State and Space Vectors of the 5-Phase 2-Level VSI

Abstract

The paper proposes a general description system of the five-phase two-level inverter. The two base methods are presented and discussed. The first one is based on the standard space vector transformation, while the other uses state vectors which enable the definition of the basic physical quantities of the inverter: current and voltage. The proposed notation system offers a general simplification of vector identification. It comprises a standardized proposal of notation and vector marking, which may be extremely useful for the specification of inverter states. The described notation system makes it possible to reach correlation between state and space vectors. It presents space and state vectors using the same digits. These properties suggest that the proposed notation system is a useful mathematical tool and may be really suitable in designing control algorithms. This mathematical tool was verified during simulation tests performed with the use of the Simulation Platform for Power Electronics Systems—PLECS.

Vector control strategy of the five-phase VSI

“…The discussed vector sequences were based on the imperative of only one switching in one phase during the whole voltage period. Three adequate examples were presented in [13]. This mathematical tool makes it easier to define state and space vectors as well as to calculate the available phase and phase-to-phase voltages and the resulting load currents.…”

“…If the phase load is fully symmetrical it is profitable to assume the equal opportunity of resistances and inductances as well: R=Ra=Rb=Rc=Rd=Re and L=La=Lb=Lc=Ld=Le. As a matter of fact, the mathematical model of the circuit is described by the system of four equations which are in [13]. Solving the system, it is possible to acquire all analytical phase voltage and current waveforms.…”

“…where coefficients 2 1 ,   are (13) The position of the successive vector is determined by its modulus Mk and the shift angle . In order to determine correctly the shift angle, it might be necessary to use additionally the arctg function (14).…”

“…According to (12) and after calculations, the modulus Mk assumes three different results: (15) In such a case among the 32 vectors there are three groups of 10 active vectors each beside two nonactive zero vectors. The parameters: moduli , coefficients , and shift angles of all 30 active vectors are collected in [13]. The moduli values are approximated.…”

“…There are many proposals relating to this [11]. The paper presents a significant development of the inverter description system idea proposed in [12], during the ICREPQ'14 conference, as well as an extended and developed version in [13]. Presented in [13] system is designed for 5-phase two level inverter and it provides a general standardization and simplification of vectors describing such an inverter.…”