Analog electrical models

This library of components is modeled after the Modelica.Electrical.Analog library.

Voltage nodes with type Voltage are the main Unknown type used in electrical circuits. voltage nodes can be single floating point unknowns representing a single voltage node. A Voltage can also be an array representing multiphase circuits or multiple node positions. Lastly, Voltage unknowns can also be complex for use with quasiphasor-type solutions.

The type ElectricalNode is a Union type that can be an Array, a number, an expression, or an Unknown. This is used in model functions to allow passing a Voltage node or a real value (like 0.0 for ground).

Example

function ex_ChuaCircuit()
    n1 = Voltage("n1")
    n2 = Voltage("n2")
    n3 = Voltage(4.0, "n3")
    g = 0.0
    function NonlinearResistor(n1::ElectricalNode, n2::ElectricalNode, Ga, Gb, Ve)
        i = Current(compatible_values(n1, n2))
        v = Voltage(compatible_values(n1, n2))
        @equations begin
            Branch(n1, n2, v, i)
            i = ifelse(v < -Ve, Gb .* (v + Ve) - Ga .* Ve,
                       ifelse(v > Ve, Gb .* (v - Ve) + Ga*Ve, Ga*v))
        end
    end
    @equations begin
        Resistor(n1, g, 12.5e-3) 
        Inductor(n1, n2, 18.0)
        Resistor(n2, n3, 1 / 0.565) 
        Capacitor(n2, g, 100.0)
        Capacitor(n3, g, 10.0)
        NonlinearResistor(n3, g, -0.757576, -0.409091, 1.0)
    end
end

y = sim(ex_ChuaCircuit(), 200.0)
wplot(y)

SeriesProbe

Connect a series current probe between two nodes. This is vectorizable.

SeriesProbe(n1, n2, name::String)

Arguments

Example

function model()
    n1 = Voltage("n1")
    n2 = Voltage()
    g = 0.0
    Equation[
        SineVoltage(n1, g, 100.0)
        SeriesProbe(n1, n2, "current")
        Resistor(n2, g, 2.0)
    ]
end
y = sim(model())

Sims/src/../lib/electrical.jl:90

BranchHeatPort

Wrap argument model with a heat port that captures the power generated by the electrical device. This is vectorizable.

BranchHeatPort(n1::ElectricalNode, n2::ElectricalNode, hp::HeatPort,
               model::Function, args...)

Arguments

Examples

Here's an example of a definition defining a Resistor that uses a heat port (a Temperature) in terms of another model:

function Resistor(n1::ElectricalNode, n2::ElectricalNode, R::Signal, hp::Temperature, T_ref::Signal, alpha::Signal) 
    BranchHeatPort(n1, n2, hp, Resistor, R .* (1 + alpha .* (hp - T_ref)))
end

Sims/src/../lib/electrical.jl:129

Basics

Resistor

The linear resistor connects the branch voltage v with the branch current i by i*R = v. The Resistance R is allowed to be positive, zero, or negative. 

Resistor(n1::ElectricalNode, n2::ElectricalNode, R::Signal)
Resistor(n1::ElectricalNode, n2::ElectricalNode, 
         R = 1.0, T = 293.15, T_ref = 300.15, alpha = 0.0)
Resistor(n1::ElectricalNode, n2::ElectricalNode;             # keyword-arg version
         R = 1.0, T = 293.15, T_ref = 300.15, alpha = 0.0)
Resistor(n1::ElectricalNode, n2::ElectricalNode,
         R::Signal, hp::Temperature, T_ref::Signal, alpha::Signal)

Arguments

Keyword/Optional Arguments

Details

The resistance R is optionally temperature dependent according to the following equation:

R = R_ref*(1 + alpha*(heatPort.T - T_ref))

With the optional hp HeatPort argument, the power will be dissipated into this HeatPort.

The resistance R can be a constant numeric value or an Unknown, meaning it can vary with time. Note: it is recommended that the R signal should not cross the zero value. Otherwise, depending on the surrounding circuit, the probability of singularities is high.

This device is vectorizable using array inputs for one or both of n1 and n2.

Example

function model()
    n1 = Voltage("n1")
    g = 0.0
    Equation[
        SineVoltage(n1, g, 100.0)
        Resistor(n1, g, R = 3.0, T = 330.0, alpha = 1.0)
    ]
end
y = sim(model())

Sims/src/../lib/electrical.jl:218

Capacitor

The linear capacitor connects the branch voltage v with the branch current i by i = C * dv/dt. 

