Nonlinear Programming: A Unified Approach

The systems modeling methodology of system dynamics is well suited to address the dynamic complexity that characterizes many public health issues. The system dynamics approach involves the development of computer simulation models that portray processes of accumulation and feedback and that may be tested systematically to find effective policies for overcoming policy resistance.System dynamics modeling of chronic disease prevention should seek to incorporate all the basic elements of a modern ecological approach, including disease outcomes, health and risk behaviors, environmental factors, and health-related resources and delivery systems. System dynamics shows promise as a means of modeling multiple interacting diseases and risks, the interaction of delivery systems and diseased populations, and matters of national and state policy.

https://ajph.aphapublications.org/doi/pdfplus/10.2105/AJPH.2005.062059

System dynamics modeling for public health: background and opportunities.

The aim of this paper is to assess the capability of the emerging synchronized phasor measurement technology in improving the overall stability of the Hydro-Quebec transmission system through supplementary modulation of voltage regulators. Following a thorough singular value and eigenvalue analysis of the system dynamic interactions, five control sites consisting of four generators and one synchronous condenser are chosen to implement new power system stabilizers with a supplementary input from remote phasor measuring units, geographically spread over nine electrically coherent areas. Since the remote feedback loops are built on top of an existing decentralized control system, this design approach results in a decentralized/hierarchical control architecture with significant advantages in terms of reliability and operational flexibility. A systematic control and measurement pairing yielded four dominant natural loops, each associated with a significant open-loop inter-area oscillatory mode at 0.06, 0.4, 0.7 and 0.95 Hz respectively. These PSSs have a speed sensitive local loop operating in the usual way, and a wide-area measurement based global loop which involves a single differential frequency signal between two suitably selected areas. The tuning and coordination technique for these advanced multiple input signals PSSs is described. Their impacts on the system is assessed using both small-signal analysis and nonlinear simulations in a transient stability program. Wide-area stabilizing controllers have a significant potential in improving the dynamic performance of the Hydro-Quebec's existing power system.

Wide-area measurement based stabilizing control of large power systems-a decentralized/hierarchical approach

Several voltage collapses have had a period of slowly decreasing voltage followed by an accelerating collapse in voltage. The authors clarify the use of static and dynamic models to explain this type of voltage collapse, where the static model is used before a saddle-node bifurcation and the dynamic model is used after the bifurcation. Before the bifurcation, a static model can be used to explain the slow voltage decrease. The closeness of the system to bifurcation can be interpreted physically in terms of the ability of transmission systems to transmit reactive power to load buses. Simulation results show how this ability varies with system parameters. It is suggested that voltage collapse could be avoided by manipulating system parameters so that the bifurcation point is outside the normal operating region. After the bifurcation, the system dynamics are modeled by the center manifold voltage collapse model. The essence of this model is that the system dynamics after bifurcation are captured by the center manifold trajectory. The behavior predicted by the model is found simply by numerically integrating the system differential equations to obtain this trajectory. >

On voltage collapse in electric power systems

This paper provides a comprehensive list of books, reports, workshops and technical papers related to voltage stability and security

Bibliography on voltage stability

A parallel method for the transient stability simulation of power systems is presented. The trapezoidal rule is used to discretize the set of algebraic-differential equations which describes the transient stability problem. A parallel Block-Newton relaxation technique is used to solve the overall set of algebraic equations concurrently on all the time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique, in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

A Gauss-Jacobi-Block-Newton method for parallel transient stability analysis (of power systems)

A new parallel algorithm for transient stability analysis is presented. An implicit trapezoidal rule is used to discretize the set of algebraic-differential equations which describe the transient stability problem. A parallel-in-time formulation has been adopted. A Newton procedure is used to solve the equations which describe the system at each time step, whereas a Gauss-Seidel algorithm relaxes the solution across the time steps. A Gauss-Seidel-like procedure can be usefully exploited in the parallel processing mode by pipelining the computation through time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

F. Torelli

Papers

A Gauss-Jacobi-Block-Newton method for parallel transient stability analysis (of power systems)

A pipelined-in-time parallel algorithm for transient stability analysis (power systems)

A generalized approach to the analysis of voltage stability in electric power systems

Quadratic probabilistic load flow with linearly modelled dispatch

State space representation of interconnected power systems for dynamic interaction studies