10. Power electronics topics¶
10.1. Switching cell¶
10.1.1. Generalized switching cell¶
In its most general form, a generalized switching cell is a set of n switches with:
the first terminals of the switches connected to n voltage source terminals, and
the second terminals of the switches forming with one terminal of a current source all the terminals of a subcircuit, so that we have \(Σ (i_K) = I_{current source}\)
An essential property of such a cell is that at all times one and only one switch must be on, and all others must be blocked. Indeed, only one of the n switches must be on (several conducting switches would create a direct path between the terminals of different voltage sources), and at least one switch must be conducting (otherwise there would be no path for the current of the current source to flow).
Discontinuous conduction mode is an exception to this rule because all switches can be blocked when the current source is zero, but only the continuous conduction mode is supported in PowerForge.
10.1.2. Elementary switching cell¶
In this document, an elementary switching cell will designate a switching cell composed of 2 switches. As a consequence of the former comment, the two switches must always be in opposite states (continuous conduction mode only).
10.1.3. Examples of use of switching cells¶
Conventional conversion circuits all use switching cells as defined above. Here are some examples:
With 2 voltage terminals
With such a cell called elementary switching cell, one can for example construct a chopper (buck, boost or buck-boost) or a half-bridge inverter.
With two of these cells, a complete bridge inverter can be constructed, and with three of these cells a three-phase voltage source inverter.
With 3 voltage terminals
Another conventional case corresponds to n = 3 and makes it possible to produce the so-called ‘current switch’ or ‘Graetz bridge’ structures.
With 3 voltage terminals and DC voltage source
There are different ways to obtain a 3-voltage terminal ‘Holtz’ or ‘T-type’ or ‘NPC’ or ‘ANPC’:
All these variants give the same operation seen from the terminals of the cell, but can use different semiconductors (series association of bidirectional-for-current switches or parallel association of bidirectional-for-voltage switches for the T-type mid-switch, for example), or even different switches to achieve the connection, (difference between T-type and NPC for example …).
10.1.4. Macro switching cell¶
10.1.4.1. Principles of association of elementary switching cells¶
A macro switching cell, or macrocell is a combination of elementary switching cells for distributing the voltage and/or the current between different cells. Different principles of association have been proposed under various and sometimes redundant denominations; it is however possible to group them into three main forms which we will call here:
flying Capacitor (index fc),
parallel (index par),
stacked (index stack).
The connection terminals of a macrocell are:
two terminals ‘+’ and ‘-’ which must be connected to a voltage source (perfect voltage source, capacitor or filter block generally requiring a DC voltage such that \(V_+ - V_- \approx constant > 0\) ),
ncell(par) terminals C which must be connected to ncell(par) star-connected reactors or a filter block.
This block also has an input receiving the duty cycle D comprised between 0 and 1 that allows varying the average potential of terminals C :
(The average potentials of the various terminals C are all identical since they are connected through inductors).
10.1.4.2. Properties common to flying capacitor, parallel and stacked associations¶
In these 3 macrocells, the switches_top1 and bot1 form a first Elementary switching cell , top2 and bot2 form another one.
These 3 macrocells all provide improved waveforms on the LV side:
voltage chopped at a frequency multiplied by two ( \(2.f_{sw}\)), where \(f_{sw}\) is the switching frequency,
amplitude of the chopped voltage divided by two ( \(V_{HV} / 2\)).
10.1.4.3. Properties common to flying capacitor and parallel associations¶
In a conversion scheme using one or more elementary switching cells with a DC voltage, each switching cell can be replaced by one of these switching macrocells. (The capacitive midpoint of the stacked structure is only compatible with inverter operation).
Some internal passive elements enable the elementary cells to be decoupled and their control signals to be phase-shifted.
