4.4
Test system
A test system is set up to validate the control methodologies described in this chapter with a focus on the proposed power reduction control. The test system, including the different voltage levels, is represented in Figure 4.4. The electrical parameters of the system are presented in Section 4.4.1.
Furthermore, WPPA and WPPB are modelled using the aggregated model shown in Figure 4.5. These aggregated models are described in [22] and neglect the collector system of the WPPs. Both wind farms aggregated models have an equal rated power generation of 63 MVA for case studies I, II, III and of 94.5 MVA for case study IV. Moreover, the DC cables are modelled using a Π equivalent while the offshore AC cables are modelled using the Γ Section equivalent [38]. Finally, regarding the onshore AC networks, these are modelled using a Thévenin equivalent composed by a three-phase voltage source and a series impedance.
Finally, the control parameters considered for the simulations are described in Section 4.4.1. Onshore Grid + Onshore Grid Onshore converter substation Offshore converter Substation Cdc + + + C + WT-GSC Substation C + Country A Country B VSC 6 WPP A equivalent VSC 5 VSC 3 VSC 4 VSC 1 VSC 2 Offshore Island Cdc Cdc Cdc Zg 150 kV 220 kV 220 kV Z g 150 kV 150 kV 150 kV 220 kV 220 kV 33 kV 33 kV
WPP B equivalent Onshore converter
substation AC Hub Offshore converter Substation L2 L3 L4 WT-GSC Substation L1
Figure 4.4: Electrical layout of the study system
C +
WT-GSC
u
dc dci
windZ
WT0.9 kV
33 kV
Colector
Bus
p
wind4.4.1 System Parameters
The parameters of the system used in the simulations are presented in this subsection. First, the electrical parameters of the system are presented. Next, the control parameters are listed.
4.4.2 Electrical Parameters
The electrical parameters of the system are listed in tables 4.1, 4.2, 4.3, 4.4 as follows:
• Onshore grid: the parameters for the Thévenin equivalent AC onshore grid are shown in table 4.1. These values have been extracted from [26] and [39].
• Onshore-VSCs, Offshore-VSCs, HVDC lines: these two converters are sized equal in the system. Further, their electrical parameters are listed in table 4.2 and are extracted from [26]. However, in this study, the rated power of the converters is 112 MVA. The maximum value for the current has been extracted from [31].
• Offshore VSC and HV cables and Power transformers: the values for the cable parameters of the offshore 150 kV grid are taken from as [21]. The transformer parameters have also been approximated from the values given in [21]. These values are listed in 4.3.
• Wind Generation, WT-GSCs and DC link values: the parameters of the wind generation system are listed in table 4.4. The rated voltage and power values and the transformer parameters, are derived from [21]. However, the p.u. values for the LC filter are extracted from [26] and [39]. The DC link capacitance has been derived from equation (4.15) considering a time constant, τ , of 5 ms [40].
Cdc =
2τ Sc,w U2
dc
(4.15)
Parameter Value unit
Rated Voltage, VLL,RM S 220 kV
Grid voltage, ug 1 p.u.
Grid inductance,Vg 0.2 p.u.
Grid resistance, rg 0.01 p.u.
Grid frequency, f 50 Hz Table 4.1: Onshore grid parameters
4.4 Test system 35
Parameter Value unit
VSC converters
Rated Power, Sc 500 MVA
Rated AC Voltage, UHV 220 kV
Rated DC voltage, Udc 400 kV
Equivalent DC Capacitor, cc
dc 150 µF
Filter resistance, rf 0.003 p.u.
Filter inductance, lf 0.08 p.u.
Filter capacitance, cf 0.2 p.u.
