Electrical Power Systems: Circuit Breakers and Machines
Transient Phenomena in Power Lines
A1. Transient Switching Phenomena
When an inductive power line is switched on, the steady-state sinusoidal current is not reached immediately. Since current through an inductance cannot change instantaneously, a transient DC component appears if the switching instant does not match the steady-state initial value. The current is defined as i(t) = i_st(t) + i_tr(t). The worst case occurs in highly inductive circuits when energization happens near voltage zero.
A2. Transient Recovery Voltage (TRV)
TRV is the voltage appearing across circuit-breaker contacts immediately after arc extinction. It is critical because if it rises faster than the dielectric strength recovers, the arc may re-ignite. For an ideal HV terminal fault, the network acts as an L-C circuit, where TRV consists of a steady-state recovery voltage plus an oscillatory transient component.
A3. Current Chopping
Current chopping occurs when a breaker extinguishes the arc before the natural current zero, typical when interrupting small inductive currents (e.g., unloaded transformers). The magnetic energy stored in the inductance is transferred to stray capacitances, causing high-frequency discharge currents and significant overvoltages.
Circuit Breaker Technologies
A4. Vacuum Circuit Breakers
Vacuum breakers extinguish arcs in a sealed, low-pressure chamber using metallic vapour. They are widely used in medium-voltage systems for short-circuit interruption, motor switching, and traction applications due to their rapid dielectric recovery.
A5. SF6 Circuit Breakers
SF6 breakers use sulphur hexafluoride, a highly electronegative gas, to capture free electrons and increase dielectric strength. They are standard in HV and EHV systems.
A6. Double-Pressure SF6 Systems
This system uses two pressure regions. During opening, a valve releases compressed gas into the arcing chamber to cool the arc and sweep away ionized particles. While effective, it is complex due to the requirement for dual-pressure storage.
A7. Single-Pressure Puffer Systems
In a puffer breaker, the mechanical motion of the contact compresses the gas. For high short-circuit currents, the thermal energy of the arc assists in pressurizing the chamber, while mechanical action dominates for small currents.
A8. Oil Circuit Breakers
These use oil as both a dielectric and arc-extinguishing medium. Due to fire risks and maintenance requirements, they have largely been replaced by SF6 and vacuum technologies.
A9. Low-Volume Oil Breakers
These concentrate oil within the interrupting chamber, reducing the total volume required and lowering fire risks compared to bulk-oil designs.
Protection and Safety
A10. Overload and Short-Circuit Protection
Overload protection manages currents slightly above rated values to prevent overheating, while short-circuit protection must act rapidly. Modern breakers often feature electronic control units for adjustable tripping.
A11. Low-Voltage Circuit Breakers
These integrate sensors and release mechanisms. Thermal bimetal releases are commonly used for overloads, where current-induced heating causes the strip to bend and trip the mechanism.
A12. Time-Current Characteristics
These curves define the relationship between fault current and disconnection time. They are essential for protection coordination, ensuring that the device closest to the fault operates first to maintain selectivity.
A13. Residual Current Circuit Breakers (RCCB)
RCCBs detect earth leakage by measuring the vector sum of currents in live conductors. If the sum is non-zero, it indicates a leakage, triggering protection against indirect contact and fire.
A14. Overvoltage Protection
Devices like surge arresters and varistors limit transient voltages from lightning or switching. They operate by switching from high to low impedance when a voltage threshold is exceeded.
Transformers and Machines
M1. Transformer Equivalent Circuit
The equivalent circuit includes copper resistances, leakage reactances, and a magnetizing branch (RFe and X1h). The induced EMF is Ui = 4.44·f·N·Φmax.
M2. Vector Groups
The vector group defines the winding connection (e.g., Yd11) and phase displacement. Matching vector groups is mandatory for parallel operation to prevent circulating currents.
M3. Parallel Operation Conditions
Transformers must have identical rated voltages, turns ratios, vector groups, and compatible short-circuit impedances to ensure proper load sharing.
M4. Instrument Transformer Safety
Rule: Never open the secondary of a current transformer (CT) while the primary is energized, and never short-circuit the secondary of a voltage transformer (VT).
