# Parameter Identification and Sliding Pressure Control of a Supercritical Power Plant Using Whale Optimizer

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Background and Motivation

#### 1.2. Literature Review and Paper Contributions

#### 1.2.1. Review on Modeling

#### 1.2.2. Control System Review

- A simplified MIMO Transfer matrix model for the sliding pressure operation mode of the supercritical power plant has been built. This model is validated for the entire OT operational characteristic.
- The second potential addition is that state-of-the-art optimization techniques will be applied to identify the parameters, which are the Whale Optimizer (WO) and Grey-Wolf Optimizer (GWO). It would be fascinating to compare these techniques against commonly used techniques, such as Genetic Algorithms, to see which one is truly more accurate for SC plants and control systems. It can be newly argued that the WO is more accurate in modeling and control than other techniques in both objectives concerned with system dynamics, energy efficiency, and cleaner operation.
- The third feasible contribution is that the study presents the design of a practically adequate multivariable PI/PD control system that is compatible with sliding pressure operation and integrates into the previously mentioned model for system dynamics and sudden load changes. This control system is capable of increasing the speed of load demand response while simultaneously lowering the plant’s fuel and feedwater consumption.

## 2. An Overview of the Whale Optimizer (WO)

#### 2.1. Inspiration

#### 2.2. Modeling and Optimization of the Algorithm

#### 2.2.1. Encircling Prey

#### 2.2.2. Hunting Technique

- 1.
- Shrinking encircling technique:

- 2.
- Spiral updating position:

#### 2.2.3. Searching for Prey

## 3. Model Structure and Parameter Identification

#### 3.1. MIMO Transfer Matrix for Sliding Pressure Mode

#### 3.2. Parameter Identification

#### 3.2.1. Genetic Algorithm

#### 3.2.2. Grey-Wolf Optimizer

#### 3.2.3. Whale Optimizer

## 4. Control Tuning and Testing

_{p}, K

_{i}, and K

_{d}, respectively. Where the constant T

_{d}is corresponded to filter time. It is worth noting that when K

_{d}= 0, PID becomes PI. Figure 13 shows the SCPP control system model.

## 5. Control System Performance Results

## 6. Conclusions

- -
- A simplified transfer matrix model for supercritical generation units has been developed with some additional blocks to capture the system nonlinearities and delays in the fuel preparation system. This structure is more suitable from a control point of view in sliding pressure operational modes.
- -
- The parameters of the transfer matrix are identified to fit a practical 600 MW SCPP via three different metaheuristic optimization techniques, which are the Whale Optimizer, Grey-Wolf Optimizer, and Genetic Algorithms. Considerable effort has been made to adjust the settings of the various optimization methods to yield the best possible results for all chosen techniques.
- -
- The Whale Optimizer has proven to be more robust and accurate than the Grey-Wolf Optimizer and Genetic Algorithms for parameter estimation. The criterion chosen for the modeling part is the NRMSE of the pressure and power responses and through a basic inspection of the depicted responses.
- -
- A robust controller has been designed and successfully implemented to govern part-load operation changes. Again, the three techniques of Whale Optimizer, Grey-Wolf Optimizer, and Genetic Algorithms have been evaluated against tuning the parameters for optimum control performance. The Whale Optimizer technique of parameter tuning is found to be better than other techniques in terms of lower fuel consumption and better output responses.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

CFP | Coal-fired Plant |

DEH | Digital Electro-Hydraulic |

FWF | Feedwater Flow |

GA | Genetic Algorithm |

GWO | Grey-wolf Optimizer |

MIMO | Multi-input Multi-output |

MSE | Mean-squared Error |

NRMSE | Normalized Mean-squared Error |

OT | Once-Through |

PID | Proportion integration differentiation |

SCPP | Supercritical Power Plant |

SLO | Sliding Pressure Operation |

DMC | Dynamic Matrix Control |

CCS | Coordinated Control System |

MST | Main Steam Temperature |

WO | Wolf Optimizer |

AGC | Automatic Generation Control |

MPC | Model Predictive Control |

ADRC | Active Disturbance Rejection Control |

SI | Swarm Intelligence |

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**Figure 1.**(

**a**) Coordinated (integrated) control mode with nearly constant pressure set-point (

**b**) Complete-range Sliding pressure mode.

**Figure 10.**Supercritical power plant input flow over 100 min (

**a**) input feedwater flow. (

**b**) input fuel flow.

Recent Studies | Plant Modeling | Algorithm | Control Strategy | Mode Coordinated/Sliding | Control System Objectives |
---|---|---|---|---|---|

Mohamed et al. (2012) | Physical model | GA | MPC | Coordinated | Enhance the overall dynamic responses |

