Nonlinear models: coal combustion efficiency and emissions control

Today’s power plants feel the pressure to limit their NOx emissions and improve their production economics. This article describes how nonlinear models are effective for process guidance of various kinds of processes, including coal fired boilers.

Abhay Bulsari, Nonlinear Solutions Oy, Turku, Finland & Antti Wemberg, Ari Anttila and

Ahti Multas, Fortum Power and Heat Oy, Naantali, Finland

The sharp increase in the price of fuels and energy in the last two years has caused renewed interest in coal fired power plants to improve their combustion efficiencies. There is also a lot of political and social pressure towards reduced NOx and other emissions. Competition in the energy markets forces the power companies to continuously improve on both these fronts. Power plant managers, therefore, would like to show continuous improvement in their processes.

Fortum’s power plant in Naantali, Finland.
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Operation of any industrial process can always be improved with more knowledge. One can never know everything about any industrial process. An infinite number of variables influence the final consequences of a process, and one can take only a few variables into consideration. Even the effects of each variable can be highly complicated, and one can always learn more and more about the effects.

For process guidance, physical modelling is not particularly effective for coal fired boilers, partly because it requires a lot of assumptions and simplifications, and partly because of the lack of deeper knowledge of the reaction kinetics and mass transfer in burning coal particles. Besides, it takes too long à‚— typically days à‚— to calculate the outputs of physical models of coal fired boilers.

Nonlinear models do not have either of these weaknesses. Empirical and semi-empirical models are based on the observed behaviour of the process, and therefore, reflect the reality better. These models can be developed from production data.

Fortum’s coal fired power plant in Naantali, Finland

The city of Turku receives much of its electricity and heat from the coal fired power plant above in the scenic coastal town of Naantali, 15 km from Turku. The Naantali power plant has been generating electric power for about 50 years. It consists of three 46 m high pulverized coal boilers with rectangular cross sections.

The Naantali 2 boiler was constructed by Sulzer and taken into use in 1964, while the turbogenerators were supplied by Kraftwerk Union of Siemens. Coal is the main fuel, while oil is normally used as the starting fuel. Saw dust is also added to coal these days, which accounts for at the most 2 per cent of the fuel value. Saw dust typically contains 45 to 55 per cent moisture.

The Naantali 2 boiler produces either 90 MW electricity and 175 MW heat, or 120 MW electricity at full load. The typical consumption of coal at full load is about 44 tonnes/hour (worth 315 MW), when the boiler produces 117 kg/sec or 421 tonnes/hour of steam at a pressure of 180 bar, and a temperature of 535 à‚°C. Depending on how much steam is taken out for industrial consumption and the amount of district heat produced, 40 to 120 MW of electricity is produced by the turbogenerator. Steam is taken out from the turbine’s intermediate pressure section. District heat is supplied in the form of water at a temperature of 75 à‚°C to 120 à‚°C, which returns at a much lower temperature.

Coal is pulverized by three coal mills numbered 4, 5 and 6, to a particle size below 0.1 mm. Each of them has a maximum capacity of 20 tonnes/hour. There are four burners at three levels, located in the corners. The burners also have provision for secondary and tertiary air flows, besides the coal conveying air which is considered to be primary air. The characteristics of coal vary with each shipment, even if it comes from the same mine. Coal is imported from several Russian mines.

Mathematical modelling with different approaches

Mathematical models are quantitative descriptions in terms of variables. In other words, they contain concise knowledge of a system about the quantitative effects of selected variables. Such models try to emulate reality and can be used instead of experimentation, if they are of a sufficiently good quality. Mathematical modelling is performed with several different approaches.

Physical models are developed by writing laws of nature in a mathematical form. For processes like combustion in a boiler, a physical model could consist of partial differential equations of heat transfer, mass transfer and fluid dynamics, coupled with multiple chemical reactions. These models usually require plenty of assumptions and simplifications. The reactions taking place at different temperatures are poorly known, let alone their kinetics. It takes a lot of time to solve these equations, making them impractical for determining good values of process variables.

Empirical and semi-empirical modelling describe the reality as observed without the need of any major assumptions or simplifications. It requires observations either from production data, or from experiments. Empirical modelling is usually carried out with linear statistical techniques, which are not very efficient at describing nonlinearities in the effects of variables. Nothing in nature is very linear, and hence it makes sense to take nonlinearities into account by using the new techniques of nonlinear modelling.

