Electrical Drives (EX-801) - Unit 3 Short Notes

UNIT 3: ELECTRICAL DRIVES - EXAM-FOCUSED SHORT NOTES

I. FUNDAMENTALS OF DRIVE SYSTEMS & STEADY-STATE ANALYSIS

A. Block Diagram & Components of Electrical Drives

A typical drive system consists of:

1. Power Supply: AC or DC source.

2. Power Converter: Modifies electrical power (voltage, current, frequency) to suit the motor (e.g., rectifier, chopper, inverter).

3. Motor: Converts electrical power to mechanical power.

4. Load: The mechanical system being driven (with its own torque-speed characteristic).

5. Controller: Generates commands for the power converter based on feedback (speed, current, torque).

6. Sensor: Measures variables (speed, current, position) for closed-loop control.

[!TIP] Exam Focus: Be prepared to draw and explain the function of each block. The power converter is the heart of modern drives.

B. Load Torque & Power Characteristics

C. Drive Classification & Quadrant Operation

• Quadrants of Torque-Speed Plane:

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

  • Quadrant II: Regenerative braking, forward (T<0, ω>0)

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

  • Quadrant IV: Regenerative braking, reverse (T>0, ω<0)

• Two-Quadrant Drive: Operates in QI & QII (forward motoring & braking) or QIII & QIV (reverse motoring & braking). Common for fan/pump drives.

• Four-Quadrant Drive: Operates in all quadrants. Required for cranes, hoists, elevators (needs forward/reverse motoring & braking).

D. Steady-State Stability of Drives

• Concept: A drive is stable at an operating point if a small disturbance (change in speed) produces a net restoring torque that brings it back to that point.

• Criterion: Stability depends on the relative slopes of the motor torque (T_M) and load torque (T_L) curves at the equilibrium point.

  • Stable: dT_M/dω > dT_L/dω at intersection.

  • Unstable: dT_M/dω < dT_L/dω at intersection.

• Mathematical Analysis (May 2024):

  Given T_M = f(ω) and T_L = g(ω), equilibrium at ω_e where f(ω_e) = g(ω_e).

  For a small perturbation Δω, net torque ΔT = [f(ω_e+Δω) - g(ω_e+Δω)].

  Using Taylor series: ΔT ≈ [f'(ω_e) - g'(ω_e)] * Δω.

  For stability, ΔT and Δω must have opposite signs → f'(ω_e) - g'(ω_e) < 0 → f'(ω_e) < g'(ω_e).

  Note: This contradicts the graphical slope rule because T = J dω/dt. If ΔT opposes Δω, drive returns to equilibrium. Graphically, if motor curve is steeper (dT_M/dω > dT_L/dω), a speed increase (Δω>0) causes T_M to drop more than T_L, so net torque negative (ΔT<0), decelerating back.

E. Load Equalization & Flywheel Design

• Necessity: To limit peak motor torque (T_Mmax) and power rating when the load torque (T_L) is intermittent (e.g., punching, shearing). A flywheel (large J) stores kinetic energy during light-load periods and releases it during heavy-load periods.

• Principle: During light load (T_L < T_M), motor accelerates, storing energy in flywheel. During heavy load (T_L > T_M), flywheel decelerates, supplying additional energy.

• Derivation of Flywheel Inertia (J_f):

  Consider a cycle with:

  • Heavy load period: t₁, T_L1 (high)

  • Light load period: t₂, T_L2 (low)

  • Maximum permissible motor torque: T_M (constant)

  • Motor inertia: J_m, no-load speed: ω₀

  • Assume linear T-ω characteristic: T_M = a - bω (a, b constants).

  Let steady-state speed fluctuation be Δω (from ω_max to ω_min).

  Energy balance over full cycle (net energy from motor = net energy to load):

  ∫(T_M - T_L) dt over cycle = 0

  (T_M - T_L1)*t1 + (T_M - T_L2)*t2 = 0 → T_M = (T_L1*t1 + T_L2*t2)/(t1+t2).

  At extreme points (ω_max and ω_min), T_M equals T_L.

  Using linear law: T_L1 = a - b ω_max, T_L2 = a - b ω_min.

  Solving: Δω = ω_max - ω_min = (T_L1 - T_L2)/(b).

