15.2 Transformer Connections & Special Transformers

15.2 Transformer Connections & Special Transformers

Standard Three-Phase Bank Configurations

Three-phase power transformation can be accomplished using either a single 3-phase transformer unit or three identical single-phase transformers connected in a 3-phase bank. The four primary three-phase winding configurations are Star-Star (Y-Y), Delta-Delta ($\Delta$-$\Delta$), Star-Delta (Y-$\Delta$), and Delta-Star ($\Delta$-Y).

                    THREE-PHASE WINDING CONNECTIONS & LINE/PHASE RELATIONS

        STAR (Y) CONNECTION                            DELTA (Δ) CONNECTION
               Phase A                                        Phase A
                 │                                              ┌─┐
                 █ Winding                                     ███│ Winding
                 │                                             ███│
          Neutral├──────┐                                Phase B│ └─┐Phase C
                 │      │                                 ┌─────┼───┼─────┐
                 █      █                                 │    ███  │    ███
                 │      │                                 │    ███  │    ███
              Phase B Phase C                             └─────┼───┘     │
                                                                └─────────┘
    V_Line = √3 · V_Phase                                V_Line = V_Phase
    I_Line = I_Phase                                     I_Line = √3 · I_Phase

Summary of Voltage, Current & Phase Relationships

Technical Features of Bank Configurations

1. Star-Star (Y-Y):
   • Requires minimum insulation per phase ($V_P = V_L / \sqrt{3}$), making it economical for extra-high voltage (EHV) systems.
   • Disadvantage: Oscillating neutral phenomenon and severe 3rd harmonic voltage distortion under unbalanced loads unless neutrals are grounded or a tertiary delta winding is added.
2. Delta-Delta ($\Delta$-$\Delta$):
   • Excellent for high-current, lower-voltage applications. Traps 3rd harmonic currents within the closed delta loop, preventing voltage distortion.
   • Can continue operating at reduced capacity in Open-Delta (V-V) if one single-phase unit breaks down.
3. Star-Delta (Y-$\Delta$):
   • Standard choice for step-down high-voltage transmission substations. The primary Y neutral can be grounded to stabilize line voltages against lightning surges.
4. Delta-Star ($\Delta$-Y):
   • Standard choice for step-up generation substations and commercial distribution systems ($400/230\text{ V}$ or $480/277\text{ V}$). The secondary Y neutral provides a 4-wire service to supply both 3-phase motor loads and single-phase lighting/receptacle loads.

Vector Groups & Standard $30^\circ$ Phase Shift

According to IEEE/ANSI standards, in Y-$\Delta$ and $\Delta$-Y transformers, high-voltage line voltage leads low-voltage line voltage by $30^\circ$ for positive phase sequence ($A-B-C$). In European IEC notation, vector groups such as Dy11 ($30^\circ$ lead) and Dy1 ($30^\circ$ lag) designate phase displacements on a 12-hour clock dial ($11 \times 30^\circ = 330^\circ \equiv +30^\circ$).

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Open-Delta (V-V) Connection Analysis

When one single-phase transformer in a 3-phase $\Delta$-$\Delta$ bank is removed due to failure or maintenance, the remaining two single-phase transformers can continue delivering balanced 3-phase power in an Open-Delta (V-V) connection.

                     OPEN-DELTA (V-V) TRANSFORMER BANK TOPOLOGY

                        Phase A ───────────────┐
                                               │
                                             ──┴──
                                         T1  │   │ Primary Winding
                                             ──┬──
                        Phase B ───────────────┼───┐
                                               │   │
                                             ──┴── │
                                         T2  │   │ Primary Winding
                                             ──┬── │
                        Phase C ───────────────┴───┘  (Third transformer T3 removed!)

