Electrical Machines and Power Electronics

Boost Converter (Step-Up DC–DC Converter)

1. Working Principle (2 marks)

A boost converter is a non-isolated DC–DC converter that steps up (increases) the input DC voltage to a higher output DC voltage. It uses an inductor, a controlled switch (MOSFET/IGBT), a diode, and a capacitor.

The operation relies on the inductor's property of storing energy in its magnetic field when current flows through it and releasing that energy when the current path is interrupted. By alternately switching the semiconductor switch ON and OFF at high frequency (tens of kHz to hundreds of kHz) and controlling the ON-time fraction (duty cycle), the average output voltage is made higher than the input voltage.

Two modes of operation:

• Switch ON: The inductor is connected across the input supply. Current flows from source → inductor → switch → back to source. The inductor stores energy. The diode is reverse-biased, so the capacitor supplies the load.
• Switch OFF: The inductor current path is broken. The inductor's induced EMF adds to the source voltage and forward-biases the diode, so energy flows through the diode to the load and charges the capacitor. The output voltage is therefore higher than the input.

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2. Circuit Layout and Derivation (5 marks)

Circuit diagram:

         L                D
  +o---/\/\/\---+------|>|------+---------+---o +
                |              |         |
   Vs          S (switch)      C         R      Vo
                |              |         |
  -o------------+--------------+---------+---o -

The inductor $L$ is in series with the source; the switch $S$ connects the inductor/diode node to the common (negative) rail; the diode $D$ feeds the output capacitor $C$ and load $R$ in parallel.

Derivation of output voltage:

Let the switching period be $T$ and the ON-time be $t_{on}$. The duty cycle is:

$D = \frac{t_{on}}{T}$

During ON-time ($t_{on} = DT$): The switch is closed. Voltage across inductor:

$V_L = V_s$

The change in inductor current during ON-time:

$\Delta I_{L,on} = \frac{V_s}{L} \cdot DT$

During OFF-time ($t_{off} = (1-D)T$): The switch is open. The inductor is in series with the source and the load, so:

$V_L = V_s - V_o$

The change in inductor current during OFF-time:

$\Delta I_{L,off} = \frac{V_s - V_o}{L} \cdot (1-D)T$

Steady-state condition: In steady state, the net change in inductor current over one cycle must be zero (volt-second balance):

$\Delta I_{L,on} + \Delta I_{L,off} = 0$

$\frac{V_s}{L} \cdot DT + \frac{V_s - V_o}{L} \cdot (1-D)T = 0$

Dividing by $\dfrac{T}{L}$:

$V_s D + (V_s - V_o)(1-D) = 0$

$V_s D + V_s - V_s D - V_o(1-D) = 0$

$V_s - V_o(1-D) = 0$

$\boxed{V_o = \frac{V_s}{1-D}}$

Duty cycle expression:

$\boxed{D = 1 - \frac{V_s}{V_o}}$

Since $0 \le D < 1$, the output voltage $V_o \ge V_s$, confirming step-up operation. As $D \to 1$, $V_o \to \infty$ (ideally), so in practice $D$ is limited to about 0.9.

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3. Suitability for Interfacing a Solar PV System with the Grid (3 marks)

A boost converter is suitable, but only as one stage — it cannot interface a PV system to the grid by itself.

Why it is suitable:

• A PV module's maximum power point voltage ($V_{mp}$) is typically 30–40 V for a single module, while a grid-tied inverter needs a DC-link voltage higher than the peak grid voltage (e.g., ~325 V peak for a 230 V rms grid). The boost converter steps up the low PV voltage to this required DC-link level.
• It performs Maximum Power Point Tracking (MPPT) by continuously adjusting the duty cycle so the PV array operates at its maximum power point, which varies with irradiance and temperature.
• The inductor at the input draws continuous current, which matches the current-source nature of a PV array and reduces stress on the panels.

Why it is not sufficient alone:

• A boost converter gives only a DC output; the grid requires AC at 50 Hz synchronized in frequency, phase, and voltage. So a DC–AC inverter stage is mandatory after the boost stage.
• It provides no galvanic isolation, which is often required for safety and grid compliance.
• It cannot perform grid synchronization, power factor control, or anti-islanding protection — these are functions of the inverter and its control system.

Conclusion: The standard grid-tied PV topology is PV array → boost converter (MPPT + voltage step-up) → DC-link → inverter → grid. The boost converter is therefore an essential but partial component, not a complete grid interface.

