Impact of Converters Interactions on Control Design in a Power Electronics Dense Network: Application to More Electric Aircraft

The aim of the work described in this paper is to analyze the impact that converters interactions, in a power electronics embedded grid, have on the control performance of each subsystem, with particular focus on More Electric Aircraft (MEA) applications. The study has been carried out on a notional electrical system composed by two three-phase power converters – a Voltage Source Inverter (VSI) and an Active Front End (AFE) which are commonly used in More Electric Aircraft applications. The analysis has been conducted in order to show the necessity of using a global control design approach in such electrical systems, rather than on individual converters. The modelling approach and controller design are presented in the paper, supported by simulation and experimental validation.


Introduction
The More Electric Aircraft concept has become one of the major trends in modern aerospace engineering [1]. Conventional devices which have been powered by pneumatic, hydraulic or mechanical power sources are being replaced by electrical systems [2]. Therefore, aircraft electrical systems are becoming increasingly complex and the number of power converters in aircraft electrical systems is rapidly growing [3]. Hence, converters may influence each other affecting the dynamic behaviour and stability of the single converter control system [4]. Consequently, aircraft control requirements (DO160, MIL 704F) might not be met.
In order to analyze the effects of converters' interactions a notional electrical system composed of two power converters has been studied. The first converter is a three-phase VSI which is supplied by 350V dc (V DC ) voltage. VSI generates 115 V (rms) 400 Hz AC grid. The second converter is a three-phase AFE which is supplied by the ac grid and loaded on its dc side by a resistive load (R LOAD ). Both converters are controlled by PI controllers designed separately for each converter. The described system is shown in the Fig. 1

Modelling
The models of the studied electrical system have been implemented in Mathworks Simulink software. The small-signal models of the converters were created on the basis of the dq-transformations concept. These models are sufficient for a design and analysis of the control system [5,6].

VSI model
The avarage model of the VSI system is derived by the equations (1) -(4) below : L,C, R are the VSI output filter inductance, capacitance and parasitic resistance respectively. I id , I iq are the output inductance current in its dq-frames, V cd ,V cq are the output capacitor voltage in its dq-frames. m d and m q are modulation indexes in dq-frame respectively, ω is the AC supply angular frequency, V dc i is the VSI dc voltage and it is assumed to be constant.

AFE model
The avarage model of the AFE system with a resistive load on its DC side is derived by the equations (5) -(7) below : L a , R a are the AFE input filter inductance and parasitic resistance, C a is the AFE output capacitance, I ad , I aq are the input inductance current in its dq-frames, V dc a is the dc-link output voltage, p d and p q are modulation indexes in dq-frame respectively, ω is the AC grid angular frequency, R L is a dc side resistive load.
The converters' filters values have been designed on the basis of power quality standards requirements in the nominal operating point. The system rated parameters are presented in the table below (Table I).

Controller Design
The designed converters control system consists of 4 control loops containing PI controllers. Two for controlling VSI output voltage and current (V cd and I iq ), other two control AFE output voltage and current (V dc a and I aq ). V cd and V dc a are set to the nominal values references V cd = 162.6 V (115 V rms), V dc = 350 V dc accordingly. I iq and I aq are set to 0 in order to keep unity power factor. The control design has been carried out individually for each converter, the appropriate gains calculation for each PI controller is derived below.

VSI controller
VSI PI controller gains are calculated by using the following equations (8) -(11) K pv V SI and K iv V SI are proportional and integral gains for VSI voltage loop PI controller, K pi V SI and K ii V SI are proportional and integral gains for VSI current loop. f v V SI and f i V SI are voltage and current loop controller bandwidths accordingly. ζ is a damping factor and is set to one in the whole analysis.

AFE controller
AFE PI controller gains are calculated by using the following equations (12) -(15) K pv AFE and K iv AFE are proportional and integral gains for AFE voltage loop PI controller, K pi V SI and K ii V SI are proportional and integral gains for VSI current loop. f v AFE and f i AFE are voltage and current loop controller bandwidths accordingly.
The simulation using dq frame representation allowed to verify whether the system meets the control requirements. The designed system based on the nominal parameters of the filters meets DO160 and MIL704F standards. The simulation results presenting output currents and voltages waveforms of the designed electrical system with PI control strategy are depicted in the Fig. 2. Figure shows dynamic behaviour of the system where the resistive load R L =80 Ω is connected at 0.2 s.

Dynamic Behaviour Analysis
The study of the passive components influence on the global behaviour of the system was performed with using the average model. In order to analyse this influence different sets of the VSI LC filter and AFE L and C filters parameters have been tested. Afterwards, the system dynamic behaviour such as both converters output voltages, voltage overshoots, undershoots and settling times for each set have been compared with the standards. The analysis has revealed that the components which have a significant influence on the global control system are the capacitors of the VSI LC filter and inductors of the AFE L filter. By reducing their values the control system performance is decreased. Fig. 3 presents the simulation results of the dynamic behaviour analysis. The resistive load R L =80 Ω was connected in each test at time 0.5s. Fig. 3a, Fig. 3b and Fig. 3c   The simulation results showed that increasing the LC filter cutoff frequency decrease the global system performance so the flexibility of changing the AFE boost inductor L a in order to maintain requirements met. In the case when cutoff frequency f c =2358 Hz, the system dynamic behaviour does not meet the requirements even with the nominal value of the AFE boost inductor L a =636.3 µH. It implies that individually designed converters' controllers which meets the requirements, might not meet the requirements when converters are connected together. This specifically underlines the need of considering both converters when designing the controller of each individual converter [7]. One of the solutions might be to increase the controllers bandwidths [8] [9], however, they are limited by the sampling frequency of the controlling unit e.g. FPGA/DSP.

Experimental Measurements
In order to verify the simulation results, a prototype VSI-AFE rig has been built (Fig. 4). During the test similar filter parameters to the those used in the simulation has been used, however, due to limitations of the VSI converter (max. input voltage 300 V dc) its reference output voltage has been set to 80 V rms instead of 115 V rms. Otherwise, the VSI controller would be saturated when supplying the VSI with 300V dc. Moreover, the resistive load has been changed to R L =19.4 Ω. The passive filter parameters which have been used in the tests are L=245 µH,C=33 µF, C=16 µF, L a =595 µH, L a =345 µH and C a =100 µH. The controller bandwidths had to be reduced due to FPGA/DSP limitations to f i V SI =800 Hz, f v V SI =80 Hz, f i AFE =500 Hz and f v AFE =30 Hz. The measurements have been performed with using ADC channels of the controller. The experiments results show the same trend to the ones obtained from the simulation, however, the changes for different sets of passive filters are lesser due to decreased values of the VSI output voltage and resistive load. Moreover, for smaller values of the filters components output voltages are more distorted so the differences are even harder to recognize. Nevertheless, we can see that increasing VSI LC filter cutoff frequency and decreasing AFE boost inductor affects the global system performance.

Conclusion
The analysis carried out in this work has revealed that the coupling between two converters affects the control performance. Due to that, both converters with individually designed control systems might not meet requirements when they are connected together. Therefore, it is necessary to either consider whole system in the control design process or design the global system controller in order to meet the aircraft requirements. To sum up, using a standard controller approach like PI, PID could not sufficient in some cases due to bandwidth or dynamic behaviour limitations. Thus, it is advised to use advanced control strategies such as LQR and H2 which represents much better performance [10].