Power factor is the ratio of active power to apparent power:
$\cos\phi=\frac{P}{S}=\frac{P}{\sqrt{P^2+Q^2}}$ A low power factor means the system draws a large reactive power (Q) for the same active power (P).

Problems associated with low power factor (2 marks)

1. Higher line current: For the same power and voltage,
   $I=\frac{P}{V\cos\phi}$ As (\cos\phi) decreases, current increases.

2. Increased (I^2R) losses: Higher current causes greater copper loss in transmission and distribution lines, reducing efficiency.

3. Poor voltage regulation and higher voltage drop: Large current increases line drop, causing low voltage at the consumer end.

4. Reduced equipment capacity: Alternators, transformers, cables and switchgear are rated in kVA. Low power factor means more kVA is used for the same kW, so useful capacity is wasted.

5. Higher capital and operating cost: Larger conductors, transformers and switchgear are required; consumers may also face low power factor penalty.

6. System instability and overloading: Excessive reactive power demand may cause voltage instability and overheating of equipment.

Remedial measures (3 marks)

1. Shunt capacitors:
   The most common and economical method. Capacitor banks are connected in parallel with the load to supply leading reactive power locally. If power factor is to be improved from (\cos\phi_1) to (\cos\phi_2), the required capacitor rating is
   $Q_c=P(\tan\phi_1-\tan\phi_2)$ This reduces reactive power drawn from the source and improves voltage.

2. Synchronous condenser:
   An overexcited synchronous motor running at no load behaves as a synchronous condenser. It supplies reactive power and gives smooth, continuous control. It is suitable for large substations and transmission systems.

3. Synchronous motors and phase advancers:
   Overexcited synchronous motors can supply leading reactive power and improve power factor. A phase advancer connected to the slip rings of an induction motor also improves its power factor.

4. Static VAR compensators and FACTS devices:
   SVC, STATCOM, TCR and TSC provide fast and dynamic reactive power compensation. They are useful where load varies rapidly and also help in voltage support.

5. Proper load management:
   Use motors of correct rating, avoid lightly loaded or idle-running induction motors, use high-efficiency and high-power-factor motors, and maintain equipment regularly.

6. Tariff incentive and penalty:
   Electricity authorities charge a penalty for low power factor and give incentives for maintaining high power factor. This encourages consumers to install compensating devices.

Conclusion:
Low power factor increases current, losses, voltage drop and cost. It is best improved by installing shunt capacitors near the load, while synchronous condensers and modern compensators are used for large or varying loads.

Load Duration Curve

Definition: A load duration curve (LDC) is a curve obtained by rearranging the load values of a load curve in descending order of magnitude, so that the loads are plotted against the percentage (or number) of time for which they are equaled or exceeded during a given period (day, month, or year).

In other words, the chronological sequence of the load curve is discarded and the loads are arranged from highest to lowest. The area under the LDC equals the total energy consumed in the period, same as the area under the original load curve.

Construction: If the load curve of a system is known, the LDC is drawn by taking the maximum load on the left and the minimum load on the right, with the horizontal axis representing the duration (hours or percentage of time) for which each load occurs or is exceeded.

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Significance in Generation Planning and System Operation

1. Determination of base load and peak load (generation planning): The LDC clearly separates the base load (the load that persists for most of the time, i.e., the flat lower portion) from the peak load (the load occurring for a short duration at the top). This helps the planner decide which plants should supply base load (nuclear, large thermal, run-of-river hydro) and which should supply peak load (gas turbines, pumped storage, diesel). Thus it guides the optimal mix of generating units.

2. Economic loading of generating units (unit commitment and dispatch): By superimposing the cost characteristics of available plants on the LDC, the planner can allocate generation so that the most efficient (cheapest per kWh) units run for the longest duration and the least efficient units run only during peak hours. This minimizes the overall cost of generation.

3. Capacity planning and reserve requirement: The maximum ordinate of the LDC gives the peak demand, which fixes the total installed capacity required (plus reserve margin). The area under the curve gives total energy demand, which is used to forecast future energy requirements and plan capacity addition in time.

4. Selection of plant type and size: The shape of the LDC indicates the load factor of the system. A high load factor (flatter LDC) justifies installation of high-capital-cost, low-running-cost plants; a low load factor (peaked LDC) favors low-capital-cost, high-running-cost peaking plants. Hence LDC is the basic tool for choosing plant type and size.

5. Scheduling of maintenance and operation: System operators use the LDC to schedule preventive maintenance of generating units during low-load periods (valleys of the curve), so that supply reliability is not affected. It also helps in planning spinning reserve and economic interchange of power between interconnected systems.

6. Tariff and load factor analysis: The LDC provides the load factor (average load / peak load), which is used in tariff design and in assessing the utilization of installed capacity. A high load factor means better utilization of plant and lower cost per unit.

Conclusion: The load duration curve is thus a fundamental tool that converts chronological load data into a form convenient for deciding plant mix, unit commitment, maintenance scheduling, and economical operation of a power system.

