regarding the sensitivity to partition points, to open the discussion on the identification of systems' weak points. Index Terms-Impedance operator, frequency domain, power converters, Nyquist stability I.

Design and Expansion Planning of Parallel Inverter Based AC Microgrids - An Approach for Improved Stability Margins

“…Application of impedance based analysis for droop controlled inverters is also investigated in [33]- [36], where emphasis is to develop an impedance model which can capture lower frequency oscillations. It has been found that impedance based analysis is highly sensitive to partition points and it has natural interactions with circuit laws which makes it a powerful tool to analyse the network easily [37]. This characteristics of impedance influenced the authors to use it for stability oriented network design of future microgrids.…”

“…After representing each element by its equivalent impedance, GNC criterion is used for stability analysis [37]. For the same, source and load equivalents at each partition bus are calculated using circuit analysis as shown in Fig.…”

“…Eigen value analysis based approach is used which is based on calculating system state matrix from state space representation. Therefore, complete microgrid system must be represented in state space form as given by (37). This can be obtained by representing equations of droop, voltage and current controllers ( 1…”

Impedance Aggregation Method of Multiple Wind Turbines and Accuracy Analysis

“…In Section 2, it was pointed out that for off-diagonal elements, the direct series connection of two impedance models will lead to the phase error, while the amplitude correctness is kept. However, when further connection such as (14) is applied, the mismatch can also be found in the impedance amplitude.…”

“…The consequences of reference frame mismatch on the impedance model aggregation which is performed in the system-level analysis are discussed in [13,14]. It was shown that the mismatch issue is an obstacle for the simple aggregation of a small-signal impedance model.…”