If the duty cycles are equal and the phase shifts are equal to 360° \(/ n_{cell}\) , the stress applied to the different cells are balanced and a number of switching frequency harmonics are cancelled. The operation can thus be assimilated to operating at a frequency multiple of the switching frequency \(n_{cell}.f_{sw}\) , with an amplitude of the square signals divided by the number of cells \(V_{HV} / n_{cell}\). For details about the comments in this last paragraph, and especially to see which harmonics are affected and how the ‘Flying capacitor’, ‘parallel’ and ‘stacked’ configurations differ, see Analysis and Design of MultiCell DC / DC Converters using Vectorized Models …
10.1.4.4. Properties specific to parallel associations¶
Only the parallel configuration improves the waveforms of the HV side current:
current chopped at a frequency multiplied by 2 (\(2.f_{sw}\)),
amplitude of the chopped current divided by 2 (\(I_ {LV} / 2\)).
As a further improvement, the star-connected inductors between the points C of the different cells in parallel can be magnetically coupled. In theory this coupling makes it possible to impose identical currents in the various windings, which, compared with uncoupled inductances, allows reducing the current ripple in the coils and corresponding Joule losses. It should also be noted that in such coupled inductors we have in the window two identical coils flowing currents with the same average values in opposite directions; this means a theoretical compensation of the amp.turns product and a field distribution that is closer to what is observed in a transformer rather than in inductors. This last comment justifies using the name ‘InterCell Transformer’ rather than ‘coupled inductors’.
10.1.4.5. Combination of the principles of association of elementary cells¶
The principles presented above can be combined within the same macrocell that can then be characterized by three indices \([ n_{cell(fc)}, n_{cell(par)}, n_{cell(stack)} ]\):
If we define \(n_{cell}\) such as \(n_{cell} = n_{cell(fc)} \cdot n_{cell(par)} \cdot n_{cell(stack)}\) , we can say that the macrocell makes it possible to build choppers and inverters:
comprising \(n_{cell}\) elementary cells per macrocell,
- with each macrocell delivering or absorbing at LV side a current spectrum equivalent to that of an elementary cell,
switching at \(n_{cell} \cdot f_{sw}\),
supplied with a voltage of \(V_{HV} / n_{cell}\) (i.e. \((n_{cell} + 1)\) LV side voltage levels) equipped with a smoothing inductor of \(L_{LV} / n_{cell}\),
- with each macrocell delivering or absorbing at HV side a current spectrum equivalent to that of an elementary cell,
switching at \(n_{cell(par)} \cdot f_{sw}\)
and outputting a current of \(I_{LV} / n_{cell(par)}\) (i.e. \((n_{cell(par)} + 1)\) HV side current levels).
10.1.4.6. High voltage and low voltage¶
In most circuits, the macrocell block is used to manage the energy exchanges between two voltage sources having a common point (usually the - terminal of these sources, but it can also be the + terminal). It is then possible to distinguish a high voltage side (between + and - terminals) and a low voltage side (between terminal C and the common terminal) since the potential of point C can only evolve between that of the + and - terminals. It is important to distinguish between filters according to the way they are connected to the switching cell because macrocell must see the HV side filter as a voltage source and the filter on the LV side as a power source. This distinction remains valid whatever the direction of transfer and it is therefore preferable to the usual input/output distinction that no longer makes sense when reversible converters are considered.
10.1.4.7. Examples¶
The same Macrocell block can be used as a building block for most conversion circuits. For example the two simplest circuits:
buck converter (P> 0),
boost converter (same circuit but P <0).
10.2. Electrothermal coupling¶
The component temperature is unknown at the first time of the calculation of losses. Yet, these losses are calculated at maximum allowed temperature, it can be shown that this approach ensures a viable solution:
the losses lead to a temperature which is higher than the allowed temperature (maximum permissible temperature of the material that was selected), the solution is rejected,
the losses lead to a temperature which is lower than the allowed temperature and the losses at calculated temperature are lower than those calculated at allowed temperature, the temperature will stabilize at a temperature lower than the calculated temperature,
the losses lead to a temperature which is lower than the allowed temperature and the losses at calculated temperature are higher than those calculated at allowed temperature; the temperature will rise above the calculated temperature and stabilize somewhere between the calculated temperature and the allowed temperature.
As a conclusion, it should be remembered that in the real world, the electrothermal coupling can lead to losses less than those calculated and to a temperature between the calculated temperature and the maximum permissible temperature.
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