The present disclosure relates to methods for calibrating a boiler having a burner to optimise efficiency.

Industrial boilers are used to generate steam, for example for power generation or for heat transfer (e.g. in medical sterilisation, industrial cooking and other industrial processes).

The burner of a typical steam boiler receives fuel (e.g. natural gas) and burns it in air to generate heat. This is known to generate emissions in a flue gas from the burner, such as oxides of nitrogen (NOx) and carbon monoxide. Stoichiometric combustion is generally not practical, and so most burners use an air-to-fuel ratio above

stoichiometric (l>1) to ensure complete combustion of the fuel. However, excessive air reduces burner temperature (“thermal dilution”) and increases net waste heat exhausted along the flue. Accordingly, it is known to reduce the air-to-fuel ratio whilst still attempting to ensure complete combustion of the fuel. This can be done by progressively reducing the air-to-fuel ratio whilst analysing the amount of excess oxygen and indicators of incomplete combustion (e.g. carbon monoxide in the flue gas). This may increase the efficiency of the burner (i.e. combustion efficiency) and may lead to a high flame temperature at the burner.

High flame temperature may cause generation of oxides of nitrogen (NOx), largely owing to nitrogen dissociating and combining with oxygen at high temperature. It is known to counteract an emissions of oxides of nitrogen (NOx) by injecting water into the burner, to reduce the flame temperature.

According to a first aspect there is provided a method of calibrating a boiler having a burner, comprising: supplying fuel to the burner at a fuel supply rate and supplying combustion air to the burner at an air supply rate, so that fuel is burnt at an air-to-fuel ratio; and supplying water to the burner at a water supply rate; adjusting burner operating variables, including adjusting both the air-to-fuel ratio and the water supply rate, to define a plurality of burner states; testing operation of the boiler at the plurality of burner states; for each burner state; determining an efficiency parameter relating to an efficiency of the boiler; monitoring emissions in a flue gas downstream from the burner; comparing the emissions to one or more emissions thresholds to determine if they are excessive or acceptable; and from a set of burner states correlated to acceptable emissions, selecting an operational burner state to optimise the efficiency parameter, for operation of the boiler.

The selected operational burner state may have a higher air-to-fuel ratio and a higher water supply rate than an optimal-efficiency burner state having excessive emissions.

Adjusting operating variables of the burner may comprise successively reducing the air-to-fuel ratio while increasing the water supply rate to counteract an increase in emissions.

The method may further comprise determining a plurality of burner states that lie on an emissions boundary in a state space of burner states in which the air-to-fuel ratio and water supply rate are state variables, the emissions boundary corresponding to the one or more emissions thresholds; and wherein the operational burner state is selected from the plurality of burner states on the boundary.

Where emissions are compared with a plurality of emissions thresholds, the emissions boundary may be a compound boundary based on each of the respective thresholds.

One or more of the burner states on the emissions boundary may be determined by calculation. In other words, when the operational burner state is selected from the plurality of burner operating states on the boundary, one or more of those burner operating states may be determined to lie on the boundary by calculation rather than by operating the burner at each respective burner operating state.

The efficiency parameter may be a flue-derived boiler efficiency determined at least partly based on a monitored level of excess oxygen and/or a monitored level of carbon monoxide and/or a monitored level of carbon dioxide in the flue gas.

The flue-derived boiler efficiency may be determined based on the fuel supply rate; the air supply rate; a flue gas parameter selected from the group consisting of level of oxygen, level of carbon dioxide, level of carbon monoxide; and a flue gas temperature. The efficiency parameter may be a boiler heat transfer efficiency determined based on the heat transfer to a working fluid of the boiler relative the heat input to the burner (i.e. a working-fluid derived boiler efficiency).

The boiler heat transfer efficiency may be determined by calculating the ratio of the thermal power difference of the working fluid to the sum of thermal power to the burner from air, fuel and water, and thermal power released by complete combustion of the fuel.

The emissions may be compared to one or more of an oxides of nitrogen (NOx) threshold; a carbon monoxide threshold; a carbon dioxide threshold; and an oxides of sulphur (SOx) threshold.

The water may be liquid as supplied to the burner, whereby the water vaporises to turbulently expand and mix at the burner.

The boiler may be in-service in an industrial plant, the boiler having a demand state corresponding to a load on the boiler, wherein the burner operating variables are iteratively adjusted to optimise the efficiency parameter.

