SPDT Relay

Single-pole, double-throw relay with delays and faults

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Description

The SPDT Relay block models a single-pole, double-throw relay. The block has three potential states:

De-energized — The common contact, C, is connected to the normally closed contact, S1.
Energized — The common contact, C, is connected to the normally open contact, S2.
Open Circuit — The relay is open. The common contact, C, is not connected to the normally closed contact, S1, or the normally open contact, S2.

You can:

Control the relay state using the physical signal input port or electrical conserving ports.
Output the relay state.
Delay the breaking and making of either or both of the connections.
Introduce a behavioral or temporal fault that results in a stuck connection, an open circuit, or degraded contact resistance.

Relay State Control

The block has two control variants:

Physical signal (PS) control — The state of the relay depends on how the value of the input physical signal compares to the relay threshold. The relay threshold, th, is the value that you by specify for the Threshold parameter.
Electrical control — The state of the relay depends on how the current through the positive and negative electrical conserving ports, which represent the relay winding, compares to the relay upper and lower thresholds. The upper and lower thresholds depend on the values that you specify for the parameters in the Winding settings.

For the PS control variant, at the start of simulation:

If the input signal, PS, is less than or equal to th, the relay is de-energized and the common contact, C, connects to the normally closed contact, S1.
If the input signal, PS, greater than th, the relay is energized and C connects to the normally open contact, S2.

After the simulation starts, if PS rises above th, the block goes from a de-energized state to an energized state :

The C–S1 connection breaks after the delay specified in Time-to-break C-S1 connection.
The C–S2 connection closes after the delay specified in Time-to-make C-S2 connection.

If the block goes from an energized state to a de-energized state, that is PS falls to or below th:

The C–S2 connection breaks after the delay specified in Time-to-break C-S2 connection.
The C–S1 connection closes after the delay specified in Time-to-make C-S1 connection.

For the electrical control variant, the upper and lower thresholds depend on the specified values for the Rated voltage, Percent rated voltage to energize, Percent rated voltage to de-energize, and Winding series resistance parameters. The rated current is:

$i_{r a t e d} = \frac{V_{r a t e d}}{r_{c o i l}} .$

The equation for the upper current threshold, i_energized, is:

$i_{e n e r g i z e d_c u r r e n t} = \frac{R a t e d V o l t a g e * P e r c e n t r a t e d v o l t a g e t o e n e r g i z e}{W i n d i n g s e r i e s r e s i s t a n c e} .$

The equation for the lower current threshold, i_de-energized, is:

$i_{d e - e n e r g i z e d_c u r r e n t} = \frac{R a t e d V o l t a g e * P e r c e n t r a t e d v o l t a g e t o d e - e n e r g i z e}{W i n d i n g s e r i e s r e s i s t a n c e} .$

At the start of simulation:

If the control current is less than i_energized, the common contact, C, connects to the normally closed contact, S1.
If the control current is greater than i_energized, the relay is energized and C connects to the normally open contact, S2.

After the start of simulation, if the current rises above i_energized, the block goes from a de-energized state to an energized state:

The C–S1 connection breaks after the delay specified in Time-to-break C-S1 connection.
The C–S2 connection closes after the delay specified in Time-to-make C-S2 connection.

If the current falls below i_de-energized, the block goes from an energized state to a de-energized state:

The C–S2 connection breaks after the delay specified in Time-to-break C-S2 connection.
The C–S1 connection closes after the delay specified in Time-to-make C-S1 connection.

Output the Relay State

To view the relay state, expose port x, a physical signal port that outputs the state of each connection. To expose the x port, in the Main settings, set State port to Visible.

The table shows how the state of the relay relates to the state of the connections. A closed connection has a state of 1. An open connection has a state of 0.

Relay and Connection States

C–S1 Connection State	C–S2 Connection State	Relay State
1	0	De-energized
0	1	Energized
0	0	Open Circuit

Connection Delays

You can specify delays for making and breaking connections in the Mechanical settings. The table shows how the make and brake time delays affect the connections between contacts S1 and S2 and the common contact, C.

