Inductor Voltage Equation The inductor voltage equation can be used to estimate the value of an inductance, in case of deterioration of inductors LCL filter. From the Fig. 1 (a), the voltage equation for inductor in LCL filter can be represented by equation (5).

(5)

Where, is the phase a voltage, and is the grid and converter inductor voltage

drop respectively for phase a and is the pole voltage of AFE with respect to neutral point

n

(a) (b)

Fig. 1 Nodes of the AFE with LCL filter and short circuit schematic of inductors

The AFE pole voltages with respect to n are given by,, and (6)

For a three phase system,

(7)

The pole voltages of the AFE is given by,

, and (8)

Where, is the DC link voltage, , and are the duty cycle of the corresponding

switches shown in Fig. 1 (a).The voltage drop across the grid and converter inductor of phase a can be represented by equation (10) and (11) respectively.

(9)

a 

b 

c 

a’ b’ c’ 

Rsc Lsc

ia ib ic

iLsc

iRsc

n

(10)

Where, and are the self-inductance of the grid and converter inductor of phase a

and are the Mutual inductance between phase a and other phases of grid inductor

and are the Mutual inductance between phase a and other phases of converter

inductor From equation (5)-(10), the phase voltages representing the grid and converter inductors are given by equation (11).

(11)

Using the value grid currents, converter currents, grid voltages and DC link voltages, the grid and converter inductor can be estimated using equation (11). Moreover, the duty information of top switches of AFE converter is required. Usually, the commercial AFE converters deployed on MPS will have provision to extract information regarding the currents, voltages and duty. Hence, the duty information can be easily extracted and utilized for grid and converter inductance estimation using equation (11). In order to study the magnetic field distribution in the inductors during short circuit, the information pertaining to the short circuit inductors are necessary. Hence, a mathematical model for short circuit inductor as shown in Fig. 1 (b) has been developed.The phase a inductor voltage can be represented as eqn. (12)

(12)

Where, ,

⇒ (13)

⇒ (14)

Representing the inductance in terms of number of turns N and reluctance 𝕽= = ⇒ (15)

Since the ⟺ ⇒ (16)

Hence, the inductance value in short circuit phase can be represented by eqn. (16), which is the function of number of shorted and healthy turns, reluctance of the air gap and short circuit resistance. The value of the inductance from eqn. (16) can be substituted in eqn. (11) and thereby emulating the operation of short circuited inductor in the LCL filter. The value of

mutual couplings ( and ( in eqn. (11) will change as they are the

function of . The same inductance eqn. (16) can be used for phases of grid and converter

inductors with appropriate changes to analyze the short circuit current.