T ABLE 51, P OSSIBLE MODULATION SCHEMES MAKING USE OF MODIFIED AND VIRTUAL VECTORS Standard modulation scheme (NTV SVM,

carrier based PWM, etc.)

Predictive optimal sequence SVM SVM based on alternate triangles (a) (b) (c) (d) D ef n it io n o f sc h em e Replace individual vectors directly by the partner states of a modified or virtual vector.

Replace complete sequence within a given triangle by a

predetermined

sequence making use of modified and virtual vectors. Evaluation of multiple sequence according to the POS (predictive optimal sequence) SVM scheme as proposed in paragraph 6.2

New small triangles can be defined based on the position of the type 1 virtual vectors. E xp la n at io n s an d co m m en ts

This works fine for modified vector and virtual vectors type 2. Virtual vectors type 1 would still need to be implemented with an alternate algorithm. This scheme is likely to generate high switching losses as it applies CM jumps without considering the rest of the modulation sequence.

This approach allows making a pre-selection of modified and virtual vectors to be applied and determines all possible sequences off line.

This scheme produces relatively low switching losses as the whole sequence can be optimized and partner states are not applied directly one after another. There is simple application at runtime, once a proper

definition of sequences has been made offline.

This approach is really an extension of the POS SVM. The systematic inclusion of modified and virtual vectors in the sequences leads to high performance regarding NP and FC control. The calculating effort is even higher than for the pure POS SVM approach.

This requires new algorithms to determine application times of states in modified and virtual vectors, as well as algorithms for the choice of modulation type. The implementation of the actual nearest three vector modulation is equivalent to standard SVM. But an optimal choice of a set of vectors to be used is complex. If multiple modified and virtual vectors are used in one triangle, up to 12 states may need to be applied.

6.1.4

Application of modified or virtual vectors

Modified or virtual vectors can be applied in different ways as indicated in TABLE 51. The most obvious approach is the use of the modified and virtual vectors as vertices in NTV SVM. However, there is a lot of redundancy. The choice of base vectors to be used is not obvious. An online optimization is quite demanding and does not necessarily result in best performance. Furthermore, a direct application of virtual vectors without specifically integrating the states within a sequence will result in high switching losses due to the jumps in CM.

An offline sequence optimization applying modified and virtual vectors according to TABLE 51 (b) offers high performance at reasonable complexity. This approach has been chosen to be implemented for simulation and experimental verification.

6.1.4.1

Virtual vector sequences generation

The development of the virtual vector sequence modulation scheme can be illustrated with the following examples.

Figure 91, Sample triangle incorporating three virtual vectors type 1

The blue triangle in Figure 91 can generate the following three virtual vectors type 1:

- {432 – 310}VV1

- {310 – 431}VV1

- {431 – 210}VV1

All these vectors can generate a current INP_b either of zero or the full phase current Iout_b. These three virtual vectors could be used for a SVM based on the blue triangle. A NTV algorithm for this small triangle could be applied. Each of the three virtual vectors would get its application time and would need to split it between the partner states. The partner state would then need to be put in an order to be physically applied.

A simpler implementation is possible based on the following observation: In all triangles incorporating modified and / or virtual vectors, some of the partner states coincide. This allows for easy optimization regarding losses. The states are simply aligned in ascending order regarding CM voltage. This results in the following sequence for the example from Figure 91:

- {210 – 310 – 431 – 432}3D

Only four states instead of 6 need to be applied. These four states describe a regular sequence of 4 of the standard size triangle. The virtual vectors are not visible anymore as such. This chosen approach does not limit the NP control capacity in comparison with a 6 vector sequence. If the redundant states of the 6 vectors are all optimized for the same NP and FC control criteria, they always reduce to only 4 states automatically. In the phase featuring the partner states, only states according to Figure 87 (a) and (b) are chosen to get either maximum or minimum NP current.

The calculation of applications times could still be done on the small triangle level. However, it seems more straight forward to do the calculation directly for the standard size triangle.

α β 100% 96.5% 81% 65% 50% Hexagon Regular Vectors Modified Vectors Virtual Vectors 1 Virtual Vectors 2

The duty cycle dxyz (= Txyz/TMP) of the two middle vectors in the sequence are given directly by the NTV SVM. The same is true for the sum of the duty cycles of the starting and the ending vectors: 431 310 432 210 d 1 d d d + = − − (80)

The two redundant states {210}3D and {432}3D need to be timed such that the FC’s stay balanced. This can be achieved by:

5 . 0 432 431 310 210+d =d +d = d (81)

This condition can be met for all space vectors within the small blue triangle and more generally for: ) 5 . 0 ( ) 5 . 0 (d₃₁₀ < AND d₄₃₁< (82)

This means that the red triangle can use the same sequence. This can also be confirmed by the analysis of the vertices of the red triangle:

- {432 – 210}MV

- {432 – 310}VV1

- {431 – 210}VV1

The resulting sequence is again (as predicted):

- {210 – 310 – 431 – 432}3D

Likewise, many other small triangles share common sequences. However, this does not matter from implementation point of view. Simply identical sequences will be stored in certain parts of a look up table. Like with an individual virtual vector, the sequence can be used to choose the NP current generated by phase b. The states to generate levels 1 and 3 in phase b can be chosen to either have zero NP current (INP_b = 0 if all states connecting to plus or minus of the DC link) or the full phase b current in the NP (INP_b = Ib for all states connecting to NP). The total NP current is the sum of the chosen phase b NP current and the phase a and phase c NP current, which depend on the state selector for the FC control in the corresponding phases. Obviously, this scheme is most powerful if the current in phase b is largest, which is the case for reactive power operation in the chosen triangle.

Outside of the star shaped area with blue dots in Figure 90, no virtual vectors type 1 are available. The proposed concept cannot be applied directly, but the same approach can be taken with larger triangles and virtual vectors type 2.

Figure 92, Sample triangle incorporating three virtual vectors type 2 The following virtual vectors type 2 can be generated with the green triangle:

- {432 – 410}VV2

- {410 – 430}VV2

- {210 – 432}VV2

The resulting virtual vector sequence is:

- {210 – 410 – 430 – 432}3D

The duty cycles of these states are easily calculated by an NTV SVM algorithm based on large size triangles. The sequence based virtual vectors type 2 is applied only, if no sequence based on virtual vectors type 1 is available. For example, the proposed triangle incorporates the small size triangles from the previous paragraph. The virtual vector 2 sequence could also be applied for those triangles, but the virtual vector 1 sequence is preferable regarding switching losses and output voltage distortion.

The yellow triangle in Figure 93 can be formed by modified and virtual vector states using partner states in any of the three phases a, b or c. Each phase offers several possible sequences with different starting point and different CM voltage. Examples for the different phases:

- Sequence for phase a: {100 – 110 – 321 – 322}3D

- Sequence for phase b: {210 – 211 – 332 – 432}3D

- Sequence for phase c: {221 – 321 – 433 – 443 }3D

The actual sequence depends on the small triangles. There will be multiple different sequences to be used within the yellow triangle. Depending on the current amplitudes in the three phases, one of the sequences can be chosen. As a consequence, this strategy is effective for any load angle for low modulation depth.

α β 100% 96.5% 81% 65% 50% Hexagon Regular Vectors Modified Vectors Virtual Vectors 1 Virtual Vectors 2

Figure 93, Sample small triangle with virtual vector sequences for all phases

TABLE 52,DEFINITION OF THE VIRTUAL VECTOR SEQUENCE MODULATION SCHEME