Department of Power Electronics and Electrical Drives Prof

Department of Power Electronics and Electrical Drives

Prof. Dr.–Ing. Joachim Böcker

Power Electronics Final Examination WS 2014 -15 Page 1 of 5

Power Electronics

31.03.2015

Surname:

Student number:

First name:

Course of study:

Task:

(Points)

1

(25)

2

(25)

3

(25)

4

(25)

Total

(100) Mark

Duration: 120 minutes

Permitted resources:

a non‐programmable calculator without graphic display

drawing materials (compasses, protractor, ruler, pens ...)

Please note:

Please prepare your student ID card (with photo) on your desk for the attendance check.

Please label each exam sheet with your name and student number. Use a new exam sheet for each task. Do

not use pencils or red pens.

With numerical calculations, the units must be considered in every step. Not following that rule will result in

deduction of points.

All solutions must be clearly documented and wherever required explained! The entry of a mere final result

without any approach will not be counted.

You can only take part in the exam, if you are registered in the PAUL system. If you take part without

registration, the exam result will not be considered.

Good Luck!

Department of Power Electronics and Electrical Drives Prof. Dr.–Ing. J. Böcker


Task 1: Buck‐Boost Converter (25 Points)

Figure 1 shows a converter which can be called buck‐boost converter. The input voltage to the

converter is U1 = 10 V. The converter supplies a DC load current of 5 A at the output. The power

switches are assumed to be ideal during conduction and blocking states (0 V during conduction

and 0 A in blocking). The converter is operated at a switching frequency of 10 kHz. The

capacitance of the capacitor C is 100 μF.

Figure 1: Buck‐Boost converter

If the duty cycle of switch S1 is chosen as 0.25, estimate the following:

1.1 The DC contents of the input current i1 and of the output voltage u2.

1.2 Evaluate the required inductance L to limit the ripple current of i1 to 20% of the DC content

(assume the output voltage approximately constant).

1.3 For what value of the inductance L does the converter operate at the boundary between

continuous and discontinuous conduction modes?

1.4 Sketch the current through the capacitor C (assume the load current approximately

constant)

1.5 Sketch uC

1.6 Determine the peak‐to‐peak voltage ripple across the capacitor C.



Task 2: Boost converter (25 Points)

Figure 2 shows a non‐ideal boost converter. The source and inductor resistances are represented

by R1 and RL respectively. The switches S1 and D1 are assumed to be ideal. The state variables are

the inductor current iL and capacitor voltage u2. The circuit is to be operated in continuous

conduction mode.

Figure 2: Boost converter

2.1 Write down the differential equations of the complete system for the two state variables

during ON state, i.e. when S1 is ON.

2.2 Write down the differential equations of the complete system for the two state variables

during OFF state, i.e. when S1 is OFF.

2.3 Using the above, write down the averaged dynamic model of the converter in state space

matrix notation.

2.4 Derive the gain /U1 at steady state as a function of duty cycle.

2.5 Evaluate the efficiency of the converter based on the average modeling,

η= ( ̅ )/(U1 ̅ )



Task 3: Four‐Quadrant Converter (25 Points)

A four‐quadrant converter (4QC) is connected to the single‐phase grid. The overhead line delivers a

single‐phase sinusoidal AC voltage with grid frequency . The two four‐quadrant converters are

operated in interleaving operation to minimize the current ripple. The traction transformer has two

primary windings connected in parallel and two secondary windings.

Figure 3: Power supply for an electric locomotive

Nominal output voltage 1.8kV Relative short circuit voltage 19%

(each secondary)

Nominal output power 2.4MW Switching frequency 500Hz

Grid voltage 25kV Grid frequency 50Hz

3.1 Draw the circuit diagram of a four‐quadrant converter, where the semiconductors are treated

as ideal switches.

3.2 Draw qualitatively the switching functions of the 4QC‐switches of two parallel four‐quadrant

converters in interleaving operation. Draw the transformer secondary voltages resulting from

the two four‐quadrant converters for a fundamental period.

3.3 Calculate the leakage inductances of the transformer. Assume that the primary leakage

inductances can be neglected. Assume that the apparent power of the transformer is 2.6 MVA.

3.4 The two four‐quadrant converters should be controlled that way that only active power is

supplied from the grid (target power factor mode). Determine the phase angle of the required

fundamental phasors of u21 , u22. Consider the case of rated load at nominal input voltage.

3.5 Calculate the minimum required transformer winding ratio for the case of 3.4.

3.6 Calculate the peak voltage stress in the transistors and the diodes of the 4QC. Explain in words

what has to be done to calculate the peak current stress (calculation not mandatory).



Task 4: Line‐Commutated Converter (25 Points)

A 3‐pulse thyristor controlled converter is connected to the 3‐phase grid via a Dy‐transformer

configuration and supplies a DC‐motor. The motor can be represented by an equivalent circuit

consisting of a DC‐voltage Ug and a resistor R of 2.8 Ω. The nominal value of the line voltage on the

primary and secondary is 400 V.

Figure 4 : Line‐commutated converter in M3 configuration

Assuming negligible losses and ideal commutations answer the following.

4.1 Assume steady state condition and DC load voltage is zero.

a) Sketch the voltage ud for a control angle 45°. Use the solution sheet in next page for the sketch.

b) Calculate the maximum and average value of the load current at 45°.

4.2 Assuming a DC output voltage Ug which is not zero but approximately constant ug= Ug,

calculate Ug :

a) for the case of a load current id, which is at the border between continuous and

discontinuous conduction mode at a control angle of 45°. b) which ensures an average load current of Id = 70 A at the maximum output voltage.

4.3 Consider the start‐up of the system. The control angle is constantly 0°, the gate is first triggered at 30° (refer to solution page). Sketch on the solution page the instantaneous load current id(t) in the interval from t = 0 to

t = 45 ms, if the counter voltage ug(t) rises as show in the figure. Assume that the

commutations are ideal and instantaneous, and the initial condition is id(0) = 0.

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Department of Power Electronics and Electrical Drives Prof