Negative resistance is a phenomenon seen in many non-linear electronic devices.  In this phenomenon, the current increases as the voltage decreases and vice versa.

This is in opposition to Ohm's law, which states that the current should vary linearly with the voltage.  This phenomenon is seen in electronic components, such as the Gunn diode, the tunnel diode and thyristors.

The fluorescent tube light is an example for negative resistance, when conduction starts, the current rises to a high level.  This is accompanied by a drop in voltage, causing the negative resistance.  To prevent the high current from damaging the device, an inductance (ballast) is connected in series.

There are no negative resistance components, such as resistors.  Certain devices exhibit negative resistance in a particular region of the VI curve.

Power system stability is the stability of a system to respond to disturbances in the system.  Power system stability is also known as synchronous stability.  Power system stability is classified into three types.

They are

  • Steady state stability
  • Transient stability
  • Dynamic stability

Steady state stability is the stability of the system to respond during minor disturbances during normal operations.  The variation in the bus voltages and the phase angles are relatively small.  Steady state stability is caused by switching small loads.

Transient stability, on the other hand, is the analysis of the response of the system to sudden and large variations in the system voltage and phase angles.  This kind of variation is caused by a sudden fault or overload, caused by a tripping of a power source.

Power flow studies need to be conducted to study the response of a power system to steady state and transient faults.

Dynamic stability is the stability which is maintained against small variations.  These variations can coalesce into large variations which can cause large fluctuations and tripping.  Dynamic stability is ensured by the use of sophisticated control equipments.

Bentonite is a naturally occurring clay.  It is used to reduce the earth resistance in earth pits.  Bentonite has the property of absorbing water. 

Bentonite is mixed with ordinary clay and placed between the earthing conductor and the earth.  Water is poured into the mixture.  Bentonite expands to many times it size as it absorbs water.

The earth resistance is reduced due to the water absorbed by Bentonite.  Bentonite will also absorb rain water and retain it for longer than the surrounding soil.  Bentonite earth pits may require water to be poured into the pit during dry seasons.  Special funnels are usually provided in these earth pits for this purpose.

The downsides are that Bentonite has many corrosive impurities, which may corrode the earthing conductors.  This may require periodic maintenance of the earth pits.

PCC (Prestressed Concrete Poles) are poles used in the tranmission and distribution of power.

PCC poles are made by placing high tensile wires in moulds.  The wires are stressed by stretching mechanisms which pull the wires apart.  When the wires are in this stressed condition, concrete is poured into the mould.  After the concrete sets, the wires are released.

A galvanized wire is run through the metal frame to provide for earthing.  This wire is connected to the earthing network.

The concrete is thus prestressed.  This kind of concrete can withstand impact and has high tensile strength.

PCC poles are more expensive than RCC poles.  They are aesthetically pleasing.  They can be manufactured at the site itself.  This will save transportation costs.

RCC (Reinforced Concrete Poles) are widely used in distribution system.  They are made of concrete with a metal reinforcement.

RCC poles are used as their are aesthetically pleasing and blend in well in urban areas with streets with buildings.

RCC poles are cheaper.  They can also be constructed at the site itself.  This reduces the cost of transportation.

RCC poles also have a long life and require less maintenance.  Sometimes, the concrete may chip and become porous.  In such conditions, water may percolate through the concreate and reach the metal reinforcement.  This can cause corrosion.

A downside is that RCC poles tend to shatter when a vehicle collides with them.  This can be prevented with the use of PCC (Prestressed Cement Concrete) poles.

Earth mat is a method of earthing,  It is used in areas with rocky soil, where it is difficult to excavate earth pits.  The earth resistance obtained with pits will also be above the required value.

Earth mats obtain the earth resistance with a large contact area.  The earth mats consists of a number of flat strips laid in the form of a grid.  The grid is placed in a trench which is about 75 cms deep.  The flats are made of mild steel and are of 75 x 8 mm size. 

The flats are welded to one another.   The low resistance is achieved by the increased contact area this method provides.

The earth resistance should ideally be less than 1 ohm.  The resistance value should be periodically checked and recorded.

Earth pits are a very widely used method of earthing electric systems.  Earth pits provide a very low earth resistance and are very reliable.

The earth pit is constructed as follows:

Excavate a pit of approximately the following dimensions 70cms x 70 cms x 250 cms. 

Place a cast iron pipe electrode that is 2.5 metres long and of size 75 -125 mm diameter.  The pipe should be about 10 mms thick.

The pipe is placed vertically. 

A mixture of Bentonite and black cotton soil is mixed in the ratio of 1:6.  The pipe is filled with this mixture.  The space surrounding the pipe is also filled with this mixture.

The earth pit is an important part of any earthing scheme.  It should be maintained properly at regular intervals.  Earth resistance measurements should be taken periodically.

Load Forecasting is an important function in power system operation.  Load forecasting is projecting the estimated load in advance.  Load forecasting can be done for a range of time periods from a few hours to many years. 

Load forecasting is done to decide which power generating units need to be taken in line in a certain period of time.  This is done to determine the best mix of generating units which will give the lowest cost of generation. 

The maintenance activities of the various power plants are also planned based on the load forecasting.  Investments for new power plants which may be required a few years down the line are also planned based on the load forecasting.

