Modelling multi-phased AC electrical system interconnexion

Quick and dirty mathematics background and rationale

We suppose that all the multi-phased electrical systems are properly balanced: .

Let's call and two multi-phased electrical systems where are respectively the number of phases, are the voltage per phase, are the total intensity and the intensity per phase.
We always have: and . So the intensities properties can be deduced one from the other.

and are interconnected serially : .

How to evaluate the properties of the resulting system ?

Let's say you only have in and . We can deduce from them.
How can we deduce ?
Division evaluation:

;

;

;

;

;

;

We can expose at leat two cases where if

Let's say you only have in and . We can deduce from them.
How can we deduce ?

So if you model an AC electrical system with the properties $ (p, V, Iph) $, you can deduce the properties of any interconnexion of them within the natural integer set.

Star topology with balanced phases

is the line current.
is the line-to-neutral voltage.
is the line-to-line voltage: .

Delta topology with balanced phases

is the phase current.
is the line current: .
is the line-to-line voltage.

Typescript code sketches

Low level class of electrical helper methods implementation:

export class ElectricUtils { public static calculateAmpTotal(nbOfPhases: number, Iph: number): number { return nbOfPhases * Iph; } public static calculatePowerPerPhase(V: number, Iph: number, cosPhi = 1): number { const powerPerPhase = V * Iph * cosPhi; if (cosPhi === 1) { return powerPerPhase; } return Math.round(powerPerPhase); } public static calculatePowerTotal(nbOfPhases: number, V: number, Iph: number, cosPhi = 1): number { return nbOfPhases * ElectricalUtils.calculatePowerPerPhase(V, Iph, cosPhi); } public static calculateAmpPerPhaseFromPower(nbOfPhases: number, P: number, V: number, cosPhi = 1): number { const power = ElectricalUtils.calculateAmpTotalFromPower(P, V, cosPhi); const powerPerPhase = power / nbOfPhases; if (power % nbOfPhases === 0) { return powerPerPhase; } return Math.round(powerPerPhase); } public static calculateAmpTotalFromPower(P: number, V: number, cosPhi = 1): number { const power = P / (V * cosPhi); if (cosPhi === 1 && P % V === 0) { return power; } return Math.round(power); } }

AC electrical component interface:

interface ElectricACComponent { nPhases: number; Iph: number; V: number; I?: number; P?: number; }

Electrical properties calculation of an electric car connected to a AC charging station implementation (the electrical properties of the connexion cable are always beyond):

const Car = { nPhases: 2, Iph: 18, V: 220, }; const ChargingStation = { nPhases: 3, Iph: 32, V: 230, }; function getCombinedElectricObject(Car, ChargingStation): ElectricACComponent { return { nPhases: Math.min(Car.nPhases, ChargingStation.nPhases), Iph: Math.min(Car.Iph, ChargingStation.Iph), V: Math.min(Car.V, ChargingStation.V), I: ElectricityUtils.calculateAmpTotal(this.nPhases, this.Iph), P: ElectricityUtils.calculatePowerTotal(this.nPhases, this.Iph, this.V), }; }

And now for example you can define a fine grained OCPP charging profile with the following schedule for the electric car connected to the charging station that will include the number of phases used and the max intensity per phase:

const ChargingSchedulePeriod = { startPeriod: 60, limit: 15, // Sanity check: ensure the limit is below getCombinedElectricalObject(Car, ChargingStation).Iph numberPhases: getCombinedElectricalObject(Car, ChargingStation).nPhases, };

Modelling multi-phased AC/DC electrical system

Rectifier modelling

Modelling multi-phased DC/AC electrical system

Inverter modelling

References

Composants symétriques : https://fr.qwe.wiki/wiki/Symmetrical_components