T ABLE 30, O PTIONS FOR THE USE OF THE REAL TIME NP CURRENT FUNCTION WITH THE EXAMPLE OF m = 0.95 AND COS (ϕϕϕϕ) = 0.86, CALCULATED WAVEFORMS

(a)

Lowest possible CM voltage

(b)

Lowest possible NP current

(c)

Optimization for output harmonics (CSPD PWM)

UCM UCM UCM

Note that PhiUI (or PhiUI) in these graphs is equivalent to ϕ, PhiU is equivalent to θ, and UCM is equivalent to s_CM. Legend (valid for all graphs of this type):

- red: maximum NP current trajectory

- blue: minimum NP current trajectory

- black: NP current trajectory based on CM injection strategy

In order to keep the desired steady state performance (according to any of the schemes in TABLE 29 and TABLE 29), the gain of the controller should not be chosen too high. With a high gain, the controller will saturate and the CM trajectory will look the same for all configurations: it will simply follow the maximum (red) or minimum (blue) NP current trajectory and switch back and forth between the two. A hysteresis control scheme applying different gain values to get good steady state performance and powerful NP control at higher NP voltage deviations is proposed in chapter 7.

The real-time piecewise linear NP current function based controller presents a significant improvement over simple unconstrained DC CM linear feedback controllers. Using the real time NP current function for NP control yields the performance shown in TABLE 23. The full physically possible range of NP currents based on standard modulation schemes can be used. The concepts gives good performance for high and low modulation depth as well as high and low cos(ϕ). However, it cannot overcome the limits shown in TABLE 23, which can be critical for very low or very high modulation depth, especially in reactive power operation. The proposals with virtual vectors in the following chapter overcome those limits. Note that the concept characterized by the real time NP current function is not limited to any specific modulation scheme. The CM values for min. and max. NP current can be used as constraints both for CB PWM and SVM schemes. The scheme is topology independent (within the frame of the 3-L DC link converters) and works independently of the number of output levels.

5.1.2.1

Simulation and experimental verification

The proposed NP control concept based on a real time NP current function has been simulated and verified experimentally with the 5-L 6kVA ANPC prototype in ANPC1 configuration. The experimental measurements are presented in the next paragraph. NP current ripple minimization according to TABLE 30 (b) is used, leading to a large 3rd _{harmonic in the CM} well visible in Figure 69 (a).

5.1.2.2

Comparison with state of the art

The calculation of a suitable CM voltage (or zero sequence voltage) has been proposed in literature by various authors. Pou [78] determines the maximum NP current points with their associated CM voltage and applies them directly depending on the sign of the deviation of the NP voltage. This gives the same result as the real-time NP current function scheme with high gain (controller in saturation). Always the maximal physically possible current is applied in that case. Some SVM schemes found in literature act in the same way (e.g. [80]). The space vector yielding the highest NP current with the correct sign is applied directly. Rodriguez [80] uses the output current reference instead of the measured current, assuming that the current controller performs as it should. The advantage is that the reference has a much lower ripple than the measured current and there are no delays from the measurement potentially degrading the performance of the NP control.

In reality, maximum NP current as obtained by the schemes above is not required. Yamanaka [81] calculates the optimal redundant states based on the output currents too, but he uses a redundancy function (duty cycle) for the application of the redundant states. This allows for the same kind of proportional feedback as with the real-time NP current function. However, the real- time NP current function offers a much higher degree of freedom in defining the PWM.

Song [76] analytically calculates the suitable zero sequence to be injected. The NP current is calculated as in (55), but rather than identifying the most interesting part of the piecewise linear function. Song uses a test-verify-revise algorithm where he starts from an initial assumption for the result of the sign functions in (55) and then revises if necessary. The actual NP control algorithms tries to generate a NP current to get to zero NP voltage deviation within one modulation period. If the controller goes into saturation, the CM voltage is only limited to the physical limitation, which will result in very poor performance of the scheme proposed in reactive power operation.

5.2

Harmonic injection NP control

The previous paragraph has described a new CM injection scheme based on the real time NP current function with all calculations done in time domain, . As an alternative, an approach in the frequency domain is proposed in this paragraph.

In active power operation, the gradient in the NP current function remains the same throughout the whole period, a DC CM offset creates a DC NP current and a linear feedback control can be used directly. In reactive power operation, a DC CM offset creates an AC NP current. To generate a DC NP current, higher order harmonics need to be injected instead. This is true also for the real-time NP current scheme presented in the previous paragraph, where the CM function is generated purely in the time domain. Also in that case, a set of higher order harmonics are injected as a result of the NP control. However, they do not need to be known at the time of application.

As an alternative, specific harmonics could be injected. A fundamental component needs to be generated in the rectified switching function to interact with the fundamental output current and generate a DC NP current (see TABLE 27). In active power operation, such a fundamental can easily be generated with a DC offset (see TABLE 24). For reactive power operation, a DC offset is not effective, as the fundamentals in the rectified switching function and the fundamental output current will have a phase shift of π/2. A fundamental without phase shift needs to be generated.

TABLE 31 gives three example of harmonic injection for the generation of a suitable fundamental component in the rectified function. The first example on the left used calculated harmonics from 2nd _{to 15}th _{order based on a pure DC and fundamental in the rectified switching} function. Obviously, the result is very powerful regarding NP control but the associated highly distorted switching function is not applicable in reality as it would generate a very large distortion in output voltage and current. In practice only zero sequence components are allowed and only with an amplitude that can physically be generated. The second column of TABLE 31 does exactly that by applying optimized multiples of 3rd _{harmonics up to the 42}nd_{. The result is close to the ideal case} which would be obtained by application of the real time NP current scheme with high gain. The CM jumps mentioned in paragraph 5.1.2 are actually nicely visible also with this harmonic injection approach (as relatively high frequencies are injected). The third column in TABLE 31 injects only a 3rd _{and a 6}th _{harmonic. The resulting waveforms resemble the ones obtained with the harmonic} injection up to the 42nd_{, but obviously it is much smoother and likely to generate less switching} losses.

It is interesting to note that both cases result in almost the same value for the fundamental component in the rectified switching function. This indicates that the 6th _{harmonic is dominant} over the higher order harmonics regarding the generation of a fundamental component.

TABLE 31,HARMONICS IN RECTIFIED SWITCHING FUNCTION ABS(S(T)) IN FUNCTION OF