M5. Transformer Inrush Current
Inrush current depends on the switching instant relative to the voltage phase. Switching at voltage zero can cause severe flux saturation and current spikes many times the rated value.
DC Machines
M6. DC Machine Principles
DC machines rely on the interaction between the magnetic field and armature current. The commutator mechanically rectifies the current to maintain consistent torque direction.
M7. Types of DC Machines
Types include separately excited, shunt, series, and compound machines, each offering different trade-offs between speed regulation and starting torque.
M8. Separately Excited Characteristics
Speed is controlled by armature voltage or field flux. Below base speed, armature-voltage control provides constant torque; above base speed, field weakening provides constant power.
M9. Armature Reaction
Armature reaction distorts the main magnetic field, causing sparking and voltage reduction. It is mitigated using interpoles and compensation windings.
M10. Basic DC Machine Equations
Key equations include E = c·Φ·ω and Ti = c·Φ·Ia, highlighting the relationship between flux, current, and mechanical output.
M11. Speed Control and Field Weakening
Speed is adjusted by varying armature voltage or field current. Field weakening reduces flux to increase speed beyond the base rating.
M12. Prohibited Operating Regimes
Loss of excitation in shunt machines leads to dangerous overspeed. Series machines must never run unloaded to avoid mechanical runaway.
M13. Reversing Rotation
Rotation is reversed by changing the polarity of either the armature or the field, but not both simultaneously.
M14. Universal Motors
These operate on both AC and DC. They are ideal for portable tools due to high starting torque and high speed.
Induction and Synchronous Machines
M15. Induction Machine Equivalent Circuit
The circuit models the stator and rotor, with rotor resistance adjusted by slip s = (n1 – n)/n1.
M16. Losses in Induction Machines
Losses include copper (I²R), iron (hysteresis/eddy current), mechanical (friction/ventilation), and stray-load losses.
M17. Torque-Speed Characteristics
Torque is proportional to the square of the supply voltage. Rotor resistance can be adjusted to shift the pull-out torque point.
M18. Starting Methods
Methods include direct-on-line, reduced-voltage (autotransformer/reactors), and external rotor resistance for wound-rotor motors.
M19. Circle Diagram
A graphical tool used to analyze induction machine performance, including power factor, efficiency, and torque, based on no-load and blocked-rotor tests.
M20. Single-Phase Induction Motors
These lack inherent starting torque. Starting is achieved via auxiliary windings, capacitors, or centrifugal switches.
M21. Braking Methods
Methods include regenerative braking (above synchronous speed), plugging (phase reversal), and dynamic braking (DC injection).
M22. Rotating Magnetic Field
Obtained by supplying three-phase windings with 120-degree phase-shifted currents. The field speed is n1 = 60·f1/p.
M23. Stator and Rotor Configuration
Stators use distributed three-phase windings. Rotors are either squirrel-cage or wound-rotor types.
M24. Synchronous Machine Types
Classified by rotor design: salient-pole (low speed) and cylindrical (high speed).
M25. V-Curves
V-curves illustrate the relationship between stator current and excitation current, showing how synchronous machines can regulate reactive power.
M26. Power Control
Active power (P) is controlled by the prime mover (turbine), while reactive power (Q) is controlled by rotor excitation.
M27. Salient vs. Non-Salient Poles
Salient-pole machines exhibit reluctance torque due to non-uniform air gaps, unlike cylindrical rotors.
M28. Static Stability
Stability is defined by dP/dδ > 0. The limit is reached at a load angle of 90 degrees.
M29. Synchronization Conditions
Generators must match the grid in phase sequence, frequency, voltage magnitude, and phase angle before connection.
M30. Excitation Systems
Systems range from traditional DC dynamos and slip rings to modern brushless and static excitation systems.
M31. Operating Area
Defined by thermal limits (stator/rotor heating) and stability limits (load angle and underexcitation).
M32. No-Load and External Characteristics
These curves define the magnetization and voltage regulation performance of the alternator.
M33. Electrically Excited vs. PM Machines
Electrically excited machines allow flux regulation, whereas permanent-magnet machines offer higher efficiency and simpler construction for specific drive applications.