Power Flow: Bus Equation Basics
This is a subtopic of the Power Flow Solution Theory Help.
Each bus in the power system model has 4 quantities associated with it that may not be know. These are
- V (Bus Voltage Magnitude)
- d Bus Voltage Angle
- P (Real Power Injection)
- Q (Reactive Power Injection)
In addition each bus may have various equations that can be used to describe it.
- Summation of Real Power Flows into the bus equal zero
- Summation of Reactive Power Flow into the bus equals zero
- Voltage equal to Voltage Setpoint
- Other (voltage tolerance has a special equation as does voltage droop control with deadband)
Typically at each bus there are then 2 unknown variables out of these 4 variables and 2 equations that are used at each bus. This makes an equal number of unknown variables as equations so the "inner power flow solution" is simply the calculation of the unknown variables from the set of equations. There are some exceptions to each bus having 2 equations that come up with remote regulation and voltage droop control, but we'll leave that for later (might have a bus with 1 equations and another with 3 equations).
PowerWorld Simulator automatically figures out which 2 equations to use and which unknown variables to solve for based on the user input parameters (mostly generator parameters). The buses are categorized into a Type or "BusCat" which is shown by default on the Bus Mismatch case information display. BusCat is a string indication as to which two equations were used in the power flow solution. BusCat has a lot of potential options described in another topic, but the most common are the following three.
- PQ: buses that have no voltage control devices such as a generator at them and are also not remotely controlled by a generator will be called a PQ bus. We call them a PQ bus because we use the equations for summation of real power (P) and reactive power (Q) at these buses and the unknown variables are then voltage angle (V) and voltage angle (d).
- PV: a bus that has a generator at it which is regulating the terminal voltage to a voltage setpoint will be called a PV bus. Again this is because the equations are the summation of real power (P) and an equation for Voltage = Setpoint (V). The unknown variables are then voltage angle (d) and the extra Q injection at the bus. The extra Q injection at the bus is then used to assign the reactive power output to the generators at the bus.
- Slack: one bus in each electrical island is chosen as the island slack bus. This bus has a fixed voltage magnitude and voltage angle. Using our notation we might call it a dV bus. The unknown variables at this bus are then the real power (P) and reactive power (Q) which are then used to assign the real and reactive power at the slack generator.
PowerWorld Simulator will also frequently add modifiers to the Bus Type string to indicate why it is behaving in a particular way. Some examples are as follows
- PV (SVC): a bus that has a switched shunt with (ShuntMode = SVC) and (SVCType = SVSMO3 or SVSMO1) configured to regulate the voltage at the terminal bus. The voltage equation will be used just as for a generator.
- PQ (Gens at Var Limit): a bus that has a generator at it regulating the terminal voltage, however presently the generator is stuck at a maximum or minimum Mvar limit and is thus no longer able to regulate the voltage. Because we are stuck at a Mvar limit, the equations used is the reactive power (Q) equation. This is an indication that the bus type would have been PV, but is not because of the generators at Mvar limits
- PQ (SVC at Limit): similar to PQ (Gens at Limit), but a switched shunt that is an SVA
- PQ (Continuous Shunts at Var Limit):: similar to PQ (Gens at Limit), but it's a continous switched shunt at limits.
This topic then gets more complex however as you add the following concepts.