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.

       In this system, two generators are connected in series, each is generating a voltage of V volts. The common point is neutral from where neutral wire is run. The voltage V of each generator is with respect to neutral which is earthed. Thus the voltage between each line and neutral is V volts while between the lines it is 2 V volts. Thus the consumers demanding higher voltage are connected to the two lines while the consumers demanding less voltage for lighting load are connected to the two lines while the consumers demanding less voltage for lighting load are connected between any one line and neutral. The Fig. 1 shows the d.c. three wire distribution system.

Fig. 1 Three wire d.c. system

       The light loads, domestic loads are connected between any of the two lines and neutral while the d.c. motor loads requiring higher voltage are connected between the lines. The neutral is earthed.

       The symbolic representation if three wire d.c. system is shown in the Fig. 2.

Fig. 2 Three wire d.c. system with balanced loads

       The Fig. 2 shows the current distribution in the system. The one line carries current I₁ while the other current carries current I₁. When the load is balanced, that is load connected on either sides of the neutral wire is exactly half of the potential between the two outer lines. Thus the positive outer wire is at V volts above the neutral while the negative outer is at V volts below the neutral.

        If the load are not balanced then the neutral carries the current. This current is the difference between the two line currents I₁ and I₂ and is called out of balance current. If the load on the positive line i.e. I₁ is greater than I₂ then neutral wire carries current equal to I₁ - I₂ if the load on the negative line is greater i.e. I₂ is greater than I₁ then the neutral wire carries current equal to I₂ - I₁. This is shown in the Fig. 3(a) and (b). The direction of I₁ - I₂ is from load end to supply end while the direction of I₂ - I₁  is from supply end to load end.

Fig. 3 Out of balance current through neutral

       In any of the two cases of out of balance current conditions, the neutral potential will not remain half of that between the two lines.

      Instead of using two generators in series, a single generator having twice the line to neutral voltage rating also can be used.

       This is shown in the Fig. 4.

       In such system, two small d.c. machines are connected across the lines in series which are mechanically coupled to a common shaft. These are called balancers.

       Normally when the load is balanced, machines work as the d.c. motors. In case of any out of balance current through neutral then the machine connected to lightly loaded side acts as motor while that connected to heavily loaded side as machine as motor drives the machine as generator. Thus the unbalance is compensated.

Fig. 4 Use of single generator in 3 wire d.c. system

       The perfect balancing can not be obtained because the working of the balancers are based on slight unbalancing of the voltages on the two sides.

1.1 Current Distribution In Three Wire D.C. System

       The Fig. 5 shows 400/200 V, three wire d.c. distribution system. The total current distribution can be understood by taking concrete values of load currents. The motor load connected across the lines demand 175 A while other loads requiring less voltage, are connected between line and neutral, on both the sides of neutral. The two loads connected between positive line and neutral take 35 and 25 A current respectively while the two loads connected between negative line and neutral take 50 A current each. Applying Kirchhoff's current law at various nodes, the current in all the section can be determined as shown in the Fig. 5.

Fig. 5  Current distribution

       It can be seen that for the selected values, I₁ = 325 A while I₂  = 275 A.

       Thus I₂ - I₁  = 275 A - 235 A = 40 A current flows at the neutral point and its direction is from neutral and towards load end. Thus knowing currents in all the sections and resistance of all the sections, the voltage across any load can be determined by applying Kirchhoff's voltage law to the appropriate loop. Such a voltage is called load point voltage. While applying Kirchhoff's voltage law, care must be taken to consider the sign of the voltage drop correctly. If the potential across two points is traced from positive to negative as a drop then it must be taken as negative while if the potential is traced from negative to positive i.e. as a rise it must be taken as positive.

Example : A three wire d.c. system takes a current of 50 A on positive side and 45 A on negative side, the resistance of each outer is 0.0004 Ω per metre while the cross-section of middle wire is half of that of each outer. If the voltage between each outer and middle wire is maintained at 220 V at the feeding end, calculate the voltage at the distant load end between each outer and middle wire. The three wires are of 100 m length.

Solution : The system is shown in the Fig. 6.

Fig. 6

       Now I₁  = 50 A and  I₂  = 45 A hence current through neutral wire is I₁ - I₂  = 5 A from load side to supply side.