  Kinetic energy change in flywheel+motor: ΔKE = ½ (J_m + J_f) (ω_max² - ω_min²) ≈ (J_m + J_f) ω_0 Δω (for small Δω).

  Energy deficit during heavy load: E_def = (T_L1 - T_M) * t1.

  This deficit is supplied by flywheel: E_def = ΔKE.

  Therefore: (T_L1 - T_M) t1 = (J_m + J_f) ω_0 Δω.

  Substitute T_M and Δω from above to solve for J_f.

  \boxed{J_f = \frac{(T_{L1} - T_M) t_1}{\omega_0 \Delta\omega} - J_m}

F. Referred Parameters & Combined Inertia

• Referred Moment of Inertia (J_eq): In a multi-mass system (motor, load, gear), all inertias can be referred to a common shaft (usually motor shaft) using gear ratios.

  If gear ratio n = N_motor / N_load (speed ratio), then:

  J_{load,ref} = J_{load} * n²

  T_{load,ref} = T_{load} / n

  J_{eq} = J_m + Σ(J_{i,ref})

• Referred Torque: Torques are referred inversely to the gear ratio to maintain power equivalence.

G. Comparison: AC vs. DC Drives

H. Constant Torque & Constant Power Operation

• Constant Torque Region (Below Base Speed): For DC motors (armature voltage control) and AC motors (V/f control with constant flux), torque capability is constant. T_max ∝ (V/f)² (constant V/f → constant T_max).

• Constant Power Region (Above Base Speed):

  • DC Motor: Field weakening (flux φ ↓) → T ∝ φ I_a, P = T ω ∝ I_a ω (since φI_a constant for max I_a). Power constant.

  • AC Motor (V/f): Above base frequency, voltage held constant (V=const), so flux φ ∝ V/f ↓. T_max ∝ φ² ∝ 1/f². To maintain same torque, current must increase, but voltage limit caps power. Hence power capability drops (not truly constant power unless with field weakening in SM). True constant power requires flux weakening (e.g., in PMSM or synchronous motor with field control).

II. DC MOTOR DRIVES

A. Starting & Conventional Methods

• Need for Starter: To limit the high starting current (I_start = V/R_a, very large as R_a is small) which can damage the armature winding and cause severe voltage dip.

• Methods:

  1. Direct-on-Line (DOL): Not used for DC motors (except very small).

  2. Series Resistor Starter: Add external resistance R_ext in armature circuit. Gradually cut out as motor gains speed. I_start = V/(R_a + R_ext).

  3. Voltage Reduction: Use a separate variable DC supply or a thyristor converter to apply reduced voltage initially.

B. Speed Control Methods

• Armature Voltage Control (Below Base Speed): Vary V_a. Speed n ∝ V_a (for constant T, hence constant I_a). Provides constant torque. Why for below base? Because field is at maximum (rated), so max torque available. Reducing voltage reduces speed without changing torque capability.

• Field Flux Control (Above Base Speed): Vary field current I_f (by varying R_f). Speed n ∝ 1/φ (for constant V_a, I_a). Provides constant power. Why for above base? Armature voltage already at maximum (V_a=V_rated). To increase speed beyond base, flux must be reduced (field weakening). This reduces torque capability (T ∝ φ I_a), so I_a can be kept at rated, making power (Tω) roughly constant.

C. Power Electronic Converters for DC Drives

1. Phase-Controlled Converters (AC-DC)

• Single-Phase Half-Controlled (Semi-Converter): 2 thyristors + 2 diodes. Unidirectional output voltage, bidirectional current (with freewheeling diode).

  • Average Output Voltage: V_dc = (V_m/π)(1 + cosα) (for α ≤ 180°), where V_m = √2 V_rms.

  • Power Factor: Displacement factor = cosα, Distortion factor < 1. Overall PF < cosα.

• Single-Phase Fully-Controlled (Full Converter): 4 thyristors. Bidirectional voltage and current (no freewheeling).

  • Average Output Voltage: V_dc = (2V_m/π) cosα (for α ≤ 90°). For α>90°, V_dc negative → regenerative braking possible.

  • Power Factor: PF = cosα (displacement only, as output is purely DC, input current is quasi-square wave → distortion present).

• Problem-Solving (Nov 2022, May 2024):

  For a separately excited motor: V_a = V_dc - I_a R_a.