Torque–Speed Characteristics of a Three-Phase Induction Motor

The torque developed by a three-phase induction motor depends on slip $s$, rotor resistance $R_2$, and rotor reactance $X_2$. The approximate torque equation is

$$T = \frac{K \, s \, E_2^2 \, R_2}{R_2^2 + (sX_2)^2}$$

where $E_2$ is the standstill rotor emf and $K$ is a constant.

Important points of the characteristic:

1. At standstill $(s=1)$:
   The rotor frequency equals the supply frequency, rotor reactance is maximum, and the motor develops the starting torque.

2. As the motor accelerates:
   Slip decreases, rotor frequency decreases, and rotor reactance decreases. The rotor current becomes more nearly in phase with the rotor emf. Hence torque increases and reaches a maximum value called the breakdown torque or maximum torque.

3. Maximum torque:
   It occurs at the slip

   $$s_m = \frac{R_2}{X_2}$$

   and its value is

   $$T_{\max} = \frac{K E_2^2}{2X_2}$$

   Thus $T_{\max}$ is independent of rotor resistance, but the slip at which it occurs depends on $R_2$.

4. Beyond maximum torque:
   If slip increases further, torque decreases. If the load torque exceeds the breakdown torque, the motor stalls.

5. At synchronous speed $(s=0)$:
   The relative speed between rotor and rotating field is zero, so no emf is induced in the rotor and torque becomes zero. Therefore an induction motor cannot run at synchronous speed.

6. Stable region:
   The portion of the curve between $s=0$ and $s=s_m$ is the stable operating region. Here, if load increases, speed falls slightly, slip increases, and motor torque increases to meet the load. The motor operates at the point where motor torque equals load torque.

7. Unstable region:
   The portion from $s=1$ to $s=s_m$ is unstable. If the motor operates here, a small increase in load causes further decrease in speed and increase in slip, leading to stalling.

8. Effect of rotor resistance:
   Increasing rotor resistance increases starting torque and shifts the maximum torque point to a higher slip. This principle is used in slip-ring induction motors by adding external rotor resistance to obtain high starting torque.

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Numerical

Given:

• Slip, $s = 4\% = 0.04$
• Supply frequency, $f = 50 \text{ Hz}$

To find:

1. Rotor frequency, $f_r$
2. Synchronous speed, $N_s$

Solution:

Rotor frequency is given by

$$f_r = s f$$ $$f_r = 0.04 \times 50$$ $$f_r = 2 \text{ Hz}$$

Synchronous speed is given by

$$N_s = \frac{120 f}{P}$$

where $P$ is the number of poles. Since the number of poles is not given in the question, the synchronous speed cannot be determined uniquely. However, for a common 4-pole, 50 Hz induction motor:

$$N_s = \frac{120 \times 50}{4}$$ $$N_s = 1500 \text{ rpm}$$

The rotor speed would then be

$$N = N_s(1-s)$$ $$N = 1500(1-0.04)$$ $$N = 1500 \times 0.96$$ $$N = 1440 \text{ rpm}$$

Answer:

• Rotor frequency, $f_r = \boxed{2 \text{ Hz}}$
• Synchronous speed, $N_s = \boxed{1500 \text{ rpm}}$ (assuming a 4-pole motor)
• Rotor speed, $N = \boxed{1440 \text{ rpm}}$

Transient in an Alternator

A transient in an alternator (synchronous generator) is the sudden, short-lived change in stator current, terminal voltage, flux and power that occurs when the operating condition of the machine is abruptly disturbed — most commonly by a sudden short circuit, sudden load throw-off/throw-on, or sudden change in excitation. During this period the machine does not obey its steady-state (synchronous) equations; instead, flux linkages cannot change instantaneously, so induced currents appear in the damper (amortisseur) windings and in the field winding, and the machine behaves as if its reactance and time constant have changed.

Causes of transient occurrence

• Sudden three-phase short circuit at the terminals or on the line
• Sudden switching of a large load (load throw-on or load throw-off)
• Sudden loss of excitation or change in field current
• Faults cleared by circuit breakers, and subsequent reclosing
• Sudden change in prime-mover input (e.g., governor action)

Various transient periods

1. Sub-transient period — first few cycles (about 1 to 2 cycles, ~0.02–0.05 s) after the disturbance. Damper winding currents dominate; the machine is represented by the sub-transient reactance (X_d'') and sub-transient time constant (T_d'').
2. Transient period — next period, lasting about 0.5 to 1 s (roughly 5 to 30 cycles). Damper currents have decayed, but field-winding induced currents still dominate; the machine is represented by the transient reactance (X_d') and transient time constant (T_d').
3. Steady-state period — after the transient decays (a few seconds). Field current and armature reaction reach their final steady values; the machine is represented by the synchronous reactance (X_d).

