Voltage Surges and Power System Grounding

Introduction to Voltage Surges and Overvoltages in Power Systems

A sudden rise in voltage for a very short duration on a power system is defined as a voltage surge or transient voltage. These overvoltages are fundamentally divided into two main categories based on their origin: internal causes and external causes. Internal causes include switching surges, insulation failure, arcing grounds, and resonance. External causes are primarily attributed to lightning discharges.

Internal Causes of Overvoltages and Switching Surges

Switching surges are overvoltages produced during switching operations. In the case of an open line, connecting an unloaded line to a voltage source sets up travelling waves. When the wave hits the terminal point A, it reflects back without a change in sign, resulting in voltage doubling. If the supply voltage is $E$ (r.m.s.), the instantaneous voltage the line must withstand is $2 \times \text{v}2 \times E$. This is temporary as line losses attenuate the wave. Similarly, switching off an unloaded line results in a momentary voltage of $2 \times \text{v}2 \times E$.

In the case of a loaded line, a sudden interruption sets up a voltage of $2 \times Z_n \times i$ across the switch, where $i$ is the instantaneous current and $*Z_n$ is the natural impedance. For example, if $Z_n = 1000\, Ω$ and $I = 100\, A$ (r.m.s.), if the break occurs at maximum current, the voltage across the breaker is calculated as:

$\frac{2 \times \sqrt{2} \times 100 \times 1000}{1000} = 282.8\, kV$

If $V_m$ is the peak line voltage in $kV$, the maximum line voltage becomes $(V_m + 282.8)\, kV$.

Current chopping is a phenomenon primarily associated with air-blast circuit breakers. Unlike oil circuit breakers, air-blast breakers maintain the same extinguishing power regardless of current magnitude. When breaking low currents, such as transformer magnetizing currents, the powerful de-ionising effect causes the current to fall abruptly to zero before the natural current zero. This creates high voltage transients, which are typically prevented by resistance switching.

Insulation failure commonly manifests as the grounding of a conductor (line-to-earth failure). If a line at potential $E$ is earthed at point $X$, two equal voltages of $-E$ travel in opposite directions with currents of $\frac{-E}{Z_n}$ and $\frac{+E}{Z_n}$. The total current to earth at the point of failure is $\frac{2E}{Z_n}$.

Arcing ground occurs in three-phase systems with ungrounded neutrals, especially in long, high-voltage lines. When a line-to-ground fault occurs, an intermittent arc is formed, producing severe cumulative transients and oscillations of three to four times the normal voltage. This can breakdown equipment insulation but is preventable by earthing the neutral.

Resonance occurs when inductive reactance equals capacitive reactance ($X_L = X_C$), resulting in unity power factor and high voltages. While rare at fundamental supply frequencies in standard lines due to small capacitance, it can be triggered by the 5th or higher harmonics if the generator e.m.f. wave is distorted, or within underground cables.

External Causes: The Mechanism and Nature of Lightning

Lightning is an electric discharge between clouds, charge centers within the same cloud, or between a cloud and the earth. It occurs when the potential gradient exceeds the dielectric strength of air (approximately $5\, kV/cm$ to $10\, kV/cm$). Charges are built up through friction between rising warm moist air and water particles; larger drops typically become positively charged and smaller drops negatively charged.

When a charged cloud passes over the earth, it induces an equal and opposite charge on the ground. The discharge process begins with a pilot or leader streamer. This streamer starts from the cloud and moves toward earth as long as there is enough charge to maintain the gradient at its tip. If the gradient fails, the leader stops and the charge dissipates. Initial leader current is low ($<100\, A$) and propagates at about $0.05\%$ the velocity of light with low luminosity.

