Electrical Drives (EX-801) - Unit 2 Short Notes

UNIT 2: ELECTRICAL DRIVES - POWER CONVERTERS AND MOTOR CONTROL

I. FUNDAMENTALS OF DRIVE SYSTEMS & STABILITY

1.1 Classification of Electric Drives

• Group Drive: Single motor drives multiple machines via a line shaft. Disadvantages: Less flexible, high losses, all machines stop if motor fails.

• Individual Drive: One motor per machine. Advantages: Flexible, independent control, suitable for modern industry.

• Quadrant Operation: Defined by direction of rotation (speed, ω) and torque (T).

  • Quadrant I: Motoring, forward (ω>0, T>0).

  • Quadrant II: Braking, forward (ω>0, T<0).

  • Quadrant III: Motoring, reverse (ω<0, T<0).

  • Quadrant IV: Braking, reverse (ω<0, T>0).

  • Two-Quadrant Drive: I & II (forward motoring & braking) or III & IV (reverse).

  • Four-Quadrant Drive: All quadrants. Needed for reversible drives (e.g., cranes, elevators).

1.2 Load Equalization & Flywheel Design

• Purpose: To limit peak motor torque ($$\displaystyle T_m $$) for loads with fluctuating torque ($$\displaystyle T_L $$) by storing/releasing kinetic energy via a flywheel.

• Principle: During light load, flywheel stores excess energy (speed increases). During heavy load, flywheel releases energy (speed decreases), reducing motor torque demand.

• Energy Balance Derivation (for periodic load):

  For a cycle with heavy load period $$\displaystyle t_1 $$ (torque $$\displaystyle T_h $$, speed drop $\Delta \omega$) and light load period $$\displaystyle t_2 $$ (torque $$\displaystyle T_l $$, speed rise $\Delta \omega$):

$$ \text{Energy deficit during } t_1 = (T_h - T_m) \cdot \frac{\theta_1 + \theta_2}{2} \approx (T_h - T_m) \cdot \theta_1 \cdot t_1 $$

$$ \text{Energy surplus during } t_2 = (T_m - T_l) \cdot \frac{\theta_1 + \theta_2}{2} \approx (T_m - T_l) \cdot \theta_2 \cdot t_2 $$

Equating: $$\displaystyle (T_h - T_m) \cdot t_1 \approx (T_m - T_l) \cdot t_2 $$

> **Flywheel Inertia Formula:**

$$ J_{flywheel} = \frac{(T_h - T_m) \cdot t_1 \cdot t_2}{(T_m - T_l) \cdot (\omega_{max}^2 - \omega_{min}^2)} \cdot \frac{1}{t_1 + t_2} \cdot (J_m + J_L) $$

Where $$\displaystyle \omega_{max}, \omega_{min} $$ are max/min speeds, $$\displaystyle J_m, J_L $$ are motor and load inertias.

\boxed{J_{flywheel} \propto \frac{(T_h - T_m) \cdot t_1}{(T_m - T_l) \cdot \Delta \omega^2}}

1.3 Steady-State Stability of Drives

• Concept: Ability of drive to return to original equilibrium speed after a small disturbance.

• Stability Criterion: At equilibrium point ($$\displaystyle T_m = T_L $$), if $$\displaystyle \frac{d(T_m - T_L)}{d\omega} < 0 $$, system is stable. If >0, unstable.

• Interpretation: Stable if motor torque decreases more rapidly than load torque with increasing speed (or vice versa).

  Exam Tip: Always plot $$\displaystyle T_m $$ vs $\omega$ and $$\displaystyle T_L $$ vs $\omega$ on same graph. Intersection points are equilibrium. Check slope difference at intersection.

1.4 Mechanical Systems Analysis

• Referred Quantities: In multi-inertia systems, all inertias and torques are referred to a common shaft (usually motor shaft).

$$ J_{eq} = J_m + J_L \left(\frac{N_m}{N_L}\right)^2 + \text{gear inertias referred} $$

$$ T_{eq} = T_m - T_L \left(\frac{N_L}{N_m}\right) \quad \text{(if load torque referred to motor shaft)} $$

• Equation of Motion: $$\displaystyle J_{eq} \frac{d\omega_m}{dt} = T_m - T_{eq} $$

1.5 Starting, Braking, and Speed Control - Key Definitions

• Starting: Bringing motor from rest to rated speed. Methods: Direct-on-line (DOL), star-delta, auto-transformer, series resistor (DC).

