Unit Conventions

The units for physical quantities are chosen for easy user input.

The units follow the general rules:

Power: MW/MVA/MVar (unless per unit of nominal power, e.g. generator.p_max_pu for variable generators is per unit of generator.p_nom)

Time: h

Energy: MWh

Voltage: kV phase-phase for bus.v_nom; per unit for v_mag_pu, v_mag_pu_set, v_mag_pu_min etc.

Angles: radians, except transformer.phase_shift which is in degrees for easy input

Impedance: Ohm, except transformers which are pu, using transformer.s_nom for the base power

CO2-equivalent emissions: tonnes of CO2-equivalent per MWh_thermal of energy carrier

Sign Conventions

The sign convention in PyPSA follows other major software packages, such as MATPOWER, PYPOWER and DIgSILENT PowerFactory.

  • The power (p,q) of generators or storage units is positive if the asset is injecting power into the bus, negative if withdrawing power from bus.
  • The power (p,q) of loads is positive if withdrawing power from bus, negative if injecting power into bus.
  • The power (p0,q0) at bus0 of a branch is positive if the branch is withdrawing power from bus0, i.e. bus0 is injecting into branch
  • Similarly the power (p1,q1) at bus1 of a branch is positive if the branch is withdrawing power from bus1, negative if the branch is injecting into bus1
  • If p0 > 0 and p1 < 0 for a branch then active power flows from bus0 to bus1; p0+p1 > 0 is the active power losses for this direction of power flow.

AC/DC Terminology

AC stands for Alternating Current and DC stands for Direct Current.

Some people refer to the linearised power flow equations for AC networks as “DC load flow” for historical reasons, but we find this confusing when there are actual direct current elements in the network (which also have a linearised power flow, which would then be DC DC load flow).

Therefore for us AC means AC and DC means DC. We distinguish between the full non-linear network equations (with no approximations) and the linearised network equations (with certain approximations to make the equations linear).

All equations are listed in the section Power Flow.