In many instances, the leader continues in jumps, giving rise to stepped leaders. These travel at velocities exceeding one-sixth the speed of light in steps of approximately $50\, m$. Upon nearing the earth, a return streamer shoots up from the ground to the cloud along the same path. This completes the circuit, causing the visible lightning spark. A single flash usually consists of multiple separate strokes with intervals between $0.0005$ and $0.5$ seconds. Statistics show $87\%$ of strokes come from negative clouds, there are approximately $100$ strokes per second worldwide, and currents range from $10\, kA$ to $90\, kA$.

Types of Lightning Strokes and Their Effects

Direct strokes occur when the discharge path is directly from the cloud to equipment. Stroke A involves a discharge between a cloud and a tall object (like an overhead line) due to induced opposite charges. Stroke B occurs when a discharge between two clouds (e.g., Cloud P and Q) triggers a sudden release of bound charge in a third cloud (Cloud R), which then discharges to ground regardless of object height. Protection against Stroke B is not possible.

Indirect strokes are more common and result from electrostatically induced charges. A charged cloud induces bound charges on a line; when the cloud discharges elsewhere, these charges become free and travel along the line in both directions as waves. This is the source of the majority of transmission line surges.

Lightning produces steep-fronted voltage waves that rise from zero to peak (up to $2000\, kV$) in roughly 1\, ́s and decay to half-peak in 5\, ́s. These waves can shatter insulators, wreck poles, and damage transformer/generator windings by "piling up" against the winding inductance and breaking down insulation. Resulting arcs can set up disturbing oscillations across the system.

Mathematical Waveforms and Overvoltage Calculations

Lightning-induced surges are unidirectional and can be modeled as the difference of two exponentials:

$v = V(e^{-at} - e^{-bt})$

Where $a$ and $b$ are constants defining the shape, $v$ is the magnitude, and $V$ is the crest value. Surges are specified by rise time ($t_1$) and decay time to half-peak ($t_2$). A 1/50\, ́s surge reaches its peak in 1\, ́s and decays to half-peak in 50\, ́s.

For a direct stroke to a phase conductor, the current $I$ splits into forward and backward travelling currents ($I/2$). The voltage surge magnitude at the strike point is:

$V = \frac{I \times Z_0}{2}$

Where $Z_0$ is the surge impedance. For $Z_0 = 400\, Ω$ and $I = 10\, kA$, $V = 2000\, kV$. For a strike on a tower, the voltage across the insulation is $V = R \times I$, where $R$ is the tower footing resistance. For high towers, inductance $L$ is included: $v = (R \times I) + (L \times \frac{di}{dt})$. For indirect strokes, the peak induced voltage is $v = E \times h$, where $E$ is the electric field ($0.5$ to $2.8\, kV/cm$) and $h$ is conductor height.

Protection of Lines and Stations Against Lightning

Overhead ground wires are the most effective protection for transmission lines. Placed above phase conductors and grounded at every pole, they intercept strokes. The potential of the tower during a strike rises to $V_t = I_1 \times R_1$. If $V_t$ is kept lower than the insulator flashover voltage by maintaining low footing resistance ($10\u201320\, Ω$), the line remains protected. Ground wires also provide damping effects and electrostatic shielding. However, they add cost and risk short-circuits if they break.

The protective ratio is the ratio of induced voltage with protection to induced voltage without it. The protective angle (typically 20
to 45
) is the angle between the vertical through the ground wire and the slanting line to the protected conductor. The protective zone is the volume (wedge) protected beneath these angles. The ground wire height should be at least $10\%$ greater than the calculated height $y$.

Station structures are protected by earthing screens (shields), which are networks of copper conductors mounted over the equipment and grounded at multiple points. While effective against direct strokes, they do not protect against travelling waves and become uneconomical at very high voltages.

lightning Arresters (Surge Diverters)

Lightning arresters are protective devices that conduct high-voltage surges to the ground. They consist of a spark gap in series with a non-linear resistor. The gap prevents conduction at normal voltages, but breaks down during a surge. The non-linear resistor offers low resistance to high surge currents but high resistance to the normal line voltage ("power-follow current") once the surge passes. Design must ensure the arc ceases post-surge and the $I \times R$ drop does not exceed equipment insulation strength.

