Washout (Discrete or Continuous)

Discrete-time or continuous-time washout or high-pass filter

• Library:
• Simscape / Power Systems / Simscape Components / Control / General Control

Description

The Washout (Discrete or Continuous) block implements a washout filter in conformance with IEEE 421.5-2016[1]. The washout is also known as a high-pass filter.

You can switch between continuous and discrete implementations of the integrator using the Sample time parameter.

Equations

Continuous

To configure the washout block for continuous time, set the Sample time property to `0`. This representation is equivalent to the continuous transfer function:

`$G\left(s\right)=\frac{Ts}{Ts+1},$`
where T is the time constant. From the preceeding transfer function, the washout defining equations are:
`$\left\{\begin{array}{c}\stackrel{˙}{x}\left(t\right)=\frac{1}{T}\left(-x\left(t\right)+u\left(t\right)\right)\\ y\left(t\right)=-x\left(t\right)+u\left(t\right)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\left(0\right)={u}_{0},\text{\hspace{0.17em}}y\left(0\right)=0,$`
where:

• u is the washout input.

• x is the washout state.

• y is the washout output.

• t is the simulation time.

• u0 is the initial input to the washout block.

Discrete

To configure the washout block for discrete time, set the Sample time property to a positive, nonzero value, or to `-1` to inherit the sample time from an upstream block. The discrete representation is equivalent to the transfer function:

`$G\left(z\right)=\frac{z-1}{z+{T}_{s}/T-1},$`
where Ts is the sample time. From the discrete transfer function, the washout defining equations are defined using the forward Euler method:
`$\left\{\begin{array}{c}x\left(n+1\right)=\left(1-\frac{{T}_{s}}{T}\right)x\left(n\right)+\left(\frac{{T}_{s}}{T}\right)u\left(n\right)\\ y\left(n\right)=u\left(n\right)-x\left(n\right)\end{array}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\left(0\right)={u}_{0},\text{\hspace{0.17em}}y\left(0\right)=0,$`
where:

• u is the washout input.

• x is the washout state.

• y is the washout output.

• n is the simulation time step.

• u0 is the initial input to the washout block.

Initial Conditions

The block sets the state initial condition to the initial input, making the initial output zero.

Bypass Filter Dynamics

Set the time constant to a value smaller than or equal to the sample time to ignore the dynamics of the filter. When bypassed, the block feeds the input directly to the output:

`$T\le {T}_{s}\to y=u\text{\hspace{0.17em}}.$`
In the continuous case, the sample time and time constant must both be zero.

Ports

Input

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Washout input signal. The block uses the input initial value to determine the state initial value.

Data Types: `single` | `double`

Output

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Washout output signal.

Data Types: `single` | `double`

Parameters

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Washout time constant. Set this value less than the Sample time to bypass the dynamics of the filter.

Washout filter sample time. Set this to `0` to implement a continuous washout block. Set this to `-1` or a positive number to implement a discrete washout block.

References

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

Introduced in R2017b

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