BGModeller All port voltages are equal; signed currents sum to zero. This junction is not a ground.
BGModeller handbook
Electrics AC
Component reference · matches the Elements library.
Electrical AC → Primitives / AdvancedV / AComplex RMS phasors
The steady-state AC solver solves voltage and current equations together, so it does not require causality assignment. Causality is therefore not assigned, and no causal strokes are shown on the diagram. You can click Simulate directly; Analyze is optional.
AC electrical components use the same bond-graph language as hydraulics, mechanics and time-domain electrics, including DC. Voltage and current correspond to pressure and flow; for steady-state AC, complex RMS phasors represent their magnitudes and phases.
Single-frequency steady-state calculation with linear elements and regulated P/Q loads using complex RMS phasors. Convention exp(+jωt); P + jQ = U conjugate(I). Positive Q is inductive. Linear composite blocks expand to 0/1/R/C/I/Se/Sf. Electronic loads add a nonlinear P/Q law. Initial conditions, end time and integration steps do not enter the calculation.
Choose Electrical AC → Advanced for the supply, cables and loads. Use 0-junctions to branch L and N. Set the common frequency and click Calculate AC. Results shows a table; Export CSV saves it. Parameter changes mark results stale.
Primitives
Common voltage
Common current
Signed branch currents are equal; signed voltages sum to zero. Endpoint order defines voltage-balance signs.
Resistance
U = R I. Positive constant resistance in Ω.
Inductance
U = j 2π f L I. Positive inductance in H. Initial state does not apply to AC.
Capacitance
U = I / (j 2π f C). Positive capacitance in F. Initial state does not apply to AC.
Voltage phasor
Specified RMS voltage and phase in degrees at the model frequency. Constant phasor only.
Current phasor
Specified RMS current and phase in degrees at the model frequency. Positive current is supplied out of the source.
Advanced
AC supply
Ports L and N. E = voltage_rms exp(j phase); VL − VN = E + (R + jωL) IL, with IL entering L. Set the internal resistance and inductance. Connect N to a neutral bus and one voltage reference. Results report terminal voltage and power delivered; source loss is R |IL|².
Two-conductor cable
Ports L1/N1 at the input and L2/N2 at the output. Each conductor has R = ρ length / area and L = inductance_per_m length. Length is one-way. Area is saved in m² and edited in mm². Approximate 20 °C resistivity: copper 1.724×10⁻⁸ Ω m; aluminium 2.82×10⁻⁸ Ω m. Both conductors contribute to loss: R (|IL1|² + |IN1|²). Output voltage is VL2 − VN2. ΔU = |Uin| − |Uout|. No heating, ampacity, mutual inductance, PE or leakage.
Constant-impedance load
Ports L and N. Set nominal RMS voltage, active power, PF (0 < PF ≤ 1), inductive/capacitive behaviour and nominal frequency. Qnom = ±Pnom tan(acos(PF)); Znom = Unom² / conjugate(Pnom + jQnom). This becomes series R–L or R–C. Physical R, L and C stay fixed when the model frequency changes. Actual power varies with voltage. No constant-power regulation, motor start or harmonics.
Electronic load (P/Q)
Ports L and N. U = VL − VN; S = P + jQ = U conjugate(IL); IN = −IL. Thus IL = conjugate(S/U). P is nonnegative AC input power in W, including conversion losses, not a DC output rating. Q in var is positive for inductive behaviour and negative for capacitive behaviour. P = Q = 0 draws zero current. Default P = 500 W, Q = 0 var, operating voltage 90–264 V RMS. Minimum voltage must be positive and maximum must exceed minimum.
The specified P/Q is maintained only within the operating voltage range. Out-of-range solutions return AC_PQ_VOLTAGE_RANGE; the model does not silently turn off or become an impedance. P/Q and PF describe the fundamental sinusoidal input, not harmonics or total distortion power factor. This block does not simulate inrush, battery state of charge, conversion control or charging stages.
The linear backbone is reduced to load-terminal voltages and current responses. Damped Newton iteration with continuation from zero P/Q solves V = V0 + H conjugate(S/V). Existing linear examples retain the direct solve. The open-circuit network must have determined voltages; disconnected loads and floating islands are errors. No usable supply gives AC_PQ_NO_SUPPLY; failure to converge or a near-singular collapse boundary gives AC_PQ_NOT_CONVERGED. Nonconvergence alone does not prove that no mathematical solution exists. The computed branch is connected to the zero-load solution; dynamic stability and uniqueness are not established.
Switch
Ports A and B. Closed: VA − VB = R IA, IB = −IA. Open: IA = IB = 0 exactly. Position is fixed during each calculation. There is no trip characteristic or switching transient. Floating islands are diagnosed, never silently grounded.
Voltage reference
One port E, VE = 0. Defines mathematical reference potential. This is not a protective-earth conductor or grounding electrode.
Voltage measurement
Ports P and N. U = VP − VN; IP = IN = 0. An ideal differential probe with no loading. Zero-amplitude phase is undefined.