Mechanical Settings Relay State C–S1 Connection State C–S2 Connection State Results, with C–S1 in Yellow and C–S2 in Blue

Parameter	Value
Time-to-break C-S1 connection	`0`
Time-to-make C-S1 connection	`0`
Time-to-break C-S2 connection	`0`
Time-to-make C-S2 connection	`0`

De-energized

Energized 0 1

Parameter	Value
Time-to-break C-S1 connection	> `0`
Time-to-make C-S1 connection	`0`
Time-to-break C-S2 connection	`0`
Time-to-make C-S2 connection	`0`

De-energized

Energized 1, 0 1

Parameter	Value
Time-to-break C-S1 connection	`0`
Time-to-make C-S1 connection	> `0`
Time-to-break C-S2 connection	`0`
Time-to-make C-S2 connection	`0`

De-nergized

0, 1

Energized 0 1

Parameter	Value
Time-to-break C-S1 connection	`0`
Time-to-make C-S1 connection	`0`
Time-to-break C-S2 connection	> `0`
Time-to-make C-S2 connection	`0`

De-nergized

1, 0

Energized 0 1

Parameter	Value
Time-to-break C-S1 connection	`0`
Time-to-make C-S1 connection	`0`
Time-to-break C-S2 connection	`0`
Time-to-make C-S2 connection	> `0`

De-nergized

Energized 0 0, 1

Faults

The block provides five fault types:

C-S1 stuck closed
C-S2 stuck closed
C open circuit (no path to S1 or S2)
Degraded contact resistance
Winding failed open circuit. This fault type is available only for the electrical control variant.

Each type of fault can take effect only when the threshold for a temporal or behavioral trigger is exceeded.

C–S1 Stuck Closed Fault

The C–S1 stuck closed fault occurs if the common contact, C, becomes mechanically, electrically, or chemically stuck to the normally closed contact, S1. Causes of this type of fault include:

Contact welding, possibly due to an inrush current or breaking current that exceeds the rating or load short circuit.
Mechanical damage.
Insulation deterioration.
Inductive voltage.

The table shows the faulted state for a C–S1 stuck closed fault.

Connection	State
C–S1	1
C–S2	0

A C–S1 stuck closed temporal fault can occur only if the simulation time exceeds the time threshold such that

$t > t_{t h_t},$

where:

t is the simulation time.
t_{th_t} is the specified value for the Simulation time after which contactors can stick parameter.

A C–S1 stuck closed behavioral fault can occur only if the load current exceeds the current threshold for a period of time that exceeds the behavioral trigger time threshold. That is, the behavioral fault can occur only if:

$i_{l o a d} > i_{t h},$

and

$t_{i > i_t h} > t_{t h_b},$

where:

i_load is the load current.
i_th is the specified value for the Maximum permissible load current parameter.
t_{i>i_th} is the time that the current threshold is exceeded.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.

When the temporal or behavioral fault thresholds are exceeded, if C–S1 is:

Closed — C–S1 remains closed for the rest of the simulation.
Open — C–S1 the fault does not take effect unless the relay becomes de-energized and the C–S1 connection closes. Once closed, the C–S1 connection remains closed for the rest of the simulation.

C–S2 Stuck Closed Fault

The C–S2 stuck closed fault occurs if the common contact, C, becomes mechanically, electrically, or chemically stuck to the normally closed contact, S2. Causes of this type of fault include:

Contact welding, possibly due to an inrush current or breaking current that exceeds the rating or load short circuit.
Mechanical damage.
Insulation deterioration.

The table shows the faulted state for a C–S2 stuck closed fault.

Connection	State
C–S1	0
C–S2	1

A C–S2 stuck closed temporal fault can occur only if the simulation time exceeds the time threshold such that:

$t > t_{t h_t},$

where:

t is the simulation time.
t_{th_t} is the specified value for the Simulation time after which contactors can stick parameter.

A C–S2 stuck closed behavioral fault can occur only if the load current exceeds the current threshold for a period of time that exceeds the behavioral trigger time threshold. That is, the behavioral fault can occur only if:

$i_{l o a d} > i_{t h},$

and

$t_{i > i_t h} > t_{t h_b},$

where:

i_load is the load current.
i_th is the specified value for the Maximum permissible load current parameter.
t_{i>i_th} is the time that the current threshold is exceeded.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.