• Braking:

  • Regenerative Braking: Motor acts as generator, feed energy back to supply. $$\displaystyle T_b < 0 $$, $$\displaystyle \omega > 0 $$ (Quadrant II). Occurs when $$\displaystyle \omega > \omega_s $$ (IM) or $$\displaystyle E_b > V_{supply} $$ (DC).

  • Dynamic (Rheostatic) Braking: Energy dissipated in external resistor. For DC: disconnect supply, connect armature to braking resistor. For AC (IM): disconnect stator, connect to DC supply (AC dynamic braking) or resistor (DC dynamic braking).

  • Plugging (Reverse Current Braking): Reverse armature/phase sequence while motor running. High braking torque, high energy loss. $$\displaystyle T_b < 0 $$, $$\displaystyle \omega > 0 $$ initially.

  Common Pitfall: Plugging reverses torque direction but speed is still positive → high braking current. Always add series resistance to limit current.

II. POWER ELECTRONIC CONVERTERS FOR DRIVES

2.1 DC Drives: Phase-Controlled Converters

• Single-Phase Semi-Converter (1-quadrant): 2 thyristors + 2 diodes. Output voltage always positive. Firing angle $\alpha \in [0°, 180°]$.

$$ V_{dc} = \frac{V_m}{\pi} (1 + \cos \alpha) \quad \text{(continuous conduction)} $$

• Single-Phase Full Converter (2-quadrant): 4 thyristors. Bidirectional voltage, unidirectional current. $\alpha \in [0°, 180°]$.

$$ V_{dc} = \frac{2V_m}{\pi} \cos \alpha $$

• Three-Phase Converter: Higher power, lower ripple. For full converter: $$\displaystyle V_{dc} = \frac{3\sqrt{6}}{\pi} V_{LL} \cos \alpha = 1.654 V_{LL} \cos \alpha $$.

• Discontinuous Conduction: Occurs at high $\alpha$, low load. Output voltage and torque ripple increase. Analysis requires solving circuit differential equations.

2.2 DC Drives: DC-DC Converters (Choppers)

• Principle: High-frequency switching (BJT, MOSFET, IGBT) to control average output voltage.

$$ V_{avg} = D \cdot V_s \quad \text{(Step-down/Buck)} $$

$$ V_{avg} = \frac{V_s}{1-D} \quad \text{(Step-up/Boost)} $$

Where $$\displaystyle D = \frac{T_{on}}{T} $$ is duty cycle.

• Motoring Operation (2-Quadrant Chopper): For separately excited motor.

  • Quadrant I (Forward Motoring): Switch $$\displaystyle S_1 $$ on (armature voltage $$\displaystyle +V_s $$), $$\displaystyle S_2 $$ off. $$\displaystyle S_2 $$ freewheels during off-time.

  • Quadrant II (Forward Braking/Regenerative): $$\displaystyle S_2 $$ on (armature connected to $$\displaystyle -V_s $$ via $$\displaystyle S_2 $$), $$\displaystyle S_1 $$ off. Energy fed back to source via $$\displaystyle D_1 $$.

• Four-Quadrant Chopper: Two-quadrant motoring + two-quadrant regenerative choppers in parallel or bridge configuration.

2.3 AC Drives: Voltage Source Inverters (VSI)

• Six-Step/Square-Wave VSI: 6 switches (IGBTs) in 3 legs. Each switch conducts for 180°. Output line voltage is 6-step, fundamental magnitude:

$$ V_{L1,rms} = \frac{\sqrt{6}}{\pi} V_d = 0.7798 V_d $$

• Pulse Width Modulation (PWM) VSI:

  • Sinusoidal PWM: Triangular carrier wave compared with sinusoidal reference. Switching frequency $$\displaystyle f_c >> f_{ref} $$. Fundamental voltage controlled by modulation index $$\displaystyle m_a $$.

$$ V_{L1,rms} = m_a \cdot \frac{V_d}{\sqrt{2}} \quad (m_a \leq 1) $$

*   **Space Vector PWM (SVPWM):** Better DC bus utilization ($$\displaystyle V_{max} = 0.907 V_d $$). Treats three-phase voltages as rotating space vector.

