Electric Drives · Lecture 6D · 4 of 4 (Final)

Static Scherbius Drive, Applications and Unified Comparative Summary

Phase-Controlled Induction-Motor Drives — Lecture 6D

Prof. Mithun Mondal BITS Pilani, Hyderabad Campus Second Semester 2025–2026
SECTION 01

Lecture 6D — Scope and Objectives

Lectures 6A–6C Recap
  • Phase control: \(\eta \leq (1-s)\); simple but fundamentally inefficient at low speed.
  • Power factor degrades with \(\alpha\); mitigation via line reactors, 12-pulse topology, or passive filters.
  • SER drive: \(T_e = K_t I_{dc}\); returns \(sP_{ag}\) to the supply.
  • SER efficiency \(> 85\,\%\) even at \(60\,\%\) speed.
  • Converter rated at only \(s_{\max}\) fraction of motor power — economical for limited speed ranges.
This (Final) Lecture
  • Historical context: Kramer and Scherbius drives
  • Static Scherbius drive: bidirectional converter, four-quadrant capability
  • Supersynchronous operation explained
  • Industrial application: large pump drives and affinity laws
  • Wind energy: DFIG concept, MPPT and reactive power control
  • Unified comparison: all three drive types side by side
SECTION 02

Historical Context — Kramer and Scherbius Drives

Evolution of Slip-Energy Recovery
Original Kramer Drive (1906)
  • Rotor slip rings connected to a rotary converter (motor–generator set).
  • The DC motor of the set was mechanically coupled back to the induction motor shaft — slip energy returned mechanically to increase shaft output.
  • Very large, heavy, with low overall efficiency due to the two machine stages.
  • Only subsynchronous motoring possible.
Original Scherbius Drive (1911)
  • Slip rings connected to a commutator (Scherbius) machine that fed power back to the AC supply electrically.
  • More flexible: speed range could span both sub- and supersynchronous operation.
  • Still required large rotating machines.
Static (Modern) Equivalents
Classical versus modern static equivalents for slip-energy recovery
Classical DriveModern Static Equivalent
KramerSER drive (diode bridge + SCR inverter)
ScherbiusStatic Scherbius drive (back-to-back VSC)
  • No rotating converter machines; higher efficiency, smaller footprint.
  • Fully controllable dynamic response.
  • Modern DFIG wind turbines are the contemporary manifestation of the Scherbius principle.
SECTION 03

Static Scherbius Drive — Four-Quadrant Operation

Bidirectional Converter for Sub- and Supersynchronous Operation

SER limitation: The diode-bridge rectifier is unidirectional \(\Rightarrow\) slip power can only flow out of the rotor, so only subsynchronous motoring is possible (\(s > 0\)).

Scherbius drive: Replace the diode bridge with a bidirectional (back-to-back) converter, allowing slip power to flow in either direction.

Power balance in all modes:

\[P_{ag} = P_{\text{mech}} + s\,P_{ag} \;\Rightarrow\; P_{\text{mech}} = (1-s)\,P_{ag}\]

When \(s < 0\) (supersynchronous), \(sP_{ag} < 0\): power is injected into the rotor from the converter, supplementing shaft output.

Bidirectional converter options:

  • Cycloconverter: anti-parallel 3-phase bridge sets; line-commutated; suited to very large power levels.
  • PWM back-to-back VSC: modern standard; sinusoidal currents; near-unity supply power factor.
Scherbius drive power flow diagram showing sub-synchronous and supersynchronous modes with bidirectional rotor converter and power directions for motoring and regenerating
Scherbius drive power flow in sub- and supersynchronous modes

Advantages: True four-quadrant operation · High efficiency across full speed range · Converter rated at only \(s_{\max}\) of motor power · Compact and cost-effective at MW scale.

SECTION 04

Supersynchronous Operation — Power Flow

What Happens When \(s < 0\)?