Chen et al. (2017) | Software-based model | - | Conventional PID | Coordinated | Maintain the fluid level under load changes |

Sarda et al. (2018) | Steady-state model | - | Conventional PID | Coordinated | Maintain main and reheater steam temperature |

Liang et al. (2018) | Physical model | GA | Multi MPC | Coordinated | improve the pulverizing system performance |

Shi et al. (2020) | Transfer function model | GA | Hybrid ADRC | Coordinated | Maintain the super-heated steam temperature |

Wu et al. (2021) | Physical model | MOGA | ADRC & PID | Coordinated | Improve the load demand following responses |

Abu Znad et al. (2022) | State-space model | - | Classical MPC | Sliding | Speed up the starting process |

This work | Data-driven model | GWO * & WO * | Multivariable PI/PD | Sliding | Enhance the load demand following responses and reduce fuel and feedwater flow usage |

GA Option | Setting |
---|---|

Population size | 30 |

Number of generations | 50 |

Crossover function | Heuristic |

Mutation function | Adaptive feasible |

Selection function | Tournament |

Migration direction | Forward |

GWO Option | Setting |
---|---|

Population size (Number ofsearch agents) | 30 |

Number of iterations | 50 |

WO Option | Setting |
---|---|

Population size (Number of search agents) | 30 |

Number of iterations | 50 |

Unknown Parameter | GA | GWO | WO |
---|---|---|---|

a_{11} | 0.77 | 0.3465 | 0.2615 |

b_{11} | 0.369 | 0.3 | 0.2297 |

c_{11} | 1.548 | 2.5 | 3.0653 |

d_{11} | 2.952 | 2.2 | 1.9263 |

e_{11} | 1.861 | 1.8 | 1.8844 |

a_{12} | 0.536 | 0.7378 | 0.7006 |

b_{12} | 0.168 | 0.201 | 0.2702 |

c_{12} | 2.804 | 1.8 | 1.9268 |

d_{12} | 68.48 | 60 | 52.1208 |

e_{12} | 6.382 | 6.5 | 7.4443 |

a_{21} | 1.942 | 1.0448 | 1 |

b_{21} | 3.967 | 2.9705 | 2.5 |

c_{21} | 6.102 | 7.5 | 6.034 |

d_{21} | 1.724 | 2.0092 | 4 |

e_{21} | 0.849 | 0.6124 | 0.998 |

a_{22} | 5.787 | 4.6825 | 4 |

b_{22} | 1.317 | 0.7091 | 0.5392 |

c_{22} | 9.434 | 8.1908 | 9.5 |

d_{22} | 30.574 | 30 | 20.8656 |

e_{22} | 2.147 | 1.2 | 0.6003 |

Response | NRMSE/GA | NRMSE/GWO | NRMSE/WO |
---|---|---|---|

Power | 0.088 | 0.0868 | 0.0561 |

Pressure | 0.0765 | 0.0735 | 0.0409 |

Parameter/Technique | GA | GWO | WO |
---|---|---|---|

K_{p1} | 7.5433 | 5.6564 | 8.0019 |

K_{i1} | 1.5321 | 0.0331 | 0.0312 |

K_{p2} | 0.2770 | 0.6726 | 3 × 10^{−6} |

K_{i2} | 0.0870 | 0.1315 | 4 × 10^{−7} |

K_{p3} | 0.8270 | 0.8404 | 0.7765 |

K_{d} | 11.4520 | 11.5471 | 11.6 |

T_{d} | 20.0010 | 24.1048 | 24.1048 |

Input/Technique | GA | GWO | WO |
---|---|---|---|

Fuel flow (Kg/s) | 73.4991 | 72.2625 | 68.8226 |

Feedwater flow (Kg/s) | 425.7973 | 428.5004 | 418.4478 |

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**MDPI and ACS Style**

Qasem, M.; Mohamed, O.; Abu Elhaija, W.
Parameter Identification and Sliding Pressure Control of a Supercritical Power Plant Using Whale Optimizer. *Sustainability* **2022**, *14*, 8039.
https://doi.org/10.3390/su14138039

**AMA Style**

Qasem M, Mohamed O, Abu Elhaija W.
Parameter Identification and Sliding Pressure Control of a Supercritical Power Plant Using Whale Optimizer. *Sustainability*. 2022; 14(13):8039.
https://doi.org/10.3390/su14138039

**Chicago/Turabian Style**

Qasem, Mohammad, Omar Mohamed, and Wejdan Abu Elhaija.
2022. "Parameter Identification and Sliding Pressure Control of a Supercritical Power Plant Using Whale Optimizer" *Sustainability* 14, no. 13: 8039.
https://doi.org/10.3390/su14138039