• VSI Fed Induction Motor (IM): Variable frequency $$\displaystyle f_s $$ and voltage $$\displaystyle V_s $$ to maintain constant $V/f$ ratio below base speed. Above base speed, $$\displaystyle V_s $$ constant, $$\displaystyle f_s $$ increased (field weakening).

• VSI Fed Synchronous Motor (SM): Requires rotor position for proper commutation (self-controlled). Can operate at leading power factor (overexcited) or lagging (underexcited).

2.4 AC Drives: Current Source Inverter (CSI)

• Principle: Large inductance in DC link maintains nearly constant current $$\displaystyle I_d $$. Thyristors (or GCTs) need forced commutation (e.g., capacitor-assisted).

• Power Circuit: DC source → inductor $$\displaystyle L_d $$ → 6-pulse thyristor bridge → 3-phase load. Commutation via auxiliary capacitors.

• Operation with IM: Output current is quasi-square wave. Speed control by varying DC link current $$\displaystyle I_d $$ (amplitude control) and frequency $$\displaystyle f_s $$.

• Comparison VSI vs. CSI:

  | Feature | VSI | CSI | | :--- | :--- | :--- | | DC Link | Capacitor (Voltage source) | Inductor (Current source) | | Switches | IGBTs/MOSFETs (self-commutated) | Thyristors (need forced commutation) | | Output | Voltage quasi-sine, Current depends on load | Current quasi-sine, Voltage depends on load | | Regeneration | Easy (anti-parallel diodes) | Difficult (needs separate converter) | | Short Circuit | High fault current | Limited by $$\displaystyle L_d $$ (inherent protection) | | Applications | General purpose, high power | High power, rugged (older tech) |

III. CONTROL OF DC MOTORS

3.1 Control Using Phase-Controlled Converters

• Steady-State Analysis (Separately Excited):

$$ V_a = V_t - I_a R_a = E_b = K_e \omega_m $$

$$ V_t = \frac{2V_m}{\pi} \cos \alpha \quad \text{(full converter)} $$

$$ T = K_t I_a \quad \text{(assuming constant flux)} $$

$$ \omega_m = \frac{1}{K_e} \left( \frac{2V_m}{\pi} \cos \alpha - R_a I_a \right) $$

• Speed-Torque Characteristics: Family of straight lines with intercept $$\displaystyle \frac{2V_m}{\pi K_e} \cos \alpha $$ on speed axis. $\alpha$ increases → speed decreases.

3.2 Control Using DC Choppers

• Steady-State (Buck Chopper, Motoring):

$$ V_a = D V_s - I_a R_a = K_e \omega_m $$

$$ \omega_m = \frac{D V_s}{K_e} - \frac{R_a}{K_e} I_a $$

• Regenerative Braking (2-Quadrant Chopper): During braking, $$\displaystyle V_a = -D' V_s - I_a R_a $$ (with $D'$ duty for braking switch). Negative voltage causes $$\displaystyle I_a $$ negative → energy fed back.

3.3 Closed-Loop Speed Control

• Block Diagram: Inner Current Loop (fast, limits $$\displaystyle I_a $$, improves torque response) + Outer Speed Loop (slow, sets current reference).

  
  Speed Ref ω* → [Speed Controller] → I_a* → [Current Controller] → Gate Pulses → Converter → Motor → ω
  
                                                                            ↑          |
  
                                                                            |          ↓
  
                                                                         [Current Feedback] [Speed Feedback]
  
  

• Advantages: Good dynamic response, immunity to supply fluctuations, precise speed regulation.

