Total impedance of a series AGL circuit from the fixtures, isolating transformers and primary cable.
A constant-current regulator drives the same current through every element, so the circuit behaves as one series impedance. This tool builds it up as a resistance and a reactance, then gives the impedance, power factor, the voltage and apparent power the regulator must deliver, and the smallest standard CCR that carries it.
Planning assumption. The loss becomes the transformer resistance.
Your own assumption. The reactive part is assigned to the transformers.
Resistance per km at 20 °C, as used in Calculator #15.
Out and back.
Placeholder. Use the cable data sheet value for your construction and frequency.
Your own rule, not a standard value.
Standard sizes 1, 2, 2.5, 4, 5, 7.5, 10, 15, 20, 25, 30, 50 and 70 kVA, treated as nominal kVA as in Calculator #16 (FAA AC 150/5345-10H lists 1 to 30 kW, with 50 and 70 kW as replacement-only; 2.5 and 5 are IEC and manufacturer sizes). Only sizes whose rated voltage (kVA ÷ current) stays within 5 kV are offered, so at 6.6 A the choice stops at 30 kVA.
| Element | R (Ω) | X (Ω) | Share of R (%) | Share of X (%) |
|---|
Quick answers on the total impedance of a series AGL circuit and the CCR duty it sets.
It builds up the total impedance of a series AGL circuit from the fixtures, isolating transformers and primary cable. A constant-current regulator drives the same current through every element, so the circuit behaves as one series impedance. The tool gives the impedance, the power factor, the voltage and apparent power the regulator must deliver, and the smallest standard CCR that carries it.
With a 1:1 current ratio, a load on the secondary appears on the primary as a resistance equal to its power divided by the current squared. The transformer loss is treated the same way, using the power divided by efficiency minus the power. The reactive power sets the transformer reactance, which is the primary power times the tangent of the arccosine of the power factor, divided by the current squared.
The cable resistance is the resistance per km at 20 degrees C, corrected for temperature with 1 plus 0.00393 times the temperature minus 20, times the length divided by 1,000. The cable reactance is the reactance per km times the length divided by 1,000. The length is the total loop, out and back, and the reactance value is a placeholder, so use the cable data sheet value for your construction and frequency.
The impedance is the square root of the sum of the squares of the total resistance and total reactance. The voltage is the current times the impedance, the apparent power is the voltage times the current, and the power factor is the resistance divided by the impedance.
The smallest standard CCR is the first size where the apparent power is within your maximum loading, which is your own rule and not a standard value. The sizes are 1, 2, 2.5, 4, 5, 7.5, 10, 15, 20, 25, 30, 50 and 70 kVA, treated as nominal kVA, where 50 and 70 are replacement-only sizes in FAA AC 150/5345-10H. Only sizes whose rated voltage, kVA divided by current, stays within 5 kV are offered, so at 6.6 A the choice stops at 30 kVA.
For 100 fixtures of 45 W at 6.6 A, 90 percent efficiency and a power factor of 0.95, the fixture resistance is 103.31 ohms, the transformer loss resistance is 11.48 ohms and the transformer reactance is 37.73 ohms. With 3,000 m of #8 AWG at 20 degrees C, the total is 120.97 ohms resistance and 38.03 ohms reactance. The impedance is 126.80 ohms, the power factor is 0.954, and the regulator must deliver 836.9 V and 5.52 kVA, so a 7.5 kVA CCR is loaded 74 percent at a 90 percent maximum.
It models the circuit at full brightness with constant impedance. Lamp resistance changes with brightness step and transformer reactance changes with loading, so the lower steps need manufacturer data. It ignores capacitance, secondary lamp-out behaviour and fault conditions.
No. Efficiency, power factor and cable reactance are planning assumptions. Final circuit design shall be verified against the CCR, isolating transformer, fixture and cable manufacturers' data.
Every step is shown so the result can be checked by hand.
With a 1:1 current ratio, a load on the secondary appears on the primary as a resistance equal to its power divided by the current squared. The transformer loss is treated the same way, and the reactive power sets the transformer reactance.
The smallest standard CCR is the first size where S is within your maximum loading.
| Item | Value |
|---|---|
| 100 × 45 W, 6.6 A, 90 %, PF 0.95 | P_fix 4.5 kW, P_pri 5.0 kW |
| Fixtures R | 103.31 Ω |
| Transformer loss R | 11.48 Ω |
| Transformer X | 37.73 Ω |
| #8 AWG, 3,000 m, 20 °C | R 6.18 Ω, X 0.30 Ω |
| Total R / X | 120.97 Ω / 38.03 Ω |
| Z, PF | 126.80 Ω, 0.954 |
| V, S | 836.9 V, 5.52 kVA |
| CCR at 90 % max | 7.5 kVA, 74 % |
It models the circuit at full brightness with constant impedance. Lamp resistance changes with brightness step, and transformer reactance changes with loading, so the lower steps need manufacturer data. It ignores capacitance, secondary lamp-out behaviour and fault conditions.
Please read before relying on any content on this page or on any result or record produced by it.