Hydraulic Turbine and Governor

A model of a hydraulic turbine and a proportional-integral-derivative (PID) control system.

hydraulic turbine and governor

Description

The Hydraulic Turbine and Governor block implements a non-linear hydraulic turbine model, a PID controller system and a servo drive [1]:

hydraulic turbine model 1

The hydraulic turbine is modelled by the following nonlinear system:

hydraulic turbine model 2

The gate servo is modelled by a second order system:

hydraulic turbine model 3

Ports

Input

# ω_ref — reference speed
scalar

Details

Reference velocity in relative units.

Data types	`Float64`.
Complex numbers support	No

# P_ref — reference mechanical power
scalar

Details

Reference mechanical power in relative units. This input can be omitted if you want to use the gate position as input to the feedback circuit instead of power rejection.

Data types	`Float64`.
Complex numbers support	No

# ω_e — actual machine speed
scalar

Details

The actual speed of the machine in relative units.

Data types	`Float64`.
Complex numbers support	No

# P_e0 — actual electrical power of the machine
scalar

Details

The actual electrical power of the machine in relative units. This input can be omitted if you wish to use the gate position as an input to the feedback circuit instead of power rejection.

Data types	`Float64`.
Complex numbers support	No

# Δω — velocity deviation
scalar

Details

Velocity deviation in relative units.

Data types	`Float64`.
Complex numbers support	No

Output

# P_m — mechanical power
scalar

Details

Mechanical power for the Synchronous Machine unit in relative units.

Data types	`Float64`.
Complex numbers support	No

# gate — gate opening
scalar

Details

Shutter opening in relative units.

Data types	`Float64`.
Complex numbers support	No

Parameters

Main

# Servo-motor [Ka Ta(s)] — gain and time constant of the first-order system

Details

The gain and time constant , in seconds (s), of the first-order system representing the servo drive.

Default value	`[10/3 0.07]`
Program usage name	`servo_motor`
Evaluatable	Yes

# Gate opening limits [gmin(pu) gmax(pu) vgmin(pu/s) vgmax(pu/s)] — shutter opening limits

Details

Limits and (pu) imposed on the gate opening and and ( ) imposed on the gate speed.

Default value	`[0.01 0.97518 -0.1 0.1]`
Program usage name	`gate`
Evaluatable	Yes

# Permanent droop and regulator [Rp Kp Ki Kd Td(s)] — constant throttle and regulator

Details

The static gain of the regulator is equal to the inverse of the constant decay in the feedback circuit. The PID controller has proportional gain , integral gain and derivative gain . The high-frequency gain of the PID controller is limited by a first-order low-pass filter with a time constant (s).

Default value	`[0.05 1.163 0.105 0 0.01]`
Program usage name	`regulator`
Evaluatable	Yes

# Hydraulic turbine [beta Tw(s)] — speed deviation damping coefficient and water start-up time

Details

Speed deviation damping factor and water start-up time (s).

Default value	`[0 2.67]`
Program usage name	`hydraulic_turbine`
Evaluatable	Yes

# Droop reference (0=power error, 1=gate opening) — feedback loop input

Details

Feedback loop input: gate position (1) or electrical power deviation (0).

Default value	`0.0`
Program usage name	`droop_ref`
Evaluatable	Yes

Initial Values

# Initial mechanical power, pu — initial mechanical power

Details

Initial mechanical power in relative units.

Default value	`0.7516`
Program usage name	`P_m_start`
Evaluatable	Yes

Literature references

[1] IEEE Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, "Hydraulic Turbine and Turbine Control Models for Dynamic Studies," IEEE® Transactions on Power Systems, Vol. 7, No. 1, February, 1992, pp. 167-179.