Examples and verification
Two PN1000M, refrigerator and air conditioner: all four loads run simultaneously on one 220 V / 50 Hz supply. Each PSU supplies 500 W DC at assumed 90% efficiency: 555.56 W AC and assumed Q = 0. The refrigerator takes 150 W / +112.5 var; the air conditioner takes 1200 W / +581.19 var electrical input. Total load power is 2461.11 W / +693.69 var before wiring losses. All values retain the assumptions in the individual examples below. Four independent L/N feeders, in that order, are 20, 12, 20 and 12 m of 2.5 mm² copper, with 0.3 μH/m per conductor and a closed 0.001 Ω switch per branch. An editable shared L/N feeder connects the source to both branch buses: assumed one-way length 10 m, copper 2.5 mm² per conductor, 0.3 μH/m per conductor. The source retains R = 0.12 Ω and L = 0.15 mH. The voltage reference is on the supply side of the feeder neutral; neither conductor is bypassed. SharedFeeder reports bus voltage, total current, loss in both conductors and ΔU = |Uin| − |Uout|. These assumed cable dimensions are illustrative, not a cable-sizing recommendation. Total source current is the magnitude of the complex sum of branch currents, not their RMS magnitudes added together. The results summary includes shared-feeder and branch-cable losses (both conductors), switch contact losses, total wiring loss and separate source internal loss. Cable loss is 2ρl|I|²/A per feeder; contact loss is R|I|². Supply terminal P equals load P plus wiring loss; ideal source power also includes its internal loss. P/Q stay fixed within the assumed 180–250 V window; starting, cycling, harmonics and control dynamics are excluded. Model: electrical_ac_combined.
Refrigerator and air conditioner — assumed running loads: both run simultaneously at 220 V / 50 Hz. Refrigerator: P = 150 W and assumed lagging displacement PF = 0.80, giving Q = +112.5 var. Air conditioner: P = 1200 W electrical input and assumed lagging displacement PF = 0.90, giving Q = +581.19 var. Q = P tan(acos(PF)); the model retains the unrounded value. These are illustrative assumptions, not manufacturer ratings or measured appliance data. Electrical input includes appliance losses; it is not cooling capacity. The existing electronic P/Q blocks hold these inputs fixed as an approximation of one running condition; they do not model motor or inverter control behavior. The 180–250 V calculation window is assumed, not a manufacturer protection specification. The 20 m refrigerator feeder and 12 m air-conditioner feeder use the illustrative cable and source parameters below. Supply power includes both loads and feeder losses. Lowering supply voltage raises current at fixed P/Q in this approximation; actual appliance behavior may differ. Starting current, cycling, defrost, speed changes and harmonic distortion are excluded. PF here is displacement PF, not total PF including harmonics. Model: electrical_ac_appliances.
Two DeepCool PN1000M — 50% DC load: two 1000 W-rated PSUs, each delivering 500 W DC. Use P = 500 / 0.90 = 555.56 W AC per PSU and Q = 0 var. The manufacturer specifies at least 90% efficiency at 50% loading and active PFC. Here 90% is a fixed scenario assumption, not a measured efficiency curve; Q = 0 assumes unity fundamental displacement factor, not zero harmonics or measured total PF. The chosen 180–250 V calculation window does not represent manufacturer protection thresholds. The 220 V / 50 Hz supply and 20 m / 12 m feeders use the illustrative wiring parameters below. Combined PSU input is 1111.11 W before wiring losses; conversion loss is 55.56 W per PSU, already included in P. To change DC loading, set active_power = DC output / assumed efficiency. Lowering the supply to 200 V increases both input currents while P/Q stay fixed.
Constant-P/Q battery charger: a 1200 W / 0 var AC input with operating range 180–250 V, beside an 800 W nominal resistive load. Lower the supply from 220 to 200 V: the charger keeps 1200 W and draws more current, while resistive power falls. This is a steady charging operating point with illustrative values; no battery or charging dynamics are modeled. The numerical tests independently solve a single P/Q feeder by a quadratic equation and check mixed and multiple-load power balances.
The example menu contains 220 V / 50 Hz and 120 V / 60 Hz circuits. A supply with R = 0.12 Ω and L = 0.15 mH feeds two parallel branches. Cables: 20 and 12 m, copper 2.5 mm², 0.3 μH/m per conductor. Closed switches have R = 0.001 Ω. At 220 V the loads are 2000 W / PF 1 and 800 W / PF 0.8 inductive; at 120 V they are 1200 W and 500 W with the same PF. These are illustrative parameters, not a cable or protection selection.
Independent example check: Zbranch = Zload + 2Zconductor + Rcontact; Y = Σ(1/Zbranch); Ubus = E/(1 + Zsource Y); Ibranch = Ubus/Zbranch. Delivered power equals load power plus cable and contact losses. Automated tests use these independent equations.
Scope
No breaker/RCD trip, fault, temperature, regulatory sizing or harmonic calculation. Electrical AC cannot be mixed with transient domains. Frequency must be positive and shared by all sources. Missing references, floating islands, conflicting ideal sources and exact ideal resonance can make the system singular; no successful result is returned in that case.