bring the system to steady state after a few cycles, without threatening the stability. The DC bus current iS is also illustrated, which is clearly a continuous current, since the AC components of the three-phase circulating currents add up to zero.
The same test has been performed for the case of the two-phase MMC and the results are displayed in Figure 2.7b. Here the effectiveness of the FAE is also well demonstrated. The orthogonal line current component iT β acts in a fast and accurate way, following closely all the transients of the actual current iT α. The circulating currents of both phase-legs contain only a DC component, and therefore lead to a constant power transfer, canceling therefore the second-order harmonic oscillating behavior of the DC-link current iS, which is also therefore a continuous quantity.
100 120 140 160 180 200
−30 0 30
Line Current [A]
100 120 140 160 180 200
−20
−10 0 10 20
Circulating and DC−link Currents [A]
Time [ms]
100 120 140 160 180
−30
−15 0 15 30
Line Current [A]
100 120 140 160 180 200
−20
−10 0 10 20
Circulating and DC−link Currents [A]
Time [ms]
Figure 2.7: MMC control system response to consecutive current reference step changes:
i) irefd from 24 to -18A at t = 140 ms, followed by ii) irefq from 0 to -15A at t = 160 ms.
Only phase-leg a-related magnitudes are depicted.
2.5 Experimental Tests
A versatile multi-phase MMC prototype has been designed and realized in the Laboratory of Industrial Electronics at EPFL. This reduced-scale laboratory setup, which has been used for the validation of the proposed concepts, is shown in Figure 2.8. It has been also extended, accordingly, in order to experimentally test the concepts that are proposed in the next chapters. The design and development of the MMC prototype is the result of a team effort and is described in detail in the Appendix A.
Figure 2.9a illustrates the results from a three-phase converter rectifying operation. The power factor is controlled to be unity, therefore the line currents are in perfect phase opposition with their respective grid phase voltages. The line-line converter voltages are
Figure 2.8: The multi-phase Modular Multilevel Converter prototype.
PWM-controlled with a triangular carrier signal of 5 kHz per branch and can comprise up to (4N+1) distinct voltage levels at high modulation indexes. The intentional second-order harmonic on the circulating current of phase a is visible, which has been imposed according to (2.20). This in turn produces a respective component on the two branch currents without, however, affecting the output current.
In a second step, the setup is reconfigured so as to have a two phase-leg converter structure connected to a single-phase voltage source. The synchronization with the grid is carried out using a SOGI-phase-locked loop (PLL) structure. The representative results for a steady state operation are shown in Figure 2.9b. The dashed-lined curves in the graphs of line current and grid phase voltage are a direct result of the FAE and SOGI utilization, respectively. As the converter is operated at a high modulation index, the measured voltage uab between the converter terminals features all the possible levels. The circulating current is very closed to being continuous, leading to almost sinusoidal branch currents, obviously in contrast with the respective figure of the three-phase counterpart.
In order to validate the accuracy of the estimation equations in the three-phase MMC studied case, the total submodule voltage ripples in both upper and lower branches of phase a are illustrated in Figure 2.10. The measured values are in good agreement with
2.5. Experimental Tests the estimated ones, although there are some slight differences which are mainly due to measurement and control inaccuracies. It is obvious, however, that the second harmonic component on the capacitive ripples has been suppressed by means of the respective harmonic injection (icirc,2).
0 10 20 30 40
Line Converter Voltages [V]
0 10 20 30 40
Grid Phase Currents [A]
0 10 20 30 40
Grid Phase Voltages [V]
0 10 20 30
Current Components of Phase a [A]
Time [ms]
Current Components of Phase Leg a [A]
Time [ms]
Figure 2.9: Experimental results for a: (a) three-phase DC/AC Modular Multilevel Con-verter and (b) two-phase DC/AC Modular Multilevel ConCon-verter hardware configurations.
Finally, the effect of a second-order harmonic injection in the circulating current is validated experimentally for the three-phase DC/AC MMC case in inverting operation.
The results for phase a are shown in Figure 2.11. Initially, the circulating current is controlled to bear a DC component. At t ≈ 0.09 s, the imposition of icirc,2 takes place according to (2.12), leading to an expected increase of the branch current peak values.
The top graph depicts the voltages for two submodules in the upper and lower branches of phase a, where the respective ripple decrease from 9 to 5.5V is visible. The capacitor voltage harmonics due to the second-order circulating current as well as third-order
common-mode voltage harmonic injections, as presented in (2.15), can be also observed.
It is noted that due to some measurement noise, the full bandwidth of the circulating current control was not reached, which is the reason for the small oscillations until the moment that the respective desired harmonic is imposed.
100 110 120 130 140 150 160
−15
−7.5 0 7.5 15
Total Submodule Voltage Ripples in Upper Branch of Phase a [V]
estimated
100 110 120 130 140 150 160
−15
−7.5 0 7.5 15
Total Submodule Voltage Ripples in Lower Branch of Phase a [V]
Time [ms]
estimated measured
measured
Figure 2.10: Experimental results for total estimated and measured submodule voltage ripples.
0 0.04 0.08 0.12 0.16 0.2
42.5 50 57.5
Submodule Capacitor Voltages [V]
0 0.04 0.08 0.12 0.16 0.2
Line and Circulating Currents [A]
Time [s]
Figure 2.11: Experimental results for capacitor voltage ripple reduction due to a second-order circulating current harmonic injection in converter inverting operation.