Explanation of the sub-transient period (in detail)

When a sudden short circuit occurs at the alternator terminals, the armature current cannot rise instantly to its final value because the flux linking the damper winding and the field winding cannot change instantaneously (Lenz's law). The sudden tendency of the armature mmf to change the air-gap flux induces large circulating currents in the damper (amortisseur) bars, which are low-resistance paths. These induced currents produce an mmf that strongly opposes the armature reaction, so the effective armature reaction is almost completely neutralised for the first few cycles. The machine therefore behaves as if it has a very small reactance — the sub-transient reactance (X_d'') — and the initial rms short-circuit current is very large:

[ I'' = \frac{E_g}{X_d''} ]

where (E_g) is the internal generated emf (behind synchronous reactance) and (X_d'') is typically only about 10–20 % of the synchronous reactance (X_d). The sub-transient current decays rapidly with the sub-transient time constant (T_d'') (usually 0.02–0.05 s), as the damper-winding currents die out due to their resistance. After this decay the machine enters the transient period, where the field winding alone opposes the armature reaction and the current is governed by the larger transient reactance (X_d'). Finally, when the field transient also decays, the steady-state short-circuit current (I_{sc} = E_g / X_d) is reached.

The sub-transient period is important because it determines the peak and initial rms values of fault current, which decide the momentary and interrupting ratings of circuit breakers, the mechanical forces on windings, and the setting of protective relays.

Corona Effect (2 marks)

Corona effect is the partial ionization of the air around a high-voltage conductor, seen as a faint violet glow and heard as a hissing sound, with an ozone smell and a power loss. It occurs when the potential gradient at the conductor surface exceeds the dielectric strength of air (about 30 kV/cm peak, or 21.1 kV/cm rms, at NTP). Because the conductor spacing is much larger than the ionized zone, breakdown is only local, so the discharge is "partial".

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Methods of Minimizing Corona (3 marks)

Corona starts when the operating voltage exceeds the critical disruptive voltage $V_c$. The design aim is therefore to keep the surface gradient low and $V_c$ high.

1. Increase conductor diameter, using larger or hollow conductors. The surface gradient falls as the radius rises.
2. Use bundled conductors (2, 3 or 4 sub-conductors per phase). This raises the effective radius and cuts the gradient, as on Nepal's 220 kV and 400 kV lines.
3. Increase conductor spacing. Wider phase spacing lowers the electrostatic stress at the surface and raises $V_c$.
4. Keep the conductor surface smooth and clean. Remove nicks, burrs and sharp edges, and use corona rings or grading shields on fittings and insulator ends.
5. Do not raise the voltage beyond $V_c$. Choose the line voltage and conductor size together so that the operating voltage stays below $V_c$, with margin for foul weather.

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Factors Affecting Corona Loss (5 marks)

1. Supply voltage. There is no loss below $V_c$. Above it the loss rises roughly as $(V - V_c)^2$.

2. Conductor size. A larger radius gives a lower surface gradient and a higher $V_c$, so the loss is smaller.

3. Conductor spacing. Wider spacing raises $V_c$ and lowers the loss. Spacing enters $V_c$ through $\ln(D/r)$.

4. Air density. The loss increases as the air density factor $\delta$ falls. Low pressure (high altitude, for example the Himalayan lines) and high temperature both lower $\delta$ and so lower the dielectric strength of air: $\delta = \frac{3.92\,b}{273 + t}$ where $b$ is the pressure in cm Hg and $t$ is the temperature in °C.

5. Weather. Rain, fog, snow and dust lower $V_c$ and sharply raise the loss. Fair weather gives the least loss.

6. Surface condition. Rough, dirty or stranded surfaces create local high-stress points. This is covered by the irregularity factor $m_0$ (about 0.72 to 0.98, and 1 for a smooth polished conductor).

7. Supply frequency. The loss increases with frequency, as the $(f+25)$ term in Peek's formula shows.

8. Line configuration. Bundling lowers the loss compared with a single conductor.

Peek's formula

$P_c = 241\times10^{-5}\,\frac{f+25}{\delta}\sqrt{\frac{r}{D}}\,(V - V_c)^2\ \text{kW/km/phase}$ $V_c = m_0\, g_0\, \delta\, r \ln\frac{D}{r}\quad(\text{kV rms per phase, } g_0 = 21.1\ \text{kV/cm})$

Here $V$ and $V_c$ are phase voltages in kV rms, and $r$ and $D$ are in the same unit.

Behavior of Medium Transmission Lines

Voltage Regulation

A medium transmission line is one whose length is roughly 80–250 km and whose operating voltage is between 20 kV and 100 kV. At these lengths the shunt capacitance is no longer negligible (as in a short line), but is not large enough to be treated as a distributed parameter (as in a long line). The line is therefore modelled with lumped parameters, the most common being the nominal-π and nominal-T models.

For the nominal-π model:

$V_S = A\,V_R + B\,I_R,\qquad I_S = C\,V_R + D\,I_R$

where

$A = D = 1 + \frac{YZ}{2},\qquad B = Z,\qquad C = Y\left(1 + \frac{YZ}{4}\right)$

with $Z = R + jX$ the total series impedance and $Y = j\omega C$ the total shunt admittance.

Key points on voltage regulation:

• Regulation is defined as $\text{Regulation} = \frac{|V_{R(\text{no load})}| - |V_{R(\text{full load})}|}{|V_{R(\text{full load})}|}\times 100\%$
• Because of the shunt capacitance, the charging current leads the voltage and produces a Ferranti effect: at light load or no load the receiving-end voltage rises above the sending-end voltage. Regulation therefore becomes negative at light loads.
• At full load the series IR and IX drops dominate, so the receiving-end voltage falls; regulation is positive and worsens as the load power factor becomes more lagging.
• The regulation curve is therefore U-shaped: it is negative at light load, passes through zero at a certain load, and becomes increasingly positive as load increases. The capacitance thus improves regulation at heavy loads (partly compensating the inductive drop) but degrades it at light loads.