Capacitor(n1::ElectricalNode, n2::ElectricalNode, C::Signal = 1.0) 
Capacitor(n1::ElectricalNode, n2::ElectricalNode; C::Signal = 1.0)

Arguments

Keyword/Optional Arguments

Details

C can be a constant numeric value or an Unknown, meaning it can vary with time. If C is a constant, it may be positive, zero, or negative. If C is a signal, it should be greater than zero.

This device is vectorizable using array inputs for one or both of n1 and n2.

Example

function model()
    n1 = Voltage("n1")
    g = 0.0
    Equation[
        SineVoltage(n1, g, 100.0)
        Resistor(n1, g, 3.0)
        Capacitor(n1, g, 1.0)
    ]
end

Sims/src/../lib/electrical.jl:286

Inductor

The linear inductor connects the branch voltage v with the branch current i by v = L * di/dt. 

Inductor(n1::ElectricalNode, n2::ElectricalNode, L::Signal = 1.0) 
Inductor(n1::ElectricalNode, n2::ElectricalNode; L::Signal = 1.0)

Arguments

Keyword/Optional Arguments

Details

L can be a constant numeric value or an Unknown, meaning it can vary with time. If L is a constant, it may be positive, zero, or negative. If L is a signal, it should be greater than zero.

This device is vectorizable using array inputs for one or both of n1 and n2

Example

function model()
    n1 = Voltage("n1")
    g = 0.0
    Equation[
        SineVoltage(n1, g, 100.0)
        Resistor(n1, g, 3.0)
        Inductor(n1, g, 6.0)
    ]
end

Sims/src/../lib/electrical.jl:341

SaturatingInductor

TBD

Sims/src/../lib/electrical.jl:356

Transformer

The transformer is a two port. The left port voltage v1, left port current i1, right port voltage v2 and right port current i2 are connected by the following relation:

| v1 |         | L1   M  |  | i1' |
|    |    =    |         |  |     |
| v2 |         | M    L2 |  | i2' |

L1, L2, and M are the primary, secondary, and coupling inductances respectively.

Transformer(p1::ElectricalNode, n1::ElectricalNode, p2::ElectricalNode, n2::ElectricalNode, 
            L1 = 1.0, L2 = 1.0, M = 1.0)
Transformer(p1::ElectricalNode, n1::ElectricalNode, p2::ElectricalNode, n2::ElectricalNode; 
            L1 = 1.0, L2 = 1.0, M = 1.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:457

EMF

EMF transforms electrical energy into rotational mechanical energy. It is used as basic building block of an electrical motor. The mechanical connector flange can be connected to elements of the rotational library. 

EMF(n1::ElectricalNode, n2::ElectricalNode, flange::Flange,
    support_flange = 0.0, k = 1.0)
EMF(n1::ElectricalNode, n2::ElectricalNode, flange::Flange;
    support_flange = 0.0, k = 1.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:501

Ideal

IdealDiode

This is an ideal switch which is open (off), if it is reversed biased (voltage drop less than 0) closed (on), if it is conducting (current > 0). This is the behaviour if all parameters are exactly zero. Note, there are circuits, where this ideal description with zero resistance and zero cinductance is not possible. In order to prevent singularities during switching, the opened diode has a small conductance Gon and the closed diode has a low resistance Roff which is default.

The parameter Vknee which is the forward threshold voltage, allows to displace the knee point along the Gon-characteristic until v = Vknee. 

IdealDiode(n1::ElectricalNode, n2::ElectricalNode, 
           Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)
IdealDiode(n1::ElectricalNode, n2::ElectricalNode; 
           Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:566

IdealThyristor

This is an ideal thyristor model which is open (off), if the voltage drop is less than 0 or fire is false closed (on), if the voltage drop is greater or equal 0 and fire is true.

This is the behaviour if all parameters are exactly zero. Note, there are circuits, where this ideal description with zero resistance and zero cinductance is not possible. In order to prevent singularities during switching, the opened thyristor has a small conductance Goff and the closed thyristor has a low resistance Ron which is default.

The parameter Vknee which is the forward threshold voltage, allows to displace the knee point along the Goff-characteristic until v = Vknee. 

IdealThyristor(n1::ElectricalNode, n2::ElectricalNode, fire::Discrete, 
               Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)
IdealThyristor(n1::ElectricalNode, n2::ElectricalNode, fire::Discrete; 
               Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:619

IdealGTOThyristor

This is an ideal GTO thyristor model which is open (off), if the voltage drop is less than 0 or fire is false closed (on), if the voltage drop is greater or equal 0 and fire is true.

This is the behaviour if all parameters are exactly zero. Note, there are circuits, where this ideal description with zero resistance and zero cinductance is not possible. In order to prevent singularities during switching, the opened thyristor has a small conductance Goff and the closed thyristor has a low resistance Ron which is default.