Rod Gap Arresters are simple but have limitations: arcs are maintained by normal voltage (causing short circuits), rods can melt, and performance depends on climate. Sphere Gap Arresters use spacing between spheres; the arc travels upward and lengthens until interrupted. Horn Gap Arresters use two horn-shaped rods; the arc is moved up by heat and magnetic effects until the gap distance is too great to sustain it. Multi-gap Arresters use a series of alloy cylinders with shunted resistances to limit power arcs.

Expulsion Type Arresters (protector tubes) use the heat of the arc to vaporize fiber tube walls, creating a high-pressure neutral gas that expels the ionized air and extinguishes the arc at current zero. Valve Type Arresters are the most advanced, using series spark gaps with grading resistors and non-linear discs (Thyrite or Metrosil). They are categorized into station type (up to $220\, kV$) and line type ($66\, kV$).

Surge Absorbers and System Grounding

A surge absorber reduces the steepness of the wave front by absorbing energy, unlike a diverter which merely redirects it. Methods include connecting a condenser between line and earth (acting as a short circuit for high frequencies) or using a parallel combination of a choke and resistance in series with the line. The Ferranti surge absorber uses an air-cored inductor surrounded by an earthed metallic sheet (dissipator), acting like a transformer with a short-circuited secondary to dissipate surge energy as heat.

Grounding is divided into system grounding and equipment grounding. Equipment grounding connects non-current-carrying metal parts to earth for safety. System grounding connects an electrical part of the power system (like a neutral point) to earth. Effective (solid) grounding has a grounding coefficient $<80\%$, while non-effective grounding (through impedance) is $>80\%$. Ungrounded systems suffer from arcing grounds and high capacitive fault currents ($I_c = 3 \times \text{Per phase capacitive current under normal conditions}$).

Neutral Grounding Methods and Resonant Grounding

Modern systems use grounded neutrals to eliminate arcing grounds and provide a clear path for protective relays. Methods include:

1. Solid Grounding: Neutral is directly earthed. It keeps healthy phase voltages at normal levels but results in high fault currents.
2. Resistance Grounding: A resistor limits earth fault current (usually to $2 \times$ full load current) and minimizes arcing grounds.
3. Reactance Grounding: Uses a reactor to limit fault current, but can cause high transient voltages.
4. Resonant Grounding (Peterson Coil): An iron-cored inductor ($L$) is tuned to the system capacitance ($C$) so that $I_L = I_C$, making the resultant fault current zero. The required inductance is:

$L = \frac{1}{3 \times (2 \times \pi \times f)^2 \times C}$

Voltage transformer grounding uses the primary of a VT in the neutral, acting as a high-reactance ground. Grounding transformers (zigzag or star-delta) are used to create a neutral point in 3-wire delta systems. These use differentially wound coils on three limbs to maintain balanced neutral currents.

Safety Grounding: Step and Touch Voltages

Equipment grounding (safety grounding) ensures metallic enclosures remain at earth potential during insulation failure. The safe limit for human body current ($I_b$) is defined by the duration of the fault ($t$):

$I_b = \frac{0.116}{\sqrt{t}}\, A$

Step voltage is the voltage between a person's feet ($0.5\, m$ apart) during a fault. Touch voltage is the voltage between a hand touching a faulted structure and the feet. Assuming body resistance $R_b = 1000\, Ω$ and soil resistivity $\rho_s$, the tolerable voltages are:

$E_{step} = (1000 + 6\rho_s) \times \frac{0.116}{\sqrt{t}}$$E_{touch} = (1000 + 1.5\rho_s) \times \frac{0.116}{\sqrt{t}}$

Actual step and touch voltages in a substation must be lower than these calculated tolerable limits to ensure safety.