Table 1: Basic parameters of PWM methods.

Control (modulation) parameterConventional schemes of vector PWMProposed method of modulation

Operating and max parameterOperating & max voltage 𝑉 and 𝑉 π‘š Operating & maximum fundamental frequency 𝐹 and 𝐹 π‘š

Modulation index π‘š 𝑉 / 𝑉 π‘š 𝐹 / 𝐹 π‘š

Duration of subcycles 𝑇 𝜏

Center of the π‘˜ -signal 𝛼 π‘˜ (angles/degr.) 𝜏 ( π‘˜ βˆ’ 1 ) (sec)

Switch-on durations 𝑇 𝛼 π‘˜ = 1 . 1 π‘š 𝑇 [ s i n ( 6 0 ∘ βˆ’ 𝛼 π‘˜ ) + s i n 𝛼 π‘˜ ] Algebraic PWMTrigonometric PWM
𝑑 𝛼 π‘˜ = 1 . 1 π‘š 𝑇 s i n 𝛼 π‘˜ 𝛽 π‘˜ = 𝛽 1 [ 1 βˆ’ 𝐴 Γ— ( π‘˜ βˆ’ 1 ) 𝜏 𝐹 𝐾 𝑂 𝜈 1 ] 𝛽 π‘˜ = 𝛽 1 Γ— c o s [ ( π‘˜ βˆ’ 1 ) 𝜏 𝐾 𝑂 𝜈 1 ]
𝛾 π‘˜ = 𝛽 𝑖 βˆ’ π‘˜ + 1 [ 0 . 5 βˆ’ 6 ( 𝑖 βˆ’ π‘˜ ) 𝜏 𝐹 ] 𝐾 𝑂 𝜈 2 𝛾 π‘˜ = 𝛽 𝑖 βˆ’ π‘˜ + 1 [ 0 . 5 βˆ’ 0 . 9 π‘š ( 𝑖 βˆ’ π‘˜ ) 𝜏 ] 𝐾 𝑂 𝜈 2
𝑑 𝑏 π‘˜ = 1 . 1 π‘š 𝑇 Γ— s i n ( 6 0 ∘ βˆ’ 𝛼 π‘˜ ) 𝛽 π‘˜ βˆ’ 𝛾 π‘˜ 𝛽 π‘˜ βˆ’ 𝛾 π‘˜

Switch-off states (zero voltage) 𝑑 0 π‘˜ = 𝑇 βˆ’ 𝑑 𝛼 π‘˜ βˆ’ 𝑑 𝑏 π‘˜ πœ† π‘˜ = 𝜏 βˆ’ 𝛽 π‘˜

Special parameters providing synchronization of the process of PWM 𝛽 ξ…ž ξ…ž = 𝛽 1 [ 1 βˆ’ 𝐴 Γ— ( 𝐾 βˆ’ 1 ) 𝜏 𝐹 𝐾 𝑂 𝜈 1 ] 𝐾 𝑠 𝛽 ξ…ž ξ…ž = 𝛽 1 Γ— c o s [ ( π‘˜ βˆ’ 1 ) 𝜏 𝐾 𝑂 𝜈 1 ] 𝐾 𝑠
πœ† ξ…ž = ( 𝜏 βˆ’ 𝛽 ξ…ž ξ…ž ) Γ— 𝐾 𝑂 𝜈 1 𝐾 𝑠 πœ† ξ…ž = ( 𝜏 βˆ’ 𝛽 ξ…ž ξ…ž ) Γ— 𝐾 𝑂 𝜈 1 𝐾 𝑠