Distributed Control and Optimization for Autonomous Power Grids

Optimal Frequency Control for Inverter-Based Micro-Grids Using Distributed Finite-Time Consensus Algorithms

“…It can be seen from (16) and (5) that λ i (θ) = λ i and P i (θ) = P i , thus the scalar form λ(θ) = λ and P (θ) = P .…”

“…are the corresponding reference values of γ − i , γ + i at equilibrium point. Similar to (16), λ i is calculated as,…”

“…Whereas, renewable resource units are in general connected through a power electronic converter, which fully or partly decouples the generator from the grid. These generation units do not inherently contribute to the total system inertia [15], [16]. The low-inertia characteristic requires a faster stabilization and operation for future micro-grid systems.…”

Steady-State Optimal Frequency Control for Lossy Power Grids with Distributed Communication

“…A class of distributed control concepts that has recently been very popular in terms of frequency regulation and balancing is real-time dynamic pricing (see [2] for a detailed survey on current research directions). Dynamic pricing is particularly advantageous in large scale networks as it enables implicit communication of momentary imbalances via a price signal, resulting in a dynamic feedback minimization [3]- [6] of the overall costs.…”

“…Moreover, from (28) it follows that λ ∈ ker D c , and as D c is an incidence matrix, all elements of λ must be equal. Summing up, it follows that all marginal prices are equal at steady state, which is the economic dispatch criterion [2]. For the sake of brevity, we denote the co-state vector z = ∇H and the dissipation vector R(z, x) = Rz + r. Then, (35) is a port-Hamiltonian descriptor system with nonlinear dissipation [17] Eẋ = J z − R(z, x) + F u. where z = ∇H(x).…”