Derivation of V-V Bank Rating & Utility Factor

Let $S_1 = V_P I_P$ be the kVA rating of one single-phase transformer. In a full $\Delta$-$\Delta$ bank of three units, the total capacity is:

$S_{\Delta-\Delta} = 3 S_1$

In the Open-Delta (V-V) bank, line current $I_L$ cannot exceed the rated phase current $I_P$ of an individual transformer winding ($I_L = I_P$). The total 3-phase apparent power delivered by the two transformers is:

$S_{V-V} = \sqrt{3} V_L I_L = \sqrt{3} V_P I_P = \sqrt{3} S_1 \approx 1.732 S_1$

1. Open-Delta Bank Capacity Ratio:

$\frac{S_{V-V}}{S_{\Delta-\Delta}} = \frac{\sqrt{3} S_1}{3 S_1} = \frac{1}{\sqrt{3}} = 0.577 = 57.7\%$

The Open-Delta bank delivers 57.7% of the full 3-phase $\Delta$-$\Delta$ rating.

2. Utility Capability Factor (Operating Efficiency of Installed Units):

$\text{Utility Factor} = \frac{\text{Open-Delta Capacity}}{\text{Total Nameplate Rating of 2 Installed Transformers}} = \frac{\sqrt{3} S_1}{2 S_1} = \frac{\sqrt{3}}{2} = 0.866 = 86.6\%$

The two installed transformers can only be loaded up to 86.6% of their combined rating ($2 S_1$) without thermal overload.

Transformer Power Factor in V-V Bank

When an Open-Delta bank supplies a balanced 3-phase load operating at power factor $\cos \phi$, the individual phase currents in the two transformers are shifted by $30^\circ$ relative to their phase voltages. Consequently, the operating power factors of the two individual transformers are unequal:

$\cos \phi_1 = \cos(\phi - 30^\circ), \quad \cos \phi_2 = \cos(\phi + 30^\circ)$

• Even if the load operates at unity power factor ($\cos \phi = 1.0$), both transformers operate at $\cos 30^\circ = 0.866$ power factor (one leading, one lagging).
• If the load power factor drops to $0.50$ lagging ($\phi = 60^\circ$), transformer T2 operates at $\cos(60^\circ + 30^\circ) = \cos 90^\circ = 0$ power factor, delivering zero active power while transformer T1 supplies the entire active load power!

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Scott-T (T-T) Winding Connection

The Scott-T (or T-T) connection converts a 3-phase system into a 2-phase system (or vice versa) using two special single-phase transformers: the Main Transformer and the Teaser Transformer.

                        SCOTT-T (T-T) TRANSFORMER VECTOR SCHEMATIC

                                Phase A (Apex)
                                      │
                                      │ Teaser Transformer (Tapped at 86.6% = √3/2)
                                      │
                                      ▼
                      Phase B ───────█████─────── Phase C
                              ▲                   ▲
                              └───── 50% Tap ─────┘
                               Main Transformer

Winding Specifications & Vector Derivations

1. Main Transformer: Connected across lines B and C of the 3-phase system ($V_{BC} = V_L$). The primary winding has $N_p$ turns and features a precise 50% center tap.
2. Teaser Transformer: Connected between line phase A and the 50% center tap of the main transformer.

From the 3-phase equilateral voltage triangle, the altitude from phase A to the midpoint of line B-C is:

$V_{\text{teaser}} = V_L \sin 60^\circ = \frac{\sqrt{3}}{2} V_L \approx 0.866 V_L$

To achieve equal primary voltage per turn and balanced orthogonal two-phase secondary voltages ($90^\circ$ phase shift), the primary winding of the teaser transformer must be tapped at $\frac{\sqrt{3}}{2} \approx 86.6%$ of total main turns ($N_{\text{teaser}} = 0.866 N_p$).

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Autotransformers: Conductive vs. Inductive Power Transfer

An autotransformer is a single-winding transformer in which a portion of the same continuous winding is common to both the high-voltage (HV) and low-voltage (LV) circuits.