Operating Principle of a 3φ Controlled Rectifier

A three-phase controlled rectifier converts three-phase AC into variable DC using thyristors (SCRs) whose firing angle α controls the average output voltage. The most common configuration is the 3-phase fully controlled bridge (6-pulse) using six thyristors.

Circuit arrangement

• Six thyristors: T1, T3, T5 form the positive group (anodes to supply phases R, Y, B); T2, T4, T6 form the negative group (cathodes to supply phases).
• Each thyristor conducts for 120°; two thyristors conduct at any instant (one from each group), so the DC current path is completed through the load.
• Thyristors are fired in sequence T1–T2–T3–T4–T5–T6 at intervals of 60°.

Operating principle

1. Natural commutation: The thyristor that is forward-biased and whose anode voltage is most positive (positive group) or most negative (negative group) is fired. Firing is delayed from the natural commutation instant by the firing angle α.
2. Conduction: Once fired, a thyristor conducts until the next thyristor in sequence is fired and reverse-biases it (line commutation).
3. Output voltage: The DC output is the difference between the instantaneous voltages of the conducting positive and negative thyristors. Its average value is

$V_{dc} = \frac{3\sqrt{3}\,V_m}{\pi}\cos\alpha = V_{d0}\cos\alpha$

where $V_m$ is the peak phase voltage and $V_{d0}=\dfrac{3\sqrt{3}V_m}{\pi}$ is the maximum (α = 0) DC voltage.

4. Control range:
   • α = 0° → maximum DC output (uncontrolled rectifier operation).
   • 0° < α < 90° → rectifier mode (power flows AC → DC).
   • α = 90° → V_dc = 0.
   • α > 90° → inverter mode (V_dc reverses, power flows DC → AC), provided a DC source exists.

Key features

• Ripple frequency = 6f (six pulses per cycle), giving low output ripple.
• Input displacement factor ≈ cos α; input power factor falls as α increases.
• Only one firing pulse per thyristor per cycle; firing circuit simple.
• Can operate in both rectifier and inverter modes — essential for HVDC.

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Application in HVDC Power Transmission

HVDC transmission uses line-commutated converters built from 3φ controlled rectifiers at each end of the DC link.

1. Rectifier station (sending end)

The 3φ controlled bridge rectifies the sending-end AC (generated at 50 Hz) into high-voltage DC. The firing angle α is adjusted to set the DC link voltage and hence the transmitted power:

$P = V_{dc}\,I_{dc}$

2. Inverter station (receiving end)

At the receiving end the same bridge is operated with α > 90° (typically α ≈ 150°), so it acts as a line-commutated inverter, converting DC back to AC at grid frequency for distribution. The two stations are connected by a DC transmission line (overhead or submarine cable).

2. Power control

Power flow direction and magnitude are controlled by the difference between the rectifier and inverter DC voltages:

$I_{dc} = \frac{V_{d0R}\cos\alpha_R - V_{d0I}\cos\alpha_I}{R_{dc}}$

By varying α_R and α_I, power can be reversed smoothly without changing the physical connection — a major advantage over AC links.

3. Reactive power and harmonics

• Controlled rectifiers absorb reactive power (≈ cos α), so shunt capacitor banks, synchronous condensers or STATCOMs are installed at both ends.
• Six-pulse operation injects 5th and 7th harmonics; 12-pulse bridges (two 6-pulse bridges in series/parallel with star-delta transformers) are used to cancel these, reducing filter size.

4. Advantages in HVDC

• Long-distance bulk transmission: lower line losses and no reactive compensation needed for very long lines.
• Submarine/underground cables: no charging current problem, so cable length is unlimited.
• Asynchronous interconnection: links grids of different frequencies or phases.
• Fast controllability: thyristor firing control gives rapid power modulation, improving transient stability and damping of oscillations.
• Power reversal: achieved by changing firing angles, useful for energy trading.

5. Limitations

• Commutation failure at the inverter during AC faults.
• Large reactive power demand and harmonic filters needed.
• Cost of converter stations is high, so HVDC is economical only beyond a break-even distance (≈ 600–800 km overhead).

Conclusion: The 3φ controlled rectifier's ability to give a controllable DC voltage and to reverse power flow by firing-angle control makes it the heart of HVDC transmission, enabling efficient, flexible and stable bulk power transfer over long distances and across asynchronous grids.