When the rotor spins faster than synchronous speed, slip is negative:

\[P_{r} = s\,P_{ag} < 0 \quad(s < 0)\]

A negative value means power is being injected into the rotor from the converter, augmenting the mechanical output.

Supersynchronous motoring (\(s < 0\)):

  • Mechanical output: \(P_{\text{mech}} = (1-s)P_{ag} > P_{ag}\).
  • Both stator and rotor converter supply power to the shaft.
  • The rotor-side converter operates as a rectifier (power flows into the rotor from the supply).
Power flow and rotor converter mode for all four operating quadrants
Mode\(s\)\(sP_{ag}\) DirectionRotor Converter
Subsync. motoring\(+\)out of rotorInverter
Subsync. regen.*\(-\)into rotorRectifier
Supersync. motoring\(-\)into rotorRectifier
Supersync. regen.\(-\)out of rotorInverter

* subsync. regen.: \(0 < s < 1\) but machine acts as a generator (braking).

Key insight: In supersynchronous generation (e.g. wind above synchronous speed), both stator and rotor deliver electrical power simultaneously. Total generation \(= P_{ag} + |s|\,P_{ag} = (1+|s|)\,P_{ag}\).

SECTION 05

Application: Large Industrial Pump Drives

Pump Affinity Laws and Energy Savings

Conventional flow control — throttle valve:

  • Pump runs at constant speed; flow reduced by partially closing the discharge valve.
  • Energy wasted as pressure drop across the valve — highly inefficient at reduced flow.

Variable-speed drive — pump affinity laws:

\[Q \propto \omega_r, \quad H \propto \omega_r^2, \quad \boxed{P_{\text{shaft}} \propto \omega_r^3}\]
💰
Energy Saving via Affinity Laws
20% Speed Reduction → 49% Power Saving

A 20% speed reduction cuts shaft power to \((0.8)^3 \approx 51\,\%\) of full-speed power — a 49% saving.

Typical large installation: Ratings 9.5 MW and 11.5 MW · Speed ranges 757–1165 rpm / 1135–1745 rpm · Supply voltage 13.8 kV · Dual series-connected 3-phase SCR bridges · Liquid-cooled auxiliary starting resistors · Flow range 60–100% \(\Rightarrow\) converter rated at \(\approx 30\,\%\) of motor power.

Power versus flow comparison showing throttle-valve control requiring constant high power at all flow rates versus variable-speed drive following cubic affinity law with significant energy savings at partial flow
Power vs. flow: throttle-valve control vs. variable-speed drive — large energy savings at partial load
SECTION 06

Application: Wind Energy Conversion — DFIG Concept

Doubly-Fed Induction Generator (DFIG)

The wound-rotor IM operating as a generator with bidirectional slip-energy exchange is the basis of the doubly-fed induction generator (DFIG), the dominant technology in grid-connected wind turbines above 1 MW.

Why variable speed matters:

  • Wind speed varies continuously; to maximise aerodynamic efficiency, rotor speed must track the wind (\(C_P\) optimisation).
  • Maximum Power Point Tracking (MPPT): \(P_{\text{aero}} \propto \omega_r^3\).
  • Fixed-speed machines waste energy whenever wind speed differs from the design point.

Key difference from pump drives: In wind turbines the speed range spans \(\approx \pm 30\,\%\) around synchronous speed (both sub- and supersynchronous generation). The bidirectional converter handles the full slip-power band in both directions.

MPPT curve versus fixed-speed operation showing shaded area of additional energy captured by variable-speed DFIG tracking optimal tip-speed ratio at all wind speeds
MPPT curve vs. fixed-speed operation: shaded area = additional energy captured by variable-speed DFIG
SECTION 07

DFIG — Reactive Power Control Capability

Independent Active and Reactive Power Control

The rotor-side converter of a modern DFIG controls both the active power (via torque) and the reactive power delivered by the stator to the grid — independently.