The parameter Vknee which is the forward threshold voltage, allows to displace the knee point along the Goff-characteristic until v = Vknee.

IdealGTOThyristor(n1::ElectricalNode, n2::ElectricalNode, fire::Discrete, 
                  Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)
IdealGTOThyristor(n1::ElectricalNode, n2::ElectricalNode, fire::Discrete; 
                  Vknee = 0.0, Ron = 1e-5, Goff = 1e-5)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:675

IdealOpAmp

The ideal OpAmp is a two-port device. The left port is fixed to v1=0 and i1=0 (nullator). At the right port, both any voltage v2 and any current i2 are possible (norator).

The ideal OpAmp with three pins is of exactly the same behaviour as the ideal OpAmp with four pins. Only the negative output pin is left out. Both the input voltage and current are fixed to zero (nullator). At the output pin both any voltage v2 and any current i2 are possible.

IdealOpAmp(p1::ElectricalNode, n1::ElectricalNode, p2::ElectricalNode, n2::ElectricalNode)
IdealOpAmp(p1::ElectricalNode, n1::ElectricalNode, p2::ElectricalNode)

Arguments

Sims/src/../lib/electrical.jl:717

IdealOpeningSwitch

The ideal opening switch has a positive pin p and a negative pin n. The switching behaviour is controlled by the input signal control. If control is true, pin p is not connected with negative pin n. Otherwise, pin p is connected with negative pin n.

In order to prevent singularities during switching, the opened switch has a (very low) conductance Goff and the closed switch has a (very low) resistance Ron. The limiting case is also allowed, i.e., the resistance Ron of the closed switch could be exactly zero and the conductance Goff of the open switch could be also exactly zero. Note, there are circuits, where a description with zero Ron or zero Goff is not possible.

IdealOpeningSwitch(n1::ElectricalNode, n2::ElectricalNode, control::Discrete,
                   Ron = 1e-5, Goff = 1e-5)
IdealOpeningSwitch(n1::ElectricalNode, n2::ElectricalNode, control::Discrete;
                   Ron = 1e-5, Goff = 1e-5)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:765

IdealClosingSwitch

The ideal closing switch has a positive pin p and a negative pin n. The switching behaviour is controlled by input signal control. If control is true, pin p is connected with negative pin n. Otherwise, pin p is not connected with negative pin n.

In order to prevent singularities during switching, the opened switch has a (very low) conductance Goff and the closed switch has a (very low) resistance Ron. The limiting case is also allowed, i.e., the resistance Ron of the closed switch could be exactly zero and the conductance Goff of the open switch could be also exactly zero. Note, there are circuits, where a description with zero Ron or zero Goff is not possible.

IdealClosingSwitch(n1::ElectricalNode, n2::ElectricalNode, control::Discrete,
                   Ron = 1e-5, Goff = 1e-5)
IdealClosingSwitch(n1::ElectricalNode, n2::ElectricalNode, control::Discrete;
                   Ron = 1e-5, Goff = 1e-5)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:813

ControlledIdealOpeningSwitch

TBD

Sims/src/../lib/electrical.jl:833

ControlledIdealClosingSwitch

TBD

Sims/src/../lib/electrical.jl:856

ControlledOpenerWithArc

This model is an extension to the IdealOpeningSwitch.

The basic model interupts the current through the switch in an infinitesimal time span. If an inductive circuit is connected, the voltage across the switch is limited only by numerics. In order to give a better idea for the voltage across the switch, a simple arc model is added:

When the Boolean input control signals to open the switch, a voltage across the opened switch is impressed. This voltage starts with V0 (simulating the voltage drop of the arc roots), then rising with slope dVdt (simulating the rising voltage of an extending arc) until a maximum voltage Vmax is reached.

     | voltage
Vmax |      +-----
     |     /
     |    /
V0   |   +
     |   |
     +---+-------- time

This arc voltage tends to lower the current following through the switch; it depends on the connected circuit, when the arc is quenched. Once the arc is quenched, i.e., the current flowing through the switch gets zero, the equation for the off-state is activated i=Goff*v.

When the Boolean input control signals to close the switch again, the switch is closed immediately, i.e., the equation for the on-state is activated v=Ron*i.

Please note: In an AC circuit, at least the arc quenches when the next natural zero-crossing of the current occurs. In a DC circuit, the arc will not quench if the arc voltage is not sufficient that a zero-crossing of the current occurs.

This model is the same as ControlledOpenerWithArc, but the switch is closed when control > level. 

