Control of DSTATCOM using reduced order-based adaptive observer under grid supply with optimized PI gains

Abstract

An adaptive observer with a decreased order is proposed in this study for use in the hardware implementation of a 3-p, 3-w distribution static compensator (DSTATCOM), which extracts grid parameters. The DSTATCOM is inculcated for attaining various functions like reactive power compensation, mitigation of current source related harmonics accompanied by the self-sufficient DC bus. A reduced order-based adaptive observer is incorporated to determine grid parameters which work under the polluted condition and does not depend on the linearization of PD output using PLL. A Lyapunov function is incorporated for ensuring the proper tracking of grid parameters under the distorted conditions which makes the system adaptive. In order to achieve the fine tuning of proportional integral gains which preserves the DC bus voltage to its craved value, Gray Wolf Optimizer is employed which utilizes very less memory and requires very less parameters reducing the computation time offering faster response in achieving the values with lower settling and rise time in comparison with manual method. Simulation in MATLAB and hardware prototy** in the laboratory with the aid of a digital signal processor are used to evaluate the control algorithm's performance, with the findings validating the control algorithm's performance.

Appendix

1.1 Parameter for the simulation of reduced order observer-based FLL on DSTATCOM for PFC Mode

AC supply: 3 phase, 50 Hz; 420 V (line to line), Nonlinear Load: Three-phase diode bridge rectifier with RL load where R = 10 ohms and L = 100mH; Passive ripple filter: $R_{{\text{f}}}$ = 5 Ω, $C_{{\text{f}}}$ = 10 $\mu F$; dc link reference voltage: 700 V; dc link capacitor ($C_{{{\text{dc}}}}$): 5000 $\mu F$; Intermediate filter inductor: $L_{{\text{f}}}$ = 3mH; Low pass filter (LPF) cut off frequency: 8 Hz, Gains of dc link controller: $k_{p}$ = 3 and $k_{i}$ = 1.5

1.2 Parameter for the simulation of reduced order observer-based FLL on DSTATCOM for ZVR Mode

AC supply: 3 phase, 50 Hz; 420 V (line to line), Nonlinear Load: Three-phase diode bridge rectifier with RL load where R = 10 ohms and  L = 100mH; Passive ripple filter: $R_{{\text{f}}}$ = 5 Ω, $C_{{\text{f}}}$ = 10 $\mu F$; dc link reference voltage: 700 V; ac link reference voltage: 339 V; dc link capacitor ($C_{{{\text{dc}}}}$): 5000 $\mu F$; Intermediate filter inductor: $L_{{\text{f}}}$ = 3mH; Low pass filter (LPF) cut off frequency: 8 Hz, Gains of dc link controller: $k_{p}$ = 2.9 and $k_{i}$ = 1.9

1.3 Parameter for hardware setup of reduced order observer-based FLL on DSTATCOM

AC supply: 3 phase, 50 Hz; 110 V (line to line), Nonlinear Load: Three-phase diode bridge rectifier with RL load where R = 30 ohms and L  = 100mH; Passive ripple filter: $R_{{\text{f}}}$ = 5 Ω, $C_{{\text{f}}}$ = 10 $\mu F$; dc link reference voltage: 200 V; Intermediate filter inductor: $L_{{\text{f}}}$ = 4mH; Low pass filter (LPF) cut off frequency: 10 rad/s; Load side inductance = 2mH.

1.4 Selection of DC link

The threshold value of the DC link voltage $V_{{{\text{dc}}}}$ of the DSTATCOM must be greater than the twice the maximum value of the phase voltage in the distribution system. The DC bus voltage can be computed as,

$$ V_{{{\text{dc}}}} = \frac{{2\sqrt 2 V_{L - L} }}{\sqrt 3 m} $$

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Here, line to line voltages are taken as 420 V, m is the modulation index with the value of 1. Substituting these values in above equation, we get,

$$ \begin{aligned} & = \frac{2\sqrt 2 \times 420}{{\sqrt 3 \times 1}} \\ & = 685.7 \cong 700 \, \text{volts} \\ \end{aligned} $$

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1.5 Selection of inductor

The choice of the AC inductance $L_{{\text{f}}}$ for voltage source converter is determined by the ripple content of the current $i_{{{\text{ripple}}}}$ which is to be considered as 15%, switching frequency $f_{{{\text{sw}}}}$ which is taken as 1.8 kHz, and DC line voltage $V_{{{\text{dc}}}}$, and it is mathematically expressed as,

$$ L_{\text{f}} = \frac{{\sqrt 3 \times m \times V_{\text{dc}} }}{{(12 \times a \times f_{\text{sw}} \times i_{\text{ripple}} )}} $$

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where a is an overloading factor with the value 1.2, substituting all the values of the parameters in the above equation, the value of the inductor for VSC can be given as,

$$ \begin{aligned} L_{\text{f}} & = \frac{\sqrt 3 \times 1 \times 700}{{12 \times 1.2 \times 1.8 \times 10^{3} \times 0.15}} \\ & = 3.11\text{mH} \cong 3\text{mH} \\ \end{aligned} $$

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