  Motor back-EMF: E_a = K_e φ ω.

  Torque: T = K_t φ I_a.

  Given V_dc from converter, solve for I_a, ω, T simultaneously. Assume continuous conduction (L_a large enough).

2. DC Choppers (DC-DC)

• Definition: Static switch (usually a single thyristor/MOSFET/IGBT) that converts fixed DC input to variable DC output.

• Step-Down (Buck) Chopper: Output voltage V_o < V_in. V_o = α V_in (α = duty cycle = T_on/T).

• Step-Up (Boost) Chopper: Output voltage V_o > V_in. V_o = V_in / (1-α).

• Types of Chopper Circuits (by quadrant operation):

  | Type | Quadrant | Switches | Application | | :--- | :--- | :--- | :--- | | Class A | I | 1 (SW) + 1 (D) | Motoring (one quadrant) | | Class B | II | 1 (SW) + 1 (D) | Regenerative braking | | Class C | I & II | 2 (SWs) + 2 (Ds) | Two-quadrant (motoring & regen) | | Class D | I & II (reversible) | 2 (SWs) + 2 (Ds) | Reversible two-quadrant | | Class E | I, II, III, IV | 4 (SWs) | Four-quadrant |

• Motoring Control (Class A or D): Switch SW1 on: V_in applied to motor. Off: motor back-EMF freewheels through D1. V_a = α V_in.

• Regenerative Braking Control (Class B or D): Switch SW2 on: motor acts as generator, current flows back to supply through D2. V_a = - (1-α) V_in (negative). Energy fed back to source.

D. Braking of DC Motors

[!TIP] Key Differentiation (Nov 2022, May 2025):

• Plugging: High current, fast stop, energy wasted as heat in R_a.

• Dynamic Braking: Moderate current, slower stop than plugging, energy wasted in external resistor.

• Regenerative Braking: Current depends on excess E_a, energy returned to supply. Requires power converter that allows reverse current (full converter, chopper Class B/D).

III. INDUCTION MOTOR (IM) DRIVES

A. Fundamentals & Speed-Torque Characteristics

• Synchronous Speed: n_s = 120f / P (rpm)

• Slip: s = (n_s - n) / n_s

• Torque-Slip Characteristic:

  • Motoring: 0 < s < 1 (n < n_s). T ∝ s for small s. Max torque at s_max = R_r' / X_eq.

  • Plugging: 1 < s < 2 (n negative). Torque negative (opposing).

  • Generating: s < 0 (n > n_s). Torque negative (opposing motion).

  • T = \frac{3 V^2 (R_r'/s)}{\omega_s [(R_s + R_r'/s)^2 + (X_s + X_r')^2]} (approx. for constant V/f).

B. Starting Methods

• DOL: Full voltage. High starting current (5-8×I_fl), high starting torque (1.5-2×T_fl).

• Reduced Voltage:

  • Star-Delta: Voltage reduced by √3, current reduced by 1/3, torque reduced by 1/3.

  • Auto-Transformer: Voltage reduced by k (turns ratio), current reduced by k², torque reduced by k².

  • Calculation (May 2024): If DOL current = I_st, torque = T_st, to get starting torque = T_fl, required voltage V_app = V_rated * √(T_fl/T_st). Starting current then = I_st * (V_app/V_rated).

C. Speed Control Methods

1. Stator Voltage Control

• Principle: For fan/pump loads (T_L ∝ ω²), torque of IM ∝ V². So, reducing voltage reduces torque, and speed drops to match load torque.

• Application: Only for loads where torque decreases rapidly with speed (quadratic). Not for constant torque loads.

• Problem (May 2024): Given T_L ∝ ω², find V, I, T at a speed ω. Use T ∝ V² and T ∝ ω² (for load) → V ∝ ω. Then from equivalent circuit, find I and T.

2. Variable Frequency Control (V/f Control)

• Below Base Speed (Constant V/f):

  • Why maintain V/f constant? To keep air-gap flux φ_m constant. From transformer EMF equation: E ≈ 4.44 f N φ_m. If V/f constant, φ_m constant. Constant flux → constant torque capability (T_max ∝ φ_m²).

  • Operation: As frequency f is reduced from f_rated, voltage V is reduced proportionally to keep V/f constant.

  • Torque-Speed: Parallel characteristics (same T_max).

