An innovative OANF–IPFC based on MOGWO to enhance participation of DFIG-based wind turbine in interconnected reconstructed power system

Abstract

Despite the affordability and popularity of doubly fed induction generator (DFIG) among the variable-speed wind turbines, it cannot follow the inertia response caused by the load perturbations and the imposed frequency fluctuations in the power system. Considering the growing participation of wind power generation, DFIG with no virtual inertia control cannot play a functional role in the frequency stability of traditional power systems. At the outset, a new inertia control strategy is proposed for DFIG to participate in system frequency control via absorption or disposal of kinetic energy based on active power control. Then after that, interline power flow controller (IPFC) known as an adaptable and complex compensator is introduced to simultaneously regulate and control the power flow of multiple lines during the large penetration of DFIGs. To enhance the damping capability of IPFC, this paper has suggested a novel optimal adaptive neuro-fuzzy (OANF). The frequency and tie-line power deviations as two prominent stability benchmarks have been considered and analysed to appraise the damping capability of the suggested controller in the affected interconnected power system. The dynamic stability problem has been formulated based on multi-objective grey wolf optimizer to optimally tune OANF-based IPFC towards simultaneous suppression of the abovementioned benchmarks. The accurate fuzzy membership functions and rules of OANF-based IPFC have been extracted during the severe perturbation in two interconnected reconstructed power systems. Eventually, the simulation results extracted from both the three-area and five-area interconnected power systems have primarily validated the inertia control-based DFIG and subsidiarily OANF–IPFC to effectively suppress the low-frequency oscillations.

Appendices

Appendix 1: DFIG-based VSWT Bhatt et al. (2017)

H_e = 3.5 p.u. MW.sec, K_ωi = 0.1, K_ωp = 1.23, R = 3, T_a = 0.2 s, T_ω = 6, C₁ = 0.5176, C₂ = 116, C₃ = 0.4, C₄ = 5, C₅ = 21, C₆ = 0.0068, V_ω = 12 m/s.

Appendix 2: Linearization process of IPFC for AGC

Based on the phasor diagram shown in Fig. 3c, the total steady-state current of area m (I_m0) can be presented by:

$$ I_{m0} = I_{mn0} + I_{mk0} $$

(42)

$$ I_{mn0} = \frac{{V_{m} \angle \theta_{m} - V_{n} \angle \theta_{n} }}{{jX_{mn} }} $$

(43)

$$ I_{mk0} = \frac{{V_{m} \angle \theta_{m} - V_{n} \angle \theta_{n} }}{{jX_{mk} }} $$

(44)

where X_mn= X_L,mn+ X_S,mn and X_mk= X_L,mk+ X_S,mk. The current angle of each area can be extracted as follows:

$$ \theta_{c,mn} = \cos^{ - 1} \left( {\frac{{V_{m} \sin \theta_{m} - V_{n} \sin \theta_{n} }}{{\sqrt {V_{n}^{2} + V_{m}^{2} - 2V_{n} V_{m} \cos \theta_{mn} } }}} \right) $$

(45)

$$ \theta_{c,mk} = \cos^{ - 1} \left( {\frac{{V_{m} \sin \theta_{m} - V_{k} \sin \theta_{k} }}{{\sqrt {V_{k}^{2} + V_{m}^{2} - 2V_{k} V_{m} \cos \theta_{mn} } }}} \right) $$

(46)

where $\cos \theta_{mn} = \cos (\theta_{m} - \theta_{n} )$, $\cos \theta_{mk} = \cos (\theta_{m} - \theta_{k} )$

Existing IPFC in multiple transmission lines (Fig. 3d), Eqs. 43 and 44 are represented as follows:

$$ I_{mn} = \frac{{V_{m} \angle \theta_{m} - V_{s,mn} \angle \alpha - V_{n} \angle \theta_{n} }}{{jX_{mn} }} = \left[ {\frac{{V_{m} \angle \theta_{m} - V_{n} \angle \theta_{n} }}{{jX_{mn} }}} \right] + \left[ { - \frac{{V_{s,mn} \angle \alpha }}{{jX_{mn} }}} \right] = I_{mn0} + \Delta I_{mn0} $$

(47)

$$ I_{mk} = \frac{{V_{m} \angle \theta_{m} - V_{s,mk} \angle \alpha - V_{k} \angle \theta_{k} }}{{jX_{mk} }} = \left[ {\frac{{V_{m} \angle \theta_{m} - V_{k} \angle \theta_{k} }}{{jX_{mk} }}} \right] + \left[ { - \frac{{V_{s,mk} \angle \beta }}{{jX_{mk} }}} \right] = I_{mk0} + \Delta I_{mk0} $$

(48)

ΔI_mn0 and ΔI_mk0 are, respectively, the complementary current terms related to the IPFC compensation voltages. The apparent power of area m is given as follows:

$$ \begin{aligned} S_{m} & = V_{m} \left( {I_{mn} + I_{mk} } \right)^{*} = S_{m0} + \Delta S_{m} \\ P_{m} + jQ_{m} & = (P_{m0} + \Delta P_{m} ) + j(Q_{m0} + \Delta Q_{m} ) \\ \end{aligned} $$

