Unit System and Conventions

Signing Convention

Loads

For loads, positive active and reactive power, $P$ and $Q$, are interpreted as consumption from the grid. Negative $P$ and $Q$ as injection into the grid.

For loads it holds that $P\ge 0$ and $Q\in \mathbb{R}$.

Generators

For generators, positive active and reactive power, $P$ and $Q$, are interpreted as injection into the grid. Negative $P$ and $Q$ as consumption from the grid.

For generators it holds that $P\ge 0$ and $Q\in \mathbb{R}$.

Power Factor

The power factor is defined as

$$pf=cos(\varphi )=\frac{P}{|S|}$$

where $cos(\varphi )$ is the power factor, $\varphi$ is the phase angle between current and voltage, $P$ is the real power and $|S|$ is the absolute value of the apparent power. It holds that $0\le pf\le 1$ since $P\ge 0$.

Depending on the sign of $Q$, $cos(\varphi )$ can be

• Overexcited: Q injection, increases voltage (capacitive)
• Underexcited: Q absorption, decreases voltage (inductive)

Power Flow

$P$ over a branch is always positive. The direction is defined by arrows:

• -->: $P$ flows from Bus 1 to Bus 2
• <--: $P$ flows from Bus 2 to Bus 1

If $Q$ is positive, it flows in the same direction as $P$. If $Q$ is negative, it flows in the opposite direction.

Frequency

The standard frequency is 50Hz. It can be changed in the Grid Editor.

Power in three-phase systems (balanced)

The power in three-phase systems is the sum of the power per phase. In balanced three-phase systems the three-phase power is 3x the single phase power:

$$S_{3\text{ph}}=3\cdot V_{\text{R}}\cdot I_{\text{R}}$$

where $S_{3\text{ph}}$ is the three-phase apparent power, $V_{\text{R}}$ is the phase to ground voltage and $I_{\text{R}}$ is the phase current. In the above equation the phase to ground voltage can be replaced by the phase to phase voltage with

$$V=\sqrt{3}\cdot V_{\text{R}}$$

where $V$ is the phase to phase voltage. Adding the second equation to the first we get

$$S_{3\text{ph}}=\sqrt{3}\cdot V\cdot I_R$$

The following conventions apply:

• Voltages entered and displayed are phase to phase, i.e. $V$.
• Powers entered and displayed are aggregated three-phase power.
• Currents entered and displayed are phase currents.

Power in 3-phase systems (unbalanced)

In unbalanced three-phase systems the power per phase is given as:

$$S_{\text{ph}}=\frac{V\cdot I_{\text{R}}}{\sqrt{3}}$$

The following conventions apply:

• Voltages entered and displayed are phase to phase, i.e. $V$.
• Powers entered and displayed are defined per phase.
• Currents entered and displayed are phase currents.

Per Unit System

Bus voltages are given as absolute or per unit values. The per unit values are relative to the phase to phase base voltage $V_{\text{nom}}$ defined for each Bus.

The default base apparent power is $S_{\text{nom}}=100\text{MVA}$. It can be changed in the Grid Editor.