Consider the two-bus power system shown in Figure P6.2. The marginal cost of production of the generators connected to buses A and B are given respectively by the following expressions:
Load flow analysis
Load flow analysis is a study or numerical calculation of the power flow of power in steady-state conditions in any electrical system. It is used to determine the flow of power (real and reactive), voltage, or current in a system under any load conditions.
Nodal Matrix
The nodal matrix or simply known as admittance matrix, generally in engineering term it is called Y Matrix or Y bus, since it involve matrices so it is also referred as a n into n order matrix that represents a power system with n number of buses. It shows the buses' nodal admittance in a power system. The Y matrix is rather sparse in actual systems with thousands of buses. In the power system the transmission cables connect each bus to only a few other buses. Also the important data that one needs for have a power flow study is the Y Matrix.
Types of Buses
A bus is a type of system of communication that transfers data between the components inside a computer or between two or more computers. With multiple hardware connections, the earlier buses were parallel electrical wires but the term "bus" is now used for any type of physical arrangement which provides the same type of logical functions similar to the parallel electrical bus. Both parallel and bit connections are used by modern buses. They can be wired either electrical parallel or daisy chain topology or are connected by hubs which are switched same as in the case of Universal Serial Bus or USB.
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ビy
Fan
D, = 2000 MW
D = 1000 MW
Figure P6.2 Two-bus power system for Problems 6.2, 6.3, 6.4, 6.10 and 6.11
6.2 Consider the two-bus power system shown in Figure P6.2. The marginal cost of
production of the generators connected to buses A and B are given respectively
by the following expressions:
MСл 3 20 + 0.03 Р, S/MWh
MCB = 15 + 0.02 Pg S/MWh
Assume that the demand is constant and insensitive to price, that energy is sold
at its marginal cost of production and that there are no limits on the output of
the generators. Calculate the price of electricity at each bus, the production of
each generator and the flow on the line for the following cases:
a. The line between buses A and B is disconnected
b. The line between buses A and B is in service and has an unlimited capacity
c. The line between buses A and B is in service and has an unlimited capacity,
but the maximum output of Generator B is 1500 MW
d. The line between buses A and B is in service and has an unlimited capac-
ity, but the maximum output of Generator A is 900 MW. The output of
Generator B is unlimited.
The line between buses A and B is in service but its capacity is limited to
600 MW. The output of the generators is unlimited.
e.
6.3
Calculate the generator revenues and the consumer payments for all the cases
considered in Problem 6.2. Who benefits from the line connecting these two
buses?
6.4 Calculate the congestion surplus for case (e) of Problem 6.2. Check your answer
using the results of Problem 6.3. For what values of the flow on the line between
buses A and B is the congestion surplus equal to zero?
6.5 Consider the three-bus power system shown in Figure P6.5 The table below
shows the data about the generators connected to this system. Calculate the
unconstrained economic dispatch and the nodal prices for the loading conditions
shown in Figure P6.5.
6.5 PROBLEMS
203
B
400 MW
80 MW
2
3
40 MW
II
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