Power Transfer Capability

The power transferred over a medium line is governed by the generalized constants:

$P_R = \frac{|V_S||V_R|}{|B|}\cos(\theta_B - \delta) - \frac{|A||V_R|^2}{|B|}\cos(\theta_B - \theta_A)$

For a lossless medium line ($R=0$), this reduces to the familiar form

$P_R = \frac{|V_S||V_R|}{X}\sin\delta$

Important consequences:

• The steady-state stability limit (maximum power) occurs near $\delta = 90^\circ$ for a lossless line; the presence of shunt capacitance effectively reduces the effective series reactance, so the power transfer capability is higher than that of a short line of the same physical length.
• The charging current supplies part of the reactive power demand of the line itself, so less reactive power must be sent from the sending end — this improves the voltage profile and allows more active power to be delivered for the same thermal limit.
• However, the series resistance causes real power loss ($I^2R$), and the shunt conductance (leakage, corona) causes additional loss, both of which reduce the net power delivered at the receiving end.
• The surge impedance loading (SIL) concept becomes meaningful: when the line is loaded near its SIL, the reactive power generated by the shunt capacitance equals the reactive power absorbed by the series inductance, giving a flat voltage profile and maximum power transfer efficiency.

Challenges in Modelling Medium Lines and Their Impact on System Performance

1. Lumped versus Distributed Parameter Approximation

The nominal-π and nominal-T models assume the line parameters are lumped at a few points. In reality, resistance, inductance and capacitance are uniformly distributed along the line. The error introduced is small for lines up to about 250 km, but it grows with length. For accurate studies the line must be treated as a distributed parameter line using hyperbolic functions:

$V_S = V_R\cosh(\gamma l) + I_R Z_c\sinh(\gamma l)$

$I_S = \frac{V_R}{Z_c}\sinh(\gamma l) + I_R\cosh(\gamma l)$

where $\gamma = \sqrt{zy}$ and $Z_c = \sqrt{z/y}$. Using the lumped model beyond its valid range leads to underestimation of the Ferranti rise and overestimation of the stability limit, which can cause voltage collapse or unintended relay operation in practice.

2. Frequency Dependence of Parameters

Line resistance varies with frequency due to skin effect and proximity effect, and inductance and capacitance also vary slightly with frequency. Since power system studies involve harmonics and transient waveforms, a single set of 50 Hz parameters is insufficient. Ignoring frequency dependence causes errors in loss calculation, harmonic propagation studies and protection settings.

3. Non-Transposition and Unbalanced Parameters

In practice, conductors are not perfectly transposed, so the three phases have slightly different self and mutual impedances and capacitances. This produces negative- and zero-sequence components, causing:

• Voltage unbalance at the receiving end,
• Circulating currents in parallel lines,
• Errors in symmetrical component based protection.

4. Corona and Shunt Conductance

At medium voltages, corona loss and leakage are not negligible. Corona loss depends on weather, conductor surface condition and voltage gradient, and is highly variable. It is difficult to represent by a fixed shunt conductance $G$, yet it affects efficiency, radio interference and insulation design.

5. Temperature and Sag Effects

Conductor resistance increases with temperature, and sag changes the effective length and hence the capacitance and inductance. These effects are ignored in standard models but become significant in long-term thermal rating and dynamic line rating studies.

6. Impact on System Performance

• Voltage regulation: Inaccurate modelling of shunt capacitance leads to wrong prediction of the Ferranti rise, causing over-voltage at light load and possible insulation failure.
• Power transfer capability: Errors in $B$ and $A$ constants directly affect the computed stability limit; optimistic estimates may lead to operation beyond the true limit, risking loss of synchronism.
• Reactive power management: Under- or over-estimation of line charging affects reactive power compensation (capacitor/reactor sizing) and voltage control at substations.
• Protection and control: Incorrect sequence impedances cause maloperation of distance relays and unbalanced current protection.
• Economic operation: Inaccurate loss models lead to sub-optimal economic dispatch and load flow results.

Conclusion

Medium lines must be modelled with lumped parameters (nominal-π or nominal-T) for routine studies, but the limitations of this approach — distributed parameters, frequency dependence, unbalance, corona and weather effects — must be recognised. For accurate stability, voltage regulation and protection studies, distributed-parameter or multi-section models are preferred. Proper modelling ensures reliable voltage control, maximises power transfer capability and prevents maloperation of protective devices.

Switchgear is the set of switching, protective and isolating devices used to control and protect equipment in a power system. The main types differ in what current they can make and break.

1. Circuit breakers. A circuit breaker can make and break a circuit under normal load and fault conditions. It extinguishes the arc in oil (OCB), compressed air (ABCB), SF₆ or vacuum (VCB), and it is the main device that clears faults. Under relay control it opens automatically and can be reclosed after a fault.