(49)

where P_m0 and Q_m0 are, respectively, the active and reactive powers lacking IPFC, i.e. (V_s,mn= V_s,mk= 0). The active power of area m flowed to area n and area k with existence of IPFC can be attained as follows:

$$ \Delta P_{mn} = \frac{{V_{m} V_{s,mn} }}{{X_{mn} }}\sin (\theta_{m} - \alpha ) $$

(50)

$$ \Delta P_{mk} = \frac{{V_{m} V_{s,mk} }}{{X_{mk} }}\sin (\theta_{m} - \beta ) $$

(51)

It is worth mentioning that V_s,mn and V_s,mk are, respectively, perpendicular to I_mn and I_mk ($\alpha = \theta_{c,mn} - \pi /2$, $\beta = \theta_{c,mk} - \pi /2$); hence, ΔP_mn and ΔP_mk are:

$$ \Delta P_{mn} = \frac{{V_{m} V_{s,mn} }}{{X_{mn} }}\cos (\theta_{m} - \theta_{c,mn} ) $$

(52)

$$ \Delta P_{mk} = \frac{{V_{m} V_{s,mk} }}{{X_{mk} }}\cos (\theta_{m} - \theta_{c,mk} ) $$

(53)

As there is no active power exchange by IPFC, the active power in the left and right sides of IPFC’s VSCs is alike:

$$ \Delta P_{mn} = \frac{{V_{m} V_{s,mn} }}{{X_{mn} }}\cos (\theta_{m} - \theta_{c,mn} ) = \frac{{V_{n} V_{s,mn} }}{{X_{mn} }}\cos (\theta_{n} - \theta_{c,mn} ) $$

(54)

$$ \Delta P_{mk} = \frac{{V_{m} V_{s,mk} }}{{X_{mk} }}\cos (\theta_{m} - \theta_{c,mk} ) = \frac{{V_{k} V_{s,mk} }}{{X_{mk} }}\cos (\theta_{k} - \theta_{c,mn} ) $$

(55)

With more simplification:

$$ \cos (\theta_{m} - \theta_{c,mn} ) = \frac{{V_{n} }}{{V_{m} }}\cos (\theta_{n} - \theta_{c,mn} ) $$

(56)

$$ \cos (\theta_{m} - \theta_{c,mk} ) = \frac{{V_{k} }}{{V_{m} }}\cos (\theta_{k} - \theta_{c,mk} ) $$

(57)

As for Fig. 3c:

$$ \cos (\theta_{n} - \theta_{c,mn} ) = \frac{{V_{m} \sin \theta_{mn} }}{{\sqrt {V_{n}^{2} + V_{m}^{2} - 2V_{n} V_{m} \cos \theta_{mn} } }} $$

(58)

$$ \cos (\theta_{k} - \theta_{c,mk} ) = \frac{{V_{m} \sin \theta_{mk} }}{{\sqrt {V_{k}^{2} + V_{m}^{2} - 2V_{k} V_{m} \cos \theta_{mk} } }} $$

(59)

Considering the aforementioned equations, ΔP_mn and ΔP_mk are, respectively, calculated as:

$$ \Delta P_{mn} = \frac{{V_{n} V_{s,mn} }}{{X_{mn} }}*\frac{{V_{m} \sin \theta_{mn} }}{{\sqrt {V_{n}^{2} + V_{m}^{2} - 2V_{n} V_{m} \cos \theta_{mn} } }} $$

(60)

$$ \Delta P_{mk} = \frac{{V_{k} V_{s,mk} }}{{X_{mk} }}*\frac{{V_{m} \sin \theta_{mk} }}{{\sqrt {V_{k}^{2} + V_{m}^{2} - 2V_{k} V_{m} \cos \theta_{mk} } }} $$

(61)

From (49)

$$ \begin{aligned} P_{m} & = P_{mn} + P_{mk} = P_{m0} + \Delta P_{m} = \left( {\frac{{V_{n} V_{m} }}{{X_{mn} }}\sin \theta_{mn} + \frac{{V_{k} V_{m} }}{{X_{mk} }}\sin \theta_{mk} } \right) \\ & \quad + \left( {\frac{{V_{n} V_{m} }}{{X_{mn} }}\sin \theta_{mn} \frac{{V_{s,mn} }}{{\sqrt {V_{n}^{2} + V_{m}^{2} - 2V_{n} V_{m} \cos \theta_{mn} } }} + \frac{{V_{k} V_{m} }}{{X_{mk} }}\sin \theta_{mk} \frac{{V_{s,mk} }}{{\sqrt {V_{k}^{2} + V_{m}^{2} - 2V_{k} V_{m} \cos \theta_{mk} } }}} \right) \\ \end{aligned} $$

(62)

Appendix 3: Three-area hydro–thermal power system Falehi et al. (2016)

