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Discrete-time or continuous-time synchronous machine ST4C static excitation system with an automatic voltage regulator

**Library:**Simscape / Electrical / Control / SM Control

The SM ST4C block implements a synchronous-machine-type ST4C static
excitation system model in conformance with IEEE 421.5-2016^{[1]}.

Use this block to model the control and regulation of the field voltage of a synchronous machine.

You can switch between continuous and discrete implementations of the block by using the
**Sample time (-1 for inherited)** parameter. To configure the
integrator for continuous time, set the **Sample time (-1 for
inherited)** property to `0`

. To configure the integrator
for discrete time, set the **Sample time (-1 for inherited)** property
to a positive, nonzero value, or to `-1`

to inherit the sample time
from an upstream block.

The SM ST4C block comprises of four major components:

The Current Compensator modifies the measured terminal voltage as a function of the terminal current.

The Voltage Measurement Transducer simulates the dynamics of a terminal voltage transducer using a low-pass filter.

The Excitation Control Elements component compares the voltage transducer output with a terminal voltage reference to produce a voltage error. This voltage error is then passed through a voltage regulator to produce the field voltage.

The Power Source component models the power source for the controlled rectifier when it is independent from the terminal voltage.

This diagram shows the overall structure of the ST4C excitation system model:

In the diagram:

*V*and_{T}*I*are the measured terminal voltage and current of the synchronous machine._{T}*V*is the current-compensated terminal voltage._{C1}*V*is the filtered, current-compensated terminal voltage._{C}*V*is the reference terminal voltage._{REF}*V*is the power system stabilizer voltage._{S}*V*is the exciter field voltage._{B}*E*and_{FD}*I*are the field voltage and current, respectively._{FD}

The following sections describe each of the major parts of the block in detail.

The current compensator is modeled as:

$${V}_{C1}={V}_{T}+{I}_{T}\sqrt{{R}_{C}^{2}+{X}_{C}^{2}},$$

where:

*R*is the load compensation resistance._{C}*X*is the load compensation reactance._{C}

The voltage measurement transducer is implemented as a Low-Pass
Filter block with the time constant
*T _{R}*. Refer to the documentation for the
Low-Pass Filter block for the exact discrete and continuous implementations.

This diagram illustrates the overall structure of the excitation control elements:

In the diagram:

The Summation Point Logic subsystem models the summation point input location for the overexcitation limiter (OEL), underexcitation limiter (UEL), stator current limiter (SCL), and the power switch selector (V_S) voltages. For more information about using limiters with this block, see Field Current Limiters.

There are two Take-over Logic subsystems. The subsystems model the take-over point input location for the OEL, UEL, SCL and PSS voltages. For more information about using limiters with this block, see Field Current Limiters.

The PI_R subsystem models a PI controller that functions as a control structure for the automatic voltage regulator and allows the representation of an equipment retrofit with a modern digital controller. The minimum and maximum anti-windup saturation limits for the block are

*V*and_{PImin}*V*, respectively._{PImax}The PI_M subsystem models a PI controller and replaces the Lead-Lag block in SM ST3C. The minimum and maximum anti-windup saturation limits for the block are

*V*and_{Mmin}*V*, respectively._{Mmax}An inner field voltage control loop is utilized to linearize the exciter control characteristic and it is composed of the gains

*K*and_{M}*K*and the time constants_{G}*T*and_{M}*T*. The minimum and maximum anti-windup saturation limits for the Low-Pass Filter block are_{G}*V*and_{Amin}*V*, respectively._{Amax}

You can use various field current limiters to modify the output of the voltage regulator under unsafe operating conditions:

Use an overexcitation limiter to prevent overheating of the field winding due to excessive field current demand.

Use an underexcitation limiter to boost field excitation when it is too low, which risks desynchronization.

Use a stator current limiter to prevent overheating of the stator windings due to excessive current.

Attach the output of any of these limiters at one of these points:

The summation point as part of the automatic voltage regulator (AVR) feedback loop

The take-over point to override the usual behavior of the AVR

If you are using the stator current limiter at the summation point,
use the single input *V _{SCLsum}*. If you are
using the stator current limiter at the take-over point, use both the overexcitation
input,

It is possible to adopt a different representation of the power source for the controlled
rectifier by selecting the relevant option in the **Power source
selector** parameter. The power source for the controlled rectifier can
be either derived from the terminal voltage (```
Position A: power source
derived from generator terminal voltage
```

) or it can be independent
of the terminal voltage (```
Position B: power source independent of
generator terminal conditions
```

).

This diagram shows a model of the exciter power source utilizing a phasor
combination of the terminal voltage, *V _{T}*,
and terminal current,

[1] *IEEE Recommended
Practice for Excitation System Models for Power System Stability
Studies.* IEEE Std 421.5-2016. Piscataway, NJ: IEEE-SA,
2016.