2. Switches. A switch is operated by hand or remotely. A load-break switch can make and break normal load current but cannot interrupt fault current, so it is normally backed by a breaker or fuses. A plain switch has no arc-quenching ability and is used only where the current is negligible or the circuit is already dead.

3. Disconnectors (isolators). A disconnector cannot interrupt load or fault current. It is opened only after the breaker has cleared the current, and closed before the breaker is closed. It gives a visible air gap so staff can work safely on the isolated section.

4. Fuses. A fuse contains an element that melts when the current exceeds its rating, so it destroys itself to break the circuit. It is cheap, simple and fast, and is used for distribution transformers, capacitors and small feeders. It must be replaced after it operates and is not suitable for repeated operation.

In practice they work together. The breaker clears faults, the disconnector gives safe isolation, the load-break switch handles routine loads, and the fuse protects small equipment.

Load factor and diversity factor — relationship

Definitions

• Load factor of a system (or consumer) over a period: $m = \frac{\text{Average load over the period}}{\text{Maximum (peak) demand over the same period}} = \frac{P_{av}}{P_{max}}$

• Diversity factor of a group of consumers: $D = \frac{\text{Sum of individual maximum demands}}{\text{Maximum demand of the combined group}} = \frac{\sum P_{max,i}}{P_{max,group}}$

Derivation of the relation

Let there be $n$ consumers connected to the system, each with individual maximum demand $P_{max,i}$ and average load $P_{av,i}$ over the same period (say 24 hours or one year).

Total energy consumed by the group in the period $T$: $E = \sum_{i=1}^{n} P_{av,i}\,T$

Average load of the group: $P_{av,group} = \frac{E}{T} = \sum_{i=1}^{n} P_{av,i}$

Load factor of the group: $m_{group} = \frac{P_{av,group}}{P_{max,group}} = \frac{\sum P_{av,i}}{P_{max,group}}$

Now write each consumer's average load in terms of its own load factor, $P_{av,i} = m_i \, P_{max,i}$: $m_{group} = \frac{\sum m_i P_{max,i}}{P_{max,group}}$

Using the definition of diversity factor, $P_{max,group} = \dfrac{\sum P_{max,i}}{D}$: $m_{group} = \frac{D \sum m_i P_{max,i}}{\sum P_{max,i}}$

If all consumers have the same load factor $m$ (i.e. $m_i = m$ for all $i$), this reduces to the simple and important result: $\boxed{m_{group} = m \cdot D}$

Interpretation

• The diversity factor is always $\ge 1$ (individual peaks occur at different times, so the group peak is less than the sum of individual peaks).
• Hence the load factor of a group (or of the generating station) is higher than the load factor of any single consumer by exactly the factor $D$.
• Physically: diversity "fills in" the valleys between individual peak periods, raising the average load relative to the peak, i.e. improving the load factor.
• Conversely, a high load factor on a system implies good diversity among its consumers; a low diversity factor (peaks coinciding) pulls the system load factor down towards the individual consumer's load factor.

Example: Two consumers each with load factor $0.5$ and maximum demand $100\ \text{kW}$. If their peaks do not coincide and the group maximum demand is $160\ \text{kW}$, then $D = 200/160 = 1.25$ and $m_{group} = 0.5 \times 1.25 = 0.625$, which is greater than $0.5$ — confirming the relation.

Protection of a substation and its equipment from lightning strokes

A substation is the most vulnerable point on a power system because it is the terminal where overhead lines, transformers, busbars and switchgear meet. A lightning stroke can reach the substation in two ways:

1. Direct stroke on the busbar, gantry, transformer tank or line near the station.
2. Indirect stroke — a stroke to the line some distance away sends a travelling wave (surge) along the line into the substation.

Protection is therefore provided in two stages: shielding against direct strokes and diversion/discharge of surge voltages before they reach the equipment insulation. The basic principle is to give the surge an easy, low-impedance path to earth at a point where the resulting voltage is still below the insulation level (BIL) of the apparatus.

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1. Protection against direct strokes — overhead shielding

• Overhead earth wires (sky wires): One or two galvanised steel earth wires are strung above the line and above the substation gantries, connected to earth at every tower/structure. They intercept the stroke and conduct it to ground, so the phase conductors and equipment are shadowed. The zone of protection is found by the protective angle method (usually 30°–45°) or by the rolling sphere method.
• Lightning masts / spikes (Franklin rods): Tall earthed masts are erected around the switchyard, especially near the transformer, so that all live parts lie within the protected cone. The mast must be bonded to the station earth grid.
• Earthing screen / cage: In important substations a mesh of horizontal earth conductors is laid above the equipment, forming a Faraday cage that shields the yard from direct strokes.
• Proper earthing of structures, tanks and fences: All steel structures, transformer tanks, gantries and fences are bonded to the earth grid so that no dangerous potential difference appears.

