Elsevier

Energy

Volume 29, Issues 12–15, October–December 2004, Pages 2239-2251
Energy

Optimization of boiler start-up using a nonlinear boiler model and hard constraints

https://doi.org/10.1016/j.energy.2004.03.022Get rights and content

Abstract

The basis for control optimization is a nonlinear modeling for a drum-type boiler consisting of furnace, economizer, evaporator, superheaters, attemperator, turbine bypass and thick-walled components such as boiler drum and superheater header. After the mathematical formulation of the boiler start-up optimization problem and of the cost function, including the related hard constraints for inputs and states, the optimal reference and input control are calculated using a multi-stage control vector parameterization method and SQP techniques. The results of this optimization process are optimal reference values and the corresponding input trajectories. The control structures applied minimize both the fuel consumption and start-up time of the boiler.

Introduction

There is a high demand for reducing start-up and shut-down costs in European thermal power plants. The main reasons are the new demands posed by a deregulated electricity market where more frequent and shorter start-ups and shut-downs are necessary in order to fulfill the short-term load requests from the electrical load dispatcher. Further reasons directly related to start-up costs of steam boilers are fuel, auxiliary load and auxiliary steam savings resulting from shorter start-up procedures which, in addition, increase the environmental compatibility of the process due to minimized overall emissions.

The major limiting factor relevant to fast power plant start-ups is the maximum admissible thermal stress for thick-walled components such as headers of superheaters and reheaters, boiler drum and the steam turbine rotor. Any violation of these limits reduces the life-time of the respective components. For this reason, both invasive and non-invasive sensors are used, complemented by dedicated thermal stress evaluation and monitoring software modules.

The new control solution presented here aims at improving of the start-up procedures of boilers and therefore explicitly takes the thermal stress values of critical components into account. Unlike other studies on power plant control [1], [2], [3], [4], mainly focusing on control improvements during load operation or hot-start conditions, this paper examines the basic start-up strategy of steam boilers, even from cold condition, considering the maximum allowable thermal stress and other constraints. These models describing the nonlinear behavior across a wide range of operating conditions are used for control optimization, either computing a priori improved reference and input values or for an on-line nonlinear model predictive controller application.

Section snippets

Boiler modeling

The model used in this paper applies for boilers for superheated steam production and includes the following process components economizer, drum, evaporator, superheaters, attemperator with spray control valve and a turbine bypass (see Fig. 1). Drum models for saturated steam production can be found in [5]. In this paper, the water drum level is assumed to be controlled properly by an inner closed-loop level controller. Therefore, it will not be modeled in an explicit way.

For practical

Thermal stress calculation

An important feature is the consideration of critical boiler components that are exposed to thermal stress. In practice, the thermal stress is calculated using invasive metal measurements as shown in Fig. 2. The most thick-walled components in power plants have a cylindrical form. During steady-state heat flux conditions and assuming a perfect thermal insulation of the outer surface, an analytic solution for the radial temperature profile T(r), ri<r<ro, in the cylinder has been found [11]:Tm−T(r

Optimization problem and numerical solution

Further limiting factors besides the thermal stress of thick-walled components for reducing start-up times in power plants are control bounds for firing change rate and control valves and other operational limitations. Therefore, it is necessary to explicitly include all relevant limitations as hard constraints into the control problem. For the start-up problem, not only the input variables but also the state and output variables are constrained.

The following formulation of the start-up

Simulation example and results

The controlled inputs of the modeled boiler are the mass flow rate qm,F of fuel, the position YHPB of the turbine bypass valve, and the position YAW of the control valve for spray water:ūT=[qm,F,YHPB,YAW]

In order to obtain continuous (stepless) inputs, one additional state variable per input has been introduced. The reason is that step-shaped inputs are not utilizable for practical purposes in power plants.

The not controlled inputs ūnc for the boiler model in this paper are the temperatures

Conclusions and outlook

The study presented here clearly shows the high impact and the potential for improvement that can be implemented if a boiler model obtained either by identification or by mathematical–physical modeling is applied. An optimized start-up strategy of the boiler leads to a new control of references and inputs which not only reduces the duration of the start-up time, but also leads to savings in fuel consumption and, consequently, to a limitation of the overall emissions into the atmosphere. The

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