When the temporal or behavioral fault thresholds are exceeded, if C–S2 is:

Closed — C–S2 remains closed for the rest of the simulation.
Open — The C–S2 the fault does not take effect unless the relay becomes energized and the C–S2 connection closes. Once closed, the C–S2 connection remains closed for the rest of the simulation.

C Open Circuit (No Path to S1 or S2) Fault

The C open circuit (no path to S1 or S2) fault occurs if the common contact, C, becomes mechanically stuck in an open position. This type of fault can happen if:

There is contact damage or deterioration.
The switch connector becomes mechanically stuck in the middle of the relay.

The table shows the faulted state for a C open circuit (no path to S1 or S2) fault.

Connection	State
C–S1	0
C–S2	0

A C open circuit temporal fault can occur only if the simulation time exceeds the time threshold such that

$t > t_{t h_t},$

where:

t is the simulation time.
t_{th_t} is the specified value for the Simulation time after which C can be open circuit parameter.

A C open circuit behavioral fault can occur only if the load current exceeds the current threshold for a period of time that exceeds the behavioral trigger time threshold. That is, the behavioral fault can occur only if:

$i_{l o a d} > i_{t h},$

and

$t_{i > i_t h} > t_{t h_b},$

where:

i_load is the load current.
i_th is the specified value for the Maximum permissible load current parameter.
t_{i>i_th} is the period of time during which the current threshold is exceeded.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.

When the temporal fault threshold is exceeded, if:

The relay is in the open-circuit state, that is, one connection has been broken, and the other connection has not yet been made, the relay remains open for the rest of the simulation.
Either the C–S1 or C–S2 connection is closed, the fault does not take effect unless the relay is energized or de-energized and the closed connection is broken. If the connection is broken, the relay becomes an open-circuit, and remains open for the rest of the simulation.

When the behavioral fault thresholds are exceeded, if:

The relay is in the open-circuit state, that is, one connection has been broken, and the other connection has not yet been made, the relay remains open for the rest of the simulation.
Either the C–S1 or C–S2 connection is closed, the relay state immediately becomes an open circuit and remains an open circuit for the rest of the simulation.

Degraded Contact Resistance Fault

Causes of the degraded contact resistance fault include:

Overuse-induced overload conditions. High inrush currents and voltages can cause overload conditions, as can excessive switching of the relay. Overload conditions ultimately trigger electrical arching, which generates heat that degrades the contact material.
Chemical contamination that interferes with the operation of the relay contacts. Contaminants, which can include oxidation films or foreign particles, tend to produce high or unstable contact resistance readings.
End of relay life.

The table shows the faulted state for a degraded contact resistance fault.

Connection	State
C–S1	0 or 1. The contact resistance is degraded.
C–S2	0 or 1. The contact resistance is degraded.

A degraded contact resistance temporal fault can occur only if the simulation time exceeds the time threshold such that

$t > t_{t h_t},$

where:

t is the simulation time.
t_{th_t} is the specified value for the Simulation time for fault event parameter.

The degraded contact resistances of S1 and S2 are:

$r_{c o n t a c t_s 1} (t) = r_{c o n t a c t_f a u l t_s 1} - (r_{c o n t a c t_f a u l t_s 1} - r_{c o n t a c t}) s e c h (\frac{t - t_{t h_t}}{τ}),$

$r_{c o n t a c t_s 2} (t) = r_{c o n t a c t_f a u l t_s 2} - (r_{c o n t a c t_f a u l t_s 2} - r_{c o n t a c t}) s e c h (\frac{t - t_{t h_t}}{τ}),$

where:

r_{contact_fault_s1} is the final value of the faulted S1 contact resistance.
r_{contact_fault_s2} is the final value of the faulted S2 contact resistance.
r_contact is the unfaulted S1 and S2 contact resistance.

A degraded contact resistance behavioral fault can occur only if the load current exceeds the current threshold for a period of time that exceeds the behavioral trigger time threshold. That is, the behavioral fault can occur only if:

$i_{S 1 - C} > i_{t h},$

and

$t_{i 1 > i_t h} > t_{t h_b},$

where:

i_load is the load current.
i_th is the specified value for the Maximum permissible load current parameter.
t_{i1>i_th} is the period of time during which the current threshold for the connection C-S1 is exceeded.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.

