Integration of Onshore Wind Farms to a Weak AC Grid Interfacing LCC HVDC Transmission

Abstract

This chapter presents three case studies relating challenges of interfacing doubly fed induction generator (DFIG)-based onshore wind farms in weak AC grids with line-commutated converter (LCC) HVDC. The first study focuses on modeling and analysis of the impact of inertia and effective short circuit ratio on control of frequency in such weak grids. In the second study, coupling between frequency dynamics of the AC systems on both inverter and rectifier side of LCC-HVDC with the rectifier station operating in frequency control is studied, along with the presence of large DFIG-based wind farms on the weak rectifier-side grid. The third study illustrates the effectiveness of converting conventional generators to synchronous condensers to improve frequency dynamics in weak grid systems following loss of infeed from a wind farm. The effectiveness of secondary frequency control through LCC HVDC is also investigated.

Appendices

Appendix 1

In an alternative form, the induction machine and the RSC dynamics can be modeled as follows (q-axis aligned with stator flux):

(4.28)

where

$$\displaystyle \begin{aligned} \begin{array}{rcl} v_{dt}&\displaystyle =&\displaystyle K_{ir} x_{rr2} + K_{pr} \left( {\frac{{L_{ss} K_{opt} \omega _{r\_dfg}^2 }}{{L_m^2 i_{ms} }} - i_{dr} } \right) \\ &\displaystyle &\displaystyle - s_l \omega \left\{ {\left( {\sigma L_{rr} + L_{fr} } \right)i_{qr}+ \frac{{L_m^2 }}{{L_{ss} }}i_{ms} } \right\} \end{array} \end{aligned} $$

$$\displaystyle \begin{aligned} \begin{array}{rcl} v_{qt}&\displaystyle =&\displaystyle K_{ir} x_{rr1} + K_{pr} \left\{ {i_{ms} + K_{vc} \left( {\left| {v_s^* } \right| - \left| {v_s } \right|} \right) - i_{qr}}\right\} \\ &\displaystyle &\displaystyle + s_l \omega \left( {\sigma L_{rr} + L_{fr} } \right)i_{dr} \\ L_{ss}&\displaystyle =&\displaystyle L_s + L_m, \quad \quad \quad \quad L_{rr}= L_r + L_m \\ K_{mrr}&\displaystyle =&\displaystyle L_m/L_{rr},\quad \quad \quad \quad \ \ \ L^{\prime}_{s}= L_{ss} - L_m/K_{mrr} \\ \sigma &\displaystyle =&\displaystyle 1 - L_m^2/(L_{ss}L_{rr}), \quad \, \ a= 1 + (L_{fr}/L_{rr}) \\ R_2 &\displaystyle =&\displaystyle K_{mrr}^2(R_{fr} + R_r), \quad \ T_r= L_{rr}/(R_{fr} + R_r) \\ i_{dr} &\displaystyle =&\displaystyle - \frac{{L_{ss} }}{{L_m }}i_{ds}, \quad \quad \quad \quad \quad i_{qr}= i_{ms} - \frac{{L_{ss} }}{{L_m }}i_{qs} \\ K_{opt} &\displaystyle =&\displaystyle 0.5\rho\pi R^5C_{Popt}/\lambda_{opt}^3 \end{array} \end{aligned} $$

The DC link and the GSC (q-axis aligned with v _s) can be modeled as described below:

$$\displaystyle \begin{aligned} \dot v_{dc}^2 &= -\frac{3}{C}\left[ { v_{dt} i_{dr} + v_{qt} i_{qr} + v_{dg} i_{dg} + v_{qg} i_{qg} } \right] \end{aligned} $$

