A Modified Extended Kalman Filter to Estimate the State of the SG4 Receiver at the Australian National University Jose Zapata 1

Transcription

1 A Modified Extended Kalman Filter to Estimate the State of the SG4 Receiver at the Australian National University Jose Zapata 1 1 Research School of Engineering, Australian National University, Canberra, ACT, 0200, Australia jose.zapata@anu.edu.au Keywords: Concentrating Solar Power, Direct steam generation, Parabolic dishes, Continuous-Discrete Extended Kalman Filter. Abstract The temperature control of direct steam generation depends on information about the dynamic heat transfer behaviour of the receiver during operation. This information may come from sensors or dynamic mathematical models of the heat transfer process taking place at the receiver. In practice, sensors are susceptible to noise and calibration errors and models suffer from uncertainty due to inexact parameter tuning and model simplification. As a result, the information generated by sensors or models contains uncertainty and may be inadequate for control purposes. This paper presents simulations and experimental runs of a modified Extended Kalman Filtering scheme that estimates the state of the mono-tube steam cavity receiver inside the SG4 steam generation system at the Australian National University. The filtering scheme combines the available measurements in the SG4 steam generation system with a dynamic model of the receiver, to compute an estimate of the receiver state suitable for closed loop temperature control. Simulations of the filtering scheme run with pre-recorded data, to evaluate and tune its performance. Experimental results demonstrate how the filtering scheme runs concurrently with the SG4 system and computes estimates of the receiver state in real time. Experimental results show that the filtering scheme performs well under the effect of noisy measurements and poor parameter calibration, and provides an estimation of the SG4 receiver state suitable for control purposes. 1. Introduction The automatic control of solar thermal power plants aims to achieve the stable operation of the plant under variable solar radiation conditions. For this purpose, controllers manipulate the plant actuators (e.g. valves, pumps, tracking mechanisms) to steer the plant behaviour in a desired manner (e.g. constant temperature at the outlet of a receiver). The extent to which the controller manipulates the plant actuators depends on the current conditions of the plant and variables that influence it [1]. The controller acquires the current conditions of the plant from measurements and/or the estimation of process variables and ambient conditions. Measurements include fluid temperatures, pressures, flows, etc., whereas estimations use a combination of measurements and calculations to predict the behaviour of process variables are inaccessible or impractical to measure. Estimated variables may be more abstract than real process variables (e.g. average reaction rates, overall heat transfer rates, etc.), but may be desirable due to their ability to predict plant behaviour and inform the decision process of the controller. A specific case of abstract estimation variables corresponds to the variables in a mathematical model of the plant. A control oriented model for a solar thermal power plant establishes the dynamic relation between the desired plant output and the inputs that influence it. In order to be useful for the controller, the model must be able to run in real time. As a result, control oriented models often simplify the physical behaviour of the plant and thus provide abstracted variables to estimate the internal behaviour of the plant [2].

