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Hydraulic Turbine and Governor

Model hydraulic turbine and proportional-integral-derivative (PID) governor system


Fundamental Blocks/Machines


The Hydraulic Turbine and Governor block implements a nonlinear hydraulic turbine model, a PID governor system, and a servomotor [1].

The hydraulic turbine is modeled by the following nonlinear system.

The gate servomotor is modeled by a second-order system.



The gain Ka and time constant Ta, in seconds (s), of the first-order system representing the servomotor. Default is [ 10/3 0.07 ].

Gate opening limits

The limits gmin and gmax (pu) imposed on the gate opening, and vgmin and vgmax (pu/s) imposed on gate speed. Default is [ 0.01 0.97518 -0.1 0.1 ].

Permanent droop and regulator

The static gain of the governor is equal to the inverse of the permanent droop Rp in the feedback loop. The PID regulator has a proportional gain Kp, an integral gain Ki, and a derivative gain Kd. The high-frequency gain of the PID is limited by a first-order low-pass filter with time constant Td (s). Default is [ 0.05 1.163 0.105 0 0.01 ].

Hydraulic turbine

The speed deviation damping coefficient β and water starting time Tw (s). Default is [ 0 2.67 ].

Droop reference

Specifies the input of the feedback loop: gate position (set to 1) or electrical power deviation (set to 0). Default is 0.

Initial mechanical power

The initial mechanical power Pm0 (pu) at the machine's shaft. This value is automatically updated by the load flow utility of the Powergui block. Default is 0.7516.

Inputs and Outputs


Reference speed, in pu.


Reference mechanical power in pu. This input can be left unconnected if you want to use the gate position as input to the feedback loop instead of the power deviation.


Machine actual speed, in pu.


Machine actual electrical power in pu. This input can be left unconnected if you want to use the gate position as input to the feedback loop instead of the power deviation.


Speed deviation, in pu.


Mechanical power Pm for the Synchronous Machine block, in pu.


Gate opening, in pu.


The power_turbine example illustrates the use of the Synchronous Machine associated with the Hydraulic Turbine and Governor (HTG) and Excitation System blocks.


[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.

Introduced before R2006a

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