The load forecasting is done using historical data and factors, such as seasonal variations, projected economic activity, population growth, etc

Shunt Capacitors Series Capacitors 
 Shunt Capacitors are used to improve the power factor of the system. They are used to offset the effect of the series reactance in the line.
 Shunt capacitors are not effective in situations where
the line reactance of the line is high.
 Series capacitors are useful in conditions of high series reactance.
 Shunt Capacitors are connected as a single bank
connected to the bus or individually near the loads.
 Series Capacitors are connected in series with the load

A bus is a set of conductors in which electrical power flows and is then distributed to different lines.
In Power Flow Analysis, buses are classified into three main types.

They are
  • The Generator Bus
  • The Load Bus and the 
  • Slack, Swing or Reference bus
The Generator Bus
As the name suggests, the generator bus is the bus producing power.  For the generator bus, the values of P, the active power and the voltage, V are given.  The reactive power, Q and the load angle, delta should be found.

The Load Bus
The load bus consumes active and reactive power.  For this bus, the active power, P and the reactive power, Q are given.  The voltage and the phase angle should be calculated.

The Swing Bus
The swing bus is the bus which has been made to take the additional active and reactive power which are used to supply the transmission losses.  Therefore, the active and reactive powers are unknown for this bus.  Only the voltage,V and the load angle, delta are given.

Bus TypeQuantities Specified Quantities to be found 
 Generator Bus P,V Q, load angle
 Load Bus P,Q V, load angle
 Swing Bus V, load angle P,Q

Static Compensators are electric circuits which are used to compensate the surge impedance in a circuit.  They are also used for load compensation.  Static compensators are used to maintain a constant voltage during varying loads.  They are also used during sudden reduction in the loads or during tripping of the source. 

Static Compensators improve the power factor and,consequently, the system stability

A simple static compensator consists of an variable inductor and a capacitor connected in parallel.  The reactive power in the system can thus be compensated using these two elements.

Thyristors are often used in series with the inductor and compensator to precisely control the reactor power flow to and from the static compensator. 

A load curve is a plot of the load in a network against time.  Load is plotted along the Y axis and time on the X-axis.

The curve shows the variation of load with time.  There can be daily load curves, monthly load curves and yearly load curve.

The area under the load curve shows the total units generated.  The tallest point in the curve shows the maximum demand.  The average load can be deduced by dividing the area under the curve by the total number of hours.

The load factor can be calculated by dividing the area under the curve by the area of the rectangle enclosing the curve.

A Load Duration curve (LDC) is a curve formed by placing the loads in descending order of their magnitude.

The curve is essentially a bar graph.  Each bar represents a specific load.  The taller bars indicating the higher loads are placed to the left.  The area under the load curve indicates the total units generated. 

The Load Duration Curve can be used in economic dispatching, system planning and reliability.

If the load on a power system is not constant but has steep variations, the cost of power generation will increase. 

More generators will have to be connected to handle the high peak loads of the system.  These generators will be idle when the load drops or they may have to operate at low loads.  This will reduce the efficiency of the prime mover and increase the fuel costs.

Increase in capital cost

More generators will have to be added to deliver the peak load.  This will result in higher capital cost.

Load - Definition

An Electrical Load is any device or component that taps energy from an electrical network.  Examples of domestic loads are domestic appliances, such as bulbs, fans and air conditioners.  Industrial loads include motors, heaters and lighting loads.

Electric loads have a range of power ratings from very low bulbs to motors which draw megawatts of power.

The vast majority of electric loads are motor loads.  The following is a classification of the types of electric loads and their quantity.

Motor devices                     - 70%
Heating and lighting loads  - 25%
Electronic devices               - 5%

Sensitivity to voltage and frequency variations

Loads are sensitive to both voltage and frequency

Motor loads are sensitive to both frequency and the voltage variations. A change in the frequency can cause the motor speed to increase or decrease.  Motor speed is directly proportional to the frequency.

When the voltage drops, a motor draws more current.  The power drawn varies as the square of the voltage.  Power is proportional to V2

Loads can be further classified based on the size, number of phases (single or three phase), and the duty cycle (constant use or intermittent use)

The Load Flow Analysis is done to determine the flow of real and reactive between different buses in a power system.  It also helps in determining the voltage and current at different locations.

To conduct a Load Flow Analysis, the components in a power system need to be modelled.  The modelling is done by developing equivalent circuits of the components, such as the generator, transmission lines and line capacitances.

The Generator equivalent circuit is shown below.

The Thevenin equivalent circuit is as shown below.

This consists of a voltage source and a resistance and an inductance in series with the load.

E = V + IZ


Z is the steady stage impedance
V is the voltage and
I is the current

The Norton equivalent circuit

The Norton equivalent circuit consists of a power source and an admittance in parallel.

INorton = V/Z

INorton = YV


The load is modelled as a resistance and inductance in a series circuit that is earth

Transmission lines

Transmission lines are modelled as

Short transmission lines (less than 80 km)

Short lines that are less than 80 kms long are modelled as a resistance and reactance in series with the load.  The line capacitances are neglected.

Medium (80 to 250 km)

Medium lines are modelled as a resistance and reactance in series.  The admittance is in parallel in two sections.

Long lines ( 250 km and above)

Long lines are also modelled as a resistance and reactance in series.  The admittance is in parallel in two sections.