2 In this study, the aim is to estimate the internal state of the mono-tube cavity receiver in the SG4 steam generation system at the Australian National University. A control oriented model of the heat transfer process taking place in the receiver has been developed by Zapata et al.[3], and it is desirable to exploit it for control purposes. The model can provide additional information about the internal state of the receiver, in the form of a state vector. The state vector is a set of variables that represent the state of the receiver through the equations of the model. The state vector can provide information about the receiver that measurements alone cannot convey. For example, sudden changes in direct normal irradiation may not translate instantly into changes in temperature, but they can be anticipated from changes to the variables in the state vector. It is possible to run the receiver model concurrently with the operation of the SG4 system, by periodically feeding it with up to date measurements from the system and recalculating the model equations. However, the state vector computed with this approach is susceptible to drift over time, subject to errors in model calibration and/or measurements. If the model parameters were not calibrated correctly, the model equations may under/overestimate the heat transfer mechanisms interacting at the absorber tube, and thus under/overestimate the steam temperature at the outlet. Similarly, if a measurement from the system (e.g. direct normal irradiation) were noisy or biased, this would also 'mislead' the computations performed by the model. This study attempts to overcome the challenge of estimating the state vector with a Modified Extended Kalman Filter (MEKF) that combines the calculations of the receiver model with additional measurements from the SG4 system 1. Extended Kalman Filters [4] are a well-established state estimation technique, with applications in concentrating solar power systems [5, 6]. This paper provides a brief description of the MEKF estimator, as well as details of its experimental implementation in the SG4 steam generation system at the Australian National University. 2. Estimating the state of the SG4 receiver 2.1. System description The SG4 steam generation system at the Australian National University (ANU) is an experimental set-up that combines the SG4 500 m 2 paraboloidal dish concentrator [7], with a hydraulic circuit. The system is currently used to perform full scale experiments for the design and operation of point-focusing concentrating solar thermal power systems. Figure 1 shows a diagram of the system. The hydraulic circuit in the SG4 system forms a closed loop to produce superheated steam at 500 C and 4 MPa at the receiver outlet. A feed-water pump draws water from a feed-water tank and feeds it to a steam cavity receiver mounted at the focal point of the dish concentrator. The steam cavity receiver absorbs concentrated radiation from the 500 m 2 dish, and turns the feed-water into superheated steam. The superheated steam returns to the feed-water reservoir through a series of pressure drop tubing and a motorised valve, and it is diffused into the reservoir with an injector. 1 The method describing this algorithm in detail is currently in preparation for a journal paper submission.

3 Figure 1: Diagram of the SG4 steam generation system at the Australian National University This set-up differs from the description provided in previous conference proceedings [8] due to the decommissioning of the steam engine in the system. The purpose of the tubing and motorised valve is to create additional back-pressure in the system, such that the steam pressure at the receiver outlet is higher than 3 MPa. Experimental runs show that the behaviour of the system is comparable to its previous configuration with the steam engine. Control and monitoring of the steam generation system is performed with a Supervisory Control and Data Acquisition system. A description of this system is provided in the experiment section of this paper Receiver Model A mathematical model of the SG4 receiver developed by Zapata et al. [3] describes the dynamic heat transfer behaviour in the absorber tube, from a simplified set of conservation equations for mass, energy and momentum. The conservation equations constitute a state-space representation of the receiver, and provide a set of variables that describe the current state of the receiver, condensed in the following state vector (for nomenclature, see appendix): x = [L 1 L 2 P h o γ T w1 T w2 T w3 ] These variables constitute an approximated representation of the boiling process in the absorber tube during the operation of the receiver. The representation consists of assuming three regions of sub-cooled, saturated and superheated flow inside the receiver tube. The prediction of steam temperature at the receiver outlet is obtained from the modelled receiver outlet enthalpy h o. The model requires a set of parameters to establish receiver dimensions (e.g. absorber tube length and gauge, heat transfer coefficients, etc.), and the following set of measurements from the system: u = [m i P i T i P o T o I sol T a ] The measurements in vector u inform the model about variables that influence the heat transfer process in the receiver, e.g. feed-water mass flow entering the receiver, or direct normal irradiation. The evolution of state variables in the receiver model depends on these variables.

