Methods of Solving A.C. Distribution Problems

As discussed in earlier section of a.c. distribution system we have take into account the power factor. This power factor can be either considered with respect to receiving end voltage or with respect to load voltage itself. Let us consider each case separately.

1.1 Power Factors Referred to Receiving End Voltage 

       Consider an A.C. distribution PQ having concentrated loads of I₁ and I₂ tapped off at point Q and R respectively. This is shown in the Fig. 1.

Fig. 1

     

A.C. Distribution Calculations

The A.C. distribution calculations and d.c. distribution calculations are different in the following respects :

1. In case of d.c. system, the voltage drop is due to resistance only which in a.c. system it is due to combined effect of resistance, inductance and capacitance.

2. The voltages or currents are added or subtracted arithmetically in case of d.c. system whereas they are added or subtracted vectorially in case of a.c. system.

3. It is required to take into account the power factor while making calculations in a.c. system which is absent in d.c. system. The distributors are normally tapped at different points with the loads having different power factors.

   

A.C. Distribution

In earlier days, d.c. system was used for the generation, transmission and distribution of electrical energy. But in case of d.c. system the voltage level cannot be changed easily unless we used rotating machinery which may not prove to be economical in many cases. This is the major disadvantages while working with d.c.

       Later on with the development of transformer, a/c/ system has become predominant. Now days a large power systems in the world are using a.c. system rather than d.c. because of many advantages of a.c. system.

       The transmission of electrical energy generated in the power station is at very high voltage with the use of 3 phase, 3 wire system. These voltages are stepped down for distribution at the substations. There are mainly two parts of the distributor system. They are primary distribution and secondary distribution. The voltage level of primary distribution system is higher than general utilization level. The secondary distribution systems receive power from primary distribution systems through distribution transformers. By distribution transformer voltage is stepped down to the normal working level and the consumers get the power with the voltage 400/230 V. The very commonly used a.c. distribution system is three phase four wire system as studied earlier.

Ring Main Distributor With Interconnector

It has been mentioned that in ring main system, the cable is arranged in the loop or ring fashion. In most simple case, the ring distributor is fed at only one point.

       But sometimes the ring main system is used to supply a large area and hence voltage drop across the various sections may become large in such case. Hence to compensate for such excessive voltage drops, the distant points of ring distributor are joined together by a conductor. This is called an interconnector. The Fig. 1 shows a ring main system with an interconnector.

Fig. 1

       The points D and G are joined by an interconnector.

       Such a case is generally analysed using Thevenin's theorem.

       Let us briefly revise the steps to use the Thevenin's theorem.

       The steps to use Thevenin's theorem :

1. Remove an interconnector DG.

2. Find the voltage V_DG without an interconnector, which is Thevenin's voltage denoted as E_o.

3. Determine the equivalent resistance as viewed through the terminals D and G, i.e. where an interconnector is to be connected. This is Thevenin's equivalent resistance denoted as R_TH.

4. Knowing the resistance of an interconnector DG, the Thevenin;s equivalent can be drawn as shown in the fed Fig. 2.

Fig. 2

5. The current I through an interconnector then can be obtained as,

       Once this current is known, current in all the sections and the voltages at load points can be determined.

D.C. Distributor With Distributed Load

This type of distributor is also classified as,

1. Distributor fed at one end

2. Distributor fed at both the ends

1.1 Distributor Load Fed at One End

      The Fig. 1 shows the single line diagram of uniformly distributed load on two wire distributor, fed at one end.

Fig. 1

     

D.C. Distributor With Concentrated Loads

This distributor is further classified as,

1. Fed at one end.

2. Fed at both the ends.

Types of D.C. Distributors

 It has been mentioned that the d.c. distributors are fed at one end or at both the ends. The voltages used to feed the distributors at both the ends may be equal or unequal. Such distributors fed at one end or both ends, with equal or unequal voltages are connected to the loads. In practice, the loads on the distributors may be concentrated or distributed.

       The loads which are acting at particular points of the distributor are called concentrated loads. The domestic load tapped at a particular point of distributor is a good example of concentrated load.

       The loads which spread over the particular distance of the distributor are called distributed loads. Practically no load is distributed in the true sense. But if number of loads having same power consumption are connected to the distributor, very close to each other then the effective load on the distributor is treated to be uniformly distributed load.

D.C. Three Wire System

It is known that higher the voltage level, lower are the transmission losses. But in case of d.c. distribution, level cannot be increased readily like a.c. Using rotating machinery, the d.c. voltage level can be increased but the method is too expensive. The d.c. three wire system can be used to double the transmission voltage, without increasing the voltage between either conductor and earth. The higher voltage demand also can be satisfied using d.c. three wire distribution system.

     

Ring Main Distribution System

Another system of distribution which eliminates the disadvantages of the radial system is used in practice called ring main distribution system.

       In such system, the feeders covers the whole area of supply in the ring fashion and finally terminates at the substation from where it is started. The feeder is in closed loop from and looks like a ring hence the name given to the system as ring main system. This is shown in the Fig. 1.

       The feeder in the ring fashion is divided into number of sections as AB, BC, CD, DE and EA. The various distributors are connected at A, B, C, D and E. Each distributor is supplied by the two feeders and hence the design is similar to the two feeders in parallel on different paths. Hence if there is any fault on any part of the feeder, still the consumers will keep on getting the continuous supply. For example, if the fault occurs at point P in the section AB of the feeder can be isolated and repaired. The feeder can be fed at one or more feeding points. Thus the disadvantages of radial system are eliminated in this system. The great saving in copper is another major advantage of the ring main system.

Radial Distribution System

The Fig. 1 shows a radial distribution system.