Iteratively adjusting the burner operating variables may comprise: obtaining a prediction of emissions and/or the efficiency parameter for a first burner state of the plurality, based on calibration data correlating emissions and/or the efficiency parameter respectively with the burner variables; determining observed data for emissions and/or the efficiency parameter; comparing the prediction and observed data to determine a performance error; defining a second burner state based on a model correlating emissions and/or efficiency to the burner operating variables to compensate for the performance offset.

The method may further comprise storing calibration data for each of the burner states at which the burner is tested, the calibration data comprising: efficiency data including the efficiency parameter; state data including: the water supply rate, the air-to-fuel ratio; and/or the fuel supply rate and the air supply rate; and emissions data relating to the emissions in the flue gas. Each of the burner operating states may correspond to the same demand state of the boiler. The demand state may correspond to a load serviced by the boiler, a heat transfer demand at the boiler (e.g. a thermal power input output to the working fluid, or a thermal power input to the burner), or a fuel supply rate, for example.

The method may comprise storing calibration data correlated to the demand state. The calibration data may comprise state data for at least the selected burner operating state, the state data including: the water supply rate; the air-to-fuel ratio, and/or the fuel supply rate and the air supply rate.

According to a second aspect there is provided a method of calibrating a boiler at a plurality of demand states comprising, for each demand state, calibrating the boiler by a method in accordance with the first aspect.

With respect to the first and second aspects, the boiler may be in a test installation remote from an industrial plant, to generate calibration data for use at an industrial plant. In other words, the boiler of the test installation may not be in-service in an industrial plant, but is instead configured for generating calibration data remotely from an industrial plant.

Alternatively, the boiler may be in-service in an industrial plant. The method may further comprise: determining a demand state of the boiler; selecting an operational burner state from the calibration data based on the demand state; and operating the boiler at the operational burner state.

According to a third aspect there is provided a method of operating a boiler having a burner, comprising: determining a demand state of the boiler; selecting an operational burner state from calibration data generated by a method in accordance with the first or second aspects, based on the demand state; and operating the burner at the operational burner state.

According to a fourth aspect there is provided a method of operating a boiler having a burner, comprising: calibrating the boiler by a method in accordance with the first or second aspects; wherein the boiler is calibrated periodically and/or in response to a stimulus selected from the group consisting of: a determination of excessive emissions in a flue gas of the boiler; a determination of a change in emissions, oxygen or carbon dioxide levels in the flue gas exceeding a respective threshold; a change in a demand state of the boiler. According to a fifth aspect there is provided a boiler controller configured to operate a boiler by: controlling a fuel supply rate of fuel to a burner of the boiler at a fuel valve; controlling an air supply rate of air to the burner at an air valve; controlling a water supply rate of water to the burner at a water supply valve; receiving emissions data from an emissions analyser of the boiler; wherein the controller is configured to carry out a method in accordance with any preceding claim.

According to a sixth aspect there is provided a boiler installation comprising: a boiler having a burner; optionally an emissions analyser for monitoring emissions in a flue gas of the boiler; a fuel valve for controlling a supply of fuel to the burner; an air valve for controlling a supply of air to the burner; a water valve for controlling a supply of water to the burner; and a boiler controller in accordance with the fifth aspect.

According to a seventh aspect there is provided a computer program comprising instructions to cause a boiler controller or a boiler installation to carry out a method in accordance with any of the first to fourth aspects.

According to an eighth aspect there is provided a non-transitory computer-readable medium storing a computer program in accordance with the seventh aspect.

The invention may comprise any combination of features described herein, except such combinations as are mutually exclusive.

The invention will now be described, by way of example, with respect to the

accompanying drawings, in which:

Figure 1 schematically shows a plot of boiler efficiency as a function of air-to-fuel ratio and water injection rate, with an overlaid emissions boundary;

Figure 2 schematically shows an example boiler installation;

Figure 3 is a flow diagram of an example method of calibrating a boiler;

Figure 4 is a flow diagram of an example method of setting an operational burner state of a burner of a boiler; and

Figure 5 is a flow diagram of an example method of calibrating a boiler.

