On the direct method for transient stability analysis of power system structure preserving models

Large-scale AC-DC hybrid power systems have become a basic pattern for power transmission in China. Currently, time-domain simulation is widely used for transient stability analysis, which has the disadvantages of high computational burdens and lack of system stability margin information. An alternative method for transient stability analysis is the direct method, which assesses transient stability from the energy point of view. Direct method requires much less computation efforts. In addition, the stability margin of the system can be obtained. Due to the challenges in system modelling, energy function construction, and determination of critical energy value, it is challenging to apply direct method for transient stability analysis of AC-DC hybrid power systems. This paper is a step in exploring the application of direct method in AC-DC hybrid power systems.

This paper presents an overview about the main advances which occurred in the application of a direct method for transient stability analysis. The text is mainly focused on the potential energy boundary surface (PEBS) and boundary controlling unstable (BCU) method. The author's opinion about future perspectives and research areas of interest are given at the end of the text.

Transient stability domain estimation of AC/DC systems considering HVDC switching characteristics based on the polynomial Lyapunov function method

The work presented in this paper describes a scheme for rescheduling pool generation and adjusting contract-transactions for dynamic security enhancement when necessary, using a power market auction mechanism. The procedure is based on the transient energy margin concept, which is estimated using the corrected hybrid method of transient stability analysis. This index is selected because of useful linearity properties which it possesses with respect to certain important problem control variables. The proposed scheme brings together both technical and economic considerations and the procedure is illustrated using the New England System data set.

Today’s power systems are operated closer to their stability limits due to the continuously growing load demands, interface to open markets, and integration of more renewable energies. In order to provide operators with clear insight on the current system situation, near real-time power systems dynamic security assessment tools are required. One of the core elements of near real-time dynamic security assessment tools is contingency screening and ranking. Most of the commercially available tools screen and rank contingencies by using the traditional numerical integration or Transient Energy Functions (TEFs) or hybrid methods. The traditional numerical integration method is accurate but computationally intensive and has a slow assessment speed which makes it difficult to identify any insecure contingency before it happens. Despite the TEF method of transient stability analysis being relatively fast, it develops less accurate results due to models simplification and assumptions. This paper introduces transient stability based on fast and robust contingency screening and ranking using an Adaptive step-size Differential Transformation (AsDTM) method. Based on the most current snapshot from Supervisory Control and Data Accusation (SCADA) data, the proposed method triggers AsDTM-based transient stability simulation for each credible contingency and evaluates Transient Stability Indices (TSI) as the normalized weighted sum of squares of errors derived from state variables and complex bus voltages at every simulation time step. Finally, contingencies are ranked based on these TSI and the worst contingency is identified for the next detail assessment. The method is tested on IEEE 9 bus and 39 bus test systems. Test results reveal that the proposed method is faster, robust, and can be used in near real-time dynamic security assessment sessions.

Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances.Important conclusions and decisions are made based on the results of stability studies.The conventional method of analyzing stability is to calculate the transient behaviour of generators due to a given disturbance.Direct methods of stability analysis identify whether or not the system will remain stable once the disturbance is removed by comparing it with a calculated threshold value.Direct methods not only avoid the time consuming solutions required in the conventional method, but also provide a quantitative measure of the degree of system stability.This additional information makes direct methods very attractive when the relative stability of different plans must be compared or when stability limits must be calculated quickly.Direct methods of transient stability analysis of a multi machine power system, using a function describing the system's transient energy, are discussed.By examining the trajectory of the disturbed system, the following fundamental questions are dealt with: the concept of a controlling unstable equilibrium point (U.E.P), the manner in which some generators tend to lose synchronism, and identifying the energy directly responsible for system separation.Resolving this issue will substantially improve transient stability analysis by direct method.

This paper presents inversion based feedforward control design for flexible multibody systems with kinematic loops and end-effector contact. The inverse model provides for a given desired output trajectories, e.g. end-effector point and contact force, the required control inputs for exact output reproduction. A very appealing and efficient model inversion approach for such multibody systems is the use of so-called servo-constraints. These can be seen as an extension of classical mechanical constraints and yield a set of differential-algebraic equations. This allows an efficient numerical solution without burdensome symbolic manipulations. In addition, the use of servo-constraints allows the straight-forward treatment of flexible multibody systems with various topologies. The arising set of differential-algebraic equations describes the inverse model. The inverse model might be purely algebraic or include a dynamical part, which is called internal dynamics in nonlinear control theory. For its numerical solution it is advisable to transform the set of differential-algebraic equations to its underlying set of ordinary differential equations. The solution method for this internal dynamics depends then on its stability. For systems with unstable internal dynamics, as considered in this paper, a solution can be computed from a boundary-value problem. The efficiency of this approach is demonstrated for a flexible multibody system with a kinematic loop and a closed end-effector contact.

Small signal stability analysis is conducted considering grid connected doubly-fed induction generator (DFIG) type. The modeling of a grid connected DFIG system is first set up and the whole model is formulated by a set of differential algebraic equations (DAE). Then, the mathematical model of rotor-side converter is built with decoupled P-Q control techniques to implement stator active and reactive powers control. Based on the abovementioned researches, the small signal stability analysis is carried out to explore and compared the differences between the whole system with the decoupled P-Q controller or not by eigenvalues and participation factors. Finally, numerical results demonstrate the system are stable, especially some conclusions and comments of interest are made.