       Applying KVL to the loop ABCNA and taking potential drop as -ve and rise as + ve we can wrire,

       Applying KVL to the loop NCDEN,

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

       Due to such system, if the fault occurs either on feeder or a distributor, all the consumers connected to that distributor will get affected. There would be an interruption of supply to all such consumers. Similarly the end of the distributor nearer to the substation will get heavily loaded than the end which is too far away from the substation. Similarly the consumers at the distant end of the distributor would be subjected to the voltage variations and fluctuations, as the load on the distributor changes. The system is advantageous only when the generation is at low voltage level and the substation is loaded at the center of the load.

       The fault on a feeder or a distributor causes interruption in supply to all the consumers connected to the distributor. This can be avoided by modifying the radial system as shown in the Fig. 2. In this system, the distributor is fed at number of points with the help of feeders. In Fig. 2, the feeders from the substation are feeding to a single distributor at points A, B and C.

Fig. 2  Modified radial system

1.1 Advantages of Radial System

       The various advantages of radial system are,

1. Simplest as fed at only end.

2. The initial cost is low.

3. Useful when the generating is at low voltage.

4. Preferred when the station is located at the centre of the load.

1.2 Disadvantages of Radial System

       Apart from its advantages, this system is suffered from the following disadvantages.
1. The end of distributor near to the substation gets heavily loaded.

2. When load on the distributor changes, the consumers at the distant end of the distributor face serious voltage fluctuations.

3. As consumers are dependent on single feeder and distributor, a fault on any of these two causes interruption in supply to all the consumers connected to that distributor.

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.

       Though the a.c. transmission and distribution is used, still for certain applications such as d.c. motors, electrochemical work, batteries, electric traction etc. the d.c. supply is must. Hence along with a.c., d.c. distribution is also equally important. In a d.c. distribution, d.c. generators are used in the generating stations or a.c. is converted to d.c. using the converters like mercury are rectifiers, rotary converters etc. at the substations. Then the d.c. supply is distributed to the consumers as per the requirement.

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.

       But with increase in transmission voltage, there will be corresponding increase in cost of insulators, transformers, switchgear and other equipments. Thus for overall economy, there is optimum transmission voltage. The economical transmission voltage is one for which cost of conductor, insulators, transformers, switchgear and other equipments is minimum.

       If the power to be transmitted, generation voltage and length of transmission are known quantities, then economical transmission voltage can be computed. Initially some standard transmission voltage is selected and costs of transformers, switchgear, conductors and other equipments are determined.

       The transformers are present at generating and receiving ends of transmission line. With increase in voltage for a given power, the cost of transformer rises. Also the cost of switchgear, lightning arrester, insulation and supports increases while the cost of conductors decreases with increase in voltage. The total cost of transmission line for a given voltage is sum of costs of transformers, switchgear, lightning  arrester, insulators, support and conductors. These costs and total cost is also computed for different transmission voltages. From this data, a graph is drawn between total cost of transmission line versus transmission voltage which is shown in Fig. 1.

Fig. 1

       The economical voltage is one for which capital cost associated with line is minimum which is point Z from the Fig. 1. Thus optimum transmission voltage is represented by OX.

       The application of this method is practice is rare as various costs associated in it can not be determined with a good degree of accuracy. Instead, an empirical formula is used for finding economical voltage. Thus the economic voltage between lines in 3 phase system is given by,

       Here V = Line voltage in KV, L = Distance of transmission line in Km, P = Maximum power per phase to be delivered to single circuit.

   The economical transmission voltage depends on length (or distance) of transmission line and power to be transmitted. With increase in distance of transmission line, the cost of equipments and apparatus increases which results in higher transmission voltage. If the power to be transmitted is large then large units of generating and transforming are required which reduces the cost per Kw of terminal equipments.

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.

1.1 Two Wire D.C. System

       The system is represented in the Fig. 1.

Fig. 1

       The voltage between the two conductors is V_m. It can be seen that there are no changes in the condition which we have discussed for two wire D.C. system for overhead system earlier in (previous post section 1.1).

       This is the base of comparison of other systems,

1.2 Two Wire D.C. System With Midpoint Earthed

       The system is shown in the Fig. Fig. 2.

Fig. 2

       it can be noted that the maximum voltage V_m exists between the two lines.

       The total copper loss is,

       Hence the total volume of copper required is,

       Thus the volume of copper required in this system is same as that required for two wire d.c. system.

1.3 Three Wire D.C. System

       The system is represented in the Fig. 3.

Fig. 3

       Again the voltage between the two lines is maximum which is V_m.

       Assume balanced load so there is no current through the neutral and there are no copper losses in neutral. So total copper loss is,

       where  A = area of cross-section of each line conductor.

