Question

Two shunt generator A and B operate in parallel and their load characteristic may be taken as straight lines. The voltage of A falls from 240 V at no-load to 220V at 200A, while that of B falls from 245 V at no-load to 220V at 150 A. Determine the current which each machine supplies to a common load of 300 A and the bus-bar at the load.

Answer 1

By equating the voltage drop per ampere for two parallel shunt generators and solving the system of equations representing their load characteristics, we found that Generator A supplies 175 A and Generator B supplies 125 A to a common load of 300 A.

Step-by-step explanation:

The question asks to determine the current supplied by each of two shunt generators operating in parallel, with given load characteristics, to a common load. To find the currents supplied by generators A and B to a 300 A load, we first need to establish the relationship between current and voltage for both generators based on their load characteristics.

For generator A, the voltage drop is 20 V when the current increases from 0 A to 200 A. This means the voltage drops by 0.1 V for every ampere of current. Similarly, for generator B, the voltage drop is 25 V when the current increases from 0 A to 150 A, meaning the voltage drops by 0.1667 V for every ampere of current.

Generator A's voltage line equation can be expressed as V_A = 240 - 0.1I_A and for generator B it's V_B = 245 - 0.1667I_B. Since they are in parallel, V_A = V_B for any load shared between them. By equating the two expressions and solving for I_A, we can find the current through each generator when they share a 300 A load.

Setting V_A equal to V_B gives us: 240 - 0.1I_A = 245 - 0.1667I_B. Since I_A + I_B = 300 A, we can solve these two equations simultaneously to find the currents I_A and I_B.

After solving, we obtain I_A as approximately 175 A and I_B as approximately 125 A. Generator A supplies 175 A and Generator B supplies 125 A to the combined 300 A load.