(4.29)

$$\displaystyle \begin{aligned} \dot i_{qg} &= - \left( {\frac{{R_{fg} + K_{pg} }}{{L_{fg} }}} \right)i_{qg} + \left( {\frac{{K_{ig} }}{{L_{fg} }}} \right)x_{g1} + \left( {\frac{{K_{pg} }}{{L_{fg} }}} \right)i_{qg}^* \\ \dot i_{dg} &= - \left( {\frac{{R_{fg} + K_{pg} }}{{L_{fg} }}} \right)i_{dg} + \left( {\frac{{K_{ig} }}{{L_{fg} }}} \right)x_{g2} - \left( {\frac{{K_{pg} }}{{L_{fg} }}} \right)\left( {\frac{{2Q_{gsc}^* }}{{3v_{qs} }}} \right) \end{aligned} $$

(4.30)

Note that v _qg and v _dg can be expressed as:

$$\displaystyle \begin{aligned} v_{qg} &= K_{ig} x_{g2} + K_{pg} \left( {i_{qg}^* - i_{qg} } \right) - \omega L_{fg} i_{dg} + v_{qs} \\ v_{dg} &= K_{ig} x_{g1} + K_{pg} \left( { - \frac{{2Q_{gsc}^* }}{{3v_{qs} }} - i_{dg} } \right) + \omega L_{fg} i_{qg} + v_{ds} \end{aligned} $$

(4.31)

The state equations of the RSC and the GSC current control loops are shown in Eq. (4.32).

$$\displaystyle \begin{aligned} \begin{array}{rcl}{} \dot x_{rr1} &\displaystyle =&\displaystyle {i_{ms} + K_{vc} \left( {\left| {V_s^* } \right| - \left| {v_s } \right|} \right) - i_{qr} } \\ \dot x_{rr2} &\displaystyle =&\displaystyle \left( {\frac{{L_{ss} K_{opt} }}{{L_m^2 i_{ms} }}\omega _{r\_dfg}^2 - i_{dr} } \right) \\ \dot x_{g1} &\displaystyle =&\displaystyle \left( {i_{qg}^* - i_{qg} } \right) \\ \dot x_{g2} &\displaystyle =&\displaystyle \left( { - \frac{{2Q_{gsc}^* }}{{3v_{qs} }} - i_{dg} } \right) \end{array} \end{aligned} $$

(4.32)

Appendix 2

4.1.1 DFIG Parameters (pu) on 1.667 MVA, 575 kV Base

$$\displaystyle \begin{aligned} \begin{array}{llll}\displaystyle L_s = 0.1714,& R_s = 0.00706,& L_m=2.904,& L_r=0.1563\\ {} R_r=0.005,& C=0.7477,& H_{t} = 3.5\,{\mathrm{s}},& H_g= 4.55\,{\mathrm{s}}\\ {} L_{fr} = 4.752,& R_{fr} = 0.0761,& L_{fg} = 2.311,& R_{fg} = 0.0338 \\ \end{array} \end{aligned}$$

$$\displaystyle \begin{aligned} \begin{array}{lll}\displaystyle C_{sh} = 0.09\,{\mathrm{{pu\,s}}}/{\mathrm{{elect\,rad}}},& K_{sh} = 0.3\,{\mathrm{pu}}/{\mathrm{{elect\,rad}}},& \lambda_{opt} = 10.5\\ \end{array} \end{aligned}$$

4.1.2 LCC-HVDC Parameters

$$\displaystyle \begin{aligned} \begin{array}{lll}\displaystyle B_i = 2,& B_r = 2, & R_{dc}= 5\,\Omega,\\ {} C_{dc} = 26~\upmu {\mathrm{F}}, & X_{ci}= 13.2062\,\Omega,& X_{cr}= 13.0956\,\Omega\\ {} L_{dc}= 1.1936~ H,& tap_i = 1, & tap_r = 1\\ \end{array} \end{aligned}$$

4.1.3 AC Grid (Dynamic Model) Parameters (pu) on 900 MVA, 20 kV Base [13]

$$\displaystyle \begin{aligned} \begin{array}{llll}\displaystyle X_d = 1.8, & X_q = 1.7,& X_l=0.2, & X^{\prime}_d=0.3\\ {} {X'}_q=0.55,& {X''}_d=0.25,& {X''}_q=0.25,& R_a=0.0025 \\ {} T^{\prime}_{d0}= 8.0\,{\mathrm{s}},& T^{\prime}_{q0} = 0.4\,{\mathrm{s}},& {T''}_{d0} = 0.03\,{\mathrm{s}},& {T''}_{q0} = 0.05\,{\mathrm{s}}\\ \end{array} \end{aligned}$$

4.1.4 State-Space Averaged Model Variables

The following are the state variables, input variables, and the algebraic variables obtained when the state-space model is linearized around the operating point (refer Table 4.2).

