# SM DC4C

Discrete-time or continuous-time synchronous machine DC4C excitation system including an automatic voltage regulator and exciter

*Since R2021b*

**Libraries:**

Simscape /
Electrical /
Control /
SM Control

## Description

The SM DC4C block models a synchronous machine type DC4C 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
block for continuous time, set the **Sample time (-1 for inherited)**
property to `0`

. To configure the block 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 DC4C block is made up of five 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 which produces and applies a field voltage to the controlled synchronous machine. The block also feeds the field voltage back to the excitation system.

The power source models the dependency of the power source for the controlled rectifier from the terminal voltage.

This diagram shows the overall structure of the DC4C 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}*SW*is the user-selected power source switch for the controlled rectifier._{1}*V*is the exciter field voltage._{B}*E*and_{FE}*V*are the exciter field voltage and current, respectively._{FE}*E*is the field voltage._{FD}

### Current Compensator and Voltage Measurement Transducer

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}*. To see the exact discrete and
continuous implementations, see Low-Pass
Filter.

### Excitation Control Elements

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 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 PID_R subsystem models a PID controller that functions as a control structure for the automatic voltage regulator. The minimum and maximum anti-windup saturation limits for the block are

*V*and_{Rmax}/ K_{A}*V*, respectively._{Rmin}/ K_{A}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. To see the exact discrete and continuous implementations, see Filtered Derivative._{F}

### Field Current Limiters

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
**V_OELscl** and an underexcitation input
**V_UELscl**.

### DC Rotating Exciter

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

In the diagram:

The exciter field current

*V*is the sum 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}

### Power Source

You can change the power source representations for the controlled rectifier with the
**Logical switch 1** parameter. The power source for the
controlled rectifier can be either derived from the terminal voltage
(```
Position A: power source derived from terminal
voltage
```

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

).

## Ports

### Input

### Output

## Parameters

## References

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

## Extended Capabilities

## Version History

**Introduced in R2021b**