4 The receiver model can also describe incomplete evaporation in the receiver tube, which is the case for the SG4 system during start-up periods and large transients caused by cloud passage. The receiver model switches between three modes, each with its own set of equations: mode '1', where the entire absorber tube is occupied by liquid water; mode '1-2' where water enters the absorber tube as liquid and exits as a saturated water/vapour mixture; and mode '1-2-3' where water enters as liquid, fully evaporates within the tube and exits as superheated steam. At any point in time during the operation of the SG4 system, it is desired to know the state vector x and the receiver mode m, from up to date measurements u, and known receiver dimensions Simulated receiver behaviour Figure 2 (next page), shows a simulation of the model using experimental data from the SG4 system to illustrate how it computes the state of the receiver. Panels (a) and (b) respectively show measurements of feed-water mass flow and direct normal irradiation. Observe in particular the amount of noise present in feed-water mass flow measurements. The cause of this noise is not currently known, but additional experiments on the SG4 system suggest that is a defect of the mass flow sensor. Panel (c) shows the dynamic temperature response generated by the model from measurements from the SG4 system, alongside actual temperature measurements from the receiver where model shows good agreement with temperature measurements (except for a brief period during the start-up transient). Panels (d) to (h) show the simulated behaviour of the variables in state vector x. Available measurements from the SG4 system are shown alongside state variables for comparison. In the case of enthalpy in panel (f), the measurement is the result of a function that calculates enthalpy from receiver outlet temperature and pressure measurements and steam properties. In panel (d) the vertical axis is tube length and the dashed line at L = 212 correspond to the total length of the absorber tube and its outlet. At the start of the simulation, L 1 equals the length of the tube, indicating that the model considers the absorber tube to be full of liquid. As the simulation progresses, L 1 shrinks and L 2 grows, modelling the appearance of two-phase flow in the absorber tube. Likewise, the boundary between the saturated and superheated regions recedes to allow superheated flow in the receiver tube. When the receiver cools, this progression occurs in reverse. By tracking different flow regions, the model is able to calculate a mass inventory in the receiver, and thus to apply different heat transfer rates, depending on fluid properties. Furthermore, each region interacts with the absorber tube wall at a different averaged temperature, which is why the model keeps track average wall temperature in each fluid region present in the model, shown in panel (h). The panels on the right side of figure 2 show a zoomed version of simulated variables. The right side of panel (a) zooms in on a period where mass flow measurements exhibit a significant amount of noise. This noise affects the model calculation of receiver outlet enthalpy h o and pressure P. The right side panel (c) zooms in on the modelled and measured receiver outlet temperatures. The temperature calculated by the model is affected by the noise in feed-water flow measurements and the fluctuations in direct normal irradiation (panel (b)). Also, there is a small discrepancy between modelled and measured temperatures caused by simplifications of the model and imperfect parameter calibration.

5 Figure 2: Simulation of the receiver model using experimental data from the SG4 steam generation system. Left side panels span full simulation time, right side panels zoom in at an intermediate time. (a) Measured feed-water mass flow. (b) Measured direct normal irradiation. (c) Measured and modelled receiver outlet temperature. (d) Modelled flow region lengths with respect to full absorber tube length. (e) Modelled receiver pressure, measured receiver inlet and outlet pressures.(f) Modelled receiver outlet enthalpy and enthalpy from measurements. (g) Modelled system mean void fraction. (h) Modelled wall temperatures for regions 1, 2, and 3.

6 2.4. Estimating the state vector with a modified Extended Kalman Filter The estimation process aims to keep track of the operation of the receiver in real time for the purpose of closed loop control. However, simulations in the previous section show that the model is susceptible to noise and calibration uncertainty. This has the potential to compute an inaccurate state vector and mislead the controller. Kalman Filters [9, 10] can overcome this limitation by comparing the estimated state vector with additional measurements from the process, and introduce small corrections to the estimated state. This study employs a modified Extended Kalman Filter (MEKF) developed specifically to work with the SG4 receiver model. The MEKF consists of three separate Continuous- Discrete Extended Kalman Filters (CDEKF) [11] interacting with the three possible modes of operation of the receiver model, and a strategy to switch between them [12]. At each time step, the MEKF performs the estimation process in two stages: a prediction stage and a correction stage. In the prediction stage, the MEKF obtains measurements from the system and uses them to update the receiver model equations, thus producing a `predicted' state vector. In the corrector stage, the MEKF compares the outputs of the model with real measurements from the SG4 system and applies a correction to all the variables, i.e. the 'corrected' state vector. The 'corrected' state vector forms the initial condition for the next time step, and the estimation process is repeated. The amount of correction effected by the MEKF depends on the quantified uncertainty of the estimation process. The MEKF expects a certain amount of uncertainty in measurements that feed the prediction stage, the predicted state vector and the measurements used in the correction stage. Furthermore, the MEKF assumes that this uncertainty is normally distributed noise added to each signal/state. Thus it is possible to quantify the expected uncertainty with a standard deviation for each measurement. Knowledge of the SG4 system, especially of the precision and past behaviour of instruments is crucial to quantify the uncertainty in the estimation process Correction measurements The filtering scheme employs measurements of pressure and temperature at the receiver to compute a correction for the receiver state estimate. The estimated average receiver pressure P can be computed as the average between measured input and output pressures. When the fluid at the outlet is either liquid water or superheated steam, the estimated receiver outlet enthalpy can be calculated from receiver outlet pressure and temperature, by consulting water and steam property tables [13]. Table 1 summarises the mapping between receiver measurements and states. Receiver Model mode Receiver pressure P Receiver enthalpy h o Mode '1' (P i + P o )/2 h = f w (P o, T o ) 2 Mode '1-2' (P i + P o )/2 n/a Mode '1-2-3' (P i + P o )/2 h = f s (P o, T o ) Table 1: Relationship between SG4 system measurements and estimated receiver states The filtering scheme selects a set of measurements based on the currently active receiver model mode for the prediction stage. 2 Not used in the experimental filtering scheme, as it hinders the transition to mode '1-2'