For a behavior-triggered fault, if $i_{S 1 - C} > i_{t h}$ continuously over the time interval t_{th_b},

$r_{c o n t a c t_s 1} (t) = r_{c o n t a c t_f a u l t_s 1} - (r_{c o n t a c t_f a u l t_s 1} - r_{c o n t a c t}) s e c h (\frac{t_{i 1 > i_t h} - t_{t h_b}}{τ}),$

where:

i_S1-C is the common contact to normally closed contact, C–S1, current.
i_th is the specified value for the Maximum permissible load current parameter.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.
r_{contact_fault_s1} is the final value of the faulted S1 contact resistance.
r_contact is the unfaulted S1 contact resistance.
τ is specified value for the Time constant for degraded contact resistance parameter.

Likewise, for a C–S2 connection, if

$i_{S 2 - C} > i_{t h}$

and

$t_{i 2 > i_t h} > t_{t h_b},$

then the degraded contact resistance is:

$r_{c o n t a c t_s 2} (t) = r_{c o n t a c t_f a u l t_s 2} - (r_{c o n t a c t_f a u l t_s 2} - r_{c o n t a c t}) s e c h (\frac{t_{i 2 > i_t h} - t_{t h_b}}{τ}),$

where:

i_S2-C is the common contact to normally closed contact, C–S2, current.
r_{contact_fault_s2} is the final value of the faulted S2 contact resistance

When the temporal fault threshold is exceeded, for both the C–S1 and the C–S2 connections, the contact resistance is immediately degraded and remains degraded for the rest of the simulation.

When the behavioral fault thresholds are exceeded for C–S1, in terms of i_S1-C, the resistance for the C–S1 connection is degraded after the specified value for the Time to fail when exceeding current parameter and remains degraded for the rest of the simulation.

When the behavioral fault thresholds are exceeded for C–S2, in terms of i_S2-C, the resistance for the C–S2 connection is degraded after the specified value for the Time to fail when exceeding current parameter and remains degraded for the rest of the simulation.

Winding failed open circuit

The open-circuit winding fault is available only for the electrical control variant. An open circuit in the winding coil can cause this type of fault.

The table shows the faulted state for a winding failed open circuit fault.

Connection	State
C–S1	1
C–S2	0

A winding failed open circuit temporal fault can occur only if the simulation time exceeds the time threshold such that

$t > t_{t h_t},$

where:

t is the simulation time.
t_{th_t} is the specified value for the Simulation time for fault event parameter.

For time fault, the relay switches depending on the winding current, which is approximated as:

$L \frac{d i}{d t} + R i = v_{w i n d i n g} * s e c h (\frac{t - t_{t h_t}}{τ}),$

where :

L is the winding inductance.
R is the winding resistance.
i is the winding current.
v_winding is the voltage across the winding.
t_{th_t} is the specified value for the Simulation time for fault event parameter.
τ is the specified value for the Time constant for winding open circuit transition parameter.

A winding failed open circuit behavioral fault can occur only if one of these conditions is met:

The winding current exceeds the current threshold for a period of time that exceeds the behavioral trigger time threshold.
The winding voltage exceeds the voltage threshold for a number of times that exceeds the threshold for the number of voltage overloads.

That is, the behavioral fault can occur only if:

$i_{w i n d i n g} > i_{t h}$

and then

$t_{i > i_t h} > t_{t h_b},$

where:

i_winding is the winding current.
i_th is the specified value for the Maximum permissible winding current parameter.
t_{i>i_th} is the time that the current threshold is exceeded.
t_{th_b} is the specified value for the Time to fail when exceeding current parameter.

or if:

$v_{w i n d i n g} > v_{t h},$

and then

$N_{v > v_t h} > N_{t h},$

where:

v_winding is the winding voltage.
v_th is the specified value for the Maximum permissible winding voltage parameter.
N_{v>v_th} is the number of times that the voltage threshold is exceeded.
N_th is the specified value for the Number of events to fail when exceeding voltage parameter.

If the temporal or behavioral fault thresholds are exceeded, the C–S1 remains closed for the rest of the simulation

Limitations and Assumptions

For behavioral faults, if time to fail when exceeding the current threshold is greater than the time between switching events, no fault is triggered because the accumulated heat is not adequate for melting or breaking the contacts or windings.
The energize and de-energize delays can differ, but the energize delay must be greater than or equal to the de-energize delay.