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2. Protection against travelling waves — surge diverters

Even with shielding, surges arrive along the incoming overhead lines. These are handled by:

• Rod gaps (air gaps): A simple air gap between the line and earth. When the surge voltage exceeds the gap breakdown value, an arc forms and the surge is diverted to earth. Cheap but crude — the arc must be extinguished by the protective relay, and the gap setting drifts.
• Horn gaps: A rod gap shaped as horns so that the arc travels upward and lengthens, helping it to self-extinguish.
• Lightning arresters / surge diverters: The main protective device. They are connected between each phase and earth, as close as possible to the equipment to be protected (especially the transformer terminals). Two types are used:
  • Valve-type arrester: Series spark gaps in series with non-linear resistance (silicon carbide) discs. At normal voltage the resistance is high and only a small leakage current flows; on a surge the gaps spark over and the non-linear resistance drops sharply, discharging the surge to earth. When the surge passes, the resistance rises again and the gaps extinguish the power-frequency follow current.
  • Metal oxide (ZnO) arrester: Uses only non-linear ZnO blocks with no series gap. It is highly non-linear, so it conducts heavily on surge and almost nothing at normal voltage. It is now preferred because it is faster, simpler and has no gap to wear out.
• Surge capacitors: Connected phase-to-earth near the transformer to flatten the steep wavefront of the incoming surge, reducing the rate of rise (dv/dt) and thus the stress on the winding insulation.
• Surge absorbers: A combination of capacitor, inductance and resistance used to absorb the surge energy and reduce steepness.

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3. Co-ordination of insulation

The arresters are not placed at random. The protective level of the arrester (the voltage that appears across it while discharging) must be lower than the basic impulse insulation level (BIL) of the equipment, with a suitable margin. The arrester is located as near as possible to the transformer so that the surge voltage reflected between the arrester and the transformer does not exceed the insulation level. This is called insulation co-ordination.

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4. Other supporting measures

• Earthing system: A low-resistance earth grid (rod electrodes, buried conductors, counterpoise wires) is essential, because the arrester can only limit the voltage to the product of surge current and earth resistance. Earth resistance should be kept as low as practicable (about 1 Ω or less for large stations).
• Overhead earth wire on the incoming line: The last 1–2 km of the line is shielded and the tower footing resistance is kept low, so that most strokes are intercepted before reaching the station.
• Neutral earthing of transformer: The transformer neutral is solidly earthed, and a surge arrester may also be provided at the neutral for protection against surges transferred through the winding.
• Protective relays and breakers: These clear faults and prevent sustained power-frequency follow current from damaging the arrester or equipment.

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Conclusion

In short, a substation is protected from lightning by overhead earth wires and lightning masts against direct strokes, and by surge diverters (rod gaps, horn gaps and lightning arresters) together with surge capacitors against travelling waves, all supported by a low-resistance earthing grid and proper insulation co-ordination so that the surge voltage reaching the equipment is always kept below its insulation level.

Demand Side Management (DSM) — Common Techniques with Examples

Demand Side Management (DSM) is the planning, implementation and monitoring of utility activities designed to influence customer use of electricity so as to produce desired changes in the utility's load shape — i.e., to reduce or shift demand rather than only build new generation. In the Nepali context (NEA system), DSM helps cut peak load, defer capacity addition and reduce load-shedding.

The common techniques are grouped below.

1. Load Shifting (Peak Clipping by shifting)

Shifting flexible loads from peak hours to off-peak hours without reducing total energy use.

• Example: Nepal Electricity Authority's Time-of-Day (TOD) tariff for industrial consumers — higher energy charge during evening peak (e.g., 6–11 pm) and lower charge at night — encourages industries to run mills, pumps and compressors at night. Similarly, time switches on irrigation pumps shift pumping to off-peak hours.

2. Peak Clipping (Direct Load Control)

The utility remotely switches off or cycles non-essential customer equipment during system peak.

• Example: Direct Load Control (DLC) of domestic air-conditioners and water heaters through ripple control or smart meters; utility-owned standby diesel generators of large consumers being started during peak. In Nepal, large industrial loads can be asked to shed load under an interruptible load tariff in return for a rebate.

3. Valley Filling

Building up load during off-peak (valley) periods to improve load factor and utilise base-load plants better.

• Example: Promoting night-time electric vehicle charging, off-peak water pumping to storage tanks, and cold storage / ice-bank air-conditioning that cools at night and discharges during the day.

3. Strategic Conservation (Energy Efficiency)

Reducing total kWh consumption through efficient end-use devices — the "negawatt" approach.

• Example: LED bulb distribution / UJALA-type programmes, promotion of 5-star labelled appliances, IE3 premium-efficiency motors and variable frequency drives (VFDs) in industries, efficient irrigation pump sets. Result: lower demand at all hours.

4. Strategic Load Growth

Deliberately increasing off-peak sales to raise revenue and load factor.

• Example: Promoting electric cooking (induction stoves) and heat pumps in areas with surplus hydro energy, especially during monsoon when Nepal has surplus power.

5. Load Curtailment / Energy Saving during emergency

Planned reduction of load when supply is critically short.

• Example: Load-shedding schedules (historical NEA practice), demand-side bidding asking industries to cut load, and public appeals to reduce lighting during peak.

6. Flexible Load Shape / Smart Grid Techniques

Using automation, smart meters and pricing signals for real-time demand response.

