In this analysis, grid currents are controlled in the switching nodes (point-B) and a typical profile of the controlled currents are shown in Figure 79. Figure 79 shows that the three currents and the three voltages are in phase, allowing an active power conversion from the DC toward the AC grid (11 kW toward the grid). The zoomed-in portion in Figure 80 shows the current in the switching node is composed of a fundamental component at 50 Hz, plus an important current ripple amplitude caused by the switching of a 2-level converter.

Figure 79 Grid Voltages and Currents of an AC/DC Converter Working at the Nominal Load of 11 kW

Figure 80 is a zoomed-in view of Figure 79 which shows the rectifier current plus the average current having a fundamental harmonic of 50 Hz.

Figure 80 Zoomed in Portion at t = 0s (Span 100μs)

Power conversion between AC and DC is achieved by means of the currents controlled at the grid frequency. Therefore, the measurement of the fundamental harmonic of the current (for example, I_L1_B_AVG) with correct amplitude and no important phase-delay needs to be delivered to the MCU. The 50-Hz or 60-Hz component can be derived by means of sampling technique as synchronous sampling, average control, and so forth. By adopting these techniques, no important phase delay in the digital control loop is introduced, allowing a faster response of the loop¹². Conversely, current sensors cannot be considered an ideal choice since current sensors have a bandwidth limitation. The current sensors can lead to important phase-delay and amplitude errors present at the MCU terminals. This error can be reflected in an error of the active and reactive powers exchanged and are expressed as in Equation 47.

where

• φ is the phase delay between the measured current and the real current
• f_e is the electrical frequency of the measured signal, which is equal for this application to 50 Hz or 60 Hz
• τ is the constant time of the low-pass filter behavior presented by the measurement chain

By using Equation 47, with a cutoff frequency higher than a hundred times the grid electrical frequency (6 kHz when having a grid at 60 Hz) a phase-angle delay lower than 0.6°can be achieved. This phase shift results in 50 Hz or 60 Hz to a negligible error of the active and reactive controlled power. The component to which the power conversion occurs, a 6-kHz bandwidth, is more than sufficient for controlling grid currents.

In general, 50 Hz or 60 Hz are not the only component to be controlled but there are higher frequency components in the grid currents introduced by the dead time in the power stage, leading to a significant increase of the THD. The high frequency component must be captured by the measurement such that the MCU can correct them, allowing a software cancellation. Increasing the dead time leads to higher distortions, in particular at the zero crossing of the current (at 11 ms) as shown in Figure 81. In this picture, current waveforms in point A drained by an AC/DC converter working at 11 kW are shown when the dead time of the controller is changed. The top graph shows the current waveform with 250-ns dead time, the bottom graph with 1.5-μs dead time.

Figure 81 Current Drained From the PCC When a Dead Time of 250ns and 1.5μs are Implemented (50-Hz Operation)

Excessive dead time can lead to significant THD which exceeds the limits set by the standards. To comply with the standards, either a large output filter is needed or adequate software control must be provided. Multiple control techniques were developed with the aim to compensate this disturbance; however, all these options require sufficient bandwidth of the current sensor. To determine the minimum bandwidth requirements, an fast Fourier transform (FFT) transformation of the current waveform is performed to analyzed the frequency content of the disturbance.

Figure 82 shows the results of FFTs of the currents in the PCC when full power is required by the grid.

Figure 82 FFT of the Currents Depicted in Figure 2-6 Plus Zoomed Portion (50 Hz)

The most important frequencies to be compensated in Figure 82 are the 5^th, 13^th, and 17^th harmonics, leading to 250 Hz, 650 Hz, and 850 Hz when the grid is working at 50 Hz. Correspondingly, when the grid operates at 60 Hz the frequencies are 300 Hz, 780 Hz, and 1020 Hz. By applying Equation 47 to the new frequencies, a minimum bandwidth from the current sensing stage of 102 kHz needs to be provided to make sure a proper compensation of the harmonics.

In conclusion, from steady-state analysis, a minimum bandwidth of 102 kHz when having a 60-Hz grid is necessary to improve the total harmonic distortion of the currents when an important dead-time is present in the PFC stage. When the grid is operating at 50 Hz, the minimum bandwidth can be scaled down to 95 kHz. The current sensor bandwidth is required in either point A or B depending where the currents are controlled because harmonic content generated by dead time is the same in both the measurement points. The reason is due to the fact that the EMI filter (see Figure 76) is optimized for much higher frequency content; therefore, no important mitigation can be achieved at low frequency.