K_P1 = K_p2 = 120 Hz/p.u MW, R₁ = R₂ = R₃ = R₄ = 2.4 Hz/p.u MW, T_g = 0.08 s, T_T = 0.3 s, T_R = 5 s, T_W = 1 s, K_P = 1.0, K_i = 5.0, K_d = 4.0, D_i = 0.00833 p.u.MW/Hz, T_w = 1.0 s, P_R1 = 1800 MW, P_R2 = 1200 MW, $G_{D} = \frac{16.5s + 16.5}{{(1/40)s^{2} + s}}$

Linearization of three-area hydro–thermal power system

For thermal areas (Falehi 2017):

$$ \Delta f_{i} \left( s \right) = \frac{{K_{pi} }}{{1 + sT_{pi} }}\left[ {\Delta P_{Gi} \left( s \right) - \Delta P_{Di} \left( s \right) - \Delta P_{i} \left( s \right)} \right] $$

(63)

$$ \Delta P_{Gi} \left( s \right) = \frac{{1 + sK_{ri} T_{ri} }}{{T_{ri} }}\Delta P_{Ri} \left( s \right) $$

(64)

$$ \Delta P_{Ri} \left( s \right) = \frac{1}{{1 + sT_{ti} }}\Delta x_{Ei} \left( s \right) $$

(65)

$$ \Delta P_{{{\text{ref}}i}} \left( s \right) = - G_{{{\text{AGC}},i}} (s)\left[ {B_{i} \left( s \right)\Delta f_{i} \left( s \right) + \Delta P_{i} \left( s \right)} \right] $$

(66)

$$ \Delta x_{Ei} \left( s \right) = \frac{1}{{1 + sT_{gi} }}\left[ {\Delta P_{{{\text{ref}}i}} \left( s \right) - \frac{1}{{R_{i} }}\Delta f_{i} \left( s \right)} \right] $$

(67)

where subscript i (i = 1, 2) is defined as every thermal area (Falehi 2017).

For hydro area:

$$ \Delta f_{3} \left( s \right) = \frac{{K_{p3} }}{{1 + sT_{p3} }}\left[ {\Delta P_{G3} \left( s \right) - \Delta P_{D3} \left( s \right) - \Delta P_{3} \left( s \right)} \right] $$

(68)

$$ \Delta x_{E3} \left( s \right) = \frac{{K_{d} .s^{2} + K_{p} .s + K_{i} }}{{K_{d} .s^{2} + \left( {K_{p} + {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {R_{3} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${R_{3} }$}}} \right).s + K_{i} }}\left[ {\Delta P_{ref3} \left( s \right) - \frac{1}{{R_{3} }}\Delta f_{3} \left( s \right)} \right] $$

(69)

$$ \Delta P_{G3} \left( s \right) = \frac{{1 - sT_{W} }}{{1 + 0.5sT_{W} }}\Delta P_{R3} \left( s \right) $$

(70)

$$ \Delta P_{ref3} \left( s \right) = - G_{AGC,3} (s)\left[ {B_{3} \left( s \right)\Delta f_{3} \left( s \right) + \Delta P_{3} \left( s \right)} \right] $$

(71)

The tie-line power deviation is (Falehi 2017):

$$ \Delta P_{12} \left( s \right) = \frac{{2\pi T_{12} }}{s}\left( {\Delta f_{1} \left( s \right) - \Delta f_{2} \left( s \right)} \right) $$

(72)

$$ \Delta P_{23} \left( s \right) = \frac{{2\pi T_{23} }}{s}\left( {\Delta f_{2} \left( s \right) - \Delta f_{3} \left( s \right)} \right) $$

(73)

$$ \Delta P_{31} \left( s \right) = \frac{{2\pi T_{31} }}{s}\left( {\Delta f_{3} \left( s \right) - \Delta f_{1} \left( s \right)} \right) $$

(74)

Furthermore (Falehi 2017),

$$ \Delta P_{1} \left( s \right) = \Delta P_{12} \left( s \right) + \alpha_{31} \Delta P_{31} \left( s \right) $$

(75)

$$ \Delta P_{2} \left( s \right) = \alpha_{12} \Delta P_{12} \left( s \right) + \Delta P_{23} \left( s \right) $$

(76)

$$ \Delta P_{3} \left( s \right) = \alpha_{23} \Delta P_{23} \left( s \right) + \Delta P_{31} \left( s \right) $$

(77)

Appendix 4: Five-area thermal power system Falehi et al. (2016)

f = 60 Hz; T_gi = 0.08 s; T_ri = 10 s; H_i = 5 s; T_ti = 0.3 s; K_r = 0.5; P_ri = 2000 MW; T_pi = 20 s; K_d = 4.0, K_p = 1.0, K_i = 5.0; D_i = 0.1283 p.u.MW/Hz; K_pi = 120 Hz/p.u MW, T_w = 1 s, a₁₂ = a₁₃ = a₂₃ = − 1 (Fig. 10).

Fig. 10

a Linearized model of reconstructed three-area hydro–thermal power system with the presence of OANF-based IPFC (Falehi et al. 2016). b Linearized model of reconstructed five-area thermal power system with the presence of OANF-based IPFC (Falehi et al. 2016)