Page 133 - Power Electronic Control in Electrical Systems

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Power electronic control in electrical systems 121

1
2 3 2 3 2 3 2 32 3 2 3
V 1 2 1 0 1 52 1 1 5
1 1
0
2
0
4 V 2 5 ˆ 4 1 3 1 5 4 5 ˆ 8 4 24 2 54 5 ˆ 8 4 5 (4:27)
V 3 0 1 2 0 12 5 0 1
4.4 The power flow theory

4.4.1 Basic concepts

From the mathematical modelling point of view, the power flow exercise consists in
solving the set of non-linear, algebraic equations which describe the power network
under steady state conditions. Over the years, several approaches have been put
forward for the solution of the power flow equations (Freris and Sasson, 1968; Stott,
1974). Early approaches were based on numerical techniques of the Gauss±Seidel
type, which exhibit poor convergence characteristic when applied to the solution of
networks of realistic size. They have been superseded by numerical techniques of the
Newton±Raphson type, owing to their very strong convergence characteristic.
In conventional power flow studies, nodes can be of three different types:
1. Voltage controlled node. If sufficient reactive power is available at the node, the
nodal voltage magnitude may be regulated and the node will be of the voltage
controlled type. Synchronous generators and SVCs may be used to provide voltage
regulation. In the case of generators the amount of active power which the gen-
erator has been scheduled to meet is specified whereas in the case of SVCs the
active power is specified to be zero. The unknown variables are the nodal voltage
phase angle and the net reactive power. These nodes are also known as PV type,
where P relates to active power and V relates to voltage magnitude.
2. Load node. If no generation facilities exist at the node, this will be of the load type.
For these kinds of nodes the net active and reactive powers are specified and the
nodal voltage magnitude and phase angle are unknown variables. These nodes are
also known as PQ type. In this case P and Q relate to active and reactive power,
respectively. If neither generation nor demand exist in a particular node, it will be
treated as a PQ type node with zero power injection. Practical design considerations
impose limits in the amount of reactive power that a generator can either supply or
absorb. If such limits are violated, the generator will be unable to regulate the nodal
voltage magnitude. To represent this practical operational condition in the power
flow algorithm, the node will change from PV to PQ type.
3. Slack node. The third kind of node in a power flow study is the Slack node. In
conventional power flow studies one node is specified to be the Slack node. The
need for a Slack node arises from the fact that both the active and reactive losses
in the power network are not known prior to the power flow solution. The
generator connected to the Slack node will generate enough power to meet the
transmission losses and to pick up any demand surplus which the other generators
in the network might not have been able to meet. To a certain extent the
specification of the Slack node is arbitrary, as long as there is sufficient generation
available in that node, or as long as such a node is a grid supply point. In this kind