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**Mumbai University > Mechanical Engineering > Sem 7 > Power Plant Engineering**

**Marks** : 10M

**Year**: Dec 2015

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Prove that economical load sharing in a power plant, the incremental rate (dI/dL) Of all generating units must be equal.

written 7.3 years ago by | • modified 7.3 years ago |

**Mumbai University > Mechanical Engineering > Sem 7 > Power Plant Engineering**

**Marks** : 10M

**Year**: Dec 2015

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written 7.3 years ago by |

An utility system has always more than one generating unit. Proper distribution of load among the generating units is a problem frequently encountered by engineers. If the load is not properly distributed, it will result in a decrease of the thermal efficiency as a whole. According to the economic scheduling principle, the load is so distributed that at any moment all generating units will have the same incremental heat rates. As the system load increases, the incremental heat rate of each unit will increase. This principle is illustrated by the example involving two generating units in the network.

Let IC be the combined input to units 1 and 2, and LC be the combined output of units 1 and 2. The combined input, IC , is a function of either L1 or L2 for a given combined output LC. When the combined input IC , is a minimum input IC is at a minimum, it must hold.

$\frac{(dI_C)}{(dL_1 )}$=0

Since, $I_C=I_1+I_2$

we have $\frac{(dI_1)}{(dL_1 )}+\frac{(dI_2)}{(dL_1 )}$=0

Now $\frac{(dI_2)}{(dL_1 )}=\frac{((dI_2)}{(dL_2 ))}×\frac{((dL_2)}{(dL_1 ))}$

Since, $L_C=L_1+L_2$

$\frac{(dL_2)}{(dL_1 )}=-1 $\frac{(dI_2)}{(dL_1 )}=-\frac{(dI_2)}{(dL_2 )}$ From Above Equation $\frac{(dI_1)}{(dL_1 )}=\frac{(dI_2)}{(dL_2 )}$ Thus, the combined input IC is a minimum only if the incremental heat rate of unit 1 is equal to that of unit. This principle can be extended to the network of multiple units. Figure 1.11 represents the input-output curves of two generating units operating in parallel and supplying common load. The corresponding heat rate curves are shown in figure 1.12. In dividing the load between these units to achieve maximum fuel economy, the principle of equal incremental heat rate is being used. Starting at zero load, the turbine B picks up the load up to LB1, while the turbine A remains ar zero load, the turbine B picks up load up to load up to LB! , while the turbine A starts to pick up load until it reaches LA1 , At the combined load LA1 + LB1, ![enter image description here][1] ![enter image description here][2] the second valve of turbine starts to open. As the load increases, the turbine B picks up the additional load, while the turbine A remains at the load LA1. For any increase beyond $L_A1+L_B2$, the turbine A starts to open the second valve and later the third valve. At the combined load $L_A3+L_B2$, the turbine A would be at a full load $L_A3$ and the turbine B starts at the load $L_B2$. If the combined load increases beyond this level, the turbine B starts to open the last valve to meet the additional demand. In a utility system with many units, to maintain continuity of service, the generating capacity in operation must be greater than the system load. The difference between these two is defined as the spinning reserve. The minimum magnitude of spinning reserves varies from one utility to another, but it is usually equal to or greater than the capacity of the largest unit in operation. To minimize the total system fuel cost, the principle of equal incremental heat rate is to be observed in distributing the system load among the operating units.

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