Whilst it has been known to (i) adjust air-to-fuel ratio to ensure complete combustion ; and (ii) inject water to a burner to reduce emissions of oxides of nitrogen (NOx), such actions in the commissioning of previously-considered boiler installations have been conducted independently and without reference to seeking optimal boiler efficiency within emissions limits. For example, a boiler installation may be commissioned by temporarily fitting an emissions analyser in the flue and adjusting the air-to-fuel ratio to target a specified level of excess oxygen in the flue gas which is thought to correspond to complete combustion at the burner. During the commissioning, if a level of oxides of nitrogen (NOx) is found to be excessive, then the burner may be setup for water injection to reduce the oxides of nitrogen to an acceptable level. Periodically (e.g. every few months), an emissions analyser may be installed in the flue and the air-to- fuel ratio may be re-adjusted to target the specified level of excess oxygen.

In a simple example of boiler commissioning, air-to-fuel ratio may be reduced in order to reduce thermal dilution at the flame (owing to excess air) whilst ensuring complete combustion. Air-to-fuel ratio may be varied based on monitoring excess oxygen in flue gas (indicative of excess air) and/or monitoring carbon monoxide in the flue gas (indicative of incomplete combustion owing to insufficient air).

This may result in a first burner state at which the air-to-fuel ratio is relatively low and a water injection rate is nil. However, the oxides of nitrogen (NOx) at this first example burner state may be excessive, for example owing to high flame temperature.

Accordingly, in this simple example, the excessive level of oxides of nitrogen (NOx) may be reduced by injecting water, to define a second burner state at the same air-to- fuel ratio but with a higher rate of water injection.

By selecting air-to-fuel ratio and water injection rates independently and without reference to boiler efficiency, a burner state may be selected during commissioning which does not represent the highest achievable boiler efficiency.

Figure 1 is a plot of boiler efficiency as a function of burner operating variables of air- to-fuel ratio and water injection rate. Overlaid on the plot (in dashed lines) is a compound emissions boundary 2 which in this example reflects burner states at which at least one type of emissions is at the respective threshold. In this particular example, the emissions boundary is a compound boundary for both a level of oxides of nitrogen (NOx) and a level of carbon monoxide (CO) in a flue gas. The applicant has found that water injection further causes carbon monoxide levels to reduce. It is thought that water injection provides additional oxygen for combustion with the fuel, thereby reducing carbon monoxide (which can be a by-product of incomplete combustion). The emissions boundary 2 indicates that burner states having a lower water injection rate or a lower air-to-fuel ratio will exceed at least one of the emissions thresholds.

The present disclosure relates to selection of an operational burner state which represents the highest boiler efficiency that can be achieved without exceeding one or more emissions thresholds. The operational burner state is shown on Figure 1 at point 4. The first and second burner states as described in the example above are shown at points 6 and 8 respectively. In this example, the first burner state 6 represents a higher boiler efficiency than the operational burner state 4, which may be because the absence of injected water leads to higher flame temperatures and heat transfer to the boiler and the working fluid (e.g. water to be converted to steam). However, the second burner state 8 represents a worse boiler efficiency than the operational burner state 4, which may be because the flame temperature is so high at burner state 4 that the water injection to reduce it to acceptable levels results in excessive thermal dilution.

Accordingly, in this example, the operational burner state 4 has a higher air-to-fuel ratio and a higher water supply rate than an optimal-efficiency burner state 6 having excessive emissions.

Figure 1 indicates the boiler efficiencies associated with each burner state as calculated based on heat transfer to the working fluid (based on the measured thermal power input to the working fluid relative to the thermal power provided to the boiler), as will be described in the example below. This may be referred to as heat transfer efficiency in the present disclosure, or a working fluid-derived boiler efficiency.

In other examples, boiler efficiency may be calculated based on monitoring (i) various gas levels in the flue gas (e.g. oxygen, carbon monoxide) and (ii) temperature of the flue gas. The various gas levels may correlate to the completeness of the combustion, whereas the temperature of the flue gas may correlate to the amount of heat released by combustion that is not transferred to the boiler. Together with information on the air- to-fuel ratio (e.g. the air supply rate and fuel supply rate) and the water supply rate, in some examples a controller may calculate or predict boiler efficiency based on flue- derived parameters, rather than direct monitoring of the thermal power input to the working fluid, as will be described in further detail below. This may be referred to as flue-derived boiler efficiency in the present disclosure - which is intended to mean an indirect calculation of boiler efficiency which uses parameters (e.g. temperature and/or gas levels) from the flue, rather than direct monitoring of the change of thermal power of the working fluid.