• Above Base Speed (Constant Voltage):

  • Why constant voltage? Because inverter/output voltage limited to rated voltage V_rated. Cannot increase V beyond V_rated.

  • Effect: Flux φ_m ∝ V/f ↓ as f increases. Hence T_max ∝ φ_m² ∝ 1/f². Torque capability decreases with speed. Constant power region (approximately, if current limit is reached before voltage limit).

• Range of Speed Control (Jun 2025): Wide. From near zero (with voltage boost at low V to overcome stator drop) to 2-3 times base speed (with field weakening).

• Derivation of Max Torque vs. Frequency (Nov 2022):

  From torque equation (approx.):

  T_max = \frac{3 V^2}{2 ω_s (R_s + \sqrt{R_s^2 + (X_s + X_r')^2})}

  For constant V/f: V ∝ f, ω_s ∝ f. So T_max ∝ (f²) / f = f. But wait, this is for constant voltage? Let's derive properly.

  Actually, T_max ∝ (V/f)² if slip at max torque s_max = R_r' / X_eq is kept constant (by keeping X_eq constant?).

  Better: T_max ∝ (V²) / (ω_s X_eq²) but X_eq ∝ f. So T_max ∝ V² / (f * f²) = V² / f³.

  If V/f constant → V ∝ f → T_max ∝ (f²) / f³ = 1/f. So max torque decreases with increase in frequency if V/f is held constant? That contradicts constant torque region.

  Correction: For constant V/f, we adjust voltage so that flux is constant. The standard result is: T_max ∝ (V/f)². How?

  From: T_max = \frac{3}{2 ω_s} \frac{(V/f)^2}{(R_s/f)^2 + (X_s + X_r')^2}? Not exactly.

  Standard Derivation:

  T_max = \frac{3 V^2}{ω_s [ (R_s + R_r'/s_max)^2 + (X_s + X_r')^2 ]}, s_max = R_r' / (X_s + X_r').

  For constant V/f: V = k f, ω_s = 2πf.

  Also, X_s = 2πf L_s, X_r' = 2πf L_r'. So (X_s + X_r') = 2πf (L_s+L_r') = k' f.

  Then T_max ∝ (k f)² / (f * (k' f)²) = k² f² / (f * k'² f²) = constant / f. Hmm.

  Wait, the key is that in V/f control, we often keep (V/f) constant, but the reactances are frequency-dependent. The correct proportionality is:

  T_max ∝ \frac{(V/f)^2}{(R_s/f)^2 + (X_{s0} + X_{r0}')^2} where X_s0, X_r0' are values at base frequency.

  If we neglect stator resistance, T_max ∝ (V/f)². So if V/f constant, T_max constant.

  Therefore: Below base speed (V/f constant), maximum torque is constant. Above base speed (V constant, f ↑), V/f ↓ → T_max ↓ as (V/f)².

3. Slip Power Recovery (Static Scherbius & Kramer Drives)

• Static Kramer Drive (Nov 2022, May 2023, May 2025):

  • Speed Range: Below synchronous speed (0 < s < 1).

  • Principle: Slip power (s * P_input) is extracted from rotor circuit via a diode bridge rectifier, then fed back to supply via a line-commutated inverter (or DC link). Rotor resistance effectively increased → speed reduced.

  • Power Circuit: Rotor terminals → diode bridge → DC link (inductor) → inverter (thyristor bridge, line-commutated) → AC supply.

  • Closed-Loop (May 2022): Speed sensor compares n with n_ref, error controls firing angle of inverter to vary slip power recovery → speed control.

  • Advantage: High efficiency (slip power recovered, not dissipated in resistor).

• Static Scherbius Drive (May 2023, May 2025):

  • Speed Range: Above synchronous speed (s < 0, generating).

  • Principle: For super-synchronous operation, slip power is injected into rotor circuit from an AC source via a cyclo-converter or dual converter. Rotor receives additional power → speed > n_s.

  • Power Circuit: AC supply → cyclo-converter or dual converter → rotor circuit (via slip rings).

  • Comparison with Conventional Scherbius: Conventional uses a DC motor in cascade with IM (Ward-Leonard). Static Scherbius uses static converters, more efficient, faster response.

• Slip-Controlled IM Drives (May 2022): General term for drives where slip power is controlled (Kramer for sub-sync, Scherbius for super-sync).

