Formal Control of New England 39-Bus Test System: An Assume-Guarantee Approach

TL;DR

This work proposes two control methods to provide guarantees for NETS: one using the principle of interconnected synchronous machines and another considering the power flows in the network between neighbouring subsystems.

Abstract

This work is concerned with an assume-guarantee approach to compositionally control a New England 39-bus Test System (NETS). The proposed scheme is based on the new notion of robust simulation functions with disturbance refinement alongside the composition of multiple subsystems to tackle the difficulties associated with scalability, also known as the curse of dimensionality. In our proposed setting, we approximate concrete subsystems with abstractions that have lower dimensions (a.k.a. reduced-order models) while providing mathematical guarantees on controller synthesis through the quantification of an upper bound on the closeness between output trajectories of original systems and their abstractions. We propose two control methods to provide guarantees for NETS: one using the principle of interconnected synchronous machines and another considering the power flows in the network between neighbouring subsystems.

Figures (13)

• Figure 1: A single-line diagram of Area $1$ of New England $39$ Bus Test System, with generators (G$2$, G$3$, G$10$), buses (thick bars), loads (thick arrows), and power lines.
• Figure 2: Top: Target range $\mathcal{T}$ is shown in green, $\mathcal{A}_{ub}$ and $\mathcal{A}_{lb}$ are shown in red as two regions that the system should never transition into (unsafe regions). The baseline controller notably improves the frequency response of the system in compare with the uncontrolled system. However, both curves still fall into the red unsafe region. Bottom: The input $u_\mathcal{V}$ is a byproduct of the simulation relation interface keeping $\Sigma_1$ and $\Sigma_2$$\epsilon$-close. Since no controller is synthesised over $\Sigma_2$, then $\mathbf{u}_2 = 0$.
• Figure 3: Top: Target range $\mathcal{T}$ is shown in green, and unsafe regions $\mathcal{A}_{ub}$ and $\mathcal{A}_{lb}$ are shown in red. The controller designed using SCOTS and the RSF with disturbance refinement successfully satisfy $\psi$, compared with the baseline controller which violates the specification. Bottom: The control input $\mathbf{u}_2$ designed using SCOTS for $\Sigma_2$ and the refined control input $\mathbf{u}_1$ for $\Sigma_1$ using our RSF.
• Figure 4: A graphical representation of NETS composed of $3$ subsystems as vertices and interconnections with neighbours as edges.
• Figure 5: Design of NETS using isolated subsystems from the principle of interconnected synchronous machines, where $i \in \{1,2,3\}$.

Theorems & Definitions (10)

• Definition 1: Subsystems
• Definition 2: Interconnected Systems
• Definition 3: Robust Simulation Functions
• Remark 1
• Lemma 1
• Theorem 1
• Theorem 2
• Remark 2
• proof : Proof of Theorem 1
• proof : Proof of Theorem 2