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In a practical power converter with real world power devices, any PWM strategy cannot be applied as it is. For example, in a two level inverter, if conventional SVPWM or even sine-triangle PWM is used, the gate pulse of upper and lower switch in an inverter leg are complimentary, i.e. one of them turns ON at the same instant the other one turns OFF in the ideal case. However, due to finite rise and fall times of voltage and current through a power electronic switch, ideal pulses transitioning at the same instant could cause short circuit of the dc bus if one switch hasn’t fully turned OFF while the other gets turned ON. To prevent this, a dead band between the two ideal gate pulses is introduced. This is demonstrated in Fig. 5.13, where qX,idl and qX′,idl are ideal gate

pulses, while qX and qX′ are final gate pulses with a dead band between them. This

dead band satisfies two criteria:

1. Prevent short circuit of the input voltage (dc link voltage for two level inverter) 2. Prevent interruption of output current (which is assumed inductive)

For a matrix converter, the first criterion means that no two input phase voltages should be short circuited. The second criterion remains the same. In a matrix converter, bidirectional switches are used. In order to satisfy the above two criteria, a different process needs to be employed instead of a simple dead band like the one in Fig. 5.13.

141 v1 v2 i 11 12 21 22 o (a) B C G E D F H q1= 0, δt A q1= 0 Q12 Q22 q2= 0 q2= 0, δt Q11 q2= 0, δt q1= 0, δt q1= 0, δt q2= 0, δt q2= 0, δt i >0, q1= 0, δt Q21Q22 Q11Q21 Q12Q22 Q11Q12 q1= 0, δt i >0, i <0, q1= 0, δt q2= 0, δt q2= 0, δt i <0,q1= 0 Q21 q2= 0 q1= 1 q2= 1 (b)

Figure 5.14: Four step commutation (a) Two bidirectional switches undergoing commu- tation (b) Conventional four-step commutation state machine

Conventional four-step commutation satisfies these two criteria. The state machine of conventional four-step commutation is presented in Fig. 5.14(b). This state machine controls the switching of the individual IGBTs of two bidirectional switches shown in Fig. 5.14(a). In Fig. 5.14(a), v1 and v2 are the input voltages, while i is the load

current, which is considered positive when flowing in the direction shown in the figure. The states in Fig. 5.14(b) are denoted by alphabets A through H.

The quantities Q11, Q12, Q21and Q22when mentioned in the states in Fig. 5.14(b),

denote that IGBTs 11, 12, 21 and 22 respectively are ON, in Fig. 5.14(a). When these quantities are not mentioned, the corresponding IGBT is OFF. For example, in state A in Fig. 5.14(b), Q11 and Q12 are mentioned which mean that IGBTs 11 and 12 in

Fig. 5.14(a) are ON, while other IGBTs, i.e. 21 and 22 are OFF. The quantity δt represents one commutation step time in seconds and q1 and q2 are ideal pulses for the

bidirectional switches in Fig. 5.14(a).

The conventional four-step commutation algorithm is described below. In the follow- ing discussion, the bidirectional switch to be turned ON is called the incoming switch, while the bidirectional switch to be turned OFF is called the outgoing switch.

142 Step 1: Turn OFF the passive IGBT (whose anti-parallel diode is conducting) of the outgoing bidirectional switch

Step 2: Turn ON the active IGBT (which will be conducting) of the incoming bidirectional switch after a delay δt

Step 3: Turn OFF the active IGBT (conducting) of the outgoing bidirectional switch after a delay δt

Step 4: Turn ON the passive IGBT (whose anti parallel diode will be conducting) of the incoming bidirectional switch after a delay δt

In the above description, the active and passive IGBTs are decided by the load current direction.

Now suppose that in Fig. 5.14(a), v1 > v2 and i > 0. Then, the four step commu-

tation process when output voltage is switching from v1 to v2 is described below:

Step 1: Turn OFF the passive IGBT (whose anti-parallel diode is conducting) of the outgoing bidirectional switch. In this case, the passive IGBT of outgoing switch is 12 and this is turned OFF.

Step 2: Turn ON the active IGBT (which will be conducting) of the incoming bidirectional switch after a delay δt. In this case, the active IGBT of incoming switch is 21 and therefore, this IGBT is turned ON. Since v1 > v2, the diode of

IGBT 22 is reverse biased. Thus, the current i keeps flowing through the first bidirectional switch and output voltage still equals v1.

Step 3: Turn OFF the active IGBT (conducting) of the outgoing bidirectional switch after a delay δt. In this case, the active IGBT of the outgoing switch is 11 and is therefore turned OFF. Due to this, the current io doesn’t have a path to

flow through first bidirectional switch and therefore is force commutated to flow through IGBT 21 and diode of IGBT 22. The output voltage is now equal to v2.

Step 4: Turn ON the passive IGBT (whose anti parallel diode will be conducting) of the incoming bidirectional switch after a delay δt. The passive IGBT of outgoing switch is 22 and is turned ON.

143 In the above example, the load current was forced to commutate from v1 to v2 when

the outgoing switch IGBT was turned OFF. This type of commutation is called forced commutation. The example case for forced commutation discussed above is illustrated in Fig. 5.15(a).

Now suppose that v1 < v2 and i > 0. Then, the four step commutation process

when output voltage is switching from v1 to v2 is described below:

Step 1: Turn OFF the passive IGBT (whose anti-parallel diode is conducting) of the outgoing bidirectional switch. In this case, the passive IGBT of outgoing switch is 12 and this is turned OFF.

Step 2: Turn ON the active IGBT (which will be conducting) of the incoming bidirectional switch after a delay δt. In this case, the active IGBT of incoming switch is 21 and therefore, this IGBT is turned ON. Since v1 < v2, the diode of

IGBT 12 is reverse biased and cannot conduct. The current naturally commutates to the second bidirectional switch and starts to flow through IGBT 21 and the anti-parallel diode of IGBT 22. The output voltage thus becomes equal to v2.

Step 3: Turn OFF the active IGBT (conducting) of the outgoing bidirectional switch after a delay δt. In this case, the active IGBT of the outgoing switch is 11 and is therefore turned OFF.

Step 4: Turn ON the passive IGBT (whose anti parallel diode will be conducting) of the incoming bidirectional switch after a delay δt. The passive IGBT of outgoing switch is 22 and is turned ON.

In the above example case, the current naturally commutates to the second bidirec- tional switch when the incoming switch IGBT is turned ON. This type of commutation is called natural commutation. The example case for natural commutation discussed above is illustrated in Fig. 5.15(b). It is concluded from this discussion, that natural commutation occurs at the second step, while forced commutation occurs at the third step of the four step process.

144 q1 q2 q11 q12 q21 q22 vo v1 v2 δt (a) q1 q2 q11 q12 q21 q22 vo v1 v2 δt (b)

Figure 5.15: Commutation examples (a) Forced commutation (b) Natural commutation

5.7

Single phase analysis for effect commutation on output