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Discrete-time or continuous-time synchronous machine DC2C excitation system including an automatic voltage regulator and an exciter

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

The SM DC2C block models a synchronous machine type DC2C excitation system
that conforms to IEEE 421.5-2016^{[1]}.

Use this block to model the control and regulation of the field voltage of a synchronous machine that operates as a generator using a DC commutator rotating exciter.

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 DC2C block is made up of four major components:

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

The voltage measurement transducer simulates the dynamics of a terminal voltage transducer by 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 exciter field voltage.

The DC rotating exciter models the DC commutator rotating exciter and produces a field voltage that is applied to the controlled synchronous machine. The block also feeds the field voltage back to the excitation system.

This diagram shows the overall structure of the DC2C 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}*E*is the exciter field voltage._{FE}*E*is the field voltage._{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
this 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), and stator current limiter (SCL) voltages. For more information about using limiters with this block, see Field Current Limiters.

The Lead-Lag block models additional dynamics associated with the voltage regulator. Here,

*T*is the lead time constant and_{C}*T*is the lag time constant. Refer to the Lead-Lag block documentation for the exact discrete and continuous implementations._{B}The Low-Pass Filter block models the major dynamics of the voltage regulator. Here,

*K*is the regulator gain and_{A}*T*is the major time constant of the regulator. The minimum and maximum anti-windup saturation limits for the block are_{A}*V*and_{Rmin}*V*, respectively._{Rmax}The Take-over Logic subsystem models the take-over point input location for the OEL, UEL, and SCL voltages. For more information about using limiters with this block, see Field Current Limiters.

The Filtered Derivative block models the rate feedback path for stabilization of the excitation system. Here,

*K*and_{F}*T*are the gain and time constant of this system, respectively. Refer to the documentation for the Filtered Derivative block for the exact discrete and continuous implementations._{F}*V*and_{T}*V_{Rmax}*V*are the minimum and maximum saturation limits for the output exciter field voltage_{T}*V_{Rmin}*E*._{FE}

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 can risk 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 an overexcitation
input

This diagram illustrates the overall structure of the DC commutator rotating exciter:

In the diagram:

The exciter field current

*V*is modeled as the summation of two signals:_{FE}The nonlinear function

*V*models the saturation of the exciter output voltage._{x}The proportional term

*K*models the linear relationship between exciter output voltage and the exciter field current._{E}

The

**Integrator**subsystem integrates the difference between*E*and_{FE}*V*to generate the output field voltage_{FE}*E*._{fd}*T*is the time constant for this process._{E}

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