Enhanced Droop Control Strategy for Three-Phase Islanded Microgrid Without LBC Lines

Abstract

In this chapter, the equivalence between secondary control scheme and washout filter-based power sharing strategy for islanded microgrid is demonstrated, and the generalized washout filter control scheme is derived. Then, the physical meaning of control parameters of secondary controllers is illustrated. Besides, a complete small-signal model of the generalized washout filter-based control method for islanded MG system is built, which can be utilized to design the control parameters and analyze the stability of MG system. Moreover, the simulation results obtained from EMTP-ATP are given to illustrate the difference between the conventional droop control scheme and the washout filter-based improved droop control scheme, and hardware-in-the-loop results are also presented to show a comparative analysis under generic operating conditions. Finally, the experimental results from a reduced-scale prototype system are provided to confirm the validity and effectiveness of the derived equivalent control scheme for three-phase islanded MG.

Appendix A

The matrix T_BPF of power stage is derived as (6.A.1), and the elements in matrix T_BPF are depicted as (6.A.2) and (6.A.3):

$$ {\mathbf{T}}_{\mathbf{BPF}}={\left[\begin{array}{ccccc}-{\omega}_h& {k}_2{\omega}_c& 0& 0& 0\\ {}0& -{\omega}_c& 0& 0& 0\\ {}0& 0& -{\omega}_c& 0& 0\\ {}-{v}_q& 0& {k}_3{v}_d& -\frac{\omega_h{v}_d^2}{v_d^2+{v}_q^2}& -\frac{\omega_h{v}_d{v}_q}{v_d^2+{v}_q^2}\\ {}{v}_d& 0& {k}_3{v}_q& -\frac{\omega_h{v}_d{v}_q}{v_d^2+{v}_q^2}& -\frac{\omega_h{v}_q^2}{v_d^2+{v}_q^2}\end{array}\right]}_{5\times 5} $$

(6.A.1)

$$ {k}_1=\frac{n_q}{1+{k}_{p E}},\kern1.6em {k}_2=\frac{m_p}{1+{k}_{p\omega}},\kern1.6em {k}_3=\frac{k_1{\omega}_c\sqrt{v_d^2+{v}_q^2}}{v_d^2+{v}_q^2}. $$

(6.A.2)

$$ {\omega}_{h E}=\frac{k_{i E}}{1+{k}_{p E}},{\omega}_{h\omega}=\frac{k_{i\omega}}{1+{k}_{p\omega}}. $$

(6.A.3)

The matrices C_V, D_V1, D_V2, and B_V2 in the inner voltage controller are derived as:

$$ {\mathbf{C}}_{\mathbf{V}}={\left[\begin{array}{cc}{k}_{iv}& 0\\ {}0& {k}_{iv}\end{array}\right]}_{2\times 2},\kern1.6em {\mathbf{D}}_{\mathbf{V}\mathbf{2}}={\left[\begin{array}{cccccc}0& 0& -{k}_{pv}& -{\omega}^{\ast }{C}_f& F& 0\\ {}0& 0& {\omega}^{\ast }{C}_f& -{k}_{pv}& 0& F\end{array}\right]}_{2\times 6} $$

(6.A.4)

$$ {\mathbf{D}}_{\mathbf{V1}}={\left[\begin{array}{cc}{k}_{pv}& 0\\ {}0& {k}_{pv}\end{array}\right]}_{2\times 2},\kern1em {\mathbf{C}}_{\mathbf{C}}={\left[\begin{array}{cc}{k}_{ic}& 0\\ {}0& {k}_{ic}\end{array}\right]}_{2\times 2},\kern1em {\mathbf{B}}_{\mathbf{V2}}={\left[\begin{array}{cccccc}0& 0& -1& 0& 0& 0\\ {}0& 0& 0& -1& 0& 0\end{array}\right]}_{2\times 6}. $$

(6.A.5)

The matrices C_C, D_C1, D_C2, and B_C2 in the inner current controller are derived as:

$$ {\mathbf{D}}_{\mathbf{C2}}={\left[\begin{array}{cccccc}-{k}_{pc}& -{\omega}^{\ast }{L}_f& 0& 0& 0& 0\\ {}{\omega}^{\ast }{L}_f& -{k}_{pc}& 0& 0& 0& 0\end{array}\right]}_{2\times 6}. $$

(6.A.6)

$$ {\mathbf{D}}_{\mathbf{C1}}={\left[\begin{array}{cc}{k}_{pc}& 0\\ {}0& {k}_{pc}\end{array}\right]}_{2\times 2},\kern1.6em {\mathbf{B}}_{\mathbf{C2}}={\left[\begin{array}{cccccc}-1& 0& 0& 0& 0& 0\\ {}0& -1& 0& 0& 0& 0\end{array}\right]}_{2\times 6}. $$

(6.A.7)

The matrices A_LCL, B_LCL1, B_LCL2, and B_LCL3 in (6.20) are derived as (6.A.8) and (6.A.9).

$$ {\mathbf{A}}_{\mathbf{LCL}}={\left[\begin{array}{cccccc}-\frac{r_{L_f}}{L_f}& {\omega}^{\ast }& -\frac{1}{L_f}& 0& 0& 0\\ {}-{\omega}^{\ast }& -\frac{r_{L_f}}{L_f}& 0& -\frac{1}{L_f}& 0& 0\\ {}\frac{1}{C_f}& 0& 0& {\omega}^{\ast }& -\frac{1}{C_f}& 0\\ {}0& \frac{1}{C_f}& -{\omega}^{\ast }& 0& 0& -\frac{1}{C_f}\\ {}0& 0& \frac{1}{L_c}& 0& -\frac{r_{L_c}}{L_c}& {\omega}^{\ast}\\ {}0& 0& 0& \frac{1}{L_c}& -{\omega}^{\ast }& -\frac{r_{L_c}}{L_c}\end{array}\right]}_{6\times 6} $$

(6.A.8)

$$ {\mathbf{B}}_{\mathbf{LCL1}}={\left[\begin{array}{cc}\frac{1}{L_f}& 0\\ {}0& \frac{1}{L_f}\\ {}0& 0\\ {}0& 0\\ {}0& 0\\ {}0& 0\end{array}\right]}_{6\times 2},\kern1em {\mathbf{B}}_{\mathbf{LCL2}}={\left[\begin{array}{cc}0& 0\\ {}0& 0\\ {}0& 0\\ {}0& 0\\ {}-\frac{1}{L_c}& 0\\ {}0& -\frac{1}{L_c}\end{array}\right]}_{6\times 2},\kern1em {\mathbf{B}}_{\mathbf{LCL3}}={\left[\begin{array}{c}{I}_{lq}\\ {}-{I}_{ld}\\ {}{V}_{oq}\\ {}-{V}_{od}\\ {}{I}_{oq}\\ {}-{I}_{od}\end{array}\right]}_{6\times 1}. $$

(6.A.9)