1. Introduction

Although there is a considerable renewable energy penetration to electrical power supply in recent years, coal fired power stations are still playing a dominant role in power generation due to its large power generation capacities and low cost. It is a worldwide big challenge for how to reduce the environmental impact brought from coal fired power generation. Supercritical boiler is one of the technologies implemented with the improved energy efficiency. Supercritical boilers have higher efficient Ranking cycle due to its high operating pressure and temperature (above critical points - for water 22.06MPa and 374.15C° pressure and temperature respectively), leading to improved thermal efficiency, lower fuel consumption and lower CO₂ emissions. Although supercritical and ultra-supercritical coal fired power generation is becoming the main choice of power generation technology for past two decades and will become a dominant technology on the long run, there are still some concerns about adopting this technology in the UK. It is required to fulfil the National Grid Code (NGC) require ments[1]. The paper is to study potential control strategies for improving SC power plant dynamic responses. The first research on optimal control of SC power plants was designed in 1978([2]) with identified state space model and dynamic programming for control task formulation. The application of nonlinear model based predictive control (NMBPC) was reported in[3] as preliminary results. Conventional dynamic matrix control (DMC) was published in[4] designed for gas fired SC power plants. However, conventional DMC may not cover the whole operating range. In[5], a simplified model for SC unit was reported for power system frequency simulation study. The performance of diagonal recurrent neural network for predictive control of coal fired SC and ultra-supercritical (USC) power plants were shown in[6-8]. This paper aims to design coordinated control system for 600MW SC coal fired plant with emphasis on the target of correcting the reference of plant local controllers. Because the model has been identified with closed loop data, the designed control signals should be used as correction to the reference of the plant local controls (the coal mill local control, the feed-water flow control, and the turbine governing system) which is extremely helpful in power plant industries. Two coordinated controllers are investigated. One is based on MPC with disturbance compensation and measurement noises generalized from prediction algorithm. This scheme has shown good performance within small load changes around nominal operating conditions. The other scheme is multivariable control system which is composed of MPC in parallel cooperation with PID fully coupled structure compensator. The use of dynamic compensator as additional means to track large steps of load changes for more reliable of power plant operation. By this, two features will be covered in handling the constraints and robust performance. Simulation results have shown the applicability of the proposed idea. It has been also proved that the coal mill local control of feeder speed and primary air fans have significant on the plant primary response of MW power output.

2. Description of the Plant Process

Table 1. Boiler Specifications

In this process, vertical spindle mills are adopted, which is a dominant type for SC coal fired power plants ([9-10]). The raw coal enters the mill inlet tube and carries the coal to the middle of grinding rotating table. Hot primary air flows into the mill from bottom to carry the coal output from grinding process to the classifier that is a multi-stage separator located at the top of the mill. The heavier coal particles fall down for further grinding and the pulverized coal is carried pneumatically to the furnace. Inside the boiler, the chemical energy released from combustion is converted to thermal energy. The heat is exchanged between the hot flue gas to the water through heat exchangers. The boiler contains thin tubes as heating surfaces which form the economizers (ECON), waterwall (WW), low temperature superheater (LSH), platen superheater (PSH), final stage superheater (FSH), and reheaters (RH). The water is forced at high pressure (SC pressure) inside the economizer and passes through all those heating sections. Since pressure is above the critical point, the sub-cooled water in the economizers is transferred to the supercritical steam in the superheaters without evaporation. The SC steam is then expanded through turbines. The high pressure (HP) turbine is energized by the steam supplied at final stage superheater and the reheaters are used to reheat the exhaust steam from the HP turbine before it returns to the IP turbine. The mechanical power is converted to electrical power by synchronous generator coupled to the turbines. The boiler specifications are shown in Table 1.

3. The Process Mathematical Model

3.1. Model Description

The power plant process is illustrated in Figure. 1. It is a complex system with multi interconnection of subsystems and components. The first task for our study is to derive the mathematical model for the process. The detailed modelling study can be found in the previous work of the authors[9-12]. The parameters, detailed model structure and the way how if is derived are all described in those references. The variables appear in Figure.1 are defined in Table.2.

The coal mill model described in[9,10] is integrated with the rest of the plant model reported in[11,12]. Because there are multiple mills operating in parallel in real power plants, a proportional gain is multiplied by the pulverized coal output to account the total pulverized coal supplied to the burners. The heat flow is basically related to fuel flow through proportional gains (K_e, K_ww, K_sh, and K_rh) as shown in the figure with 1^st order lag transfer function. For more details about modelling, please refer to[11, 12].

