Technical Background

The power-flow problem is the computation of voltage magnitude and phase angle at each bus in a power system under balanced three-phase .

From the single-line diagram of a N-bus power system, an N*N admittance matrix Y can be constructed:

• Diagonal elements Yii = sum of admittances connected to bus i;

• Off-diagonal elements Yij = - (sum of admittances connected between buses i and j)

Using Y, we can write nodal equations for a power system network:

where:

• I: the N vector of source currents injected into each bus;

• V: the N vector of bus voltages.

For any specific bus ‘i’, the complex power delivered to it will be:

where:

• P: active power

• Q: reactive power.

Since

where:

	bus voltage magnitude at bus i and j
	bus voltage angle at bus i and j
	the value of the admittance between bus i and j
	the angle of the admittance between bus i and j

In other words:

For each node i, four variables need to be determined in these two equations: 

The user must define two variables as inputs for the other two to be solved.

The buses are categorized into three types, based on their nature:

Usually, generator buses are considered as the Swing bus or PV buses since real power and voltage magnitude levels are controlled to the fixed values. PQ type is also supported for generator buses if necessary.

Load buses are considered PQ buses (rated load capacity, fixed P and Q, dynamic voltage).

HYPERSIM load flow calculation is an iterative process based on the Newton-Raphson method. For more precise results, the user may adjust the "Tolerance" parameter. However, reducing tolerance will increase the number of iterations, and may not lead to a converging load flow solution within the maximum iterations.

The load flow calculation allows to initialize the system very close to the calculated operating point, But it is still possible that the system, when simulated, may go through small oscillations and stabilize around the closest stable operating point. This is because:

• There are components which are not included in the load flow analysis.

• Load flow calculation is performed considering a linear system, thus all non-linear components (saturable transformer, arrester, synchronous machine saturation) may affect the actual operating point.

• Load flow calculation is performed at the base frequency with the positive sequence circuit values, any unbalanced load, untransposed line or coupled line may affect the actual operating point.

Configuration of Components

Components' Mask Load Flow Tab

When a component is supported in the load flow calculations, it has a load flow tab, and it often looks like the following:

Open

• In the drop-down menu of Type, the user can select the bus type of the bus, as defined in the table above, where this component is selected. 

• Two out of the four variables (V, θ, Q, and P) must be specified according to the bus type.

• The Q limits are used to define the range of values within which the actual value of Q is restricted. For these limits to be effective, the Use Qmin and Qmax limits options must be enabled in Load Flow. 

Tips and Tricks for Various Components