By monitoring boiler efficiency and emissions together, burner operating variables (i.e. air-to-fuel ratio and water injection rate) can be adjusted to calibrate a boiler for optimum efficiency within emissions limits.

Figure 2 shows an example boiler installation 10 for conducting burner calibration testing as described in outline with respect to Figure 1. In this example, the boiler installation 10 is not in-service (i.e. for servicing a load), but is installed remote from an industrial plant, or is in a calibration or commissioning phase of an industrial plant, in order to generate calibration data for subsequent use.

The boiler installation 10 comprises a boiler 12 configured to receive a working fluid, and a burner 14 configured to burn fuel in the presence of air to transfer heat to the working fluid.

In this particular example, the boiler is for generating steam and has an inlet 16 for receiving liquid water and an outlet 18 for discharging steam. A flue 20 extends from the burner 14 to discharge flue gas outside of the boiler 12.

The burner is configured to receive fuel from a fuel inlet pipe 22, to receive air from an air inlet pipe 24, and to receive water from a water injection pipe 26.

The boiler installation 10 further comprises a controller 50 configured to control operation of the burner 14. The controller 50 comprises a non -transitory machine- readable medium 52 which in this example stores instructions for controlling the boiler installation 10, and optionally calibration data recorded at the boiler installation 10 (although in other examples such data may be stored remotely).

The controller 50 is coupled to control equipment throughout the boiler installation, including:

a combined flow controller and temperature sensor for fuel 23 installed on the fuel inlet pipe 22;

a combined flow controller and temperature sensor for air 25 installed on the air inlet pipe 24;

a combined flow controller and temperature sensor for water 27 installed on the water injection pipe 26;

a temperature sensor 17 installed at the water inlet pipe 16 to the boiler;

a temperature sensor 19 installed at the steam outlet pipe 18 from the boiler; and an emissions analyser 21 installed along the flue 20.

In other examples, separate flow controllers and temperature sensors may be used. The controller 50 is configured to control a fuel supply rate at which fuel is supplied to the burner 14, an air flow rate at which air is supplied to the burner 14, and a water injection rate at which water is injected to the burner 14, as will be described below with respect to the example methods of boiler calibration.

Figure 3 shows a first example method of boiler calibration in which the controller tests operation of the boiler of Figure 2 at a plurality of burner states. In this particular example, a matrix of burner states are defined for testing the boiler, for example at 8 different air-to-fuel ratios (e.g. between 1.01 and 1 .06) and at 8 different water injection rates (e.g. between nil and 10% of the fuel flow rate). However, in other examples, a different range of air-to-fuel ratios may be defined. For example, it may be appropriate to specify a higher and/or wider band of air-to-fuel ratios, such as between 1 .04 to 1.32 (which may correspond to excess oxygen of between 0.5% and 5%, for example). A higher air-to-fuel ratio may be necessary where there is a particularly low emissions limit for oxides of nitrogen. In yet further examples, burner states may be defined differently, for example: iteratively to maximise an efficiency parameter, or by successively reducing the air-to-fuel ratio and raising the water injection rate to compensate for emissions.

In block 302 of the method, one of the burner states of the matrix of burner states is determined for test operation of the boiler. The burner state defines the water injection rate and the air-to-fuel ratio. As will be appreciated, the air-to-fuel ratio can be varied by either adjusting the air supply rate, the fuel supply rate, or both (in this example, air supply rate is varied).

In block 304, the controller 50 tests operation of the boiler at the determined burner state by controlling the respective flow controllers 23, 25, 27 to set the respective rates for fuel, air and water supply and operating the burner whilst monitoring various parameters for storage as calibration data over a test period, for example 30 minutes or 1 hour.

In this example, the boiler is out of service and is configured for testing. It is operated at a constant demand state corresponding to supply of 10 tonnes of steam per hour (2.78kg/s) at a pressure of 3bar. The demand state is constant in that the load and operating conditions of the boiler - and thereby the heat transfer to the burner to the working fluid - does not vary between successive tests of the boiler at the burner states.

