# VOLTAGE-CURRENT RELATION

The separately-excited dc motor, when armature reaction is neglected, has the V-I relation:

V = IRa + E (1)

where :

E : induced EMF = Ka ф w

Ф : motor flux; constant for constant excitation.

Ka : induced EMF and torque constant (for SI units).

I : armature current.

Ra : armature resistance, w : motor speed.

The PV generation is a nonlinear device that converts the solar insolation directly to electrical energy. The V-I equation is given by :

V = – I Rs + К In (( Io + Iph – I ) / Io ) (2)

where :

Io : saturation current of the PV generator.

Iph: photocurrent of PV generator, proportional to solar insolation.

I : PV generator current.

К : constant, temperature dependent.

Rs : PV generator series resistance.

When the dc motor and the PV generator are directly connected, the armature resistance Ra and the series resistance of the PV generator are connected in series. Thus, the motor armature resistance can be combined with the PV generator to form the system resistance given by Khater (1989) as :

Rs’ = Ra + Rs

As a result, the system V-I relation is expressed as:

E = – I Rs’ + К In (( Io + Iph – I ) / Io ) (3)

At constant excitation, which is the case of a separately excited dc motor, the induced emf E is proportional to the motor speed. Equation (3) can be rewritten as a relation between the current I and the motor speed w as given by :

w = і – I Rs’ + К In ((Io + Iph – I) / Io)] / Ka ф (4)

Updated: August 23, 2015 — 8:17 am