Engee documentation

Filtered Derivative (Discrete or Continuous)

A derivative filtered in discrete or continuous time.

blockType: SubSystem

filtered derivative discrete or continuous

Path in the library:

/Physical Modeling/Electrical/Control/General Control/Filtered Derivative (Discrete or Continuous)

Description

Block Filtered Derivative (Discrete or Continuous) implements a derivative with filtering in accordance with the IEEE 421.5-2016 standard [1].

You can switch between continuous and discrete block implementations using the parameter Sample time (-1 for inherited).

The equations

notable mode

To configure the filtered derivative to work in continuous mode, set the parameter Sample time (-1 for inherited) meaning 0. This representation is equivalent to a continuous transfer function.

where

  • — gain factor;

  • — time constant.

The above transfer function implies a system of equations defining the derivative:

where

  • — the input signal of the unit;

  • — condition;

  • — the output signal of the unit;

  • — simulation time;

  • — the initial value of the input signal of the block.

discret mode

To configure the derivative with filtering to work in discrete mode, set the parameter Sample time (-1 for inherited) positive non-zero value or value −1 to inherit the sampling period from the upstream block. The discrete representation is equivalent to the transfer function

where

  • — gain factor;

  • — time constant;

  • — the sampling period.

Based on the discrete transfer function, the derivative equations with filtering are determined using the direct Euler method.:

where

  • — the input signal of the unit;

  • — block status;

  • — the output signal of the unit;

  • — time step of the simulation;

  • — the initial value of the input signal of the block.

Determining the initial conditions

The initial conditions of the block can be set using the parameter Initialization. Set the value:

  • Inherited from block input — the unit will set the initial conditions of the status and output signal equal to the initial input value;

  • Specify as parameter — the block will set the initial condition of the state equal to the value of the parameter Initial state.

Output signal limitation

To limit the output signal to the derivative with filtering, set the final values for the parameters Upper saturation limit and Lower saturation limit.

Unlike other typical blocks listed in the IEEE 421.5-2016 standard, saturation methods with error accumulation are used for the derivative with filtering («windup») and with suppression of error accumulation («anti-windup») do not differ. The output signal can immediately respond to a change in the sign of the input signal when it is saturated.

Ports

Input

# u — derivative input signal with filtering
vector

Details

The input signal is a derivative with filtering. The block uses the initial value of the input signal to determine the initial value of the state.

Data types

Float32, Float64
Complex numbers support

I don’t

Output

# y — derivative output signal with filtering
vector

Details

The output signal is a derivative with filtering.

Data types

Float32, Float64
Complex numbers support

I don’t

Parameters

Main group

# Gain — gain coefficient of the derivative

Details

The gain of the derivative with filtering.

Default value

1.0
Program usage name

K
Evaluatable

Yes

# Time constant — the time constant of the derivative

Details

The time constant of the derivative with filtering. To ensure acceptable accuracy, set this parameter to at least 10 times more than Sample time (-1 for inherited).

Default value

0.1
Program usage name

T
Evaluatable

Yes

# Upper saturation limit — upper limit of the output signal

Details

The upper limit of the output signal of the derivative with filtering. Set the value Inf for an unsaturated upper limit.

Default value

Inf
Program usage name

upper_saturation_limit
Evaluatable

Yes

# Lower saturation limit — lower limit of the output signal

Details

The lower limit of the output signal of the derivative with filtering. Set the value −Inf for the unsaturated lower limit.

Default value

-Inf
Program usage name

lower_saturation_limit
Evaluatable

Yes

# Minimum time constant to sample time ratio — the discrete ratio

Details

The minimum allowable ratio of the time constant to the sampling period. As the sampling period approaches the time constant, the accuracy of the block decreases. Use this parameter to set the tolerance for this ratio.

Default value

10.0
Program usage name

T_to_sample_time_ratio
Evaluatable

Yes

# Initialization — the method of setting the initial state
Inherited from block input | Specify as parameter

Details

Select the initial state for this block. For more information, see Determining the initial conditions.

Values

Inherited from block input | Specify as parameter
Default value

Inherited from block input
Program usage name

initial_option
Evaluatable

Yes

# Initial state — initial state

Details

The initial state of the block.

Dependencies

To use this parameter, set for the parameter Initialization meaning Specify as parameter.

Default value

0.0
Program usage name

initial_state
Evaluatable

Yes

# Sample time (-1 for inherited) — block sampling period

Details

The time between consecutive block executions. During execution, the block generates output signals and, if necessary, updates its internal state.

For the inherited discrete time mode, set this parameter to −1. For discrete mode, set this parameter to a positive integer. For continuous mode, set this parameter to 0.

To ensure acceptable accuracy, set this parameter to at least 10 times less than Time constant.

Default value

-1
Program usage name

sample_time
Evaluatable

Yes

Literature

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