Nonlinear modelling

One of the main purposes of this article is to improve the awareness about the new techniques of nonlinear modelling. Many readers of this magazine have probably seen the article on nonlinear modelling of desulphurization in the May 2008 issue of Power Engineering International1.

Nonlinear modelling has been successfully used in several industrial sectors including plastics, metals, concrete, glass, pharmaceuticals, medicine, semiconductors, biotechnology, mineral wools and food. It has been utilised for a variety of purposes including quality control, product development, process guidance, software sensors and fault detection. Process modelling for process development, however, is the most common purpose.

Nonlinear modelling is empirical or semi-empirical modelling that takes at least some nonlinearities into account. The older techniques include polynomial regression, linear regression with nonlinear terms, and nonlinear regression. These techniques have several limitations unlike the new techniques of nonlinear modelling based on free-form nonlinearities.

Figure 1. A typical feed-forward neural network has an input layer, an output layer and one or two hidden layers.
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The new techniques of nonlinear modelling include: feed-forward neural networks, series of basis functions, and multivariate splines. Among these new techniques, feed-forward neural networks have turned out to be particularly valuable in process modelling2 primarily because of their universal approximation capability3. It is usually possible to produce nonlinear models with some extrapolation capabilities with feed-forward neural networks. Artificial neural networks consist of neurons or nodes, usually arranged in layers and directionally connected to others in the adjacent layers. The multilayer perceptron (Figure 1) is a kind of a feed-forward neural network.

Nonlinear modelling of industrial processes

As mentioned in the previous section, nonlinear models of processes are developed for a few different purposes including process development, process guidance, process control, fault detection, and estimation of variables, which are difficult to measure. For a power plant, the operators would like to know the suitable values of process variables, which will result in good combustion leading to a high combustion efficiency and low emissions. Every time the load changes, or when a new shipment of coal arrives, the optimal conditions change, and operators would like to determine the best conditions, as well as the possibility to study what-if scenarios.

Determining the best operating conditions is an optimization problem, with constraints on process variables as well as on consequences like emissions. In addition, there are fixed values of disturbance variables like coal characteristics and the load. The objective function could be the consumption of coal, or cost of fuel per hour.

Different industrial processes may have different raw materials, different products, different process variables, different kinds of chemical reactions. The process may be a batch process, a continuous process or a fed-batch one. However, process modelling of various kinds of processes have several common features. Various consequences of a process depend on the feed characteristics and process variables (Figure 2). In case of coal fired boilers, the consequences of interest include emissions, efficiency, and the cost of fuel.

Figure 2. A typical model configuration for process guidance of a coal fired boiler.
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Operation data from the Naantali 2 boiler

Nonlinear models are developed from observations of a process. These observations could be taken from production data, or experiments could be carried out to produce even better data. Sometimes data from a few experiments is added to selected production data. In case of the Naantali 2 boiler, well-selected production data was used for much of the model development work. Production data tends to be dilute in information content, so it helps to select observations which result in sufficient variety in them.

Figure 3. A typical model structure for a coal fired power plant.
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Which variables to include is not always clear from the beginning, so it is common to develop a large number of models with different sets of input variables. Figure 3 shows one possible set of variables. The input variables have to be independent variables, while the output variables are dependent variables, which depend on the input variables. The input variables should be the causes of the consequences, which are represented by the output variables, if we want the models to be useful for process guidance or control. The dependent variables do not have to be independent of each other.

This project was called the A4 project à‚— based on the first names of the four persons working on it, the co-authors of this article. It was started by listing the possible input and output variables, which could be included in the models. The fuel flow rates, fraction of sawdust, air flow rates and the load had to be taken into account. The actual energy output of the plant was measured in terms of feed water flow rate, which was taken as an output variable, since it depends entirely on the heat produced by the boiler.

NOx content in the flue gas was another important output variable. In the beginning, production data containing a larger number of variables was collected for use. Many observations were picked manually from the database to ensure a good variation in several variables of interest.

