UCM | Substation Modeling

• In each substation, there are passive components interpreted as RLC elements which can be linear or non-linear, circuit-breakers, different kinds of generation interpreted as voltage and current sources equipped with control systems.
• Machines and motors are considered sources with control systems.
• Besides control systems, other equipments are power elements working at the power system level voltages and currents.
• Power elements of a substation are interconnected together via nodes. Power elements are not simulated sequentially one by one but rather simultaneously all together in a single equation called the node equation:

YV=I

• where Y is the substation admittance matrix, V is a vector of node voltages and I is a vector of node currents (currents injected to nodes).
• Control systems are modeled using the block diagram principle, either under graphic form (HYPERSIM ® block diagram and Simulink block diagram) or coded in C/C++. Their inputs can be node voltages and currents while their outputs can be used to control sources and switches.

RLC element

Trapezoidal integration

HYPERSIM as EMTP, uses the trapezoidal integration technique, it means that:

is evaluated as

where T is the calculation time step. By the same rule, the derivative 

is approximated as a difference deduced from the equation

L Branch

For an L branch connected between node k and node m, the following equation is applied:

OR

Using the trapezoidal integration rule given by the equation above, we get

with

As shown, an L branch is equivalent to resistor R_eq in parallel to historic current source i_hist. One can see that the historic current depends only on the voltage and current values of the previous step.

For a fixed inductor, L is constant, therefore R_eq is constant and need not be recalculated at every time step.

C branch

The current of a C branch connected between nodes k and m is given by

Replace the derivative by the difference equation from page 7 and we get:

or

with