Supply System & Per Unit System | Power Systems - Electrical Engineering (EE) PDF Download

Introduction to Power System

Power generation systems are power generators and related systems that are used in power plants or large-scale facilities. When applying an AC drive and motor to an application; the characteristics of the drives load such as horsepower, torque and speed occur.

Electric power supply system in a country comprises of generating units that produce electricity; high voltage transmission lines that transport electricity over long distances; distribution lines that deliver the electricity to consumers; substations that connect the pieces to each other; and energy control centers to coordinate the operation of the components.

Transmission and Distribution Lines

• The power plants typically produce 50 cycle/second (Hertz), alternating-current (AC) electricity with voltages between 11kV and 33kV. At the power plant site, the 3-phase voltage is stepped up to a higher voltage for transmission on cables strung on cross-country towers.
• High voltage (HV) and extra high voltage (EHV) transmission is the next stage from the power plant to transport A.C. power over long distances at voltages like; 220 kV & 400 kV. Where transmission is over 1000 kM, high voltage direct current transmission is also favoured to minimize the losses.
• Sub-transmission network at 132 kV, 110 kV, 66 kV or 33 kV constitutes the next link towards the end user. Distribution at 11 kV / 6.6 kV / 3.3 kV constitutes the last link to the consumer, who is connected directly or through transformers depending upon the drawn level of service.

 Cascade Efficiency

• The primary function of transmission and distribution equipment is to transfer power economically and reliably from one location to another. 
• Capacitors are used to correct power factor by causing the current to lead the voltage. When the AC currents are kept in phase with the voltage, operating efficiency of the system is maintained at a high level. Circuit-interrupting devices are switches, relays, circuit breakers, and fuses. Each of these devices is designed to carry and interrupt certain levels of current.
• Making and breaking the current carrying conductors in the transmission path with a minimum of arcing is one of the most important characteristics of this device. Relays sense abnormal voltages, currents, and frequency and operate to protect the system.
• Transformers are placed at strategic locations throughout the system to minimize power losses in the T&D system. They are used to change the voltage level from low-to-high in step-up transformers and from high-to-low in step-down units.
• The power source to end-user energy efficiency link is a key factor, which influences the energy input at the source of supply. If we consider the electricity flow from generation to the user in terms of cascade energy efficiency, typical cascade efficiency profile from generation to 11 – 33 kV user industry will be as below:

Single line representation of power system 

Trying to represent a practical power system where a lot of interconnections between several generating stations involving a large number of transformers using three lines corresponding to R, Y, and B phase will become unnecessary clumsy and complicated. To avoid this, a single line along with some symbolical representations for generator, transformers substation buses are used to represent a power system rather neatly.

Distribution System

• Till now we have learnt how power at somewhat high voltage (say 33 kV) is received in a substation situated near load center (a big city). Loads of a big city are primarily residential complexes, offices, schools, hotels, street lighting etc.
• These types of consumers are called LT (low tension) consumers. Apart from this, there may be medium and small scale industries located in the outskirts of the city. LT consumers are to be supplied with single phase, 220 V, 40 Hz. We shall discuss here how this is achieved in the substation receiving power at 33 kV.
   Power receive at a 33 kV substation is first stepped down to 6 kV and with the help of underground cables (called feeder lines), power flow is directed to different directions of the city. At the last level, step down transformers are used to step down the voltage from 6 kV to 400 V. These transformers are called distribution transformers with 400 V, star connected secondary. 

Per Unit System

It is usual to express voltage, current, volt-amperes and impedance of an electrical circuit in per unit (or percentage) of a base or reference values of these quantities. The Per Unit System Definition value of any quantity is defined as:

Consider first a single-phase system. Let 

Base Volt-Ampere = (VA)_B VA

Base Volt = (V)_B

So Base Current I_b = (VA)_B/(V)_B Amp

Base Impedance Zb= (V)_B/I_b = {(V)_B}²/(VA)_B Ohm

If the actual impedance is Z (ohms), its Per Unit Value value is given by

For a power system, practical choice of base values are:

Base Megavolt-Ampere = (MVA)_B 

OR Base Kilovolt-Ampere = (kVA)_B

Similarly Base kilovolt = (kV)_B

In a three-phase system rather than obtaining the Per Unit System values using per phase base quantities, the per unit values can be obtained directly by using three-phase base quantities. Let

Three-phase base Mega Volt-amperes = (MVA)_B

Line-to-line base kilovolts = (kV)B

Assuming star connection (equivalent star can always be found),

When MVA base is changed from Old (MVA)_B, to New (MVA)_B, B, new, and kV base is changed from (KV)B old, Old  to (kV)B new, new, the new per unit impedance

Per Unit Representation of a Transformer

• It has been said a three-phase transformer forming part of a three-phase system can be represented by a single-phase transformer in obtaining per phase solution of the system.
• The delta connected winding of the transformer is replaced by an equivalent star so that the transformation ratio of the equivalent single-phase transformer is always the line-to-line voltage ratio of the three-phase transformer.

For a transformer

Z_1(p.u) = Z_2(p.u) = Z_(p.u)

which shows that the per unit transformer impedance of a transformer will remain same in either side of the transformer.

Per Unit Impedance Diagram of a Power System

From a one-line diagram of a power system we can directly draw the impedance diagram by following the steps given below:

1. Choose an appropriate common MVA (or kVA) base for the system.
2. Consider the system to be divided into a number of sections by the Choose an appropriate kV base in one of the sections. Calculate kV bases of other sections in the ratio of transformation.
3. Calculate per unit values of voltages and Impedance in each section and connect them up as per the topology of the one-line diagram. The result is the single-phase per unit impedance diagram.
   

