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.

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The electrical power grid is a fundamental infrastructure in today’s society. The synchronization of the frequency to nominal frequency over all the network is essential for the proper functioning of the power grid. The current transition to a more distributed generation by weather dependent renewable power sources, which are inherently more prone to fluctuations, poses great challenges to the functioning of the power grid. Among these fluctuations, the frequency fluctuations negatively affect the power supply and stability of the power grid. In this thesis, we focus on load frequency control laws that can effectively suppress the frequency fluctuations, and methods that can improve the synchronization stability...@en

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.

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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.

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To balance the power supply and demand with optimized control cost and nominal synchronized frequency, we propose a secondary frequency control approach, named Power-Imbalance Allocation Control (PIAC), for power systems with lossless networks, consisting of synchronous machines, frequency dependent power sources and passive loads. With Proportional-Integral control, the power imbalance is estimated by a coordinator with aggregated frequency deviations and the control inputs are optimally allocated to the controllers after solving an economic power dispatch problem on-line. The advantage of the approach is that the estimated power imbalance converges to the actual power imbalance exponentially with neither overshoot of control inputs nor unnecessary oscillations of the frequency. In addition, the convergence speed only depends on a control coefficient which is independent of any other parameters of the power systems and of the economic power dispatch problem.@en

For secondary frequency control of power systems with lossless networks, we proposed a method named Power-Imbalance Allocation Control (PIAC) to restore the nominal frequency after a disturbance. PIAC has shown a good transient performance where under a constant power imbalance, the overshoot problem and unnecessary oscillations of frequencies are eliminated. In this paper, we evaluate the performance of PIAC on power systems with time-varying power imbalance, which is more realistic since the power supply and load are continuously changing. Analysis and numerical simulations show that PIAC is able to closely track the power imbalance and effectively controls the global frequency to a desired range for slowly changing and Lipschitz-continuous power imbalance.@en

Synchronization is essential for the proper functioning of power grids, we investigate the synchronous states
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.@en