K. Xi
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A consensus-control-based multi-level control law named Multi-Level Power-Imbalance Allocation Control (MLPIAC) is presented for a large-scale power system partitioned into two or more groups. Centralized control is implemented in each group while distributed control is implemented at the coordination level of the groups. Besides restoring nominal frequency with a minimal control cost, MLPIAC can improve the transient performance of the system through an accelerated convergence of the control inputs without oscillations. At the coordination level of the control groups, because the number of the groups is smaller than that of nodes, MLPIAC is more effective to obtain the minimized control cost than the purely distributed control law. At the level of the control in each group, because the number of nodes is much smaller than the total number of nodes in the whole network, the overheads in the communications and the computations are reduced compared to the pure centralized control. The asymptotic stability of MLPIAC is proven using the Lyapunov method and the performance is evaluated through simulations.
For system identification of a continuous-time polynomial system, a subalgebraic identification procedure is defined. The procedure is motivated by the needs of system identification of the life sciences. The approach is inspired by the subspace identification algorithm which is adjusted to the subset of continuous-time polynomial systems. The procedure makes use of the subalgebraic procedure for system identification of a discrete-time polynomial system. An example illustrates the approach.
The traditional secondary frequency control of power systems restores nominal frequency by steering Area Control Errors (ACEs) to zero. Existing methods are a form of integral control with the characteristic that large control gain coefficients introduce an overshoot and small ones result in a slow convergence to a steady state. In order to deal with the large frequency deviation problem, which is the main concern of the power system integrated with a large number of renewable energy, a faster convergence is critical. In this paper, we propose a secondary frequency control method named Power-Imbalance Allocation Control (PIAC) to restore the nominal frequency with a minimized control cost, in which a coordinator estimates the power imbalance and dispatches the control inputs to the controllers after solving an economic power dispatch problem. The power imbalance estimation converges exponentially in PIAC, both overshoots and large frequency deviations are avoided. In addition, when PIAC is implemented in a multi-area controlled network, the controllers of an area are independent of the disturbance of the neighbor areas, which allows an asynchronous control in the multi-area network. A Lyapunov stability analysis shows that PIAC is locally asymptotically stable and simulation results illustrate that it effectively eliminates the drawback of the traditional integral control based methods.
Power-imbalance allocation control of power systems
A frequency bound for time-varying loads
Synchronization of Cyclic Power Grids
Equilibria and Stability of the Synchronous State
and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stability of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous
state. We find that the energy barrier depends on the network size ($N$) in a more complicated fashion compared to the linear stability. In particular, when the generators and consumers are evenly distributed in an alternating way, the energy barrier decreases to a constant when $N$ approaches infinity.
For a heterogeneous distribution of generators and consumers, the energy barrier decreases with $N$. The more heterogeneous the distribution is, the stronger the energy barrier depends on $N$. Finally, we find that by comparing situations with equal line loads in
cyclic and tree networks, tree networks exhibit reduced stability. This difference disappears in the limit of $N\to\infty$. This finding corroborates previous results reported in the literature and suggests that cyclic (sub)networks may be applied to enhance power
transfer while maintaining stable synchronous operation. ...
and their stability for cyclic power grids. We calculate the number of stable equilibria and investigate both the linear and nonlinear stability of the synchronous state. The linear stability analysis shows that the stability of the state, determined by the smallest nonzero eigenvalue, is inversely proportional to the size of the network. We use the energy barrier to measure the nonlinear stability and calculate it by comparing the potential energy of the type-1 saddles with that of the stable synchronous
state. We find that the energy barrier depends on the network size ($N$) in a more complicated fashion compared to the linear stability. In particular, when the generators and consumers are evenly distributed in an alternating way, the energy barrier decreases to a constant when $N$ approaches infinity.
For a heterogeneous distribution of generators and consumers, the energy barrier decreases with $N$. The more heterogeneous the distribution is, the stronger the energy barrier depends on $N$. Finally, we find that by comparing situations with equal line loads in
cyclic and tree networks, tree networks exhibit reduced stability. This difference disappears in the limit of $N\to\infty$. This finding corroborates previous results reported in the literature and suggests that cyclic (sub)networks may be applied to enhance power
transfer while maintaining stable synchronous operation.