D. Braking of Induction Motors

• Regenerative Braking (Nov 2022):

  • Condition: Rotor speed n > n_s (s < 0). Motor operates as an induction generator.

  • With VSI: If supply is from a VSI, regenerative braking is possible by controlling the inverter to accept power (e.g., by reducing frequency below instantaneous rotor frequency).

  • Speed-Torque: Torque is negative (braking) in generating region (s<0). Torque magnitude increases with speed above n_s up to a point.

• AC Dynamic Braking (Two Lead Connection) (Nov 2022):

  • Connection: Motor disconnected from supply. Two supply leads connected to a resistor (or to each other via resistor? Actually, "two lead connection" means connecting two stator terminals to a resistor, with the third terminal left open? No, standard AC dynamic braking: disconnect supply, connect stator to a single-phase AC source (often a capacitor or a resistor-capacitor network) to create a rotating field. But "two lead connection" specifically: connect any two stator leads to a resistor, and the third lead left disconnected? That creates a single-phase pulsating field, not rotating. That's not effective.

  • Correction: Standard AC dynamic braking for 3-phase IM: disconnect from 3-phase supply, reconnect stator to a single-phase supply (or to a capacitor to create a phase-shifted supply). This creates a pulsating magnetic field that is approximately synchronous with rotor speed, inducing currents that produce braking torque. The "two lead connection" might refer to connecting two leads to a resistor-capacitor network to create a phase shift? I need to check.

  • Actually, common method: Disconnect from supply, connect stator to a resistive load (three resistors, one per phase) or to a single-phase supply. The "two lead" might be a misnomer. Perhaps it means connecting two leads to a capacitor and the third to a resistor? Let's stick to standard: AC dynamic braking uses a single-phase supply (or capacitor) to produce a stationary field. The rotor cuts this field at slip s ≈ 1 (since field is stationary, synchronous speed = 0), so high slip, high braking torque.

  • Better to describe: In AC dynamic braking, the stator is disconnected from the 3-phase supply and connected to a single-phase AC source (or a capacitor). This produces a pulsating magnetic field (synchronous speed = 0). The rotor, still spinning, cuts this field at a slip s ≈ 1 (since n_s=0), inducing high rotor currents and thus high braking torque. Braking torque is proportional to square of applied voltage.

E. Current Source Inverter (CSI) Fed Drives (Nov 2022)

• Power Circuit: A DC link inductor (large) to maintain constant current, followed by a thyristor bridge inverter (6-pulse or 12-pulse).

• Operation: The inductor makes the DC link current nearly constant (ripple small). The inverter switches connect this constant current to the motor phases in sequence, producing a quasi-square wave current in the stator. Voltage is generated by the motor's back-EMF.

• Advantage: Naturally suited for high-power applications, inherently provides current control, regenerative braking possible with dual converter.

• Disadvantage: Poor power factor at light loads, more harmonics, larger inductor.

F. Self-Controlled (Commutatorless) IM Drives (May 2022)

• Principle: The IM is fed from a load-commutated inverter (LCI) or a cyclo-converter such that the stator current waveform is synchronized with the rotor position. The motor behaves like a synchronous motor with a slip that is always very small (almost synchronous). The rotor flux is "locked" to the stator MMF.

• Advantage: High efficiency, good power factor, simple control (like synchronous motor).

• Application: Large power drives (e.g., mills, compressors).

IV. SYNCHRONOUS MOTOR DRIVES

A. Starting & Pull-in Phenomenon

• Need for Damper Winding: To provide starting torque (like a squirrel-cage) and to damp oscillations during operation.

• Starting Methods:

  1. Asynchronous Starting: Use damper winding. Start as induction motor, then apply DC field when speed near synchronous (pull-in).

  2. Pony Motor: Small auxiliary motor brings rotor to near sync speed.

  3. Variable Frequency Starting: Start with very low frequency supply.

• Pull-in: When DC field is applied at a speed close to synchronous, the rotor "pulls in" and locks to the rotating field. Condition: Rotor speed must be within pull-in range (typically 2-5% of n_s). If applied at much lower speed, the large slip torque oscillations prevent synchronization.

B. Variable Frequency Control

• Below Base Speed: Constant V/f control to maintain constant air-gap flux. Same principle as IM.