Figure 1. Illustration of a SC power plant process mathematical model

Table 2. List of Symbols in Figure.1

3.2. Computer Implementation and Parameter Identification

Figure 2. Mass flow(Kg/s) Data set.1(identification)

Figure 3. Frequency Deviation(identification)

Figure 4. Electrical Power Data set.2 (verification)

Figure 5. Electrical Power Data set.3(verification)

Figure 6. Main Steam pressure Data set.3(verification)

Figure 7. Main Steam temperature Data set.4(verification)

The model has been implemented in MATLAB and SIMULINK environment for model response study and testing the new control strategies. The implementation has been carried out using different blocks of summing points, integrators, differentiators, first order lags, gains and so on. The identification of each subsystem has been carried out using optimization approach based on Genetic Algorithms (GAs) with data recorded on closed loop operation. It has been proved that GA is a robust optimization technique for multi-objective optimization and simultaneous parameter adjustments. Initially, the GA produces a random initial population. Then, it calculates the corresponding fitness function to recopy the best coded parameter in the next generation. The GA termination criteria depend on the value of the fitness function. If the termination criterion is not met, the GA continues to perform the three main operations which are reproduction, crossover, and mutation. More details about this technique can be found in[13].

The model has been verified over wide operating range. Some identification and verification results are shown in Figure.3 and .4 respectively. The detailed coal mill parameter identification is described in[9,10]. The measured data for identification and verification of boiler parameters are: 1) main steam temperature; 2) main steam pressure; 3) reheater pressure; 4) steam flow rate. The measured variable data for identification of turbine /generator parameter optimization are: 1) output power; 2) system frequency. The plant data from a 600MW SC power plant is used for identification. Some results of the boiler-turbine-generator unit are reported in[11,12]. Data set.1 has been used for identification which represents an increase in the load demand from 35% to 100% of load demand. Data sets 2, 3 and 4 are used for further model investigations. Figures 2 and 3 represent some identification results while figures 4, 5, 6, and 7 show some verification results for different sets of data.

4. Generalized Predictive ControllerSet-up

A model based predictive control is developed with provisions of unmeasured disturbances and measurement noises to be used for compensation around the investigated operating conditions. Here, the linear time invariant model is used for the MPC algorithm while the process mathematical model has been used to simulate the power plant responses. GA has been used again to develop the internal model of the MPC which initially has the following form:

(1)

(2)

The model has four states x^T=[x₁ x₂ x₃ x₄]^T, three inputs or manipulated variables u^T=[u₁ u₂ u₃]^T, and three outputs’=[y₁ y₂ y₃]^T =[x₂ x₃ x₄]^T. A, B, and C, are the normalized state space model matrices. The parameters of the digitized model are:

,

The inputs and the outputs which have been used for identification of the controlled plant are chosen as:

4.1. The Generalized Predictive controller

In this research, the generalized predictive controller algorithm described in[14] is adopted which has been widely used for chemical or thermodynamic process control[14-17]. The prediction model has been upgraded as follows:

(3)

(4)

where v is the measured disturbance and w is the unmeasured disturbance vector, z is the measurement noise. The adopted predictive control algorithm is quite analogous to LQG procedure, but with implication of the operational constraints. The prediction is made over a specific prediction horizon. Then the optimization program is executed on-line to calculate the optimal values of the manipulated variables to minimize the objective function below:

(5)

The weighting coefficients (Q and R), control interval(Hw), prediction horizon (Hp) and control horizon (HC) of the performance objective function will affect the performance of the controller and computation time demands. The terms r represents the demand outputs used as a reference for MPC model and Δu is the change in control values for HC number of steps. Zero-order hold method is then used to convert the control signals from discrete time to continuous time to be fed to the plant. The inputs/outputs constraints are determined according to the power plant operation restrictions, which are expressed as the maximum and the minimum allowable inputs:

(6)

(7)

The optimization problem is to find the control moves for each manipulated variable, i.e. the MPC control law:

Subject to (6) and (7).

Figure 8. Generalized Predictive controller scheme

The quadratic programming (QP) solver, with active set method or interior point method, is commonly used to solve control law problem of the MPC. In the interest of predictive controllers for thermal power stations, the generalized MPC approaches and DMC algorithms are reported for control of power plants once-through and drum type units.[3-5,7, 14-18]. To show the influences of coal mill control on the plant output responses, a controller is implemented to regulate the primary air fan and the other is implemented to regulate the coal feeder speed. Both receive the MPC coal flow signal as adjuster for their reference. With the MPC strategy described above, simulations have been conducted. The whole package of the proposed strategy is shown in figure.8. Simulation results are presented in the next section.