7 3. Experimental implementation of the filtering scheme The filtering scheme was implemented and tested in the SG4 system. The filtering scheme was implemented in GNU Octave for simulations, and then converted to C++ for deployment in the SG4 SCADA system. The experimental version of the filtering scheme ran concurrently with the operation of the SG4 system, computing estimates at 2s intervals Supervisory control and data acquisition system The SG4 supervisory control and data acquisition (SCADA) system monitors, records and coordinates the operation of the SG4 steam generation system. The SCADA system consists of a server connected to control and data logging devices via a 10Mb Ethernet link. The devices in the SG4 steam generation system are two Yokogawa programmable logic controllers (PLC) and one Yokogawa data acquisition (DAQ) device. Figure 4 shows a diagram of the SCADA system. Figure 3: Supervisory control and data acquisition system diagram for the SG4 steam generation system The cavity receiver DAQ device is mounted at the back of the steam cavity receiver. It acquires over 40 thermocouple measurements from the receiver tube, inlet and outlet pressures, plus an anemometer. The Dish PLC monitors and controls the 2 axis tracking mechanism of the SG4 500m 2 dish concentrator, the feed-water mass flow pump, and acquires temperature/pressure measurements along the feed-water and steam lines. The Balance of Plant (BOP) PLC monitors and controls the motorised valve before the feedwater tank reservoir, and acquires temperature and pressure measurements for the pressure drop tubing, feed-water tank and cooling tower. The SCADA server is a personal computer running the Yokogawa FAST/TOOLS SCADA suite. The SCADA server has access to all sensor measurements and actuators from both PLCs and the DAQ device via the 10Mb Ethernet link. The SCADA server maintains a historic database of selected sensors, alarms and other data from the SG4 system, recorded at 2 second intervals for analysis following experimental runs. The SCADA server features a graphical interface to display measurements from the SG4 system and issue commands to the tracking system and the steam generation equipment.