       Let area of cross-section of neutral wire is half of the area of cross-section of each conductor i.e. 0.5 A.

        Hence the total volume of copper required is

       Thus the volume of copper required for this system is 1.25 times that that required for 2 wire d.c. system. So 25% more copper is required in this system.

1.4 Three Phase Three Wire A.C. System

       Consider a star connected three phase three wire a.c. system as shown in the Fig. 4. Note that the voltage between the line conductors is V_m. Thus the line voltage is V_m.

Fig. 4

        The r.m.s. value of the phase voltage is,

       The power transmitted per phase is,

       Let cosΦ be the load power factor.

        The total copper loss is,

        Hence the volume of copper required is,

       Thus the volume of copper required in this system depends on the load power factor and it is 1.5/cos²Φ times that that required for two wire d.c. system.

       The resultant remains same whether the system is star or delta connected.

1.5 Three Phase Four Wire A.C. System

        The system is shown in the Fig. 5. The neutral is available for the load connection. As the load is assumed to be balanced, the neutral current is zero and the copper losses in neutral are zero. Note that the voltage between the lines is V_m.

Fig. 5

       Hence the r.m.s. value of the phase voltage is,

       The power per phase is given by,

        This is same as obtained for three phase three wire system. The total copper loss is,

       Let the cross-section of the neutral wire be half of the cross-section of each line conductor i.e. 0.5 A.

       Hence the total volume of copper required is

       Thus the volume of copper required in this system is 1.75/cos²Φ times the volume of copper required for two wire d.c. system.

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.

      Based on these assumptions, let us compare the various types of systems for the volume of copper required.

1.1 Two Wire D.C. System With One Line Earthed

       The system is represented in the Fig. 1.

Fig. 1

       The maximum voltage between the conductors is V_m, as one material is earthed.

       Where P = Power transmitted 

       Let R = resistance of each conductor

      Total copper losses in both the lines are,

        Volume of copper required is

       The volume of copper required for other systems is compared by taking volume of copper required for this system as base. Let it be constant K and volume of copper required for other systems can be expressed interms of K.

1.2 Two Wire D.C. System With Midpoint Earthed

       The system is represented in the Fig. 2.

Fig. 2

       As power transmitted is same as P, the current in each conductor is,

       The total copper loss in both the lines is,

      where A = area of cross-section of each line.

The total volume of copper required is,

       Thus the volume of copper required in this system is one fourth the volume of copper required for two wire d.c. system with one line earthed.

1.3 Three Wire D.C. System

       The system is represented as shown in the Fig. 3.

Fig. 3

       When the load is balanced, current through the third neutral wire is zero.

       Let A = Cross-section of outer conductors 

       The total copper loss is,

       Let area of cross-section of the middle neutral wire is half of the area of cross-section of the outer conductor.

       Hence the total volume of copper

               = Volume of copper for outer wires + volume of copper for neutral wire

       Thus the volume of copper required in this system is 0.3125 times the volume of copper required for two wire d.c. system with one line earthed.

1.4 Three Phase Three Wire A.C. System

       This is most commonly used system for the transmission. The three phase three wire star connected system with neutral earthed is shown in the Fig. 4.

Fig. 4

         The maximum voltage between each line conductor and the neutral is V_m as shown in the Fig. 4.

         The R.M.S. value of the voltage per phase given by,

        Then total power transmitted is P watts hence per phase power transmission is,

        Let cosΦ be the load power factor

         Hence the total copper loss is,

        The volume of the copper required is

        Thus the volume of copper required depends on power factor of the load and it is 0.5/cos²Φ times the volume of copper required by twp wire d.c. system with one line earthed. This system may be delta connected but irrespective of the method of connection star or delta, the result derived remains same.

1.5 Three Phase Four Wire A.C. System

       This system is popularly used for secondary distribution. The neutral is also made available for the connection of the load. The system is shown in the Fig. 4.

Fig. 5

        Assuming the load balanced, there is no current flowing through the neutral.

       The cross-section area of neutral is half the cross-section of each conductor i.e. 0.5 A where A is cross-section of each conductor.

       The maximum voltage between any conductor and the neutral is V_m hence r.m.s. voltage per phase is,

       The power transmitted per phase is,

       Hence all the calculations upto the copper losses and expression of A remain same as derived for three  phase three wire system.

       The total volume of copper requires is,
                        = Volume of copper for 3 lines + copper required for neutral

       Thus the volume of copper required is 0.583/cos²Φ times the volume of copper required by two wire d.c. system with one line earthed.