4.2. Simulation Study 1 (small load change)

The results are mentioned in figures 9.10.11. Case.A represents the improved case with embedded plant controllers while Case.B represents the existing milling and plant performance. It is clearly seen that the control strategy speeds-up the plant power primary response with significant improvements. Furthermore, the boiler pressure and temperature respond with less fluctuation and are kept within supercritical conditions to ensure optimal efficiency despite load variation. In figure 11, the various mill variables are presented. It seems that the mill should draw higher current than normal case in order to provide better grinding capability. In addition, higher differential pressure of the mill and primary air pressure are created to carry more pulverized coal to the furnace. In the next section, the plant will be equipped with robust compensator and tested with large load changes.

Figure 9. Controlled variables of the SC Power Plant

Figure 10. Input variables to the boiler-turbine-generator system

Figure 11. Variables of each mill in service

5. The MIMO Compensator Design and Incorporation

The plant model embeds high nonlinear features. The MPC performs well on small load change even with consideration of constant disturbance and measurement noises in prediction. The performance of MPC alone for large load change or partial load rejections was totally unacceptable. The MIMO compensator is designed by using Genetic Algorithms. This compensator has no function except compensating control errors resulting form large load changes. It has been located in parallel with the MPC. The procedures are given in the next section.

5.1. MIMO compensator design

The parallel structure MIMO PID with coupled structure can be designed and reported in many research articles[19-21], the generalized form for n×n system is then described by:

(8)

In which the input to thus matrix is the errors vector, the output is the signal required for compensation. Each s function in the matrix has the normalized proportional + integral + differential parameters which can be written as:

(9)

Then, another performance index to be minimized is written as:

(10)

Table 3. MIMO Compensator Parameters Cab kp ki kd C11 2.88 0.0393 0 C12 0.074 0 0 C13 0.0041 0 0 C21 0.0209 0 0 C22 0.0054 2.8×10-8 0.2×10-6 C23 0.0054 0 0 C31 0.0862 0 0 C32 7.74×10-8 0 0 C33 0.0054 7.1571×10-8 0.2×10-6

Figure 12. Multivariable controller scheme

The final optimal control law for robust solutions becomes:

where e is the error remaining from plant severe nonlinearity and the subscripts to indicate the outputs responses of pressure, Power, and Temperature, respectively. w₁, w₂ , w₃ are the weighting coefficients used in optimization. In our work, the matrix K is only 3×3 matrix. The major steps performed by GA to reach the optimal solution can be found in[13]. The dynamic compensator parameters are listed in Table.3. The additional corrections to the MPC control signals are introduced to simulate large load event (See figure.12).

5.2. Simulation study 2 (Large load changes)

Simulation results are mentioned in the same two cases in section 5.1 to show the performance of the control strategy proposed including the effect of milling dynamics. Again the improvements in the primary response of the plant power can be seen even with large load variation. Then, this configuration merits application on SC power plant to improve its dynamic response with emphasis on the issue of National Grid Code compliance.

There are other parallel schemes reported in the literature of chemical process control[22, 23]. In[22], an adaptive neuro controller is located in parallel with MPC to increase the controller robustness while in[23] extra PID scheduled loops are installed in parallel with MPC to compensating the plant nonlinearity. The slow dynamics of the mill can be handled by its local control system.

Figure 13. Electrical power dynamic response

Figure 14. Pressure and Temperature

Figure 15. Manipulated Variables

Figure 16. Variables for each mill in service

6. Conclusions

A mathematical model of a coal fired supercritical power plant is described in the paper. Simulation study indicates the model can predict the main dynamic response variation trends of the 600MW SC power plant process. A coordinate control is proposed and tested through simulation study with relatively large load changes. The control considers the milling process as a key stage for power plant dynamic response improvement. From the study, it is convinced that better control of the milling process can improve the power plant load following capability and/or primary response of the plant power. As future recommendations, more accurate and detailed models will be developed to simulate SC power plant and Ultra-supercritical (USC) power plants for more complicated studies.

ACKNOWLEDGEMENTS

The work of the paper was supported in part by UK EPSRC grant (EP/G062889/1) and AWM/ERDF Birmingham Science City Energy Efficiency and Demand Reduction project.