3.4 Plugging & Dynamic Braking Calculations (DC Motor)

• Plugging: Reverse supply polarity while motor running.

  • Initial Braking Torque: $$\displaystyle T_b = -K_t I_a $$ (opposite to rotation). $$\displaystyle I_a = \frac{V + E_b}{R_a + R_{ext}} $$ (large).

  • Braking Current Limit: Add series resistance $$\displaystyle R_{ext} $$: $$\displaystyle I_{b,max} = \frac{V + E_{b0}}{R_a + R_{ext}} \leq k \cdot I_{rated} $$.

  • Torque at Zero Speed: $$\displaystyle E_b=0 $$, $$\displaystyle I_a = \frac{V}{R_a+R_{ext}} $$, $$\displaystyle T_b = -K_t \frac{V}{R_a+R_{ext}} $$ (still braking until current reversed).

• Dynamic Braking (Resistor): Disconnect supply, connect armature to resistor $$\displaystyle R_b $$.

  • $$\displaystyle I_a = \frac{E_b}{R_a + R_b} $$ (decays exponentially).

  • Initial Braking Torque: $$\displaystyle T_b = -K_t \frac{E_{b0}}{R_a + R_b} $$.

  • Torque at Zero Speed: $$\displaystyle E_b=0 \Rightarrow T_b=0 $$ (torque becomes zero as speed reaches zero).

IV. CONTROL OF INDUCTION MOTORS

4.1 Variable Frequency Control (V/f Control)

• Principle: Maintain constant air-gap flux $$\displaystyle \phi_m \propto \frac{V_s}{f_s} $$. Prevent core saturation (excess flux) or low torque (weak flux).

$$ \frac{V_s}{f_s} = \text{constant} \quad \text{(below base speed)} $$

• Speed-Torque Characteristics:

  • Below Base Speed ($$\displaystyle f_s < f_{base} $$): Constant $V/f$. Max torque $$\displaystyle T_{max} $$ constant. Speed control by varying $$\displaystyle f_s $$.

  • Above Base Speed ($$\displaystyle f_s > f_{base} $$): $$\displaystyle V_s = V_{rated} $$ constant. Flux weakens $$\displaystyle \propto 1/f_s $$. $$\displaystyle T_{max} \propto 1/f_s^2 $$. Constant power region.

• Derivation of Max Torque vs. Frequency:

$$ T_{max} = \frac{3}{\omega_s} \frac{(V_s^2 / 2)}{(R_r'/s_{max} + \sqrt{R_r'^2 + (X_{eq})^2})} \approx \frac{3}{\omega_s} \frac{V_s^2}{2 \sqrt{R_r'^2 + (X_{eq})^2}} $$

With $$\displaystyle V_s/f_s = \text{const} $$, $$\displaystyle V_s \propto f_s $$, and $$\displaystyle X_{eq} \propto f_s $$:

$$ T_{max} \propto \frac{f_s^2}{f_s \cdot f_s} = \text{constant} \quad \text{(below base)} $$

Above base ($$\displaystyle V_s = \text{const} $$): $$\displaystyle T_{max} \propto \frac{1}{f_s^2} $$.

4.2 Slip Power Recovery Drives

• Principle: Recover slip power ($$\displaystyle s \cdot P_{in} $$) from rotor circuit instead of dissipating in rotor resistor.

• Static Kramer Drive:

  • Circuit: Wound Rotor IM → Diode bridge (in rotor) → DC link inductor → Inverter (thyristor bridge) → Grid.

  • Operation: Rotor slip frequency AC rectified to DC, inverted to fixed frequency AC fed back to grid. Speed controlled by changing inverter firing angle $\beta$.

  • Speed Range: $$\displaystyle s_{max} \approx 0.05 - 0.1 $$ (limited by commutation). Below synchronous speed only.

  • Power Flow: Stator → air-gap → rotor → diode bridge → DC link → inverter → grid.

  • Closed-Loop: Speed controller sets inverter firing angle $\beta$.