• Example: Advanced Metering Infrastructure (AMI) with Real-Time Pricing (RTP) or Critical Peak Pricing (CPP); demand response aggregators curtailing load of a group of consumers within minutes. In Nepal, smart meters under NEA's AMI pilot allow remote load limiting.

7. Renewable / Distributed Generation at customer side

Customer-owned solar PV, net metering and captive generation reduce net utility demand.

• Example: Rooftop solar with net metering (NEA Net Metering Guideline, 2075) — a household or industry meeting part of its load locally, thereby reducing feeder demand at peak.

Summary Table

Conclusion: In Nepal, the most practical DSM tools are TOD tariff, energy-efficient appliances (LED, IE3 motors, VFDs), rooftop solar net metering and direct load control of air-conditioning — together they clip the evening peak, improve load factor and defer costly generation and transmission investment.

Step Potential and Touch Potential

Step Potential

Step potential is the potential difference that exists between two points on the earth's surface separated by a distance of one pace (about 1 metre) when fault current flows into the ground through an earthing electrode. A person standing near the earthing point with feet apart bridges these two points, and the voltage difference drives current through the body from one foot to the other, along a path that includes the legs and lower body.

If the current flowing into the earth is $I$ and the soil resistivity is $\rho$, the potential at a distance $x$ from the electrode (hemispherical electrode model) is:

$V_x = \frac{\rho I}{2\pi x}$

Hence the step potential between points at distances $x$ and $x+1$ m is:

$V_{step} = \frac{\rho I}{2\pi}\left(\frac{1}{x} - \frac{1}{x+1}\right)$

Step potential is maximum close to the electrode (where the potential gradient is steepest) and falls rapidly as distance increases. It is the main cause of fatalities to cattle and to people walking near a faulted tower or substation.

Touch Potential

Touch potential is the potential difference between the energised metallic structure (equipment enclosure, tower leg, or any metal part connected to the earthing system) and a point on the earth's surface within reach of a person's outstretched hand (about 1 metre). It is the voltage appearing across the hand and the feet when a person touches a faulted structure.

$V_{touch} = V_{electrode} - V_{x=1\,m} = \frac{\rho I}{2\pi}\left(\frac{1}{r} - \frac{1}{1}\right)$

where $r$ is the radius of the earthing electrode. Touch potential is dangerous because the current path is hand-to-feet, passing through the heart and other vital organs.

Permissible Limits

As per IEEE 80 / IS 3043, for a person of body weight 50 kg (with surface layer resistivity $\rho_s$):

$E_{step,50} = (1000 + 6\rho_s)\frac{0.116}{\sqrt{t_s}}$

$E_{touch,50} = (1000 + 1.5\rho_s)\frac{0.116}{\sqrt{t_s}}$

where $t_s$ is the fault duration in seconds. For 70 kg body weight the factor 0.116 is replaced by 0.157.

Mitigation Measures

1. Reduction of earth resistance — Use a low-resistance earthing system (multiple rods, ring earth, deep-driven electrodes, chemical/backfill compounds). Lower $I$ through the electrode reduces both step and touch potentials.

2. Increase the area of the earthing grid — A large mesh (grid) spreads the current over a wide area, flattening the potential gradient at the surface. This is the standard practice in substations.

3. Mesh/ground grid design — Provide closely spaced conductors at the periphery and adequate number of ground rods; keep mesh voltage and step voltage within limits as per IEEE 80 design procedure.

4. Surface layer (insulating) treatment — Spread a high-resistivity layer such as crushed stone/gravel (typically 75–100 mm thick, resistivity 2500–5000 Ω·m) over the surface. This increases contact resistance between feet and earth, raising the tolerable step and touch voltages.

5. Equipotential bonding (bonding mats) — Bond all metallic structures, fences, and equipment to the earthing grid so that no dangerous potential difference develops. Provide ground mats at operating handles and switchgear.

6. Insulated gloves, mats and tools — For operating personnel, use insulating mats and gloves as a secondary (personal) protection.

7. Restrict access and use barriers — Fence off high-gradient areas; use warning signs. Keep people and animals away from electrodes during faults.

8. Reduce fault current and clearing time — Fast-acting protective relays and circuit breakers reduce $t_s$, which directly reduces the permissible (and actual) energy dissipated in the body.

9. High-resistance surface near towers — In transmission line towers, provide gravel/stone layer or a ring earth to reduce step potential for people and animals.

10. Separate earthing — Keep the lightning earthing and the power earthing properly designed so that potential rise is controlled; use surge arresters and neutral grounding resistors to limit fault current.

Conclusion

Step potential acts between the two feet of a person on the ground, while touch potential acts between the hand and the feet when a person touches a faulted structure. Both arise from the potential gradient set up by fault current entering the earth. They are mitigated primarily by reducing earth resistance, enlarging and properly designing the earthing grid, providing an insulating surface layer, and bonding all metallic parts to a common equipotential system, supplemented by fast fault clearing and personal protective measures.

