The filter configurations differ at the level of modularity. Modularity can be studied from a number of perspectives, which are for instance changes in attenuation, resonances, and energy and further, the maintenance perspective.
The first perspective consists of two subviews; modularity by design and modularity by retrofit. The first one relates to a situation where the filtering is optimized in the design
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phase for a particular range of paralleled inverters, whereas the second view relates to a situation where the filters are not designed according to the modular design criteria but for instance the application power is increased by adding more inverters in parallel.
From the perspective of maintenance, the modularity of each design is analysed based on how much components have to be changed in the case of faulty components, excessive tolerances in component values, or redesign changes in the filter configuration. In the modular design, the maintenance modularity is at highest when the least number of components have to be replaced. A good analogy would be that a passenger car is modular from the maintenance point of view whereas a television is not. When a car breaks, parts are replaced in order to make the car run again, but when a television breaks, normally the whole TV set is replaced.
The configuration that experiences the least resonance shift can be considered the most modular one from the viewpoint of resonance shift. A similar principle applies also to the other properties. The configuration that can be maintained by changing the least components is the most modular one from the viewpoint of maintenance. Further, the attenuation is closely connected to the location of the resonance peak fr2. The lower the frequency is, the better the attenuation at high frequencies is.
Considering the resonance shift for each configuration, there are some clear differences between the configurations. In the L-configuration, there is no resonance shift in the lower resonance frequency. However, the higher resonance shifts towards higher frequencies, which may become a problem if the frequency is already close to the upper limit of fr2 ≤ fsw /2.
In other configurations, both frequencies shift towards lower frequencies as the number of paralleled inverters increases. The LLCL configuration experiences the least resonance shift in both resonance frequencies amongst the LCL, LC, and LC+L configurations. The LLCL configuration clearly benefits from the additional resonance frequency produced by the third inductor in series with the capacitor. As the number of paralleled inverters is increased, it can be seen that the difference between the LLCL and LCL configurations remains approximately the same for lower resonances, but for higher resonances the difference increases as n increases.
The LC and LC+L configurations have the same resonance shift in the lower resonance frequency but the LC+L configuration shows less shift in the higher resonance because of the common grid-branch inductor in the configuration. However, this benefit is diminished by the very large energy stored in the component rendering the configuration impractical.
The L-configuration does not present an interactive cross-coupling resonance, which generally can be taken as an advantage in control design. From the other configurations, LLCL and LCL benefit from their grid-side inductors in cases where the inductance value is larger enough to push the cross-coupling resonance low enough. In section 3.3.3, the
equations yielding the grid-side inductor value were presented. The LC and LC+L configurations do not have grid-side inductors. However, the cables connecting the filters in parallel presents some inductance, which can place the cross-coupling resonance over the switching frequency thereby causing destructive operating conditions. In the case of several inverters in parallel, it is possible that the cabling that connects inverters in parallel becomes longer, potentially increasing the inductance. However, compared with the LCL and LLCL cases, the LC and LC+L configurations lack some modularity considering this resonance and its potential problems.
The smaller the inverter-side current ripple is made by increasing the L1 inductor value, the less resonances are shifted. However, the smaller the ripple is, the larger losses are caused in the inductors itself. On the other hand, the larger the ripple can be, the more losses are caused in the inverter bridge by switching of larger currents. The effect of L1
on the modularity is part of a larger optimization problem, which involves aspects not studied in this dissertation.
Considering the energies of the components, compared with the LCL case, the LLCL configuration presents a slightly larger total energy. This difference is due to the additional capacitor branch inductor. The difference in the calculations was minimal partly because the calculations were made at the fundamental frequency. Assuming a maximum ripple current flowing into the capacitor branch, the energy of the inductor is in the range of 0.001 pu with the nominal filter values used in the calculations. Moreover, when taking the switching frequency ripple account, the other components such as the inverter-side inductor store a significantly larger proportion of energy rendering the additional inductor energy insignificant.
When comparing the total energies, the LC configuration changes least as n increases.
The LCL and LLCL ones are close to the LC configuration, whereas the L and LC+L configurations have the second largest and largest energies. In the weak grid case, where the grid-side inductor and capacitor values are smaller, the LCL and LLCL experience less change than the LC but the L and LC+L configurations remain the least modular.
Both the resonance shift and energy and their change can be influenced by component changes. However, the inverter-side inductor is a fixed design married normally to the inverter, being seldom a component that can be changed. Moreover, in many cases the whole filter is an integrated structure, which means that single components cannot be changed for retrofit or maintenance reasons. This holds for the LCL, LLCL, LC, and LC+L configurations with the exception that the common grid-branch inductor of the LC+L can be changed as it is an individual component.
