• Energy Research

When emergency controls cannot keep the stability of the whole system, it is a critical and efficient way to split the whole system into several small isolated islands. Moreover, the generators in the same island are synchronous. In this work, a mixed integer linear programming (MILP) model is set up to analyze the splitting strategies for power system islanding operations with the objective of minimizing total load shedding. Furthermore, graph theory is employed to transform the splitting strategy into a partition problem, which gives the splitting constraints for a given number of islands. In addition, the budget set is introduced to control the size of each island, which gives a more practical strategy. Finally, IEEE 30-bus, 118-bus, and 300-bus test systems with given groups of asynchronous generators are studied. The results show that a global optimal solution can quickly be achieved by using the MILP model and the branch-and-bound method.

Real-time damping estimation for a dominant inter-area mode is important for situational awareness of potential angular instability in power systems. Electromechanical oscillations energized by large disturbances often manifest obvious nonlinearities in measurements on first several swings. Traditional methods based on linear system theory often discard first several swings intentionally to avoid nonlinearity; if not, the estimated damping ratios often vary with the length and starting point of the measuring window. By identifying a nonlinear oscillator to fit a dominant mode, this paper proposes a new measurement-based approach utilizing complete post-disturbance data for robust damping estimation independent of the measuring window. Case studies on the IEEE 9-bus system and a 48-machine Northeast Power Coordinating Council system validate the proposed approach for providing accurate and robust damping estimation compared with existing methods including the Prony's method. Meanwhile, three factors influencing damping estimation in practical applications are also addressed, including measurement noises, limited coverage of PMU measurements, and existence of multiple dominant modes.

This paper proposes a novel approach for power system dynamic simulation based on the Differential Transformation (DT). The DT is introduced to study power systems as high-dimensional nonlinear dynamical systems for the first time, and is able to avoid computations of high-order derivatives with nonlinear differential equations by its transform rules. This paper first proposes and proves several new transform rules for generic non-linear functions that often appear in power system models, and then uses these rules to transform representative power system models such as the synchronous machine model with trigonometric functions and the exciter model with exponential and square root functions. The paper also designs a DT-based simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy and time performance of the proposed new DT-based simulation approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system.

This paper proposes a novel method for power system dynamic simulation that solves power system differential algebraic equations by a semi-analytical and semi-numerical approach using continued fractions. The method implements a two-stage scheme to enhance online performance of simulation: the offline derivation stage finds approximate analytical solutions, so-called “semi-analytical solutions,”for state variables of dynamic devices, such as generators in the form of power series of time with symbolic coefficients about system conditions; the online evaluation stage substitutes values on actual system conditions for symbolic coefficients, then transforms the solution into a continued fraction to prolong its time interval of accuracy, and finally calculates the system's trajectory over consecutive, adaptive time intervals for expected simulation results. A priori error bound for continued fractions is proposed to enable the simulation on adaptive time intervals. Compared with the conventional numerical simulation methods, the proposed continued fraction-based method has a fast simulation speed and a good suitability for parallel computing. The method is demonstrated and tested on the IEEE 9-bus system, the IEEE 39-bus system, and Polish 327-generator 2383-bus system.

This paper explores an alternative, semi-analytical approach to solution of the initial value problem of differentialalgebraic equations modeling a power system. Different from the traditional numerical integration based approach, this new approach applies the Adomian Decomposition Method to derive an approximate solution, called a semi-analytic solution (SAS), as a closed-form explicit function of time, the initial state and parameters on the system condition. Such a solution directly gives the power system's dynamic trajectory starting from an initial state that is accurate over a certain time window. Then, a multi-stage scheme evaluating the same SAS repeatedly for sequential time windows is able to give the system's trajectory for a desired simulation period without iterative computations as numerical integration does. The new approach is tested for power system transient stability simulation on a 3-machine, 9-bus power system and the IEEE 10-machine, 39-bus system, and its accuracy and time performance are compared with the 4th order Runge-Kutta method.

In the risk assessment of cascading outages, the rationality of simulation and efficiency of computation are both of great significance. To overcome the drawback of sampling-based methods that huge computation resources are required and the shortcoming of initial contingency selection practices that the dependencies in sequences of outages are omitted, this paper proposes a novel risk assessment approach by searching on Markovian Tree. The Markovian tree model is reformulated from the quasi-dynamic multi-timescale simulation model proposed recently to ensure reasonable modeling and simulation of cascading outages. Then a tree search scheme is established to avoid duplicated simulations on same cascade paths, significantly saving computation time. To accelerate the convergence of risk assessment, a risk estimation index is proposed to guide the search for states with major contributions to the risk, and the risk assessment is realized based on the risk estimation index with a forward tree search and backward update algorithm. The effectiveness of the proposed method is illustrated on a 4-node power system, and its convergence profile as well as efficiency is demonstrated on the RTS-96 test system. To appear in IEEE Transactions on Power Systems

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e., within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. The simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, a mathematical tool that can obtain power series coefficients by transformation rules instead of calculating high order derivatives and has proved to be effective in solving state variables of nonlinear differential equations in our previous study. This paper further solves non-state variables, e.g. current injections and bus voltages, directly with a realistic DAE model of power grids. These non-state variables, nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their differential transformations are proved to satisfy formally linear equations in this paper. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model with ZIP loads. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical methods. Published by IEEE Transactions on Power Systems in 2019

Semi-analytical simulation (SAS) is a methodology that derives power series as an approximate solution in power system steady-state or dynamic analysis. Pade approximation is able to further improve the efficiency of SAS, while its computation for large-scale power systems is time-consuming. This letter proposes a vectorized fast algorithm for computing Pade approximation of a large-scale SAS. The Levinson algorithm is used to reduce the temporal and spatial complexities. Considering the structural homogeneity of computation, a vectorized version of Levinson algorithm is realized to achieve instruction-level parallelism. The novel approach is tested on the SAS of Polish 2383-bus system, which verifies the advantage of Levinson algorithm and vectorization in boosting the computation speed of SAS.

Abstract Growing penetration of intermittent resources such as renewable generations increases the risk of instability in a power grid. This paper introduces the concept of observability and its computational algorithms for a power grid monitored by the wide-area measurement system (WAMS) based on synchrophasors, e.g. phasor measurement units (PMUs). The goal is to estimate real-time states of generators, especially for potentially unstable trajectories, the information that is critical for the detection of rotor angle instability of the grid. The paper studies the number and siting of synchrophasors in a power grid so that the state of the system can be accurately estimated in the presence of instability. An unscented Kalman filter (UKF) is adopted as a tool to estimate the dynamic states that are not directly measured by synchrophasors. The theory and its computational algorithms are illustrated in detail by using a 9-bus 3-generator power system model and then tested on a 140-bus 48-generator Northeast Power Coordinating Council power grid model. Case studies on those two systems demonstrate the performance of the proposed approach using a limited number of synchrophasors for dynamic state estimation for stability assessment and its robustness against moderate inaccuracies in model parameters.