There are two prominent features in the process of temperature control in solar collector field. Firstly, the dynamic model of solar collector field is nonlinear and complex, which needs to be simplified. Secondly, there are a lot of random and uncontrollable, measurable and unmeasurable disturbances in solar collector field. This paper uses Taylor formula and difference approximation method to design a dynamic matrix predictive control (DMC) by linearizing and discretizing the dynamic model of the solar collector field. In addition, the purpose of controlling the stability of the outlet solar field salt temperature is achieved by adjusting the mass flow of molten salt. In order to further improve the ability of the system to suppress unmeasured disturbances, a steady-state Kalman filter is designed to estimate state variables, so that the system has better stability and robustness. The simulation verification results show that the DMC control system based on Kamlan filtering has better control effect than the traditional DMC control system. In the case of large fluctuations in solar radiation intensity and consideration of undetectable interference, the overshoot of the system is reduced by 4% and the rise time remains unchanged.

As an environmentally and widely available renewable energy, solar energy has broad development prospects. At present, many countries use solar energy to generate electricity by establishing photovoltaic power stations or solar thermal power stations. The focused solar thermal power station focuses the solar energy through the collector, and then heats the heat transfer working medium inside the collector. The heated heat transfer working fluid generates steam through the heat exchanger and drives the steam turbine to generate electricity. In order to ensure stable power output, the outlet temperature of the solar thermal field must be able to maintain the set operating point. Due to the non-linearity, complexity, delay and strong random interference characteristics of the solar heat collection field, the control of the outlet temperature of the heat transfer working fluid in the heat collection loop has become a hot and difficult problem in the research field of solar thermal power generation.

This paper studies solar power plants with linear Fresnel (LF) collectors. The LF collector is an improvement and simplification of the trough collector. Its heat collection system is mainly composed of a condenser and a glass-metal vacuum heat sink. The concentrator can be regarded as the linear segmentation discretization of the parabolic trough reflector, it reflects the incident light from the sun and gathers it on the focal line of the linear strip mirror. The heat sink is installed above the focal line and heating the heat transfer fluid, and finally realize the conversion of solar energy to thermal energy [

In response to the problem of temperature control of LF collector field, many scholars at home and abroad have done a lot of research, including traditional PID control, model-based predictive control (MBPC) [

Since the factors that affect the overall efficiency such as direct solar radiation, specular reflectance and metal absorptance can only be measured locally, and other unmodeled factors such as wind speed, it is necessary to consider these interferences in the process of controlling the salt temperature at the outlet of the collector to improve the control effect [

The Dacheng Dunhuang LF Power Station is currently composed of a heat collection field, a heat storage system and a power generation system. The heat collecting field uses binary molten salt as the heat transfer medium, with a total of 80 parallel circuits and a total mirror area of 1.27 million m^{2}.

After general simplification and assumptions, the distributed LF collector field can be described by a distributed parameter model about temperature. This distributed parameter model includes the energy balance equation of the metal heat absorption tube and the energy balance equation of the heat transfer fluid in the heat absorption tube [

where _{f} is the convective heat transfer coefficient between the molten salt and the absorbor tube; _{m} is the wall temperature of the metal absorbor tube; _{a} is the ambient temperature; _{f} is the temperature of molten salt fluid;

Since the heat transfer effect between the metal absorbor tube and the heat transfer fluid is good, it is assumed that the metal absorbor tube temperature is equal to the heat transfer fluid temperature [_{m}(_{f}(

where, _{fi} is the inlet molten salt temperature, _{fo} is the outlet molten salt temperature,

Symbol | Name | Value |
---|---|---|

_{m} |
absorbor density | 7930 kg/m^{3} |

_{m} |
absorbor specific heat capacity | 500 J/kg·K |

_{m} |
absorbor cross-sectional area | 0.0064 m^{2} |

G | collector opening diameter | 24.4 m |

reflection factor | 61.2% | |

_{f} |
molten salt fluid density | 1734 kg/m^{3} |

_{f} |
molten salt fluid specific heat capacity | 1539.2 J/kg·K |

_{f} |
absorbor internal cross-sectional area | 0.0053 m^{2} |

L | absorbor tube length | 22 m |

_{a} |
convection heat transfer coefficient | 40 W/m^{2}·K |

Since linear discrete model is used in the predictive control algorithm, it is necessary to linearize and discretize the energy balance equation given in

Using Taylor linear approximation, select an appropriate operating point to linearize the model and the result is shown in

Then use the differential approximation of the derivative to discretize the

The linearized and discretized transfer function is shown in

where,

In order to solve the control object with large inertia, large delay and nonlinearity such as solar thermal field, so that it still has good control effect in the case of model mismatch, this paper proposes a DMC predictive control with steady-state Kalman filter algorithm (KFDMC). The KFDMC control structure diagram of the LF collector is shown in