       When the distributor is connected to substation on one end only with the help of feeder, then the system is called radial distribution system. The feeders, distributors and service mains are radiating away from the substation hence name given as radial system. There are combinations of one distributor and one feeder, connecting that distributor to the substation. In Fig. 1, distributor 1 is connected only at one end to substation through a feeder at point A. Similarly the other feeder is feeding the distributor 2, only at one point B.

Fig. 1 Radial distribution system

     

General D.C. Distribution System

The Fig. 1 shows a general distribution system in d.c. form where d.c. generators are used at the generating stations.

Fig. 1  General D.C. distribution system

       As explained earlier, the feeders are used to feed the electrical power from the generating stations to the substations. The distributors are used to distribute the supply further from the substations. The service mains are connected to the distributors so as to make the supply available at the consumers permises. This is the simplest two wire distribution system used to supply the consumers. One more type of d.c. distribution system is also used in practice which is d.c. there wire system. Though for d.c. distribution, mainly two systems are used, the various types of distributors are used in these systems.

Requirements of a Good Distribution System

The necessary requirements of a good distribution system are,

1. The continuity in the power supply must be ensured. Thus system should be reliable.

2. The specified consumer voltage must not vary more than the prescribed limits. As per Indian Electricity Rules, the variation must not be beyond ± 5 % of the specified voltage.

3. The efficiency of the lines must be as high as possible.

4. The system should be safe from consumer point of view. There should no be leakage.

5. The lines should not be overloaded.

6. The layout should not affect the appearance of the site or locality.

7. The system should be economical.

     

Economic Choice of Transmission Voltage

The cost of conductor material required can be reduced with reduction in volume of conduction           material which is possible with increase in transmission voltage. The volume of conductor material is inversely proportional to transmission voltage as seen in previous posts. So it may be economical from point of view of cost of conductor material to go for maximum possible transmission voltage.

     

Comparison of different transmission systems

The comparison of different transmission systems based on the volume of material required is summarized below in table 1.

       Though D.C. system is more economical, due to practical difficulties three phase a.c. system is used for the transmission and distribution.

Comparison of Volume of Copper in Underground System

In case of underground system, the maximum stress exists between the line conductors. Hence the various assumptions for such comparison are,

1. The maximum voltage (V_m), between the conductors is same.

2. The power (P) transmitted in all the systems is same.

3. The distance ( l  ) over which the power is transmitted is same.

4. The copper losses (w) are same in all the systems.

Comparison of Volume of Copper in Overhead System

The selection of a particular type of a.c. or d.c. system for the transmission and distribution is based on comparison of amount of material i.e. copper necessary for the various systems. As mentioned earlier, the maximum stress in the overhead system exists between the conductor and earth. Hence comparison of material required is done assuming the maximum voltage between any conductor and earth being the same. The assumptions made for the comparison are :

1. The power (P) transmitted by all the systems is same.

2. The distance ( l  ) over which the power is transmitted is same.

3. The power loss (W) in all the systems are same.

4. The maximum voltage (V_m) exists between any conductor and the earth, in all the systems.

   

DC Transmission and Distribution

Though a.c. is extensively used everywhere, there are few applications like operation of d.c. motors, batteries, charging where d.c. supply is must. It can be obtained by using rectifiers or by d.c. generators at substations.

The d.c. systems are further classified as,

1. Two wire d.c. system

2. Two wire with midpoint earthed d.c. system

3. Three wire d.c. system

AC Transmission

The a.c. system which is very commonly used for the transmission of power till substations and local distribution centre is three phase three wire system. While for the secondary distribution, the universally adopted a.c. system is three phase four wire system.

1.1 Three Phase Three Wire System

       The three phase three wire system may be star or delta connected. If it is star connected, then its neutral is grounded. The Fig. 1 shows the scheme of three phase three wire system for the primary distribution. The large consumers like factories which need bulk supply are directly supplied from the substations. The power is also distributed to other substations and distribution centres.

Fig. 1 Three phase three wire scheme

Types of Transmission

In general two types of systems are used for the transmission.

1. Overhead system            2. Underground system

1.1 Overhead System

        In this system, the transmission of electrical power is by using overhead transmission lines over long distances. In such system, the appropriate spacing is provided between the conductors, at the supports as well as at the intermediate points. This spacing provides insulation which avoids an electric discharge to occur between the conductors. The transmission by overhead system is much cheaper than the underground system. The overhead transmission lines are subjected to the faults occurring due to lightening, short circuits, breakage of line etc. but overhead lines can be easily repaired compared to underground system. It is also true that though such faults are rare, if occurred it is very difficult to find exact point of fault as transmission lines are very long. In the overhead system, the insulation must  be provided between the conductor and supporting structure. Hence the maximum stress exists between conductor and earth.

1.2 Underground System

        The cables are generally preferred in underground system. All the conductors must be insulated from each other in the underground system. As voltage level is high, insulation required is more. Hence due to insulation difficulties, the voltage level used in underground system is below 66 KV while the voltage level used in overhead transmission lines can be as high as 400 KV. The maintenance cost of the underground system is less compared to overhead system. In crowded areas, overhead system using bare conductors is not practicable where underground system using cables is preferred. The line surges are suppressed by using the cables hence cable must be used for the last part of the connection which can save transformers and generators from the damage due to line surges.

       In the underground system, the maximum stress exists on the insulation between the conductors.

Effect of High Voltage in Transmission System

Looking at the advantages and disadvantages of the two systems, it can be conclude that high voltage transmission is advantageous. Let us steady the effect of increased voltage level of transmission on

1. Volume of copper used for transmission

2. Efficiency of the line

3. The line voltage drop