I believe that the simplification of the mathematical model of the plant. In addition, some frames of references such as dq allow control laws simple and easy to implement in DSPs, FPGAs, etc.

One of the main advantages of dq frame is that it allows instantaneous compensation of reactive power, because it waives the need for averaging.

Dear Juan and Amin

thanks for your responses. I want to know that is there any condition in which we are forced to use a specific reference frame?

I am not expert in control, but I believe that I know something about modeling. In modeling, the reference frame is selected according the phenomena that you want to know. For example, if you want to study harmonics, then you probably want to use an EMTP type models in the time-domain (phase or dq, among others), or one of the harmonic domain approach can also be used. Of course, this models are very detailed and consequently are complex and time-consuming. In practice, we select the simplest model that retain the information that we are interested with, therefore, we should start with a complex model and then simplify it step by step until we are sure that this is the simplest and also retain the information and phenomena that we want to study.

In control of power electronic converters, and probably in control applications, the plant model is simplified in order to use the available control theory and to develop lots of awesome mathematical equations, theorems, etc. I know that there are some control approaches tackling nonlinear, periodic and switched systems (realistic power networks with power electronic converters and controls); however, the theory is probably much more difficult and the developed controllers are more complex and consequently difficult to implement.

Hello Mr. Sadeghkhani 

before that I wana to explaine your answer, I should tell to you that, often, alpha, beta frame is used in unbalance condition. at least what I saw in the papers.

Dependence on voltage feed-forward and cross-coupling blocks are the major drawbacks of the control structure implementd in synchronous reference (dq) frame. The phase angle of the grid voltage should be extracted in this implementation. In the stationary reference frame (alpha, beta)  if PR controllers are used for current regulation, the complexity of the control becomes less compared to the structure implemented in the dq frame. also, the phase angle information is not necessary and filtered grid voltages can be used as templates for the reference current waveform. In the natural frame, the control system complexity will be increased if an adaptive hysteresis band controller is used for current regulation. A simpler control schem can be achieved by implementing a dead-beat controller instead. Note that for this control structure, each phase can be controlled independently if three single-phase PLLs are used to generate the current reference.

Dear Mehdi

Hello and thanks for your response. Can we said that in unbalanced condition, we should use stationary reference frame and natural frame is not applicable?

Hi,

Synchronous Reference Frame (SRF): In many cases a dq synchronous frame current regulator is preferred because there is a natural link between the real/reactive power and dq references. 

Using abc to dq transformation (or AlphaBeta to dq transformation) allows simple PI structures to be used for the power and current controllers, since they operate on “dc” converter variables in the synchronous frame and hence can achieve zero steady-state error because of the infinite DC gain of a PI regulator. Furthermore, only two regulator structures are required, in the d and q axes only, because the floating neutral connection of the utility grid means that the three phase currents must always sum to zero, and hence there is no fundamental zero-sequence current flowing through the inverter system.

Stationary Frame: In this frame in order to regulate the current, a resonant part should be added to the controller to compensate for the fundamental frequency component in the reference signal (which is  ac). So Proportional + Resonant (PR) controllers are basically used for this purpose.

Unbalanced: when the voltage is unbalanced, negative sequence component appear (in balanced systems negative sequence component is zero) as well as the positive sequence component. So proper current reference calculation and regulation is required to fully control the system. Briefly for unbalanced conditions, 4 current regulators are required (using simple PI regulator) in SRF and in stationary frame 2 regulators (PR regulator) are required. 

For more detailed controller design and implementation refer to:

balanced:

[1]     Zmood, D.N.; Holmes, D.G., "Stationary frame current regulation of PWM inverters with zero steady-state error," Power Electronics, IEEE Transactions on , vol.18, no.3, pp.814,822, May 2003.

unbalanced:

[2]     Kabiri, R.; Holmes, D.G.; McGrath, B.P., " Double Synchronous Frame Current Regulation of Distributed Generation Systems under Unbalanced Voltage Conditions without Sequence Current Separation," Applied Power Electronics Conference and Exposition (APEC), 2015 Thirtieth  Annual IEEE , vol., no., pp., 15-19 March 2015.

[3]     Kabiri, R.; Holmes, D.G.; McGrath, B.P., "Control of Distributed Generation Systems under Unbalanced Voltage Conditions," IPEC-Hiroshima 2014 -ECCE Asia, May. 18 2014 May. 21 2014.

Mr. Sadeghkhani 

in my opinion, Each frame can be used for transformation, but will consider your model complexity. as metioned above, using of  PI controller is ssociated with complexity of transfer function.