  
  [Rotor AC] → [Diode Bridge] → [DC Link] → [Thyristor Inverter] → [Grid]
  
              sP_rotor         P_dc          P_inv
  
  

• Static Scherbius Drive:

  • Circuit: Cycloconverter (direct AC-AC) replaces diode bridge + inverter. Or two back-to-back thyristor bridges in DC link.

  • Operation: Rotor AC directly converted to variable frequency, variable voltage AC fed back to grid. Speed control by varying cycloconverter output frequency.

  • Speed Range: Wider than Kramer, can reach supersynchronous speeds (above $$\displaystyle n_s $$).

  • Comparison:

    | Feature | Kramer Drive | Scherbius Drive | | :--- | :--- | :--- | | Converter | Diode bridge + Inverter | Cycloconverter / Dual converter | | Speed Range | Sub-synchronous only | Sub & Super-synchronous | | Power Factor | Poor (diode bridge) | Better (controllable) | | Cost | Lower | Higher | | Applications | Fan/pump drives | High power, wide range |

4.3 Rotor Resistance Control (Wound Rotor IM)

• Principle: Insert external resistance $$\displaystyle R_{ext} $$ in rotor circuit via slip rings.

$$ T \propto \frac{s R_r' / R_{ext}}{(R_r'/R_{ext})^2 + (s X_{eq})^2} \quad \text{at constant } V_s, f_s $$

Increasing $$\displaystyle R_{ext} $$ shifts max torque to higher slip, reduces $$\displaystyle T_{max} $$.

• Closed-Loop Speed Control: Speed sensor → controller → adjust $$\displaystyle R_{ext} $$ (via thyristor-controlled resistors or chopper) to maintain speed.

4.4 Regenerative Braking of Induction Motors

• With VSI/CSI: Reduce inverter frequency $$\displaystyle f_s $$ below rotor frequency ($$\displaystyle n > n_s $$). Motor enters generating mode. Power flows: mechanical → air-gap → stator → inverter → DC link → source (if VSI with regenerative capability).

• Speed-Torque Curve: For constant $V/f$, braking region appears for $$\displaystyle \omega_m > \omega_s $$. Torque negative (braking).

V. CONTROL OF SYNCHRONOUS MOTORS

5.1 Self-Controlled Synchronous Motor Drives

• Principle: Inverter frequency $$\displaystyle f_i $$ exactly equals rotor speed ($$\displaystyle f_i = \frac{p n}{60} $$). Rotor "locks" to rotating magnetic field. No "hunting" (like conventional synchronous motor).

• Load-Commutated Inverter (LCI) Fed Drive:

  • Circuit: DC source (or rectifier) → inductor → thyristor bridge (inverter) → SM.

  • Commutation: Load commutation (SM's overexcited synchronous reactance provides reactive power). Requires leading power factor operation (overexcited).

  • Advantage: Simple, robust, high power (MW range). Disadvantage: Low power factor at light loads, torque ripple.

• VSI Fed Synchronous Motor Drive:

  • Circuit: VSI (IGBTs) → SM.

  • Control: Requires rotor position (resolver/encoder) for proper commutation. Can operate at any power factor (field controlled).

  • Block Diagram: Speed loop → torque/current reference → PWM modulator → VSI → SM with position feedback.

5.2 Variable Frequency Control

• Below Base Speed: Constant $V/f$ ratio to maintain constant flux $\phi$. Torque capability constant.

$$ V_t \approx 4.44 f N \phi K_w \Rightarrow \frac{V_t}{f} = \text{const} $$

• Above Base Speed: Terminal voltage $$\displaystyle V_t $$ constant (limited by insulation). Flux weakens $\propto 1/f$. Torque capability reduces $$\displaystyle \propto 1/f^2 $$. Constant power region.

• Numerical Problem Approach:

  1. Determine base speed $$\displaystyle n_b $$ at rated $$\displaystyle V_t, f $$.

  2. For given $n$, find $$\displaystyle f = \frac{p n}{60} $$.

  3. If $$\displaystyle f \leq f_{base} $$, $$\displaystyle V_t = V_{rated} \cdot (f/f_{base}) $$ (constant $V/f$).

  4. If $$\displaystyle f > f_{base} $$, $$\displaystyle V_t = V_{rated} $$ (constant voltage).

  5. Compute $$\displaystyle E_f \propto f \cdot I_f $$ (if field current $$\displaystyle I_f $$ constant, $$\displaystyle E_f \propto f $$).