• Above Base Speed: Terminal voltage held constant (V=rated). Flux decreases (φ ∝ V/f). Torque capability decreases.

• Self-Controlled Synchronous Motor Drives (May 2024, May 2023):

  • The stator supply frequency is controlled to be exactly equal to the rotor speed (in electrical rad/s). So the motor runs at synchronous speed always (s=0). The torque angle δ (load angle) is controlled by adjusting the magnitude of stator current or field current.

  • Advantage: No hunting, stable operation, fast response.

  • Implementation: Use a cyclo-converter or a PWM inverter with rotor position feedback (resolver/encoder).

C. Power Electronic Converter Fed Drives

1. Voltage Source Inverter (VSI) Fed (May 2023, May 2024)

• Power Circuit: DC link capacitor (voltage source), then 6-switch IGBT/MOSFET bridge (PWM or square wave).

• Operation: Produces variable frequency, variable voltage AC output. For regenerative braking, the inverter operates in inverting mode (power flows from motor to DC link, then back to AC supply via a separate converter or using regenerative PWM).

• Closed-Loop Block Diagram (May 2023, May 2024):

  
  Speed Ref ──► [Controller] ──► Frequency Ref ──► V/f Pattern Generator ──► PWM Modulator ──► VSI ──► Synchronous Motor
  
                                                                    ▲
  
                                                                    │
  
  Speed Sensor ───────────────────────────────────────────────────────┘
  
  

  The V/f pattern ensures constant flux below base speed.

• Regenerative Braking (Nov 2022): When motor speed > synchronous speed (δ increases beyond 90°), it enters generating mode. The VSI must be capable of inversion (power flow from DC link to AC supply). This requires a regenerative converter (e.g., a PWM inverter with bidirectional switches or a separate line-side converter).

2. Current Source Inverter (CSI) Fed (May 2022)

• As described in IM section, but feeding a synchronous motor. The constant DC link current produces quasi-square wave stator currents. Torque is proportional to sinδ. Requires forced commutation or load commutation (if motor power factor leading).

3. Load-Commutated Inverter (LCI) / Self-Commutated (May 2023)

• LCI: Uses the synchronous motor's own back-EMF to commutate the thyristors. Requires motor to operate at leading power factor (over-excited). No need for forced commutation circuits.

• Self-Commutated: Uses IGBTs/MOSFETs that can be turned on/off independently (e.g., PWM VSI). No dependency on motor back-EMF. More common nowadays.

• Comparison: LCI suitable for very high power, low speed; self-commutated (PWM VSI) for medium power, wide speed range.

D. Braking of Synchronous Motors

• Regenerative Braking with VSI (Nov 2022): As above. When load drives motor beyond synchronous speed (e.g., downhill hoist), δ becomes negative, motor generates. VSI inverts power back to supply.

• Speed-Torque Characteristic: In generating region (δ negative), torque is negative (braking). The characteristic is similar to motoring but in negative torque quadrant.

E. Advanced Problem (May 2023)

• For salient-pole motor under V/f control: T = \frac{3 V^2}{2 ω_s} \frac{(X_d - X_q) \sin 2δ + 2 X_q \sin δ}{2(X_d X_q \sin^2 δ + X_q^2 \cos^2 δ)} (approx). Need to calculate δ from load torque, then find currents, power factor, etc. Remember: I_d = (V - E_q)/jX_d, I_q = -E_d/jX_q (in d-q frame). E_q = V + jI_d X_d, E_d = V + jI_q X_q.

V. SPECIAL MOTORS & DRIVES

A. Switched Reluctance Motor (SRM) (Nov 2022, May 2024, May 2023)

• Construction: Stator has concentrated windings (each phase excited separately). Rotor is salient, no windings, no magnets (just laminated iron).

• Principle of Torque Production: T = ½ I² dL(θ)/dθ. Torque is produced by the tendency of the rotor to align with the excited stator pole (magnetic attraction). Sequence of excitation causes rotation.

• Power Circuit & Switching: Each phase has one switch (or two for asymmetry). Switching sequence: energize phase when rotor pole approaches aligned position, de-energize when it leaves.