Ports

The type, visibility, and location of the block ports depend on how you configure these parameters in the Main settings:

Control port — Choose between a physical signal input port, PS, or electrical conserving ports, + and -, for relay control.
State port — Set the visibility for the relay state physical signal output port, x.
Common port — Set the location of the common port, C, relative to the contact ports S1 and S2.

Control port	State port	Common port
`PS`	`Hidden`	`Adjacent to switch ports`
	`Hidden`	`Adjacent to switch ports`
	`Visible`	`Across from switch ports`
	`Visible`	`Across from switch ports`
`Electrical`	`Hidden`	Not applicable
`Electrical`	`Visible`	Not applicable

Input

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`PS` — Physical signal control
physical signal

Physical signal input port that energizes and de-energizes the relay.

Dependencies

This port is visible only when, in the Main settings, the Control port parameter is set to PS.

Output

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`x` — Relay state
physical signal

State of the relay in terms of the C–S1 and C–S2 connections:

1 — Closed connection
0 — Open connection

Dependencies

This port is visible only when, in the Main settings, the State port parameter is set to Visible.

Conserving

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`S1` — Normally closed contact
electrical

Electrical conserving port associated with the normally closed contact.

`C` — Common contact
electrical

Electrical conserving port associated with the common contact.

`S2` — Normally open contact
electrical

Electrical conserving port associated with the normally open contact.

`+` — Winding positive terminal
electrical

Electrical conserving port associated with the winding positive voltage terminal. The current through the winding controls the relay state.

Dependencies

This port is visible only when, in the Main settings, the Control port parameter is set to Electrical.

`-` — Winding negative terminal
electrical

Electrical conserving port associated with the winding negative voltage terminal The current through the winding controls the relay state.

Dependencies

This port is visible only when, in the Main settings, the Control port parameter is set to Electrical.

Parameters

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Main

`Control port` — Input port choice
`PS` (default) | `Electrical`

Relay state control method:

PS — PS physical signal input port
Electrical — + and - electrical conserving ports associated with the relay winding terminals

Dependencies

If this parameter is set to:

PS — The PS port and related parameters in the Main and Faults settings are visible. For more information, see Control Port Parameter Dependencies.
Electrical — The + and - ports, related parameters in the Main and Faults settings, and the Windings settings are visible. For more information, see Control Port Parameter Dependencies, Faults Parameter Dependencies, and Winding.

The table shows how this parameter affects the visibility of other parameters in the Main settings. To learn how to read the table, see Parameter Dependencies.

Control Port Parameter Dependencies

Control port
`PS`	`Electrical`
Closed resistance	Closed resistance
Open conductance	Open conductance
Threshold	Open conductance
State port	State port
Common port	State port

`Closed resistance` — Connected contact resistance
`0.01` `Ohm` (default) | positive scalar

Resistance across closed relay contacts. The parameter value must be greater than zero.

`Open conductance` — Open-circuit conductance
`1e-8` `1/Ohm` (default) | positive scalar

Conductance across open relay contacts. The parameter value must be greater than zero.

`Threshold` — Relay threshold
`0` (default) | nonnegative scalar

If the physical signal input is above the threshold value, the relay is energized. Conversely, if the physical signal input falls is the threshold value, the relay is de-energized.

Dependencies

This parameter is visible only if the Control port parameter is set to PS.

`State port` — Relay state output port visibility
`Hidden` (default) | `Visible`

Visibility of the physical signal port that outputs the relay state. The port outputs a vector of length two, with the first element corresponding to the C–S1 connection and the second to the C–S2 connection. The elements are 1 if the corresponding connection is closed, and 0 otherwise.

Dependencies

The x port is visible only if this parameter is set to Visible.

`Common port` — Common port location
`Adjacent to switch ports` (default) | `Across from switch ports`

Location of the common port, C, relative to the S1 and S2 ports.

Dependencies

This parameter is visible only if the Control port parameter is set to PS.

Winding

The Winding settings are visible only if, in the Main settings, the Control port parameter is set to Electrical. For more information, see Control port.

`Rated voltage` — Rated voltage
`5` `V` (default) | positive scalar

Standard voltage applied to the operating coil under normal operating conditions. The current threshold depends on the value of this parameter.