DefiniteTimeRelay

A definite-time relay with optional lockout. Each relay models one element.

Notes

• Designed to measure a BranchBreakers terminal current, a bus voltage, or a frequency, and to drive a BranchBreakers trip1 or trip2 input.

• The element operates above \(M_\mathrm{pickup}\) if \(M_\mathrm{pickup} > M_\mathrm{ref}\) and below it otherwise.

• With lockout, the relay commits to trip once \(x\) passes \(1/2\), so it may measure the current it interrupts.

Model Parameters

Symbol	Units	JSON	Description	Typical Value	Note
\(M_\mathrm{pickup}\)	[p.u.]	Mpickup	Pickup level		Required
\(M_\mathrm{ref}\)	[p.u.]	Mref	Reference level		Required; 0 for current, 1 for voltage and frequency
\(T_\mathrm{trip}\)	[s]	Ttrip	Trip time		Required; time to \(x = 3/4\) for \(p = 1\)
\(s_\mathrm{lock}\)	[boolean]	Lockout	Lockout selector	true	true = lockout, false = self-reset

Parameter Validation

\[\begin{split}\begin{aligned} M_\mathrm{pickup} &> 0 \\ M_\mathrm{ref} &\ge 0 \\ M_\mathrm{pickup} &\ne M_\mathrm{ref} \\ T_\mathrm{trip} &\ge 0 \end{aligned}\end{split}\]

All real parameters must be finite.

Model Derived Parameters

\[\begin{split}\begin{aligned} \epsilon_T &= 10^{-3}\ \mathrm{s} \\ T_\mathrm{trip} &\leftarrow \max(T_\mathrm{trip}, \epsilon_T) \\ T_\mathrm{latch} &= \dfrac{T_\mathrm{trip}}{\ln 4} \end{aligned}\end{split}\]

Model Ports

Name	Port	Init	Description
mr	Input	Known	Required measured quantity, real component
mi	Input	Known	Measured quantity, imaginary component
trip	Output	Known	Required trip command

Unattached mi defaults to zero, so absolute frequency uses mr alone.

Model Variables

Internal Variables

Differential

Symbol	Units	Description	Note
\(x\)	[-]	Relay latch

Algebraic

Symbol	Units	Description	Note
\(s\)	[-]	Trip command	trip

External Variables

Differential

None.

Algebraic

Symbol	Units	Description	Note
\(m_r\)	[p.u.]	Measured quantity, real component	mr
\(m_i\)	[p.u.]	Measured quantity, imaginary component	mi

Model Equations

Smooth functions: above, latch, logistic (\(\sigma\)).

For readability, define:

\[\begin{aligned} p &= \text{logistic}\left(\dfrac{m_r^2 + m_i^2 - M_\mathrm{pickup}^2}{M_\mathrm{pickup}^2 - M_\mathrm{ref}^2}\right) \end{aligned}\]

Internal Equations

Differential

\[\begin{aligned} 0 &= -\dot{x} + \dfrac{1}{T_\mathrm{latch}}\text{latch}(x, p, (1 - s_\mathrm{lock})(1 - p)) \end{aligned}\]

Algebraic

\[\begin{aligned} 0 &= -s + \text{above}(x; 3/4) \end{aligned}\]

External Equations

None.

Initialization

\[\begin{split}\begin{aligned} x &\leftarrow 0 \\ s &\leftarrow \text{above}(x; 3/4) \end{aligned}\end{split}\]

All internal derivatives initialize to zero.

Monitors

Monitor	Units	Description	Note
m	[p.u.]	Measured quantity magnitude	\(\sqrt{m_r^2 + m_i^2}\)
x	[-]	Relay latch	\(x\)
trip	[-]	Trip command	\(s\)