Table 1 Overview of voltage regulation, max-consensus and communication network variables
From: Max-consensus protocol to determine the regulated node in distributed voltage regulation
Variable | Description | |
|---|---|---|
\(n \in \mathbb {N}\) | Number of voltage measurement nodes | |
\(d \le n\) | Number of DRES nodes | |
\(\overline{Q}_i\) \(\in \mathbb {R}\) | Reactive power limit of DRES i [VAr] | |
\(Q_i\) \(<\overline{Q}_i\) | Reactive power values of DRES i [VAr] | |
\(\overline{U}\) \(\in \mathbb {R}\) | Maximum allowed voltage value [V] | |
\(db \in \mathbb {R}\) | Dead-band below \(\overline{U}\) [V] | |
\(S \in \mathbb {R}^{n\times d}\) | Sensitivity matrix | |
\(d^{up}\) \(\in \mathbb {N}^{n\times d}\) | Delay time up (\(d^{up}_{j,i}\): DRES i and regulated node j) | |
\(d^{down}\) \(\in \mathbb {N}^{n\times d}\) | Delay time down | |
\(\Delta ^{delay}\) \(\in \mathbb {N}\) | Delay time constant | |
\(U^{loc}\) \(\in \mathbb {R}^n\) | Local voltage values [V] | |
\(U \in \mathbb {R}^n\) | Known maximum voltage values [V] | |
\(r \in \{1,\ldots ,n\}^n\) | Known regulated node at each agent | |
\(t \in \mathbb {N}^n\) | Node sequence numbers | |
\(m_i\) \(=(U_i, r_i, t_{r_i})\) | Information state at agent i, initially \((U_i^{loc}, i, t_i)\) | |
\(\Delta ^{volt}\) \(\in \mathbb {N}\) | Voltage measurement interval | |
\(m \ge n\) | Number of communication vertices | |
\(\mathcal {V}\) \(=\{v_1,\ldots , v_m\}\) | Communication vertex set | |
\(\mathcal {E}\) \(\subseteq \mathcal {V} \times \mathcal {V}\) | Edges connecting communication vertices | |
\(\mathcal {G}\) \(=(\mathcal {V}, \mathcal {E})\) | Communication network graph | |
\(\mathcal {V}'\) \(\subseteq \mathcal {V}\) | Consensus vertex set | |
\(\mathcal {E}'\) \(\subseteq \mathcal {V}' \times \mathcal {V}'\) | Edges connecting consensus vertices | |
\(\mathcal {G}'\) \(=(\mathcal {V}', \mathcal {E}')\) | Consensus overlay network graph | |
\(\Delta ^{com}\) \(\in \mathbb {N}\) | Communication interval | |