How reactive power is controlled:

In rotor flux-oriented (vector) control, the rotor current is decomposed into two orthogonal components:

  • \(i_{rq}\): component in quadrature with rotor flux \(\Rightarrow\) controls electromagnetic torque.
  • \(i_{rd}\): component in phase with rotor flux \(\Rightarrow\) controls magnetising current and stator reactive power.
  • Increasing \(i_{rd}\) causes the stator to export reactive power (capacitive — voltage support).
  • Decreasing \(i_{rd}\) causes the stator to absorb reactive power (inductive).

Reactive power operating range:

\[-Q_{\max} \leq Q_s \leq +Q_{\max}\]

independently of active power output, subject to rotor converter current rating. Unity power factor at the stator terminals is achievable at any wind speed.

Grid-code requirement: Modern grid codes require wind farms to provide dynamic reactive power support during voltage disturbances (fault ride-through, FRT). The DFIG's independent \(P\)\(Q\) control is what enables FRT compliance — a squirrel-cage generator cannot do this without a full-rated reactive compensator.

SECTION 08

Comparative Summary — All Three Drive Types

Unified comparison of stator resistance control, phase (SCR) control and slip-energy recovery
Feature Stator Resistance Control Phase (SCR) Control Slip-Energy Recovery
Control variable External \(R_{\text{ext}}\) Firing angle \(\alpha\) Firing angle \(\alpha\) (rotor back-EMF)
Efficiency at low speed Very poor (\(\ll 1{-}s\)) Poor (\(\approx 1{-}s\)) High (\(> 85\,\%\) typical)
Input power factor Moderate Poor (degrades with \(\alpha\)) Good (VSC version: unity)
Rotor type Squirrel-cage or wound Squirrel-cage Wound-rotor (slip rings)
Converter cost Very low Low Moderate
Quadrant operation 1 1 or 3 (reversible ctrl.) 1 basic; 4 with Scherbius
Harmonic content Low Moderate Moderate (6th harmonic)
Supply harmonics Low Moderate Moderate (12-pulse mitigates)
Controller complexity Simple Moderate Moderate (DC-drive-like)
Typical applications Starting resistor only Fans, pumps, soft-starters Large pumps, MW-scale wind
SECTION 09

Key Takeaways — Complete Lecture Series

Stator Voltage (Phase) Control
  • Air-gap power partition: rotor copper loss \(= s\,P_{ag}\); ceiling \(\eta\leq(1-s)\) is fundamental.
  • SCR waveforms non-sinusoidal for \(\alpha>\phi\); harmonics govern thermal rating.
  • Input power factor degrades with \(\alpha\); mitigation essential in large drives.
  • Stability: operating point must lie on the low-slip side of peak torque.
  • Open-loop speed range \(\approx 6\,\%\); closed-loop cascade control mandatory.
  • NEMA D motors extend the stable region.
Slip-Energy Recovery (SER)
  • Returns \(sP_{ag}\) to supply — breaks the \((1-s)\) efficiency barrier.
  • \(T_e \propto I_{dc}\): single-variable control (DC-drive analogy).
  • Converter cost \(\propto s_{\max}\): economic only for limited speed ranges (\(\leq 30\,\%\)).
  • Supply harmonics mitigated by 12-pulse topology or line reactors.
  • Static Scherbius extends to four-quadrant sub- and supersynchronous operation.
  • Modern DFIG adds independent reactive power control for grid support and fault ride-through.
End of Lecture Series · Electric Drives · BITS Pilani
"The recovery of slip energy transforms the induction machine from a variable-speed workhorse into a high-efficiency, controllable industrial drive system."
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Series-Wide Conclusion
When Are These Drives Justified?

Both schemes remain cost-effective for large wound-rotor IM systems where the required speed range is limited (\(\leq 30\,\%\) of rated speed), where a full-rated PWM-inverter drive would be disproportionately expensive.

L1: Power circuits & steady-state  ·  L2: Load interaction & efficiency  ·  L3: SER analysis & harmonics  ·  L4: Scherbius & applications