This paper proposes a critical clearing time (CCT) estimation method by the domain of attraction (DA) of a state-reduction model of power systems using sum of squares (SOS) programming. By exploiting the property of the Jacobian matrix and the structure of the boundary of the DA, it is found the DA of the state-reduction model and that of the full model of a power system are topological isomorphism. There are one-to-one correspondence relationships between the number of equilibrium points, the type of equilibrium points, and solutions of the two system models. Based on these findings, an expanding interior algorithm is proposed with SOS programming to estimate the DA of the state-reduction model. State trajectories of the full model can be transformed to those of the state-reduction model by orthogonal or equiradius projection. In this way, CCT of a grid fault is estimated with the DA of the state-reduction model. The calculational burden of SOS programming in the DA estimation using the state-reduction model is rather small compared with using the full model. Simulation results show the proposed expanding interior algorithm is able to provide a tight estimation of DA of power systems with higher accuracy and lower time costs.

This paper presents an Expanding Annular Domain (EAD) algorithm combined with Sum of Squares (SOS) programming to estimate and maximize the domain of attraction (DA) of power systems. The proposed algorithm can systematically construct polynomial Lyapunov functions for power systems with transfer conductance and reliably determine a less conservative approximated DA, which are quite difficult to achieve with traditional methods. With linear SOS programming, we begin from an initial estimated DA, then enlarge it by iteratively determining a series of so-called annular domains of attraction, each of which is characterized by level sets of two successively obtained Lyapunov functions. Moreover, the EAD algorithm is theoretically analyzed in detail and its validity and convergence are shown under certain conditions. In the end, our method is tested on two classical power system cases and is demonstrated to be superior to existing methods in terms of computational speed and conservativeness of results.

Large-scale cooling energy system has developed well in the past decade. However, its optimization is still a problem to be tackled due to the nonlinearity and large scale of existing systems. Reducing the scale of problems without oversimplifying the actual system model is a big challenge nowadays. This paper proposes a dimension reduction-based many-objective optimization (DRMO) method to solve an accurate nonlinear model of a practical large-scale cooling energy system. In the first stage, many-objective and many-variable of the large system are pre-processed to reduce the overall scale of the optimization problem. The relationships between many objectives are analyzed to find a few representative objectives. Key control variables are extracted to reduce the dimension of variables and the number of equality constraints. In the second stage, the many-objective group search optimization (GSO) method is used to solve the low-dimensional nonlinear model, and a Pareto-front is obtained. In the final stage, candidate solutions along the Pareto-front are graded on many-objective levels of system operators. The candidate solution with the highest average utility value is selected as the best running mode. Simulations are carried out on a 619-node-614-branch cooling system, and results show the ability of the proposed method in solving large-scale system operation problems.

With variation of parameters, DC-DC converters may change from a stable state to an unstable state, which severely degrades the performances of the converter system. In this article, by establishing the state-space average model, the stability and bifurcation of a boost and a buck-boost converter with energy balance control (EBC) is studied, respectively. Then the stability boundary and stable parameter domains are accurately predicted. The obtained stability region provides a parameter regulating range for converter design. Furthermore, compared with the one-cycle control (OCC) method, the EBC possesses an extended stable parameter domain, while avoiding unstable behaviors such as Hopf bifurcation, Quasi-periodic Oscillation even chaos, etc. The theoretic analysis is well validated through simulation and experiment.

In this paper we construct an energy function for multi-machine power systems with doubly-fed induction generator-based wind turbine (DFIGWT) according to a synchronous-generator-mimicking (SGM) model of the DFIGWT. An SGM model is proposed to approximate the dynamics of a DFIGWT. Similar to the modelling of a synchronous generator (SG), the internal dynamics of a DFIGWT are also described with differential equations of newly constructed virtual rotor angle and internal electromotive force (EMF) in the SGM model. Moreover, the power flow of a DFIGWT is expressed by nonlinear functions of its virtual rotor angle and internal EMF. The SGM model bridges the gap between the irregular and complex modelling of DFIGWTs and the well-developed energy function construction techniques for SG models. Based on the SGM model, a numerical energy function is constructed for power systems with DFIGWT generation. Both theoretical analysis and numerical studies were undertaken to validate that the proposed energy function satisfies the necessary conditions for an energy function of a power system.