In other examples, the demand state may vary owing to variation of a real load serviced by the boiler (e.g. variation in a flow rate at which steam is drawn from the boiler, or variation of the pressure at which the steam is demanded), or by virtue of variation of the operating conditions of the boiler (e.g. variation of the supply rate of feed-water to the boiler, and/or the temperature of feed-water as supplied to the boiler, and/or the amount of water in the boiler).

Boiler controllers conventionally control fuel supply in response to variable real loads and operating conditions. A boiler controller may control fuel supply rate based on a feedback loop targeting an operational supply pressure of steam. A boiler controller may further control the fuel supply rate based on the supply rate, temperature of feed- water and/or the amount of water in the boiler (which may be maintained by a separate control loop between a maximum and a minimum).

The demand state as described herein is related to the heat transfer demanded at the boiler, and may vary according to the same principles underlying the above-described variation of fuel supply rate. In particular, the demand state may vary in dependence on downstream demand (e.g. load serviced by the boiler) and/or upstream operating conditions (e.g. the temperature and/or flow rate of feed-water, quantity of water in the boiler).

In examples, the demand state may be characterised (i.e. for correlation and data storage) in different ways. For example, the demand state may be specified in terms of the actual rate of heat transfer to the working fluid (i.e. the thermal power output in watts, as determined based on the thermodynamic properties of the working fluid into and out of the boiler). The demand state may otherwise be specified in terms of the actual rate of heat transfer (i.e. thermal power in watts) input to the burner (e.g. the sum of the calculated thermal power released by combustion, and the thermal power of the fuel, water and air supplied to the burner). As will be appreciated, the thermal power input to the burner is transferred to the working fluid at an efficiency less than unity, for example owing to power losses by conduction through the apparatus, and heat which is rejected to the flue. In some examples, the demand state may be specified by the fuel flow rate.

In such examples where the demand state varies between successive tests of the boiler, the calibration data may be correlated both by burner state and demand state to either permit calibration data to be generated for a plurality of burner states at each respective demand state, or to permit interpolation of results at different demand states (i.e. mapping observations from one demand state to another demand state based on predetermined relationships).

During operation of the boiler, calibration data 350 relating to the performance of the boiler is stored, correlated to the burner state (and optionally the demand state, as mentioned above). In this example, the calibration data stored for each burner state comprises the demand state, the burner state, an efficiency parameter 352 relating to the efficiency of the boiler at the burner state, and emissions data 354 relating to the emissions in the flue gas.

In this particular example, the efficiency parameter is a heat transfer efficiency (or working fluid derived boiler efficiency) of the boiler determined as the proportion of the thermal power transferred to the working fluid (in this example, liquid water vaporising to steam) relative to the input power. It is calculated as:

_ * L-*'R water

heat -transfer ^~ Tj

' input R _wate r is the thermal power transferred to the working fluid between the water inlet 16 and the steam outlet 18, and is calculated based on the flow rate and the temperature of the working fluid at the sensors 17, 19.

Pin _p u _t is the input power and, in this example, is calculated as the total of the thermal power of each of the fuel (i.e. not including combustion), air, water as supplied to the burner, together with the thermal power released by complete combustion of the fuel.

The heat transfer efficiency (or working fluid derived boiler efficiency) may be relatively slow to settle upon change of a demand state or burner state, as the thermal mass of the boiler equipment is relatively high and so it can take a relatively long period (for example, between 30 minutes and 2 hours, for example 1 hour) to reach a steady state condition in which heating or cooling of the boiler equipment is negligible and there is a steady state thermal loss through the boiler equipment.

The emissions data comprises a level (e.g. a concentration, such as parts per million (ppm)) of oxides of nitrogen (NOx), a level of carbon monoxide, a level of carbon dioxide and a level of oxides of sulphur (SOx), all of which are determined by the emissions analyser 21 in the flue 20.

The emissions in the flue are directly related to the conditions at the burner, and so are relatively fast to settle after a change of demand state or burner state. Emissions data for a burner state may be recorded based on a 2 minute average 5 minutes after a change to the respective burner state.

In this example, the calibration data is stored in a memory 52 of the controller. In other examples the calibration data may be stored remotely from the boiler installation, for example in cloud storage accessible over an internet connection.

In block 306 of the method, the controller determines whether the boiler tests are complete - in particular by determining whether the boiler has been operated at each burner state of the matrix of burner states. If not, the method returns to block 302 for a further burner state of the plurality. Otherwise, the method continues to block 308.