ControlledOpenerWithArc(n1::ElectricalNode, n2::ElectricalNode, control::Signal,
                        level = 0.5,  Ron = 1e-5,  Goff = 1e-5,  V0 = 30.0,  dVdt = 10e3,  Vmax = 60.0)
ControlledOpenerWithArc(n1::ElectricalNode, n2::ElectricalNode, control::Signal;
                        level = 0.5,  Ron = 1e-5,  Goff = 1e-5,  V0 = 30.0,  dVdt = 10e3,  Vmax = 60.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:929

ControlledCloserWithArc

This model is the same as ControlledOpenerWithArc, but the switch is closed when control > level. 

ControlledCloserWithArc(n1::ElectricalNode, n2::ElectricalNode, control::Signal,
                        level = 0.5,  Ron = 1e-5,  Goff = 1e-5,  V0 = 30.0,  dVdt = 10e3,  Vmax = 60.0)
ControlledCloserWithArc(n1::ElectricalNode, n2::ElectricalNode, control::Signal;
                        level = 0.5,  Ron = 1e-5,  Goff = 1e-5,  V0 = 30.0,  dVdt = 10e3,  Vmax = 60.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:995

Semiconductors

Diode

The simple diode is a one port. It consists of the diode itself and an parallel ohmic resistance R. The diode formula is:

i  =  ids * ( e^(v/vt) - 1 )

If the exponent v/vt reaches the limit maxex, the diode characterisic is linearly continued to avoid overflow.

Diode(n1::ElectricalNode, n2::ElectricalNode, 
      Ids = 1e-6,  Vt = 0.04,  Maxexp = 15,  R = 1e8)
Diode(n1::ElectricalNode, n2::ElectricalNode; 
      Ids = 1e-6,  Vt = 0.04,  Maxexp = 15,  R = 1e8)
Diode(n1::ElectricalNode, n2::ElectricalNode, hp::HeatPort,
      Ids = 1e-6,  Vt = 0.04,  Maxexp = 15,  R = 1e8)
Diode(n1::ElectricalNode, n2::ElectricalNode; hp::HeatPort;
      Ids = 1e-6,  Vt = 0.04,  Maxexp = 15,  R = 1e8)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:1047

ZDiode

TBD

Sims/src/../lib/electrical.jl:1072

HeatingDiode

The simple diode is an electrical one port, where a heat port is added, which is defined in the Thermal library. It consists of the diode itself and an parallel ohmic resistance R. The diode formula is:

i  =  ids * ( e^(v/vt_t) - 1 )

where vt_t depends on the temperature of the heat port:

vt_t = k*temp/q

If the exponent v/vt_t reaches the limit maxex, the diode characterisic is linearly continued to avoid overflow. The thermal power is calculated by i*v.

HeatingDiode(n1::ElectricalNode, n2::ElectricalNode, 
             T = 293.15,  Ids = 1e-6,  Maxexp = 15,  R = 1e8,  EG = 1.11,  N = 1.0,  TNOM = 300.15,  XTI = 3.0)
HeatingDiode(n1::ElectricalNode, n2::ElectricalNode; 
             T = 293.15,  Ids = 1e-6,  Maxexp = 15,  R = 1e8,  EG = 1.11,  N = 1.0,  TNOM = 300.15,  XTI = 3.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:1135

Sources

SignalVoltage

The signal voltage source is a parameterless converter of real valued signals into a source voltage.

This voltage source may be vectorized.

SignalVoltage(n1::ElectricalNode, n2::ElectricalNode, V::Signal)

Arguments

Sims/src/../lib/electrical.jl:1180

SineVoltage

A sinusoidal voltage source. An offset parameter is introduced, which is added to the value calculated by the blocks source. The startTime parameter allows to shift the blocks source behavior on the time axis.

This voltage source may be vectorized.

SineVoltage(n1::ElectricalNode, n2::ElectricalNode, 
            V = 1.0,  f = 1.0,  ang = 0.0,  offset = 0.0)
SineVoltage(n1::ElectricalNode, n2::ElectricalNode; 
            V = 1.0,  f = 1.0,  ang = 0.0,  offset = 0.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:1217

StepVoltage

A step voltage source. An event is introduced at the transition. Probably cannot be vectorized.

StepVoltage(n1::ElectricalNode, n2::ElectricalNode, 
            V = 1.0,  start = 0.0,  offset = 0.0)
StepVoltage(n1::ElectricalNode, n2::ElectricalNode; 
            V = 1.0,  start = 0.0,  offset = 0.0)

Arguments

Keyword/Optional Arguments

Sims/src/../lib/electrical.jl:1249

SignalCurrent

The signal current source is a parameterless converter of real valued signals into a current voltage.

This current source may be vectorized.

SignalCurrent(n1::ElectricalNode, n2::ElectricalNode, I::Signal)

Arguments

Sims/src/../lib/electrical.jl:1284