Switching Overvoltage and Its Generation in a Power System

Switching overvoltage (also called switching surge) is a transient overvoltage that appears across the insulation of system equipment when a circuit is deliberately switched — i.e., when a circuit breaker or isolator opens or closes, or when a fault is cleared. Unlike lightning overvoltage, which originates from an external source (the atmosphere), switching overvoltage originates within the system itself. Its magnitude is typically 2.5 to 3.5 times the peak value of the normal system voltage (sometimes up to 4 p.u. in EHV systems), and its waveform is oscillatory with a much longer front and duration (hundreds of microseconds to a few milliseconds) than a lightning surge (1–2 µs front). Because of this longer duration, switching overvoltages are more severe for internal insulation (transformers, bushings, cables) than for external air clearance.

How Switching Overvoltages Are Created

1. Energization (closing) of an unloaded line or capacitor bank: When a long transmission line or a capacitor bank is switched on, the voltage wave travels down the line and reflects at the open (receiving) end. The superposition of the incident and reflected waves can raise the receiving-end voltage to nearly 2 p.u., and with three-phase coupling and trapped charge effects it may reach 2.5–3 p.u. This is the most important source of switching overvoltage on EHV lines.

2. Interruption of small inductive currents (current chopping): When a circuit breaker interrupts a small inductive current (e.g., magnetizing current of an unloaded transformer or shunt reactor), the current is "chopped" before a natural current zero. The magnetic energy stored in the inductance, ½Li², is transferred to the capacitance of the circuit, producing a high-frequency oscillatory voltage of magnitude v = i·√(L/C), which can be several times the normal voltage.

3. Interruption of capacitive currents (capacitor bank / unloaded line switching): When a capacitor bank or unloaded line is disconnected, the capacitance retains its charge (trapped charge). If the breaker restrikes during the recovery voltage, the capacitor voltage can build up cumulatively — each restrike adding to the trapped charge — producing overvoltages up to 3–4 p.u. across the breaker contacts.

4. Fault clearing and restriking: When a fault is cleared, the sudden interruption of a large current causes an oscillatory transient (transient recovery voltage) across the breaker contacts and along the line. If the breaker restrikes, travelling waves are set up that can double the voltage at points of reflection.

5. Load rejection: Sudden loss of load causes the generator to speed up (voltage and frequency rise) and the Ferranti effect on the line raises the receiving-end voltage, giving sustained overvoltage.

6. Out-of-phase switching and single-pole reclosing: Reclosing a line with trapped charge, or closing out of phase, can produce a voltage step of nearly 2 p.u. which then doubles at the open end.

Protection of the System and Installations Against Switching Overvoltage

1. Surge arresters (metal-oxide / ZnO arresters): The primary protective device. A surge arrester is connected between each phase and earth at the line entrance to substations and near transformers. It presents a very high resistance at normal voltage (negligible leakage) but becomes highly conducting when the voltage exceeds its protective level, discharging the surge energy to earth and limiting the voltage across the equipment insulation to a safe value. Modern gapless ZnO arresters have a flat, well-defined protective characteristic and are widely used on EHV systems.

2. Switching overvoltage control by circuit breakers:

   • Pre-insertion resistors: A resistor (typically 400–1200 Ω) is inserted in series with the breaker contacts for a few cycles during closing, damping the travelling-wave oscillations and reducing the overvoltage to about 1.5–2 p.u.
   • Controlled/synchronized closing: The breaker is closed at the instant when the supply voltage is near zero, minimizing the trapped charge and the resulting overvoltage.
   • Single-pole or three-pole reclosing with a delay to allow trapped charge to decay before reclosing.
   • Resistor or reactor switching to limit current chopping and restriking.

3. Damping circuits and drain coils: On long EHV lines, shunt reactors with neutral grounding resistors, or surge-impedance damping resistors, are used to absorb the trapped charge and reduce the oscillatory overvoltage.

4. Shunt capacitors and shunt reactors: Shunt reactors compensate the Ferranti effect and reduce sustained overvoltage on long lines; shunt capacitors are switched in steps to keep voltage within limits.

5. Insulation coordination: The insulation levels of transformers, bushings, cables and switchgear are chosen (BIL/SIL) so that they are higher than the arrester protective level by a suitable protection margin, ensuring the insulation is never stressed beyond its withstand value. The basic impulse insulation level (BIL) and switching impulse level (SIL) are selected accordingly.

6. Earthing (grounding) of the neutral: Solid or low-resistance neutral grounding reduces the overvoltage on the healthy phases during a single line-to-ground fault and limits the switching surge magnitude.

7. Shielding and surge capacitors: Overhead earth wires shield against lightning; surge capacitors connected at transformer terminals slow down the steepness of the incoming surge front (reduce dv/dt), protecting the winding insulation from steep-fronted switching surges.

8. Transformer protection: Surge diverters/arresters at transformer terminals, together with inter-turn insulation designed for the expected switching surge, protect the transformer. Neutral grounding resistors and surge capacitors are also used.

9. Operating practices: Avoiding energization of long lines from the weak end, using series capacitors to reduce the effective line length and hence the surge magnitude, and reclosing only after the trapped charge has decayed are operational measures.

By combining surge arresters, controlled switching, damping resistors/reactors and proper insulation coordination, the system and its installations are kept safe against switching overvoltages.