8 The SCADA server also hosts the experimental implementation of the modified Extended Kalman Filtering scheme Experimental results Figure 3 displays the output of the filtering scheme for an experimental run of the SG4 system performed on the 25 th of October The filtering scheme estimates all the variable in the receiver model state vector x, but are presented with relevant measurements from the system. The feed-water mass flow signal shows significant variation due to the nature of the test, which was to evaluate the experimental filtering scheme in conjunction with a temperature control system. The estimates computed by the experimental filtering scheme maintained very good agreement with measurements throughout the test. Panels (a) and (b) of figure 3 respectively show the feed-water mass flow and measured direct normal irradiation. Both signals exhibit a moderate amount of noise within the acceptable operating range for the SG4 system. Panel (c) shows estimated and measured receiver outlet temperatures. The filtering scheme produces very good agreement with measurements. The right hand side of panel (c) shows a close up where this agreement is evident. The filtering scheme attenuates the influence of noise from both mass flow and DNI signals on the temperature estimate. There is, however, disagreement between temperature estimates during the start-up of the receiver. This disagreement appears as the filtering scheme underestimates the rate at which the pressure inside the receiver builds up as boiling flow appears in the system. It is thought that the disagreement stems from the receiver model in the prediction stage of the filtering scheme. Current temperature control algorithms for the SG4 system are only applied when the outlet is superheated, and thus this temporary disagreement does not detract from the main result. Panel (d) shows the filtering scheme estimation of fluid region lengths during the experimental run. Estimated region lengths change according to the mass inventory in the receiver, and relate to the amount of liquid, saturated and superheated flow in the absorber tube. In comparison to model-only estimations in figure 2, these region length estimates experience faster changes during large transients. Panel (e) in figure 3 shows the average receiver pressure estimated by the experimental filtering scheme, alongside measurements of pressure at the inlet and outlet of the absorber tube. The pressure estimate is consistent with the assumption that P = (P i + P o ) 2 throughout the experimental run, due to the corrective effect of pressure measurements in the filtering scheme. Other quantities in the receiver model that depend on average receiver pressure (e.g. water and steam properties) also benefit from this correction. Panel (f) in figure 3 shows the receiver outlet enthalpy estimated by the filtering scheme. Temperature and pressure measurements aid the filtering scheme to compute a corrected estimate for this state. Note also that the enthalpy estimate is not affected by noise introduced by mass flow and DNI measurements. Panels (g) and (h) of figure 3 show the remaining variables in the estimated state vector: system mean void fraction γ and wall temperatures T w1, T w2 and T w3. The filtering scheme also attenuated the noise introduced by input measurements into these state estimates, when compared to model-only simulations.

9 Figure 4: Experimental results of the filtering scheme during an experimental run with the SG4 system on the 25th of October Left side panels span full simulation time, right side panels zoom in at an intermediate time. (a) Measured feed-water mass flow. (b) Measured direct normal irradiation. (c) Measured and modelled receiver outlet temperature. (d) Modelled flow region lengths with respect to full absorber tube length. (e) Modelled receiver pressure, measured receiver inlet and outlet pressures.(f) Modelled receiver outlet enthalpy and enthalpy from measurements. (g) Modelled system mean void fraction. (h) Modelled wall temperatures for regions 1, 2, and 3.

10 4. Summary The challenge of estimating the internal state of the SG4 receiver during operation for control purposes has been addressed by employing a modified Extended Kalman Filtering scheme. The filtering scheme improves the estimating ability of a non-linear model of the SG4 receiver, by introducing additional measurements from the system. Experimental results on the SG4 system show that filtering scheme attenuates the effect of noise in state estimates, reduces the error between estimated variables and output measurements, and offers a practical implementation platform to observe the state of the receiver in real time. Future work on this topic will concentrate on improving the performance of the filter during large (e.g. start-up) transients in the system. 5. Acknowledgements The author wishes to thank Dr. Jochen Trumpf from the Research School of Engineering (RSE) at the ANU for his guidance and support in the development of this study and Mr. Greg Burgess, also from the RSE for his assistance and support for the experimental part of this project. Appendix A Nomenclature L 1 : L 2 : P: h o : γ : T w1 : T w2 : T w3 : T i : T o : P i : P o : m i: I sol: T a : Sub-cooled region length in receiver model Saturated region length in receiver model Average receiver pressure in receiver model Enthalpy at receiver tube outlet in receiver model System mean void fraction for saturated region in receiver model Tube wall temperature for sub-cooled region in receiver model Tube wall temperature for saturated region in receiver model Tube wall temperature for superheated region in receiver model Feedwater temperature at receiver inlet Fluid temperature at receiver outlet Fluid pressure at receiver inlet Fluid pressure at receiver outlet Feedwater mass flow at receiver inlet Direct normal irradiation Ambient temperature References [1] E.F. Camacho, M. Berenguel, F.R. Rubio, and D. Martinez. Control of Solar Energy Systems. Springer, [2] Gene F Franklin, J David Powell, and Abbas Emami-Naeini. Feedback Control of Dynamics Systems. Upper Saddle River [N.J.]: Pearson, 6th edition, 2010.

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