  6. Use phasor diagram: $$\displaystyle V_t = E_f - j I_a X_s $$ (neglect $$\displaystyle R_a $$) to find $$\displaystyle I_a $$, power factor, torque $$\displaystyle T = \frac{3 V_t I_a \cos \phi}{\omega_m} $$.

5.3 Regenerative Braking with VSI

• Reduce inverter frequency $$\displaystyle f_i $$ below mechanical speed ($$\displaystyle n > n_s $$). Motor operates as generator. Power fed back to DC link, then to source via regenerative front-end converter (PWM rectifier).

5.4 Permanent Magnet Synchronous Motor (PMSM)

• Construction: PM rotor (surface-mounted or interior), stator with 3-phase windings.

• Back EMF: $$\displaystyle E_f = K_e \omega_m $$ (sinusoidal for SPMSM, trapezoidal for BLDC).

• Torque Production: $$\displaystyle T = K_t I_q $$ (torque proportional to $q$-axis current in $d-q$ model). Requires rotor position for field-oriented control (FOC).

VI. SPECIAL MOTORS & STEPPER MOTORS

6.1 Switched Reluctance Motor (SRM)

• Construction: Salient poles on both stator and rotor. No PMs, no windings on rotor.

• Principle: Variable reluctance. Torque produced by tendency to align rotor pole with stator pole. $$\displaystyle T \propto I^2 \frac{dL(\theta)}{d\theta} $$.

• Power Converter: Typically asymmetric bridge (4 switches per phase). Each phase energized sequentially.

• Switching Scheme: Rotor position sensor (or sensorless) triggers switching. Phase energized when $$\displaystyle dL/d\theta > 0 $$ (motoring).

• Advantages over AC Drives:

  • Robust, simple construction (no brushes, PMs).

  • High torque/speed range.

  • Fault-tolerant (phase failure not catastrophic).

  • Low cost (no rare earth magnets).

• Torque-Speed: High starting torque, constant torque region up to base speed, constant power above.

6.2 Brushless DC Motor (BLDC)

• Construction: PM rotor (usually surface-mounted), stator with concentrated windings, Hall effect sensors (or sensorless).

• Operation & 6-Step Commutation: Each phase conducts for 120°. Hall sensors determine rotor position → sequence energizes phases.

  
  Hall: 101 → 001 → 011 → 010 → 110 → 100 → (repeat)
  
  Phase: A+ B- → C+ A- → B+ C- → ...
  
  

• Torque: Trapezoidal back EMF, quasi-rectangular current → constant torque.

• Comparison:

  | Feature | BLDC | PMSM | | :--- | :--- | :--- | | Back EMF | Trapezoidal | Sinusoidal | | Current | Rectangular (6-step) | Sinusoidal (FOC) | | Control | Simpler (6-step) | Complex (FOC) | | Torque Ripple | Higher | Lower | | Applications | Fans, pumps, appliances | High-performance (robotics, EVs) |

6.3 Stepper Motors

• Variable Reluctance (VR) Stepper:

  • Construction: Stator with multi-phase windings, rotor with soft iron teeth (no PM).

  • Operation: Sequential excitation of stator phases pulls rotor teeth into alignment.

  • Step Angle: $$\displaystyle \theta_s = \frac{360°}{m \cdot N_r} $$ where $m$ = phases, $$\displaystyle N_r $$ = rotor teeth.

• Microstepping:

  • Principle: Divide full step into smaller increments by controlling phase currents proportionally (sinusoidal/cosine waveforms).

  • Waveform Synthesis: $$\displaystyle I_a = I_m \sin \theta $$, $$\displaystyle I_b = I_m \cos \theta $$ for 2-phase motor.

  • Advantage: Smooth motion, reduced resonance, finer resolution.