• Advantages over other AC drives:

  1. Simple, rugged, low cost rotor.

  2. High starting torque.

  3. Torque-speed characteristics can be shaped by control.

  4. Fault tolerant (failure of one phase doesn't stop motor, just reduces torque).

  5. Wide speed range.

  6. No permanent magnets (no demagnetization, low cost).

• Disadvantages: High torque ripple, acoustic noise, needs position sensor (or sensorless control).

B. Permanent Magnet Synchronous Motor (PMSM) (May 2024)

• Construction: Stator similar to synchronous motor (3-phase winding). Rotor has permanent magnets (surface-mounted or interior).

• Working Principle: Same as synchronous motor. Rotor field from permanent magnets. Stator currents produce rotating field that locks with rotor field. Torque T ∝ I_q (q-axis current) for surface PMSM (L_d=L_q). For interior PMSM (L_d≠L_q), torque has reluctance component.

• Control: Field-oriented control (FOC) similar to DC motor: d-axis current controls flux, q-axis current controls torque.

C. Brushless DC Motor (BLDC) (Jun 2025)

• Construction: Stator has 3-phase concentrated windings. Rotor has permanent magnets (usually surface). Hall effect sensors on stator detect rotor position.

• Operation: Similar to PMSM but with trapezoidal back-EMF and trapezoidal current. The controller energizes phases in sequence based on Hall signals to produce constant torque.

• Switching Scheme: 120° conduction (each phase conducts for 120° electrical). Six-step commutation.

• Difference from PMSM: BLDC has trapezoidal back-EMF and current, PMSM has sinusoidal. BLDC uses Hall sensors, PMSM often uses encoder/resolver for FOC.

D. Stepper Motors

1. Variable Reluctance (VR) Stepper Motor (Nov 2022)

• Construction: Stator has multiple phases (usually 2 or 3) with concentrated windings. Rotor is salient, no windings, no magnets (high permeability iron).

• Operation: When a stator phase is excited, rotor aligns to minimize reluctance (teeth align). By sequentially exciting phases, rotor steps.

• Switching Sequence (for 3-phase, 6/4 poles): Example: A→B→C→A gives clockwise rotation. Step angle = 360° / (number of rotor teeth). For 6/4, step angle = 15°.

• Microstepping (Nov 2022): Instead of full-step (on/off), the current in each phase is proportionally controlled to produce intermediate positions. This smooths motion, reduces resonance, increases resolution. Achieved by PWM control of phase currents.

2. Load Angle Control (May 2024)

• Principle: In a stepper motor, torque is proportional to sin(θ_e), where θ_e is the load angle (difference between rotor position and equilibrium position for the excited phase). By controlling the magnitude of phase current, the maximum torque (holding torque) changes, thus controlling the load angle for a given load torque. Used in closed-loop stepper systems.

VI. ADVANCED TOPICS & APPLICATIONS

A. Digital Control of Drives (May 2024, May 2023, May 2022)

• Block Diagram:

  
  Ref (speed/torque) ──► Digital Controller (DSP/FPGA/MCU) ──► PWM/Space Vector ──► Power Converter ──► Motor
  
                                                                    ▲
  
                                                                    │
  
  Sensors (current, speed, position) ──► ADC ───────────────────────┘
  
  

• Advantages over Analog:

  1. Flexibility (easy to change control algorithms).

  2. High accuracy and repeatability.

  3. Implementation of complex control (vector control, predictive control).

  4. Self-diagnostics, communication (fieldbus).

  5. Cost-effective for complex control.

B. Industry-Specific Drive Schemes

1. Cement Industries (Jun 2025):

• Applications: Raw mill, kiln, cement mill, fan, conveyor.

• Drive Requirements: High torque at low speed (kiln), constant torque (mill), quadratic load (fans).

• Typical Drives: Large slip-ring IM with slip power recovery (Kramer) for mills; VFDs for fans; DC drives for older kilns.

2. Steel Industries (Jun 2025):

• Applications: Blast furnace fan, rolling mill (stand drives), crane, conveyor.

• Drive Requirements: High torque, frequent starting/braking, four-quadrant operation (cranes, reversing mills).

• Typical Drives: DC drives (historically), now AC drives with vector control (IM or synchronous). For main rolling mills, large synchronous motors with load-commutated inverters (LCI) or VSI.

C. Electric Traction Drives (May 2023)

• Overview: Drives for locomotives, EMUs, trams.