Maximum current, imax 1.08 p.u. HVDC Lines Cable resistance, Rdc 0.011 Ω/km Cable inductance, Ldc 2.615 mH/km Cable capacitance, Cdc 0.1908 µF/km L3 length 200 km L4 length 200 km
Table 4.2: Onshore-VSC and Offshore-VSC parameters and HVDC lines
Parameter Value unit
HV Cable 150 kV
Rated AC Voltage, UM V 150 kV
Cable resistance, Rac 0.06 Ω/km
Cable inductance, Lac 0.44 mH/km
Cable capacitance, Cac 0.14 µF/km
Cable length WPP1 to Offshore hub AC, L1 25 km Cable length WPP2 to Offshore AC hub, L2 25 km
Transformer 33/150 kV Transformer Resistance, rtr1 0.12 % Transformer Inductance ltr1 2 % Transformer 150/220 kV Transformer Resistance, rtr2 0.12 % Transformer Inductance ltr2 2 %
Table 4.3: AC cables parameters and transformers parameters
Parameter Value unit
Rated Power, Sc,w 6.3 MVA
Rated AC Voltage, Uac 0.9 kV Rated DC voltage, Udc 2 kV Equivalent DC Capacitor, cc dc 16 mF Transformer Resistance, rtr 0.8 % Transformer Inductance ltr 6 %
Filter resistance, rf 0.003 p.u.
Filter inductance, lf 0.08 p.u.
Filter capacitance, cf 0.2 p.u.
4.4.3
Control Parameters
The different values for the control parameters used in Onshore-VSCs, Offshore-VSCs and WT-GSCs are listed down below in tables 4.5, 4.6 and 4.7 respectively. These values are tuned using a trial and error method in order to obtain a good dynamic performance as in [33]. As stated before, each pair of VSC is considered equal hence their control parameters are the same. The control parameters for the power reduction controllers are listed in the following Section together with the droop gain of the outer controller of the onshore-VSCs, kdcg .
Furthermore, the active power measured signal is filtered through a LPF which time constant is included in 4.6. The power synchronization droop value is small to limit the frequency rise of the offshore grid.
Parameter Value unit
PLL
filter cut off frequency, ωg
LP,P LL 500 p.u.
Proportional gain PLL controller, kp,pllg 0.0844 p.u. Integral gain PLL controller, ki,pllg 4.6908 p.u.
Inner loop
Proportional gain current controller, kg
p,cl 1.2732 p.u.
Integral gain current controller, kg
i,cl 14.25 p.u.
Active damping gain, kg
ad 0.5 p.u.
udc outer loop
Considered Current droop gain controller kg
dc 0.0 / 0.025 / 0.55 / 0.2 p.u.
Proportional gain udc controller, k g
p,dc 1.0885 p.u.
Integral gain udc controller, k g
i,dc 590.93 p.u.
q outer loop
Proportional gain reactive power controller, kg
p,q 0.01 p.u.
Integral gain reactive power controller, kg
i,q 897.67 p.u.
Table 4.5: Control Parameters of the Onshore-VSC Converters
Parameter Value unit
Power Synchronization loop
PSL Droop gain, kf 0.002 p.u.
Power measurement filter time constant, τp 40 ms Alternating-Voltage controller
AVC droop gain, ku 30 p.u.
Voltage-Vector Control Law
High pass filter kv 0.2 p.u.
High pass filter αv 70 p.u.
4.4 Test system 37
Previous to the simulation, a Power flow is performed on the study system with the wind generation values of each WPP as an input obtaining the initial values for the currents, power and voltages of the system that are used as signals in the control strategies. Moreover, the eigenvalues of the system are calculated from the small-signal model of the system to check the stability of the system.
Parameter Value unit
PLL
filter cut off frequency, ωg
LP,P LL 50 p.u.
Proportional gain PLL controller, kg
p,pll 0.0084 p.u.
Integral gain PLL controller, kg
i,pll 0.0469 p.u./s
Inner loop
Proportional gain current controller, kg
p,cl 1.2732 p.u.
Integral gain current controller, kg
i,cl 14.25 p.u./s
Active damping gain, kg
ad 0.5 p.u.
udc outer loop
Proportional gain udc controller, kgp,dc 1.0885 p.u.
Integral gain udc controller, ki,dcg 590.93 p.u./s q outer loop
Proportional gain reactive power controller, kg
p,q 0.01 p.u.
Integral gain reactive power controller, kg
i,q 897.67 p.u.