Geometry of Distance Protection

Abstract

Distance relays detect faults on transmission lines. They face uncertainty from the fault's location and resistance, as well as the current from the line's remote terminal. In this paper, we aggregate this uncertainty with the Minkowski sum. This allows us to explicitly model the power grid surrounding the relay's line, and in turn accommodate any mix of synchronous machines and inverter-based resources. To make the relay's task easier, inverters can inject perturbations, or auxiliary signals, such as negative-sequence current. We use Farkas' lemma to construct an optimization for designing inverter auxiliary signals.

Figures (5)

• Figure 1: Circuit representation of an ag fault. The fault loop is from phase a of the local bus to ground.
• Figure 2: Circuit representation of an ab fault. The fault loop is from phase a to phase b of the local bus.
• Figure 3: Diagram of the Minkowski sum, $\vec{\mathcal{Z}}_{\textrm{A}}^{\textrm{ab}}=\mathcal{Z}_{\textrm{T}}\oplus\vec{\mathcal{Z}}_{\textrm{F}}^{\textrm{ab}}$.
• Figure 4: For ag and ab faults, the post-test uncertainty sets, their zonogon relaxations, and the cut $\textrm{Im}[z]\textrm{Re}[z_{\textrm{A}}^{\eta}]\geq \textrm{Re}[z]\textrm{Im}[z_{\textrm{A}}^{\eta}]$.
• Figure 5: Left: separating auxiliary signals for the pair $(\textrm{N},\textrm{ag})$ ($\bullet$), the pair $(\textrm{N},\textrm{ab})$ ($\blacktriangledown$), and pairs $(\textrm{N},\textrm{ag})$, $(\textrm{N},\textrm{ab})$, and $(\textrm{ag},\textrm{ab})$ (+). Right: Separating auxiliary signals for all LG faults ($\bullet$), all LL faults ($\blacktriangledown$), and all LG and LL faults (+).

Theorems & Definitions (15)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• Lemma 5
• Lemma 6
• proof