Preparation
To calculate parameters for all power elements and the substation’s node equation, the preparation operations are:
- Read each element’s parameters from the parameter form
- Define node signals: voltages and currents
- Define element’s signals: voltages (except node voltages), currents (source, historic), control signals
- Calculate the fixed part Yini as initial admittance of all elements, as well as other element’s parameters needed during the simulation
- Calculate the fixed part YINI and initialize the substation admittance matrix Y to this value
- Reorder Y so that varying elements will affect only the lower right part of Y
- Download YINI: Yini, and other simulation parameters needed by the simulation program
Simulation
At each simulation step, the following operations are required to simulate power elements and solve the node equation of a substation:
- Determine the switch commands (used to turn them on or off)
- Determine states of switches
- If needed (some switches have changed their state or some non-linear elements have changed their operation point), determine the area of matrix Y that needs to be re-evaluated due to elements that have changed their operating point.
Re-calculate this part of Y.
- If needed (as above), perform the LDU decomposition of the lower-right bloc of the YLDU matrix
- Calculate source’s currents (voltage sources and current sources)
- Add source’s currents to node currents I.
- Solve YV = I to calculate node voltages V.
- Determine if a non-linear element changes its operating point. If it is the case, calculate its new Yadd and update Yeq=Yini+Yadd for that element.
- Calculate element’s historic current Ihist as well as all other signals it needs.
- Re-initialize node currents I to [0] for the next step
- Add element’s historic currents Ihist to node current I.
- Calculate control functions
Parallel tasks in HYPERSIM®
As mentioned in the line modeling section, lines are equivalent to current sources in parallel to resistors at each line end. Current sources at each end depend only on the past value of line voltages and currents of both ends. Variations at one end will therefore affect the other end at one transmission delay later. The transmission speed is about light speed, which is 300 000 km/s. A 30km line has a transmission delay of 100 µs.
Due to the transmission delay, in a network composed of lines and substation (as shown), the following tasks can be performed in parallel:
- Substation tasks solving substation node equations, which also include line-end equivalents (current sources in parallel with resistors) and simple control systems,
- Line tasks calculating line equivalents at each line end.
Certain complex substations can have complex control systems, such as an AC-DC conversion station, generation station with machine models. These substations are simulated with many tasks: one for solving the node equation and others for control systems.
In non-real-time mode running in a single processor, all tasks are given to the same processor. With a parallel computer, tasks are distributed among parallel processors using a task mapping algorithm based on following criteria: execution time of each task, available time of processor, communications needed and communication link available, I/O needed and I/O availability, etc.