• Load Angle & Step Rate: Load angle $$\displaystyle \theta_L $$ is deviation from equilibrium position. Step rate (pulses/sec) determines speed. Maximum step rate limited by torque-speed curve.

VII. SYSTEM APPLICATIONS & ADVANCED CONTROL

7.1 Industrial Drive Schemes

• Cement Industry: Crushers, mills, fans, kilns. Drives: Large wound rotor IM (slip power recovery), synchronous motors (high power, constant speed).

• Steel Industry: Rolling mills (high torque, four-quadrant), cranes, conveyors. Drives: DC drives (historically), large AC drives (VSI-fed IM/SM with vector control).

• Textile: Spinning, weaving (constant speed). Drives: Small IM with V/f control.

• Rolling Mills: Requires constant torque in both directions (four-quadrant). High starting torque, fast response. Drive: DC or high-performance AC (vector-controlled IM/SM).

7.2 Electric Traction Drives

• Requirements: High starting torque, wide speed range, regenerative braking, ruggedness.

• Types: DC series motors (older), 3-phase IM (modern), PMSM (high efficiency).

• Control: V/f control for IM, field-oriented control for PMSM. Regenerative braking essential.

7.3 Digital Control of Drives

• Block Diagram:

  
  [Speed Ref] → [Speed PI Controller] → [Torque/Current Ref] → [Current PI Controller] → [PWM/Space Vector] → [Power Converter] → [Motor]
  
                                                                            ↑                              |
  
                                                                            |                              ↓
  
                                                                         [Current Sensors]         [Rotor Position/Speed Sensor]
  
  

• Role of DSP/Microprocessor: Implements control algorithms (PI, FOC, DTC), PWM generation, protection, communication.

• Advantages over Analog: Flexibility, accuracy, multiple control loops, diagnostics, adaptive control.

7.4 Constant Torque & Constant Power Operation

• Constant Torque Region: Below base speed (for AC: constant $V/f$; for DC: constant flux). Torque capability constant. $P \propto \omega$.

• Constant Power Region: Above base speed. Flux weakened. Torque capability $$\displaystyle \propto 1/\omega^2 $$, so $P \approx \text{constant}$.

• Applications:

  • Constant Torque: Hoists, conveyors, rolling mills (at low speeds).

  • Constant Power: Machine tools (spindle), traction (high speed).

7.5 Energy Recovery Systems

• Regenerative Braking to Grid: Energy from braking fed back to AC supply via regenerative converter (VSI with bidirectional capability or CSI with separate rectifier).

• Applications: Electric vehicles, elevators, cranes, downhill conveyors.

• Benefit: Significant energy saving (up to 30% in frequent start-stop applications).

7.6 Computer Numerical Control (CNC)

• Basic Concept: Microprocessor-based system controlling machine tool axes (position, speed) via drives.

• Role in Drives: Generates reference signals for individual axis drives (position/speed loops). Interpolates tool path. Coordinates multi-axis motion.

Final Exam Strategy:

1. Derivations First: Be perfect with Load Equalization energy balance, V/f max torque derivation, referred inertia.

2. Waveforms & Diagrams: Practice drawing single-phase semi/full converter waveforms, VSI six-step/PWM, chopper waveforms, Kramer/Scherbius circuits.

3. Numerical Problems: Master formulas for:

*   Chopper: $$\displaystyle V_a = D V_s - I_a R_a $$

*   Phase converter: $$\displaystyle V_t = \frac{2V_m}{\pi} \cos \alpha $$

*   Plugging/Dynamic braking: $$\displaystyle I = \frac{V \pm E_b}{R_{total}} $$

*   V/f: $$\displaystyle V/f = \text{const} $$, $$\displaystyle T_{max} \propto 1/f^2 $$ above base.

*   Synchronous: $$\displaystyle V_t = E_f - j I_a X_s $$.

4. Comparisons: Know VSI vs CSI, Kramer vs Scherbius, BLDC vs PMSM, regenerative vs dynamic vs plugging braking.

5. Applications: Link drive type (DC, IM-VSI, SM, SRM) to industrial/traction requirements (torque, speed range, quadrant).