In the L-configuration, the capacitor and the grid-side inductor can both be individual components, or they can be integrated into one unit. Regardless of which of these options is the basis for the design of the L-configuration, the modularity of the configuration is very high, especially from the perspectives of retrofit and maintenance. The inverter-side inductor can be integrated into the inverter module while for a particular number of
parallel-connected inverters, either the capacitor, grid-side inductor, or both can be changed to accommodate the requirements of the application. Of course, the integrated CL circuit option would be better from the viewpoint of component optimization because the connections between the components can be minimized or at least optimized. The capacitor and the grid-side inductor can be designed in such a way that the resonances and attenuation stay within the designed range for a few paralleled inverters. When more inverters are added in parallel, a new CL circuit will be chosen, which will work again for a few more paralleled inverters.
For the other configurations, the filters can be designed in such a way that they provide adequate attenuation and resonances are kept within the desired range for instance by using a capacitor value that suits for a range of paralleled inverters. In section 3.4.2 this was referred to as ‘average filter design’ or ‘average capacitor’ to be accurate. The capacitor value can be chosen as an average over a certain range of numbers of parallel-connected inverters. In this way, the resonances can be kept within a chosen range while the attenuation is not compromised. If the average capacitor is used for a number of paralleled inverters at the low end (n = 2−3) of the range, the resonances are higher and the attenuation is less than in the middle of the range. Similarly, at the high end (n = 4−6) of the range, the resonances are lower but the attenuation is greater than in the middle.
The best configuration for the average filter design is the LLCL one because of its additional resonance, which should be placed at the switching frequency. Although this third resonance changes the increase rate of the attenuation to 20 dB/dec after the resonance, it ensures that the attenuation around the switching frequency and above it is not lost with the average capacitor at the low end of the range of paralleled inverters.
When the capacitor is changed, the series inductor also has to be changed. However, with the average capacitor being fixed, the inductor is also fixed and it evens out the shift.
Because of the lack of a grid-side inductor, the LC configuration generally requires a larger capacitor to achieve fr2 ≤ fsw /2. Generally, the average capacitor is smaller than it would be for a single filter, which means that the applicability of the average capacitor design for this configuration is more limited than for the LLCL, LCL, and LC+L cases, where the grid-side inductor allows the use of smaller capacitances.
From the perspective of maintenance, the L-configuration is the best one. This is naturally due to the fact that it presents more components that can be changed if broken, or even better, which are about to break. The common capacitor can be replaced or both capacitor-inductor on the grid side can be replaced. For the other configurations, all filter components of a single filter are more likely to be changed in case of failure. Of course, the filters can be designed in such a way that for instance capacitors can be changed from the integrated design, but this may not be the best solution as it most certainly will take more time than changing the whole filter. The LC and LC+L configurations can present better modularity by maintenance compared with the LCL and LLCL configurations.
Considering a situation where L1 or Cf (which can be assumed to be integrated components) fail, the module is replaced, leading to a maximum of two components to
be replaced at a time. With the LCL and LLCL configurations, the filter as a whole is replaced because it is often integrated into one unit.
However, both the common capacitor and the common grid-side inductor are crucial components for the operation of the whole system. If one of them fails, all inverters with individual inductors are down, whereas in the other configurations, only the failed inverter is off-line while the others can operate at least with partial power.
To summarize the discussion on the modularity of each configuration, the following observations were made
The L-configuration presents great modularity from all aspects discussed above, especially from the perspectives of retrofit and maintenance. Furthermore, the L-configuration does not present cross-coupling resonance, which does not have to be taken into account when changing components.
The common capacitor and grid-side inductor make the L-configuration least redundant. If either of them fails, none of the inverters can feed power to the grid. Similarly, the LC+L configuration suffers from decreased redundancy caused by the common grid-side inductor.
The LLCL configuration is the most modular one because of its third resonance frequency at the switching frequency, which keeps the high-frequency
attenuation at a good level even if the capacitor was designed for a broader range of paralleled inverters.
The LC+L configuration benefits from the grid-side inductor compared with the LC configuration. However, the grid-side inductor leads to more energy stored in the filter components, and thus, a larger filter configuration.
The LC configuration needs a larger capacitor to place the filter resonance low enough, which limits the modularity of this configuration to a narrower range of paralleled inverters.