One needs to keep in mind the objective of the models while developing the models. The models are going to be used to determine suitable values of process variables, particularly the coal flow rates and air flow rates, such that the emissions stay below desired limits, and the cost of fuel is minimized. The optimal operating conditions change every time a new shipment of coal arrives, or when the load changes. Variables which appear in the constraints or the objective function should be included in the models, and not dropped out at any stage.

Analysis and pre-processing of data

Production data almost always needs some pre-processing. However, it is good to preprocess and analyze experimental data also. With production data, there can be simpler issues like missing values in observations and obviously wrong observations. Since the observations were more or less hand-picked, the data was relatively clean. Plots of each variable against each other variable can point out some relevant things.

Some of the input variables that should be independent may still show a strong correlation. It takes a few seconds to calculate the correlation matrices, and it is good to go through them. Cluster analysis is also performed when the amount of data is relatively large. In this case, there were some internal correlations among the selected input variables, but were not too strong. These actions also increase the familiarity with the data, which helps significantly during the real model development work.

Nonlinear models of consequences of coal combustion

Nonlinear models of different structures were developed at different stages of this work. Various subsets of the input variables shown in Figure 3 were used, and as a start, coal characteristics were not taken into account, considering that their variation was not large. Even though plain production data was utilised, nonlinear models could predict NOx emissions and feed water flow rate (a measure of power generated) quite well, with fairly high correlation coefficients. Unlike linear models, it is easy to ensure that the nonlinear models will not predict negative values of NOx emissions.

Figure 4. Effect of secondary air on NOx emissions at different values of flow rate from coal mill 4 as predicted by the nonlinear model.
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Figure 4 shows the reducing effect of secondary air on NOx emissions at different values of the fuel flow rate from coal mill 4, while keeping other input variables constant. The reducing effect of the fraction of saw dust on feed water flow rate at different values of fuel flow rate from coal mill 6 is seen in Figure 5.

Figure 5. Effect of the fraction of saw dust on feed water flow rate at different values of flow rate from coal mill 6 as predicted by the nonlinear model.
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Figure 6 shows the combined effects of secondary air and fuel flow rate from coal mill 6 on unburnt carbon in ash in the form of contours. There is a relatively large acceptable region (bluish area in Figure 6) for operation, from the point of view of unburnt carbon in ash.

Figure 6. Effect of secondary air and fuel flow rate from coal mill 6 on unburned carbon-in-ash.
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The equations of nonlinear models are not simple. One cannot expect the users of nonlinear models to be familiar with the mathematics involved. A set of software components has been constructed by Nonlinear Solutions over the years to help users utilize the nonlinear models efficiently. Different software components can be useful for different purposes. When assembled together into a single programme, we refer to it as a LUMET system.

The plots in Figures 4, 5 and 6 were produced by a LUMET system containing some of the models developed for the Naantali 2 boiler. In some cases, a software component allowing for updating the models is also included. LUMET systems can also have facilities for calculating the best values of process variables in presence of constraints and optimization objectives.

Mathematical models can always be improved. More variables can be taken into account, ranges of the variables can be widened, and nonlinearities could be better approximated. The models developed so far have already contributed to our knowledge of the process, but the development does not end here. More variables will be included in near future, experiments will be carried out to widen the ranges of the variables, as well as study the cross term effects of input variables.

All industrial processes, including combustion in boilers can be operated more efficiently with better quantitative knowledge of the effects of important process variables and feed characteristics on the relevant consequences of the processes. The relations between the variables are fairly complicated in the case of coal fired boilers.

Nonlinear models, which have proved to be highly effective for a large variety of processes in several industrial sectors, are well-suited for coal fired power plants as well. When implemented in suitable software, nonlinear models emerge as powerful tools for the power plant operators as well as for R&D engineers. They can help improve the combustion efficiency while keeping emissions under allowable limits, with little extra effort.


[1] A. Bulsari and J. Hagstràƒ¶m, “Fine tuning FGD via nonlinear modelling”, Power Engineering International, Vol. 16, No. 4 (May 2008) 136-140.

[2] A . Bulsari (ed.), Neural Networks for Chemical Engineers, Elsevier, Amsterdam, 1995.

[3] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, Vol. 2, (1989) 359-366.

[4] P. E. Gill, W. Murray and M. H. Wright, Practical Optimisation, Academic Press, London (1981) 133-140.

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