A two-dimensional approach to multibody free dynamics in space environment

This study proposes a novel equivalent modelling method of wind farm (WF), which can be used for small‐signal stability analysis and researches on damping control of low‐frequency oscillation. First, a complete WF model described with a set of differential algebraic equations is established, then its linearised model is obtained at one of the steady‐state operating points. Next, the eigenanalysis and the modal participation factor (MPF) analysis methods are adopted to evaluate the low‐frequency oscillation modes and the corresponding modal participation in each wind turbine generator (WTG). A feature vector for each WTG, describing its oscillation characteristics, is extracted based on the MPFs. Afterwards, all WTGs are clustered into some groups via a clustering algorithm, then the WTGs in the same groups are aggregated into a single WTG, using the weighted summation method. Furthermore, the criterion for the validity of the equivalent model is studied. The proposed modelling and validation methods are verified by simulations.

Recent efforts to apply direct methods of transient stability analysis to multimachine power systems have used the so-called "energy functions." These functions describe the system transient energy causing the synchronous generators to depart from the initial equilibrium state, and the power network's ability to absorb this energy so that the synchronous machines may reach a new post-disturbance equilibrium state. Recent results have shown that not all the transient energy contributes to system separation. Indeed it has become increasingly evident that system separation depends on the energy of certain individual machines or groups of machines, which comprise the critical group, and which tend to separate from the rest of the machines (which make up the noncritical group). Thus there is a need for generating energy functions for individual machines (or for groups of machines). Using a center of inertia frame of reference, the energy function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_{i}</tex> for machine <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</tex> is derived. A procedure for first swing transient stability assessment is developed using the energy function of individual machines and groups of machines. The method is tested extensively on two realistic power networks (the 20-generator IEEE System and the 17-generator reduced Iowa System). An analytical justification for using the critical energy of individual machines in stability assessment is provided using an invariance principle for ordinary differential equations. Power system transient stability is analyzed using the energy function of the critical group of machines. This energy function is dependent on all state variables of the power system, and satisfies the hypotheses of the invariance theorem of La Salle, enabling us to deduce the asymptotic stability of the post-disturbance equilibrium of the entire power system. It also enables us to obtain an estimate of the domain of attraction of this equilibrium of the entire power system. The methodology advanced herein, which combines computer-aided techniques with analytical tools, yields less conservative results than were obtained in previous works that used total system energy. It is to be noted that the present results are preliminary in the sense that the mechanism of separation of the critical group of machines from the rest of the system needs further investigation.

This paper proposes a decoupling based direct method to analyze the post-contingency transient stability for a general multi-machine power system. A linear decoupling transformation is used to construct the same number of independent single machine infinite bus (SMIB) power systems as oscillation modes. Each SMIB system carries stability information regarding one oscillation mode of the original system at the equilibrium. Then, the transient energy function method is applied on all decoupled SMIB systems to calculate stability margins, the smallest of which indicates the stability margin of the original system. Case studies on an IEEE 9-bus power system and a WECC 179-bus power system demonstrate the validity of the proposed method.

A comparison of numerical methods for solving multibody dynamics problems with frictional contact modeled via differential variational inequalities

SUMMARYThe study of inertial forces effects at high speeds in flexible parallel manipulators, which generate undesired deviations, is a challenging task due to the coupled and complicated equations of motion. A dynamic model of the Revolute Prismatic Revolute (RPR) planar manipulators (specifically 3-RPR, 2-RPR and 1-RPR) with flexible intermediate links is developed based on the assumed mode method. The flexible intermediate links are modeled as Euler-Bernoulli beams with fixed-free boundary conditions. Using the Lagrange multipliers, a generalized set of differential algebraic equations (DAEs) of motion is developed. In the simulations, the rigid body motion of the end-effector is constrained by some moving constraint equations while the vibrations of the flexible intermediate links cause deviations from the desired trajectory. From this analysis, the dynamic performance of the manipulators when tracking a desired trajectory is evaluated. A comparison of the results indicates that in some cases, adding each extra RPR chain in the n-RPR planar manipulators with flexible intermediate links reduces the stiffness and accuracy due to the inertial forces of the flexible links, which is opposite to what would be expected. The study provides insights to the design, control and suitable selection of the flexible manipulators.

The recent work presents the motion control of a pendulum like under—actuated service robot AC ROBOT ER. This robot is designed to be applied in indoor environments, where it can perform pick and place tasks autonomously and/or with close cooperation with humans. It can also serve as a platform that carries other service robots with lower mobility. The cable suspended robot has a complex structure and its dynamics is difficult to model using conventional robotic approaches. Instead, in this paper natural (Cartesian) coordinates are used to describe the configuration of the robot, while its dynamics is modeled as a set of differential algebraic equations. The method of computed torque control with a PD controller is applied to the investigated under—actuated system. The inverse dynamics solution is obtained via direct discretization of the DAE system. Results for a real parameter case study are presented by numerical simulations.