                    AUTOTRANSFORMER VOLTAGE AND CURRENT FLOW

                     I_H ───►  ┌───────────┐ Common Winding Portion
       V_H (Input)             │ Primary   │ (Series Winding N_se)
                               └─────┬─────┘
       ──────────────────────────────┼───────────► I_L (Output)
                                     │
                               ┌─────┴─────┐ Common Winding (N_c)
                               │ Secondary │ Current = I_L - I_H
                               └─────┬─────┘
       ──────────────────────────────┴───────────► Neutral

Transformation Ratio ($K$)

Let $V_H$ be the higher terminal voltage and $V_L$ be the lower terminal voltage. The autotransformer ratio is defined as:

$K = \frac{V_L}{V_H} < 1$

Apparent Power Capacity Advantage

When a standard two-winding transformer of rating $S_{\text{two-winding}}$ is reconnected as an autotransformer, its effective output kVA capacity increases dramatically according to:

$S_{\text{auto}} = \frac{S_{\text{two-winding}}}{1 - K}$

Division of Transferred Power

Power transferred from primary to secondary side in an autotransformer occurs via two distinct physical mechanisms:

$\text{Total Transferred Power: } S_{\text{auto}} = P_{\text{ind}} + P_{\text{cond}}$

1. Inductively Transferred Power ($P_{\text{ind}}$) (via magnetic flux coupling through core): $P_{\text{ind}} = (1 - K) S_{\text{auto}} = S_{\text{two-winding}}$
2. Conductively Transferred Power ($P_{\text{cond}}$) (via direct electrical connection): $P_{\text{cond}} = K S_{\text{auto}}$

Quantitative Advantages & Isolation Hazard

• Copper Saving: $\frac{\text{Weight of copper in auto}}{\text{Weight of copper in 2-winding}} = 1 - K$.
• Higher Efficiency: Internal $I^2 R$ losses decrease because only a fraction $(1-K)$ of power is transformed inductively.
• Lower Percentage Impedance: Results in superior voltage regulation, but increases available short-circuit fault current ($I_{\text{sc}} = I_{\text{rated}} / Z_{\text{pu}}$).
• FATAL ISOLATION HAZARD: Primary and secondary circuits are electrically tied together. A break in the common winding exposes low-voltage load equipment to full high-voltage potentials, requiring solid neutral grounding.

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Voltage Tap Changers

To compensate for line voltage drops caused by varying load currents along power distribution feeders, transformers are equipped with tap changers on their high-voltage windings (where current is lower, minimizing arc erosion).

1. No-Load Tap Changers (NLTC / Off-Circuit Tap Changers): Tap setting can only be manually adjusted while the transformer is completely de-energized. Typically provides $\pm 2.5%$ and $\pm 5.0%$ voltage adjustments.
2. On-Load Tap Changers (OLTC): Adjusts tap positions dynamically while carrying full load current. Employs selector switches and diverter switches with transition resistors or reactors to prevent breaking load current or short-circuiting adjacent tap turns during tap transitions.

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Grounding Transformers (Zig-Zag Connection)

Utility distribution systems fed by $\Delta$-connected transformer secondaries lack a physical neutral conductor. To establish a stable neutral point on an ungrounded 3-phase 3-wire network, a Grounding Transformer is installed.

                  ZIG-ZAG (INTERCONNECTED STAR) GROUNDING TRANSFORMER

                 Phase A             Phase B             Phase C
                    │                   │                   │
                   ███ a1              ███ b1              ███ c1
                    │                   │                   │
                   ███ c2              ███ a2              ███ b2
                    └───────────────────┼───────────────────┘
                                        │
                                        ▼ Ground Neutral (N)

Operating Principle of Zig-Zag (Interconnected Star) Winding

• Each phase limb contains two equal winding sections wound in opposite directions on different core limbs ($a_1, c_2; b_1, a_2; c_1, b_2$).
• Normal Balanced Conditions (Positive/Negative Sequence): Equal opposing currents in each limb cancel magnetizing flux, presenting extremely high magnetizing impedance and drawing negligible no-load current.
• Ground Fault Conditions (Zero Sequence $I_0$): Zero-sequence fault currents flow in phase through all three lines simultaneously. The opposing winding arrangement allows zero-sequence current to pass through with very low impedance, providing a safe path to ground and enabling protective relays to clear phase-to-ground faults.