02 Uncontrolled AC to DC Converters(2)

# Is the angle between the fundamental components of

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is the angle between the fundamental components of input current and voltage, is called displacement angle, the Displacement factor (DF) is defined as: D 𝐹 = cos The Harmonic factor (HF) of the input current is defined as ?𝐹 = 𝐼 𝑠 2 −𝐼 𝑠1 2 𝐼 𝑠1 2 = 𝐼 𝑠 𝐼 𝑠1 2 − 1 Where, I s1 is the fundamental component of input current I s1 (rms value). The input Power factor (PF) is defined as P 𝐹 = V s I s1 V s I s cos For a resistive load, it can be written as, P 𝐹 = P ac V s I s

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11 D IODE R ECTIFIERS How can we calculate the Power Factor (PF)? Linear System i s ( t ) v s ( t ) a b v s ( t ) i s ( t ) 𝜋 2𝜋 ? Power Electronics Lecture 2
12 D IODE R ECTIFIERS How can we calculate the Power Factor (PF)? Nonlinear System i s ( t ) v s ( t ) a b v s ( t ) i s ( t ) Power Electronics Lecture 2

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13 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R load) 2 2 2 2 (0.318 ) (0.5 ) (0.318 ) 40.5% (0.5 ) m dc m ac m m V P R V P R V V Rectification efficiency: ? = 𝑃 ?? 𝑃 𝑎? Power Electronics Lecture 2 Power factor: 𝑃𝐹 = 𝑅?𝑎? 𝑃???? 𝐴??𝑎???? 𝑃???? = 𝑃 𝑎? 𝑉𝐴 = 0.5 2 0.707 × 0.5 = 0.707
14 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R load) Diode voltage drop The conduction angle 𝜃 c is that part of the cycle during which the diode is conducting Power Electronics Lecture 2

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15 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R-L load) Current continues to flows for a while even after the input voltage has gone negative Power Electronics Lecture 2 Due to the presence of inductor, the conduction period of diode will extend beyond 180°, until the current becomes zero.
16 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R-L load) Example : Find the average output voltage of the following circuit assuming the conduction angle of degree: Power Electronics Lecture 2

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17 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R-L load) Power Electronics Lecture 2 𝑉 ?? = 1 2𝜋 0 𝜋+𝜎 𝑉 𝑚 sin 𝜔? ?𝜔? = 𝑉 𝑚 2𝜋 0 𝜋+𝜎 sin 𝜔? ?𝜔? = 𝑉 𝑚 2𝜋 −cos(𝜔?) 𝜋 + 𝜎 0 = 𝑉 𝑚 2𝜋 1 − cos(𝜋 + 𝜎)
18 D IODE R ECTIFIERS Single phase half-wave diode rectifier (R-L load) Compare the load current waveform with the one in the previous circuit. (without free- wheeling diode) Average output voltage depends on the load parameters. Power Electronics Lecture 2

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19 D IODE R ECTIFIERS Battery charger with a resistive current limiter R D 1 Diode D 1 is turned off when v s < E at Power Electronics Lecture 2 Diode D 1 is turned on when v s > E at
20 D IODE R ECTIFIERS Battery charger with an inductive current limiter Current begins to flow when the input voltage exceeds Ed. Current continues to flows for a while even after the input voltage has gone below Ed. Power Electronics Lecture 2

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21 D IODE R ECTIFIERS Single phase full-wave diode rectifier with center-tapped transformer, (R load) Power Electronics Lecture 2 - +