Coal fired power plants currently account for more than 50% of the electricity generation in the US. Coal is abundant and cheap relative to other sources of fossil energy. Unfortunately the carbon foot-print is large. In the long run it is desirable to phase out coal based power generation as nuclear and renewable energy systems are developed. In the short run it is imperative that the coal based fleet is operated as efficiently as possible to minimize the emission of greenhouse gases and other pollutants like fly-ash, NOX and SOX.
Advanced process control and optimization have not made significant inroads into power plant control. Most power plants are operated using old control system structures using PI controllers that may be poorly tuned and some feed-forward. These control system structures were adequate for steady state operation. In the current, deregulated market power plants are subject to frequent load changes. Shortcomings in the classical control system designs have become evident and there is a need to implement advanced, model based control systems which can be used for stabilization and setpoint tracking.
Power generation systems are highly integrated internally and the dynamics change considerably due to strong integration with the power grid. The dynamics display a wide range of time-scales ranging from millisecond in the turbine and electrical systems to seconds and minutes in the steam temperature, combustion and emission control systems. All the time-scales must be modeled and controlled to ensure stable and safe power plant operation.
Classical approaches to power plant modeling use intensive variables like pressure and temperature to represent the system state [3-4]. Unfortunately, several approximations have to be made to implement such models, thermodynamic calculations often become cumbersome and the model structure becomes complex and non-intuitive. Nonlinearities are present in the state equations and it is difficult to develop systematic methods for modeling the network interconnections. Control system design can becomes cumbersome since inherent passivity properties, which facilitate simple control system design, may be lost.
In the passivity based approach we choose the inventories (the so-called Gibbs ensemble {U,V,N}) to represent the system state. The conservation laws are represented in the control affine form which can be connected with the passive systems theory. Network structures are easy to develop since the state space consisting of the extensive variables, can be described using concepts from affine geometry [5] [6]. Thermodynamics, chemical reaction and transport are described using algebraic constraints. The second law of thermodynamics can be used to show that the resulting DAE system has index 1, which means that open and closed loop dynamics can be solved using well tested integration methods suitable for stiff systems like ODE15s in MATLAB.
In the paper we use the passivity based approach to develop a dynamic model and multivariable control systems for a Rankine cycle power plant. The model components include the water-wall, riser and drum-boiler complex. We include multiple super-heaters, turbines with steam extraction, condenser, furnace, feed and air heaters. Each component is modeled as a system of DAEs with standard interconnects which allow accurate representations of the material and energy flows. The resulting model system maintains the invariant (Hamlitonian) structures which can be derived from the mass and energy conservation laws. The resulting model has been verified against data from a 600MW power plant system in the Pittsburgh region.
We furthermore prove that the state space spanned by the intensive variables such as temperature and pressure is isomorphic to the space spanned by extensive variables such as the mass and energy inventories for a single component system. This result allows us to develop a passivity-based inventory control scheme the power plant system. The asymptotic stability of the closed-loop system is proved using Lyapunov stability theory using a thermodynamic based dissipation function.
The proposed inventory controller has been tested in two typical tests: step response test and area regulation test. In the step response test, the power plant model is subjected to a set-point change in the mass or energy inventory of a unit operation. The area regulation (AR) test is a standard test and frequently used in the daily operation of a power station. The AR test signals consist of several ramps, which fluctuate around the base loading with a maximum deviation of ±10%. The numerical simulations suggest the performance and efficiency of the inventory controllers in power plant systems.
[1] A. van der Schaft. L2-Gain and Passivity Techniques in Nonlinear Control. Springer-Verlag, New York, second edition, 2000.
[2] K. R. Jillson and B. Erik Ydstie. “Process networks with decentralized inventory and flow control” Journal of Process Control, vol. 17:399-413, 2007.
[3] K. J. Astrom and R. D. Bell. “Drum-boiler dynamics, ” Automatica, 36:363-378, 2000
[4] M. E. Flynn , M. J. Oapos Malley. “A drum boiler model for long term power system dynamic simulation, ” IEEE Transactions on Power Systems, vol. 14:209-217, 1999
[5] E.D. Gilles. Network theory for chemical processes. Chem. Eng. Technol., 21(2):121–132, 1998.
[6] C. A. Farschman, K. P. Viswanath, B. Erik Ydstie. “Process systems and inventory control,” AIChE Journal, Vol. 44(8):1841-1857, 1998
[7] K. L. Chien, E. I. Ergin , C. Ling and A. Lee. “Dynamic analysis of a boiler,” ASME Transactions 80:1809-1819, 1958.