Importance of Lab Testing of an Electric Machine

Lab testing of an electric machine is carried out to verify its design, performance, and safety before it is put into service. Its importance can be summarised as follows:

1. Verification of design and performance: Tests confirm whether the machine meets the guaranteed ratings (power, voltage, current, speed, efficiency, temperature rise) specified in the design or purchase order.
2. Determination of losses and efficiency: Losses (copper loss, iron loss, friction and windage loss) cannot be measured directly in service; lab tests separate these losses and allow accurate calculation of efficiency at any load.
3. Prediction of performance characteristics: Parameters obtained from tests (equivalent circuit constants, regulation, torque–speed characteristics) allow the behaviour of the machine at various loads to be predicted without actually loading it.
4. Quality control and comparison: Routine tests on identical machines ensure uniformity of production and help detect manufacturing defects such as loose windings, poor insulation, or wrong core material.
5. Safety assurance: Insulation resistance, dielectric, and temperature-rise tests ensure the machine will not fail dangerously in service, protecting personnel and connected equipment.
6. Basis for maintenance and fault diagnosis: Test results form a baseline record; later deviations indicate insulation deterioration, winding faults, or core damage, allowing timely maintenance.
7. Economy: Testing avoids the cost of failure in the field, prevents oversizing or undersizing of machines, and helps select the most efficient machine for a given duty.

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Routine Tests of a Transformer by Open Circuit and Short Circuit Tests

The two tests together give the equivalent circuit parameters and hence the efficiency and regulation of the transformer without actually loading it. Both are carried out at rated frequency with sinusoidal supply.

(a) Open Circuit (No-Load) Test

Purpose: To determine the iron (core) loss (P_i) and the no-load (shunt) branch parameters (R_0) and (X_0).

Connection: LV winding is supplied at rated voltage; HV winding is left open. Wattmeter, voltmeter and ammeter are connected on the LV side.

Procedure:

1. Apply rated voltage (V_1) at rated frequency to the LV winding, keeping the HV winding open.
2. Record the ammeter reading (I_0), voltmeter reading (V_1), and wattmeter reading (W_0).
3. Since (I_0) is only 2–5 % of full-load current, the copper loss in the LV winding is negligible. Hence the wattmeter reading gives the iron loss: [ P_i = W_0 ]
4. Compute the no-load power factor: [ \cos\phi_0 = \frac{W_0}{V_1 I_0} ]
5. The shunt branch parameters (referred to LV side): [ I_w = I_0 \cos\phi_0,\qquad I_\mu = I_0 \sin\phi_0 ] [ R_0 = \frac{V_1}{I_w},\qquad X_0 = \frac{V_1}{I_\mu} ]

(b) Short Circuit (Impedance) Test

Purpose: To determine the full-load copper loss (P_{cu}) and the series (impedance) parameters (R_{eq}) and (X_{eq}).

Connection: LV winding is short-circuited through an ammeter; a reduced voltage is applied to the HV winding. Wattmeter and voltmeter are connected on the HV side.

Procedure:

1. Apply a reduced voltage (about 5–10 % of rated) to the HV winding so that rated current flows in both windings.
2. Record voltmeter reading (V_{sc}), ammeter reading (I_{sc}) (rated current), and wattmeter reading (W_{sc}).
3. Since the applied voltage is very low, the core flux is far below normal, so iron loss is negligible. Hence the wattmeter reading gives the full-load copper loss: [ P_{cu} = W_{sc} ]
4. Compute the equivalent impedance, resistance and reactance referred to the HV side: [ Z_{eq} = \frac{V_{sc}}{I_{sc}},\qquad R_{eq} = \frac{W_{sc}}{I_{sc}^2} ] [ X_{eq} = \sqrt{Z_{eq}^2 - R_{eq}^2} ]
5. These values are then transferred to the LV side using the turns ratio (K = V_1/V_2): [ R_{eq2} = \frac{R_{eq1}}{K^2},\qquad X_{eq2} = \frac{X_{eq1}}{K^2} ]

(c) Use of the Test Results

• Efficiency at any load fraction (x): [ \eta = \frac{x,(\text{kVA})\cos\phi}{x,(\text{kVA})\cos\phi + P_i + x^2 P_{cu}} ]
• Regulation: [ %,\text{Regulation} = \frac{I_2 R_{eq2}\cos\phi \pm I_2 X_{eq2}\sin\phi}{V_2}\times 100 ] (plus for lagging, minus for leading power factor).

Precautions

1. Use low-range wattmeter and ammeter on the LV side for the OC test; use rated-current instruments on the HV side for the SC test.
2. The SC test must be performed quickly to avoid overheating of windings.
3. Supply must be at rated frequency and sinusoidal.
4. Readings should be taken at steady conditions; meters must be properly calibrated.

Thus the OC and SC tests are the standard routine lab tests that yield the complete equivalent circuit, efficiency, and regulation of a transformer without loading it.