1. Specification of internal control system for blade pitch and electrical power
1.1. Description of internal control system
The implemented control system is based on the choice of a conventional variablespeed, variable bladepitchtofeather configuration wind turbine and consists of two basic control systems: a generator torque controller and a full span rotorcollective bladepitch controller. The two control systems are designed to work independently. The objective of generatortorque controller is to maximize power capture below the rated operation point. The goal of the bladepitch controller is to regulate generator speed above the rated operation point.
Control measurement filter
Both the generator torque and blade pitch controllers use the generator speed as the sole feedback input. A recursive, singlepole lowpass filter exponential smoothing to reduce the high frequency excitation of the control systems is provided. The discrete time recursion equation for this filter is
\(\mathrm {\omega _{f.k}=\alpha \omega _{f.k1}+(1\alpha )\omega _K}\)
where
\(\mathrm {\alpha =exp((\Delta t)/(TC))}\)
where \(\mathrm {\Delta t}\) is the discrete time step, \(\mathrm {TC}\) is the filter time constant, \(\mathrm {\alpha }\) is the lowpass filter coefficient \(\mathrm {\omega _f}\) is low pass filtered generator speed and \(\mathrm {k}\) indicates the time step. The relation between the filter time constant and the cut off (corner) frequency \(\mathrm {f_C}\) is given by:
\(\mathrm {TC=\frac{1}{2\pi f_C}}\)
Generator torque controller
The generator torque is computed as a tabulated function of the filtered generator speed, incorporating five control regions: 1, 1 1/2, 2, 2 1/2 and 3 as illustrated in the figure `Illustration of the variable speed controller  Generator torque versus generator speed' below. Region 1 is a control region before cutin wind speed, where the generator torque is zero and no power is extracted. Instead, the wind is used to accelerate the rotor for startup. Region 2 is a control region for optimizing power capture. Here, the generator torque is proportional to the quare of the filtered generator speed to maintain a constant (optimal) tipspeed ratio. In region 3, the generator torque or the generator power is held constant. In case of constant power the generator torque is inversely proportional to the filtered generator speed.
Blade pitch controller
In region 3, the collective blade pitch angle commands are computed using a gainscheduled proportionalintegral (PI) control on the speed error between the filtered generator speed and the rated generator speed. The PI regulator is represented by the Laplace transform: \(\mathrm {(K(s+a))/s}\) where \(\mathrm {K}\) and \(\mathrm {a}\) are the proportional gain and the integrator gain. The corresponding and simple regulator algorithm is given by
\(\mathrm {R(t+\Delta t)=R(t)+\Delta \omega \Delta t}\)
\(\mathrm {\theta =K_P\Delta \omega aK_PR(t\Delta t)=K_P\Delta \omega K_IR(t\Delta t)}\)
where \(\mathrm {\Delta t}\) is the regulator time step, \(\mathrm {\Delta \omega }\) is the rotor speed error, i.e. the difference between filtered rotor speed and rated rotor speed. \(\mathrm {R}\) is accumulated time integrated speed error which is set to zero for filtered generator speed less than rated generator speed. \(\mathrm {\theta }\) is the instructed/required collective blade pitch angle.
Gain scheduling
Gain scheduling is introduced because the optimal proportional and integrator gains are dependent of the blade pitch angle. At each step the gain will be corrected based on the pitch angle applied in the previous step. The user may specify a gain scheduling law or choose to apply the default law presented in the table `The defaults gain scheduling law'. For intervening generator speeds, linear interpolation is used.
Illustration of the variable speed controller  Generator torque versus generator speed.
1.2. Input description
Engine Data, Generator, One input line
GBRATIO GNS_RATE TRQ_RATE RGN3MP

GBRATIO: real >= 1
: Gear box ratio. Number of rotations of the high speed shaft for one rotation of the low speed shaft, i.e. generator versus rotor 
GNS_RATE: real > 0
: Rated generator speed \(\mathrm {[rad/T]}\) 
TRQ_RATE: real > 0
: Rated generator torque \(\mathrm {[FL]}\) 
RGN3MP: real
: Minimum pitch angle for which electrical torque versus generator speed will stay in region 3 \(\mathrm {[deg]}\)
Engine Data, Generator One input line
RGN15SP RGN20SP RGN25SP RGN30SP TRQRGN2

RGN15SP: real > 0
: Transitional generator speed between region 1 and 1 1⁄2. Start speed for extracting power. \(\mathrm {[rad/T]}\) 
RGN20SP: real > RGN15SP
: Transitional generator speed between region 1 1⁄2 and 2. \(\mathrm {[rad/T]}\) 
RGN25SP: real > RGN20SP
: Transitional generator speed between region 2 and 2 1⁄2 \(\mathrm {[rad/T]}\) 
RGN30SP: real > RGN25SP
: Transitional generator speed between region 2 1⁄2 and 3 \(\mathrm {[rad/T]}\) 
TRQRGN2: real > 0
: Generator torque constant in region 2\(\mathrm {[FL/(rad/T)^2]}\)
Engine Data, Generator One input line
METRGN3

METRGN3: character(6)
: Method for power extraction in region 3
POWER
: Constant Power 
TORQUE
: Constant Torque

Engine Data, Generator actuator One input line
TRQ_MAXRAT TRQ_MAX

TRQ_MAXRAT: real > 0
: Maximum torque rate \(\mathrm {[FL/T]}\) 
TRQ_MAX: real > 0
: Maximum electrical torque \(\mathrm {[FL]}\)
Blade pitch Controller/actuator One input line
PC_MINPIT PC_MAXPIT PC_MAXRAT

PC_MINPIT: real
: Minimum pitch setting in pitch controller \(\mathrm {[deg]}\) 
PC_MAXPIT: real
: Maximum pitch setting in pitch controller \(\mathrm {[deg]}\) 
PC_MAXRAT: real
: Maximum pitch rate \(\mathrm {[deg/T]}\)
Controller Data (PI regulator : K(s+a)/s One input line
KP KI G_SHEDULE TC

KP: real
: Proportional gain at zero pitch angle 
KI: real
: Integral gain 
G_SHEDULE: character
: Gain scheduling; Default or Tabulated
= D
: Default 
= T
: Tabulated


TC: real
: Time constant for first order low pass filter, \(\mathrm {TC=1/\omega }\) \(\mathrm {[s/rad]}\)
Input refer to lowspeed shaft
Gain scheduling (G_SHEDULE=T) One input line
GSNumber

NOP_GST: integer > 0
: Number of points in gain scheduling table. The maximum is currently 30.
Gain Scheduling; Gain correction factors. NOP_SGST input lines
BPITCH GCF

BPITCH: real
: Blade pitch angle \(\mathrm {[deg]}\) 
GCF: real
: Gain correction factor
Example input for control system
‘ 'gbratio gnsrate trq_rate rgn3mp 97 122.911 43.09355 1.0 'rgn15sp rgn20sp rgn25sp rgn30sp trqrgn2 70.16 91.208 119.0137 121.6805 0.002332288 'metrgn3 TORQUE 'trq_maxrat trq_max 15.0 43.09355 'pcminpit pcmaxpit pcmaxrat 1. 90. 8. 'kp ki g_shedule TC 0.006275604 0.000896514 D 0.6366 ‘ ‘dtsamp 0.0125