4.1.4.1 State Variables, x ₀

$$\displaystyle \begin{aligned} \begin{array}{llll}\displaystyle \hat \theta_2 = 0.046\,{\mathrm{{pu}}},&x_{rr1} = -0.020,& \normalsize{x_{pll(2)} = 0,}& i_{qs} = 8.340\,{\mathrm{{pu}}}\\ {} i_{ds} = 4.532\,{\mathrm{{pu}}},&x_{rr2} = 0.045,&x_{rf} = 0,&i_{ms} = 3.962\,{\mathrm{{pu}}},\\ {} v^2_{dc} = 5.928\,{\mathrm{{pu}}},&\normalsize{i_{qg} = 0.951\,{\mathrm{{pu}}},}&i_{dg} = 0,&\normalsize{\theta_{tw} = 2.683\,{\mathrm{{rad}}}.}\\ {} \omega_t = 1.180\,{\mathrm{{pu}}},&x_{g1} = 0.005,&x_{g2} = 0,&\normalsize{\omega_{r-dfg} = 1.18\,{\mathrm{{pu}}}}\\ {} e^{\prime}_{qs} = 0.908\,{\mathrm{{pu}}},&x_{i1} = 0.036,&I_{dr} = 2~A,&i_{qg}^* = 0.951\,{\mathrm{{pu}}}\\ {} e^{\prime}_{ds} = 0.292\,{\mathrm{{pu}}},&x_{r1} = 0.030, &I_{di} = 2~A,&v_{dm} = 504.5\,{\mathrm{{kV}}}\\ \end{array} \end{aligned}$$

4.1.4.2 Input Variables, u ₀

$$\displaystyle \begin{aligned} \begin{array}{llll}\displaystyle I_d^* = 2\,{\mathrm{A}},&\left| {v_s^*} \right| = 0.817\,{\mathrm{{pu}}},&V_w =13.2\,{\mathrm{m}}/{\mathrm{s}}, &{\theta_2 = 0.046\,{\mathrm{{pu}}},}\\ {} {Q_{gsc}^* = 0,}&{\big(v_{dc}^*\big)^2 = 5.928\,{\mathrm{{pu}}},}&{\gamma _i^* = 0.263\,{\mathrm{rad}}.}\\ \end{array} \end{aligned}$$

4.1.4.3 Algebraic Variables, z ₀

$$\displaystyle \begin{aligned} \begin{array}{lll}\displaystyle {\left| {v_s } \right| =1.035\,{\mathrm{{pu}}},}&{v_{qs}= 1.035\,{\mathrm{{pu}}},}&{E_{acr} = 367.0\,{\mathrm{{kV}}},}\\ {} {E_{aci} = 231.8\,{\mathrm{{kV}}},}&{\alpha_{r0} = 367.0\,{\mathrm{{kV}}}}\\ \end{array} \end{aligned}$$

4.1.5 Pitch Angle Control

The parameters of the pitch angle controller (Fig. 4.42) are: K _pp = 1 deg, K _ip = 40 deg sˆ-1

Fig. 4.42

Schematic of the pitch angle (β) controller [15]

4.1.6 Parameters for Case Study II

Inverter-side system: H _G2 = 7.0 s, R _gov2 = 0.005 (Hz∕pu −MW), P _L = 1700 MW, nominal P _G2 = 774.01 MW and rating of G ₂ = 900 MW.