Design of Main Circuit Parameters for Modular Multilevel Matrix Converter in LFAC System

Comprehensive optimization framework for transmission expansion planning with fractional frequency transmission system

“…Based on the mathematical model of M3C [15] and the design of main circuit parameters [11], in engineering practice, M3C is often equivalently represented as a back‐to‐back Voltage Source Conver inverter in steady state. According to the operational data of the M3C fractional frequency transmission demonstration project already built in China, the loss rate of M3C is less than 1%, which can be ignored for planning purposes.…”

“…Equations ( 6) and ( 7) represent the constraints of the transmission capacity, which ensures that the apparent power does not exceed the allowable value. (11) Equations ( 8) to (11) express the relationship between the transmission power and the grid voltage and power angle, which represent the AC power flow equation. Equations ( 10) and (11) introduce a large value 'M ' to express the logical relationship between v l and power flow.…”

“…(11) Equations ( 8) to (11) express the relationship between the transmission power and the grid voltage and power angle, which represent the AC power flow equation. Equations ( 10) and (11) introduce a large value 'M ' to express the logical relationship between v l and power flow.…”

“…Drawing on the flexible DC transmission technology of Modular Multilevel Converter (MMC), the Modular Multilevel Matrix Converter (M3C) was adopted as the core equipment for fractional frequency transmission. At the theoretical level, the design of its main circuit and selection of parameters were completed [11]. The flexible four‐quadrant operation capability of the M3C provides the system with reactive power support and fault ride‐through capability [12].…”

Design and control of modular multilevel matrix converter with symmetrically integrated energy storage for low frequency AC system

“…All the arms are named after the phases connected at both ends, like the arm Aa in Figure 1. Taking arm Aa as example, the input current i Aa ( t ) and the output voltage u Aa ( t ) of cascaded SMs, referred to as the arm current and voltage, can be expressed as [5]: $$$$\begin{equation}{i}_{{\mathrm{Aa}}}\left( t \right) = \frac{1}{3}{i}_{{\mathrm{VA}}}\left( t \right) + \frac{1}{3}{i}_{{\mathrm{va}}}\left( t \right),\end{equation}$$$$ $$$$\begin{equation} \def\eqcellsep{&}\begin{array}{l} {u}_{{\mathrm{Aa}}}\left( t \right) = {u}_{{\mathrm{GA}}}\left( t \right) - {L}_{\mathrm{T}}\frac{{d{i}_{{\mathrm{VA}}}\left( t \right)}}{{dt}} - {L}_{{\mathrm{arm}}}\frac{{d{i}_{{\mathrm{Aa}}}\left( t \right)}}{{dt}}\\[4pt] \;\;\;\;\;\;\;\;\;\;\; - {L}_{\mathrm{t}}\frac{{d{i}_{{\mathrm{va}}}\left( t \right)}}{{dt}} - {u}_{{\mathrm{ga}}}\left( t \right) \end{array} .\end{equation}$$$$where u GA ( t ), i VA ( t ) are the LFS side AC bus voltage and input current at phase A; u ga ( t ), i va ( t ) are the PFS side AC bus voltage and output current at phase a. L arm represents the arm inductance. L T and L t denote the leakage inductances of the LFS side and the PFS side converter transformers which are generally required for grid‐connection.…”