Лапидус А.А. Схемы соединения обмоток трансформаторов. Серия роликов "Вопрос из Грозного"

Scientific concepts / nature phenomena presented

Transformer winding connection schemes

• Star (Y)
• Delta (Δ)
• Zigzag (Z)
• Star with neutral (“star-zero”, Y0) and delta with no neutral

AC power system design and phase systems

Why three-phase AC is preferred

• A balanced three-phase system via phase currents 120° apart
• Produces a rotating magnetic field (key advantage for motor operation)

Neutral grounding modes and their consequences

• Neutral is typically:
  • Grounded at 110 kV and above
  • Isolated at 6–35 kV
  • Grounded at < 1 kV (e.g., low-voltage distribution)
• The choice of grounding/isolating the neutral determines which transformer connection types are feasible (e.g., Y0 vs Δ vs Z).

Harmonics and power quality standards

• Voltage waveform non-sinusoidality arises because transformer magnetization is nonlinear.
• Standards (GOST 3244-2013) specify power quality of electrical energy, including:
  • a sinusoidal / non-sinusoidality coefficient
  • separate limits/coefficients for harmonics 2–40
• Harmonic behavior via sequence components:
  • Direct (positive), reverse (negative), and zero sequence are discussed relative to the fundamental (50 Hz) and then extended to harmonics.
  • Some harmonics behave “like” reverse/positive sequence depending on their order (e.g., 2nd ≈ reverse, 3rd ≈ direct).

Transformer magnetization nonlinearity → harmonic generation

• Transformer core steel has a nonlinear magnetization curve (the saturation “knee”).
• This yields non-sinusoidal flux, which adds harmonic components to voltage.
• A key family discussed is the 3rd harmonic family: 3rd, 6th, 9th, …
• Since flux is proportional to voltage, non-sinusoidal flux implies non-sinusoidal voltage.

Why 3rd-harmonic matters for transformer connections

• Transformer design can “route/contain” problematic harmonics internally by selecting winding connections.
• The lecture emphasizes the 3rd harmonic (and multiples of 3) and how different connections treat zero-sequence 3rd-harmonic currents.

Behavior of short circuits / asymmetrical loads across sides

• Unequal phase loading and single-phase short-circuits to ground can create zero-sequence currents/flows in star-connected systems.
• Depending on the HV/LV winding connection combinations, zero-sequence components may:
  • circulate internally (often with Δ involvement),
  • cancel, or
  • not cancel, causing neutral/phase-voltage displacement.
• As a consequence, an LV single-phase short can appear like a two-phase short on the HV side because sequence components are transformed through the winding group.

Kirchhoff’s current law constraint for zero-sequence

• A star with isolated neutral (“impassable” to 3rd-harmonic zero-sequence currents) cannot satisfy the required current summations at the neutral node unless the circuit provides a harmonic current path.

Winding group concept and phase shift

• Connection group numbering, especially group 11, is emphasized.
• A typical 30° phase shift is noted between vector diagrams for certain connection groups (e.g., triangle-star with group 11 vs other groups).

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Methodology / design logic outlined (as rules)

Step 1: Choose phase system

Use three-phase AC because it allows:

• balanced compensation of currents
• a rotating magnetic field (120° separation)

Step 2: Decide neutral grounding mode by voltage class

• 110 kV and above (neutral grounded):
  • use star with neutral grounded (Y0)
  • triangle without neutral is generally not applicable
• 6–35 kV (neutral isolated):
  • choose between:
    • star (with isolated neutral)
    • delta (triangle often preferred to address harmonic-related issues)
• 0–1 kV (neutral grounded):
  • use star with neutral (Y0) or sometimes zigzag with neutral (Z0)

Step 3: Use at least one delta winding to control harmonics

• “In any case, at least one transformer winding should be connected in a delta circuit.”
• Purpose: confine 3rd-harmonic-related problems (multiples of 3) within the transformer instead of polluting the external network.

Step 4: Handle zero-sequence and asymmetry correctly

• Star–star-zero:
  • can be inappropriate for single-phase faults/asymmetric loading
  • because zero-sequence currents/flows distort phase voltages (neutral displacement)
• Triangle involved (e.g., delta-star-zero):
  • zero-sequence effects can be transformed/cancelled
  • helps avoid neutral displacement and keeps LV phase voltages normal

Step 5: Accept trade-offs

• Triangle circuits:
  • better harmonic/sequence control
  • can introduce winding complexity
  • may cause connection group phase shift (e.g., 30°), affecting differential protection settings
• Zigzag:
  • can help with certain neutral/voltage balancing under asymmetrical loads
  • but is more expensive/complex

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Researchers / sources featured (named)

• Mikhail Osipovich Dolivo-Dobrovolsky — defended alternating current, promoted three-phase systems; proposed a star-based approach
• Thomas Edison — advocated direct current
• Nikola Tesla — advocated two-phase systems (referenced in the context of AC system rivalry)
• GOST 3244-2013 — state standard referenced for quality of electrical energy and harmonic limits/coefficients