Advantages of Per Unit System

There are mainly two advantages of using the Per Unit System.

• The parameters of the rotating electrical machines and the transformer lie roughly in the same range of numerical values irrespective of their ratings if expressed in per unit system of their ratings.
• It relieves the analyst of the need to refer circuit quantities to one or other side of the transformer, making the calculations easy.
• In per unit system, the quantities on single phase basis & three phase basis will remain same.
• Per unit impedance of the transformer will remain same in either side of the transformer.

Power Generation and Load Characteristics

Hydro Power Plant

The generated electric power (P) in a hydropower plant is given by
 

where, Q = Discharge in m³/S

H = Water head in metre
η = Efficiency of plant
Power output of tidal scheme

P = Q_pgH in watt

where, Q = Quantity of water flow in m³/s
p = Density of sea water = 1025 kg/m³
g = Acceleration due to gravity = 9.81 m/s²
H = Water head in meter

Specific Speed of Turbine

Specific speed of a turbine is the speed of a scale model of turbine which develops 1 metric horse power under head of 1 m.

where, Ns = Specific speed in metric unit
N = Speed of turbine in rpm
P1 = Output in metric horse power
H = Effective head in meter

A Classification of Turbines According to Range of Head and Specific Speed

Nuclear Power Plant

The nuclear power plant is only the source which can supply the future energy demands of the world. The nuclear power plant use nuclear fission process in which atomic weight material nucleus splits into metals of lower atomic weight and releases the huge amount of energy

There are following main parts of nuclear plant

1. Nuclear reactor
2. Heat exchanger
3. Steam turbine
4. Condenser
5. Alternator

Fuel the radioactive element are used as fuel in the reactor. Generally, U235 and Pu239 are used as fuel.

Moderator Graphite, heavy water and beillium can be used as moderator. Control rods The most common used materials for control rods are cadmium, boron and helium.

The load characteristics depends upon the following factors

Demand Factor = Maximum demand / Total connected load

• Demand Factor is always changed with the time to time or hours to hours of use and it will not constant.
• The connected load is always known so it will be easy to calculate the maximum demand if the demand factor for a certain supply is known at different time intervals and seasons.

The word “demand” itself says the meaning of Demand Factor. The ratio of the maximum coincident demand of a system, or part of a system, to the total connected load of the system.

Average Load or Average Demand

Load Factor

Group Diversity Factor

Utilisation Factor

Capacity Factor
 

or
 

Load Factor

Plant Capacity

Ferranti Effect

• In general practice we know, that for all electrical systems current flows from the region of higher potential to the region of lower potential, to compensate for the potential difference that exists in the system.
• In all practical cases the sending end voltage is higher than the receiving end, so current flows from the source or the supply end to the load. But Sir S.Z. Ferranti came up with an astonishing theory about medium or long distance transmission lines suggesting that in case of light loading or no load operation of transmission system, the receiving end voltage often increases beyond the sending end voltage, leading to a phenomena known as Ferranti effect in power system.

Corona

Electric-power transmission practically deals in the bulk transfer of electrical energy, from generating stations situated many kilometers away from the main consumption centers or the cities. For this reason the long distance transmission cables are of utmost necessity for effective power transfer, which in-evidently results in huge losses across the system. Minimizing those has been a major challenge for power engineers of late and to do that one should have a clear understanding of the type and nature of losses. One of them being the corona effect in power system, which has a predominant role in reducing.

Factors Affecting Corona

The phenomenon of corona is affected by the physical state of the atmosphere as well as by the conditions of the line. The following are the factors upon which corona depends :

• Atmosphere: As corona is formed due to ionisation of air surrounding the conductors, therefore, it is affected by the physical state of atmosphere. In the stormy weather, the number of ions is more than normal and as such corona occurs at much less voltage as compared with fair weather.
• Conductor size: The corona effect depends upon the shape and conditions of the conductors. The rough and irregular surface will give rise to more corona because unevenness of the surface decreases the value of breakdown voltage.
• Spacing between conductors: If the spacing between the conductors is made very large as compared to their diameters, there may not be any corona effect. It is because larger distance between conductors reduces the electrostatic stresses at the conductor surface, thus avoiding corona formation.
• Line voltage: The line voltage greatly affects corona. If it is low, there is no change in the condition of air surrounding the conductors and hence no corona is formed. However, if the line voltage has such a value that electrostatic stresses developed at the conductor surface make the air around the conductor conducting, then corona is formed.

Critical disruptive voltage: It is the minimum phase-neutral voltage at which corona occurs. Consider two conductors of radii r cm and spaced d cm apart. If V is the phase-neutral potential, then potential gradient at the conductor surface is given by

where 

g₀ =  breakdown strength of air at 76 cm of mercury and 25⁰C  
= 30 kV/cm (max) or 21.2 kV/cm (r.m.s)

∴ Critical disruptive voltage, 

Correction must also be made for surface condition of the conductor. This is accounting for multiplying the above expression by irregularity factor m_o.

∴ Critical disruptive voltage 

where mo = 1 for Polished Conductor
= 0.98 to 0.92 for Dirty Conductor
= 0.87 to 0.80 for Stranded Conductor

Visual Critical Voltage

It is the minimum phase neutral voltage at which corona glow appears all along the line conductor. It has been seen that in case of parallel conductor the corona glow does not glow at the Disruptive Voltage V_c but at higher voltage called Visual Critical Voltage.

Power Loss Due to Corona

f = frequency of the Supply
V_c = Critical Disruptive Voltage(r.m.s)
V = Phase to Neutral Voltage (r.m.s)