In block 308, the controller 50 determines an operational burner state which is selected from a plurality of the burner states having acceptable emissions, so as to optimise efficiency with respect to the efficiency parameter. The term“operational burner state” is intended to denote a burner state for continued operation of the boiler or a like boiler having a like burner. In this example, the controller 50 evaluates the calibration data for each of the burner states and determines a subset having acceptable emissions. The controller then determines the burner state from the subset which has the highest efficiency.

In some examples, the controller may interpolate one or more burner states based on a plurality of neighbouring burner states in the state space (i.e. of air-to-fuel ratio and water injection rate) in order to predict a burner state having high efficiency and acceptable emissions.

In some examples, the controller may interpolate one or more burner states that lie on an emissions boundary in the state space of air-to-fuel ratio and water injection rate. It is thought that such burner states may include the burner state having the highest boiler efficiency, and therefore a search of burner states which is limited to those lying on the emissions boundary may be faster.

Whilst an example has been described in which burners states belonging to a matrix of burner states are tested, in other examples other testing schemes may be conducted to generate calibration data. For example, burner states may be iteratively tested (i.e. with each successive burner state being defined based on the results of previous tests) to determine a local maximum for the respective efficiency parameter. In an example, burner states along the emissions boundary may be tested (for example on or close to the boundary), for example by defining a next burner state to test based on a basic predictive model of emissions of the burner.

As described above, the example boiler installation 10 of Figure 2 is out of service and configured for generating calibration data only, which may be used for the control of other boiler installations having a like burner and boiler. The method of Figure 3 may nevertheless be applied to an in-service boiler configured to service a load to generate calibration data for use in mapping the emissions and efficiency performance of the boiler to burner operating variables, for use in determining suitable operating burner states of the boiler (e.g. for various demand states of the boiler, or for like boilers).

Figure 4 shows an example method of controlling an in-service boiler of an industrial plant based on calibration data. In this example the in-service boiler is as described above with respect to Figure 2, except that it is installed in an industrial plant to provide steam for an in-service load. In some examples, the in-service boiler may omit some of the sensors as described above with respect to Figure 2. As will become clear from the example described below, emissions data is not required in order to select a suitable operational burner state for operation of the burner based on previously- determined data (as opposed to generating such data). Accordingly, the emissions analyser of Figure 2 may be omitted. Such emissions analysers may only be required for initial calibration testing to determine operational burner states (i.e. to determine using testing which burner state from a plurality should be used to optimise efficiency), and may not be required to select an operational burner state based on previously- generated such calibration data.

In block 402, the controller 50 obtains a demand state for the boiler (e.g. a current thermal power output required to the working fluid). In block 404, the controller 50 obtains an operational burner state correlated to the demand state based on calibration data 450 generated by a method as described above.

Figure 5 shows a further example method of calibrating an in-service boiler based on a model which maps an efficiency parameter and emissions data to burner operating variables including the air-to-fuel ratio and the water supply rate. Such a model may be generated based on prior operation of the boiler (e.g. during normal in-service operation, or an initial or periodic period of commissioning, including as described above with respect to the method of Figure 3).

The utility of the method of Figure 5 reflects that a mapping of boiler efficiency and/or emissions to burner operating variables may become inaccurate, for example owing to changing performance or operation of the boiler, but the underlying behaviour of the boiler in terms of the way that emissions and efficiency vary in response to burner operating variables may be substantially unchanged. By way of example only, the method will be described with respect to an in-service boiler which is otherwise substantially as described above with respect to Figure 2.

In block 502, the controller 50 obtains a first burner state for the boiler (i.e. a first set of burner operation variables), which may be a current burner state of the boiler. In block 504, the controller obtains predictions for emissions and an efficiency parameter based on previously-stored calibration data 550. In block 506, the controller tests operation of the boiler at the first burner state and stores observed data 560 including observed emissions data and an observed efficiency parameter.