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

• Typical Drives: DC series motors (older), now 3-phase IM drives with VVVF inverters (IGBT-based). For high-speed trains, synchronous motors (PMSM) with vector control.

• Key Feature: Regenerative braking essential for energy saving.

D. Computer Numerical Control (CNC) (May 2023, May 2022)

• Role in Drive Systems: CNC provides position and speed references to individual axis drives (usually servo drives - PMSM or high-performance IM). It coordinates multiple axes for precise motion (machining, cutting).

• Interface: CNC sends pulse train (step/direction) or analog/digital setpoints to drive controllers. Drive closes inner current and speed loops.

E. Energy Recovery Systems (May 2022, May 2023)

• Principle: During braking, kinetic energy is converted to electrical energy and fed back to the supply or to a common DC bus to be used by other motoring drives.

• Implementation: Requires regenerative converters (full converters, PWM inverters with regenerative capability). In multi-drive systems, a common DC bus with a regenerative unit (or a bidirectional converter) allows energy sharing.

• Benefit: Significant energy saving, especially in cranes, elevators, and machines with cyclic operation.

F. Group & Individual Drives (May 2023)

• Group Drive: One motor drives multiple machines via belts, shafts, etc.

  • Advantages: Lower initial cost, simpler control.

  • Disadvantages: Less flexible, all machines stop if motor fails, inefficient (motor sized for peak load of group).

• Individual Drive: Each machine has its own motor.

  • Advantages: Flexible, independent operation, higher efficiency (motor sized for individual load), better speed control.

  • Disadvantages: Higher initial cost, more complex control.

• Selection: Individual drives preferred for modern, flexible, efficient systems. Group drives for simple, low-cost applications.

VII. SYNTHESIS & COMPARATIVE QUESTIONS

A. Comparative Analysis

1. AC vs. DC Drives (Jun 2025)

2. Two-Quadrant vs. Four-Quadrant Drives (May 2023)

3. Conventional Scherbius vs. Static Scherbius Drive (May 2023)

4. VSI vs. CSI Fed Synchronous Drives (May 2022)

5. Self-Controlled BLDC/AC vs. Conventional Drives (May 2022)

• Conventional: Motor speed determined by supply frequency (for synchronous) or voltage/frequency (for IM). Slip exists in IM.

• Self-Controlled (e.g., BLDC, self-controlled synchronous): Supply frequency exactly tracks rotor speed (s=0 for synchronous). Torque controlled by current magnitude/phase. No slip, no hunting, faster response.

B. Conceptual Explanations & Derivations

1. Derivation of Max Torque vs. Frequency in V/f Control (Nov 2022)

As derived in III.C.2:

For constant V/f: V = k f.

T_max ∝ V² / (ω_s X_eq²).

ω_s ∝ f, X_eq ∝ f (since X = 2πfL).

So T_max ∝ (k² f²) / (f * (k' f)²) = k² / (k'² f).

But if we neglect stator resistance and assume X_eq constant? That's not right. Standard Result: T_max ∝ (V/f)².

Proof: From torque equation:

T = \frac{3 V^2}{ω_s} \frac{(R_r'/s)}{(R_s + R_r'/s)^2 + (X_s + X_r')^2}

At max torque: s_max = R_r' / \sqrt{R_s^2 + (X_s + X_r')^2}.

Substitute: T_max = \frac{3 V^2}{2 ω_s \sqrt{R_s^2 + (X_s + X_r')^2}}.

Now, ω_s ∝ f, X_s + X_r' ∝ f.

So T_max ∝ V² / (f * f) = V² / f².

If V/f constant → V ∝ f → T_max ∝ (f²) / f² = constant.

If V constant → T_max ∝ 1/f². Therefore: Below base speed (V/f constant), T_max constant. Above base speed (V constant), T_max ∝ 1/f².

2. Explanation of Load Equalization with Derivations (Nov 2022, May 2024)

See Section I.E above. The derivation shows how flywheel inertia J_f is calculated to limit motor torque T_M to a specified value for a given cyclic load.

3. Steady-State Stability Dependence on Combined Characteristics (May 2024)

See Section I.D. The equilibrium point is stable if the motor torque curve is steeper than the load torque curve at that point (dT_M/dω > dT_L/dω). This means the drive system's stability is a combined property, not just motor or load alone.

END OF UNIT 3 NOTES