According to the linear collector model established in 2.2, the KFDMC controller was designed. Use _{fo}; _{a}, and inlet salt temperature _{fi};

KFDMC algorithm is a model-based control algorithm and applies the principle of online optimization. The online calculation of KFDMC consists of an initialization module and a real-time control module. The initialization module detects the actual output y of the object in the first step of operation and sets it to the predicted initial value

The DMC system uses the step response of the system to calculate the output predicted value. For the SISO system, the open-loop prediction output at time

where,

At time

Satisfy the condition:

Then it is obtained by

where,

Since the step model does not include wind speed and other unmeasured (unmodeled) factors that interfere with stable controlled variables, it will inevitably lead to tracking errors. In order to eliminate errors and suppress unmeasured interference, a steady-state Kalman filter is introduced into the DMC algorithm to realize the estimation of system state variables containing unmeasured interference.

To design a steady-state Kalman filter, consider the following state-space model to describe the dynamic system:

where,

Assume 2.1

where,

Assume 2.2

Assume 2.3

Theorem 2.1 (Steady state Klaman filter) System

Call

where,

From

Take modeling time domain

where,

The optimization process of predictive control is repeated online, and the optimization criterion is minimized at each moment to achieve optimization, that is, rolling optimization. Choose the optimal objective function as follows:

s.t.:

The molten salt fluid selected in the project is composed of 60% _{3} and 40% _{3}. Its melting point is about 220°C, and its vaporization point is about 600°C. The expected operating temperature range is 290°C to 550°C. The molten salt flow rate varies from 0 kg/s to 50 kg/s. From

According to the necessary conditions for taking extreme values

where,

So far, DMC has obtained the optimal control variable matrix that should be applied at each time, but DMC uses rolling optimization. At each time

The collector model verification is carried out by comparing with the actual operating data of Dacheng Dunhuang Linear Fresnel Power Plant. Use the solar radiation intensity _{a}, the collector molten salt inlet temperature _{fi} and the molten salt flow rate

Experimental parameter | _{f}(°C) |
_{f}(°C) |
Relative deviation | ||||
---|---|---|---|---|---|---|---|

^{2}) |
_{a}(°C) |
_{i}(°C) |
|||||

1 | 788 | 31 | 292.7 | 6.78 | 549.4 | 550.5 | 0.2% |

2 | 848 | 30 | 291.7 | 7.63 | 549.3 | 549.9 | 0.1% |

3 | 920 | 34 | 293.1 | 8.01 | 549.5 | 551.3 | 0.3% |

4 | 955 | 36 | 293.4 | 8.39 | 549.5 | 551.3 | 0.3% |

In this section, two different weather conditions are used to analyze the performance of the controller. Take the sampling time Ts = 1 min, use

The simulation data of the measurable disturbances _{a} and _{fi} used to simulate a day with clear weather and no cloud cover is shown in

Simulate a day with cloud cover and strong radiation intensity interference, the simulation data of the measurable disturbances _{a} and _{fi} used are shown in ^{2} and 874.06 W/m^{2}, and the fluctuation is small. During this period, the maximum overshoot of the outlet salt temperature of the DMC control algorithm is 0.42%, and the maximum overshoot of the KFDMC control algorithm outlet salt temperature is 0.27%, and the maximum deviation of the outlet salt temperature of the KFDMC controller is 63.26% of the maximum deviation of the outlet salt temperature of the DMC algorithm. In the 100th to 110th minutes, DNI dropped sharply from 877.89 W/m^{2} to 520.47 W/m^{2}, with large fluctuations. During this period, the maximum overshoot of the DMC algorithm was 7.14%, the maximum overshoot of the KFDMC controller was 3.39%, and the maximum deviation of the KFDMC controller outlet salt temperature was 47.5% of the maximum deviation of the DMC algorithm outlet salt temperature.

The observation result of the Kalman filter is shown in

This paper proposes a DMC predictive controller with unmeasured interference estimation. By adding a steady-state Kalman filter in DMC, the LF heat collection system can effectively suppress the influence of measurement errors and unmodeled interference on the control effect. This article carries out simulation analysis for two different interference conditions. The results show that under the condition of clear weather and no cloud cover, the classic DMC predictive control algorithm has a good control effect, and its performance is better than PID controller. When there is cloud cover and the intensity of solar radiation fluctuates strongly throughout the day, considering measurement errors and model mismatch, the DMC predictive controller with unmeasured interference estimation has better control than the classic DMC predictive controller effect.