In block 508, the controller defines a second burner state based on a comparison between the calibration data and the observed data for the first burner state. For example, the controller may determine a vector in the mapping of the calibration data to move from a point representing the observed emissions and efficiency performance to a point representing the predicted emissions and efficiency performance, and thereby determine an offset in the burner operating variables (i.e. air-to-fuel ratio and water injection rate) corresponding to the vector. For example, if the controller determines that the observed emissions are higher than predicted but the efficiency is substantially the same, then the controller may determine a vector in the mapping corresponding to marginally increasing the air-to-fuel ratio and marginally increasing the water supply rate, in order to reduce the emissions in a way that maximises efficiency. In a further example, the controller may determine that the observed emissions are lower than predicted and the efficiency is lower than predicted, and the controller may analyse the mapping of efficiency and emissions in the calibration data to determine a vector to return the performance the predicted emissions and efficiency, which may correspond to reducing the air-to-fuel ratio to maximise the efficiency without exceeding the emissions boundary. The calibration data is updated based on the test operation of the boiler to re-map the emissions and efficiency performance.

In block 510, the controller determines whether the boiler should continue to be operated at the second burner state defined at block 508, or whether a further cycle of iteratively defining a new burner state as described above with respect to blocks 502 to 508 should be repeated. In this example, the criteria for continuing operation is that the differences in each of the burner operating variables between the first burner state and the second burner state should be below a predetermined threshold (e.g. 0.005 for air- to-fuel ratio, 10ml/min for water injection rate) - indicating that the burner state has settled. The threshold difference for water injection may vary depending on the size of the boiler installation and the range of water injection. For example, in larger installations the minimum increment between burner states may be 50ml/min.

Although examples of the invention have been described with respect to monitoring heat transfer efficiency of the boiler (also referred to herein as working fluid derived boiler efficiency), in other examples other efficiency parameters may be used. For example, a flue-derived boiler efficiency may be calculated based on:

• fuel supply rate;

• air supply rate;

• water supply rate; • a fuel gas parameter (e.g. concentration of oxygen or carbon dioxide or carbon monoxide levels in the flue gas)

• temperature of the flue gas;

• temperature of supply air.

The fuel gas parameter may be used in conjunction with the fuel supply rate and the air supply rate to determine whether combustion is complete. For example, given a known quantity of fuel and air, the concentration of oxygen and carbon dioxide owing to complete combustion is readily predictable. Alternatively, a correlation between carbon monoxide levels and completeness of combustion may be used. Carbon monoxide tends to increase when combustion is incomplete. Alternatively, complete combustion may be assumed, and a fuel-derived boiler efficiency may be calculated based on the flue gas temperature and a fuel gas parameter that correlates with the air supply rate (i.e. the concentration of carbon dioxide or the concentration of oxygen). The temperature of supply air and the water supply rate may be taken into account to improve accuracy of the fuel-derived efficiency.

Fuel supply rate, air supply rate and water supply rate may be used to determine a thermal power into the burner. The thermal power input from the fuel has two components: the thermal power of the fuel itself, and the thermal power released from complete combustion.

The temperature difference between the supply air and the flue gas, together with the air supply rate, may be used to deduce the thermal power rejected from the burner into the flue. The thermal power transferred to the boiler can therefore be calculated as the thermal power input to the boiler, less the thermal power rejected into the flue.

A model for flue-derived boiler efficiency may take into account heat transfer losses at the boiler - for example by specifying a thermal power loss at the boiler, which may be constant or a function of operating temperature of the boiler.

In some examples, a model for flue-derived boiler efficiency may approximate or ignore one or more of the above parameters. By calibrating a boiler having a burner as discussed above, an operational burner state for operation of the boiler can be found and/or selected for use. The methods described herein permit an efficient burner state of a boiler to be found based on dynamic operation and/or testing of the boiler, and for a burner state to be changed dynamically in response to changes in a demand state of the boiler in operation.

Calibration data may be generated at a first boiler having a particular configuration (e.g. a combination of burner type and boiler type), and used for selecting an efficient operational burner state for a second boiler having a like configuration (e.g. the same combination of burner type and boiler type). Initial calibration testing to determine an operational burner state for a particular demand state (e.g. iteratively) may be done using a temporarily-installed emissions analyser to provide feedback on emissions data. However, subsequent selection of a (previously-determined) operational burner state based on a demand state of the same or a different boiler installation may be done without need of an emissions analyser. Accordingly, operation of a boiler installation can be dynamically updated to optimise efficiency with acceptable emissions, without necessarily re-commissioning the boiler in a way that necessitates installation of an emissions analyser.