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This paper focuses on the stability problems in a hydropower station. To enable this study, we consider a nonlinear hydropower generation system for the load rejection transient process based on an existing hydropower station. Herein we identify four critical variables of the generation system. Then, we carry out the dynamic safety assessment based on the Fisher discriminant method. The dynamic safety level of the system is determined, and the evolution behavior in the transient process is also performed. The result demonstrates that the hydropower generation system in this study case can operate safely, which is in a good agreement with the corresponding theory and actual engineering. Thus, the framework of dynamic safety assessment aiming at transient processes will not only provide the guidance for safe operation, but also supply the design standard for hydropower stations.

Safety problems in hydropower stations generally cause power supply failures, economic loss of plants, and injury of workers [

There are two operation types for the HGS including the small variation and large variation transient process. Generally, the large variation transient processes (i.e., load rejection, load increase/decrease, start-up, and shut-down) often result in unsteady operating conditions of the HGS, which may lead to the safety problems in the hydropower station. For example, the turbine flow and torque rapidly decrease during the load rejection transient process, which results in the fact that the system easily loses its control ability when system variables strongly change. Thus, we should pay more attention to the safety study of the HGS in the transient process, especially in the large variation.

Safety assessment has been extensively studied in many fields and has also obtained significant outcomes [

In light of the above consideration, this paper aims to assess the dynamic safety levels of the nonlinear HGS using the Fisher discriminant method. From the literature [

We have three innovations to make our paper attractive compared with the existing papers such as [

The rest of the paper is organized as follows. In Section

Hydropower generation system (HGS) as an important part in hydropower station is directly related to the safety of power grid. HGSs are complex system integrated with multiple nonlinear structures. In general, a complete nonlinear HGS is composed of seven typical structures, that is, reservoirs, penstock systems, governors, generators, hydraulic turbine, surge tanks, and draft tubes, which can be shown in Figure

Diagram of an elementary hydropower generation system.

In fact there are two operating types for HGSs in the practical hydropower station, which are the small and large variation transient processes [

The load rejection transient herein is a study case to further investigate the safety of HGS. As is known to all, the variable of system fluctuates dramatically because the HGS is a high coupled nonlinear system in the load rejection transient. For example, during this transient process, the flow and the torque of hydraulic turbine decrease rapidly with the close of guide vane. Meanwhile, the speed of hydraulic turbine first increases and then decreases. Figure

Schematic diagram of the change laws of variables in the nonlinear HGS during the load rejection transient process.

In this paper, we study the performance of HGS based on an existing hydropower station. Therefore, the closing law of guide vane for the load rejection transient is shown in Figure

Closing law of an existing HGS in the load rejection transient process.

Based on the above consideration, we adopt the experimental data and HGS model presented in [

Based on the working mechanism of the characteristic line shown in Figure

The working mechanism of the characteristic line.

Here, the pressure

In this study, a universal Fisher discriminant method [

Schematic diagram of Fisher discriminant method.

The primary formula of Fisher discriminant method can be described as follows: we assume that there is a linear discriminant function

The objective function

Meanwhile, the linear discriminant function

To obtain the final linear discriminant function, we make the objective function

To conclude, the overall methodology of this paper is performed in Figure

Preparatory work: to enable the dynamic safety assessment, we should analyze the accident of the HGS and also obtain the training and predictive HGS data.

Use the Fisher discriminant method to judge the safety level of the predictive data at the transient time

Update the safety level of the HGS by repeating step

Understand the safety evolution process and obtain the dynamic safety level of the HGS in the transient process.

Overall methodology of this work.

In this paper, the safety assessment of a nonlinear HGS is carried out on the basis of an existing hydropower station, and its basic information including the head level and hydraulic turbine is listed in Tables

Head level information of an existing HGS.

Parameters of the HGS | Values |
---|---|

Normal water level of upstream reservoir | 1300 m |

Designed flood level of upstream reservoir | 1300.53 m |

Check flood level of upstream reservoir | 1301.56 m |

Dead water level of upstream reservoir | 1280 m |

Designed flood level in tailrace outlet | 1152.85 m |

Check flood level in tailrace outlet | 1155.52 m |

Hydraulic turbine information of an existing HGS.

System parameters | Values/information |
---|---|

Type of hydraulic turbine | HLFI034-LJ-176 |

Nominal head | 129 m |

Nominal speed | 428.6 r/min |

Installation height | 1147.5 m |

Maximum head | 149 m |

Minimum head | 119 m |

Nominal power | 20.62 Mw |

Moment of inertia | 320 t⋅m^{2} |

To enable this dynamic safety assessment, the training date and predictive data of the HGS for the load rejection transient process are, respectively, performed in Table

Training data of the HGS in the load rejection transient process.

Relative values of variables in HGS (p.u.) | ||||
---|---|---|---|---|

Speed of hydraulic turbine | Pressure of spiral case | Pressure of draft tube | Pressure of surge tank | Safety level |

1 | 1.0547 | 0.94 | 0.9948 | Safety |

0.2971 | 0.9867 | 0.8389 | 0.9995 | Safety |

0.2121 | 0.9965 | 0.8052 | 0.9986 | Safety |

0.149 | 0.9942 | 0.8354 | 0.9976 | Safety |

0.1271 | 1.0017 | 0.9234 | 1.0005 | Safety |

0.1065 | 1.0194 | 1.0009 | 1.0033 | Safety |

0.1175 | 1.0397 | 0.9063 | 1.004 | Safety |

0.1 | 1.0192 | 0.9 | 1.0046 | Safety |

1.2282 | 1.075 | 0.9908 | 0.9995 | Tolerable |

1.2913 | 1.1025 | 0.9637 | 1.0059 | Tolerable |

1.3543 | 1.143 | 0.9063 | 1.0113 | Tolerable |

1.2282 | 1.317 | 1.2917 | 0.9998 | Tolerable |

1.1651 | 1.2843 | 1.3692 | 1.004 | Tolerable |

1.1116 | 1.2516 | 1.4265 | 1.0084 | Tolerable |

0.9951 | 1.2111 | 1.43 | 1.0097 | Tolerable |

0.921 | 1.1731 | 1.3827 | 1.0062 | Tolerable |

0.8264 | 1.1329 | 1.3284 | 1.0033 | Tolerable |

0.7524 | 1.1178 | 1.2238 | 0.9989 | Tolerable |

0.6783 | 1.0949 | 1.1226 | 0.9967 | Tolerable |

0.5713 | 1.09 | 1.0784 | 1.0024 | Tolerable |

0.4767 | 1.0773 | 1.0075 | 1.0062 | Tolerable |

0.4136 | 1.0472 | 0.9365 | 1.0052 | Tolerable |

0.3286 | 1.0092 | 0.9063 | 1.0008 | Tolerable |

1.4188 | 1.1708 | 0.8389 | 1.0141 | Unstable |

1.4394 | 1.2464 | 1.021 | 1.0027 | Unstable |

1.4078 | 1.287 | 1.0854 | 0.9963 | Unstable |

1.3653 | 1.317 | 1.1599 | 0.9935 | Unstable |

1.3228 | 1.3625 | 1.2273 | 0.9957 | Unstable |

1.4503 | 1.1859 | 0.8288 | 1.0126 | Risk |

1.4928 | 1.1908 | 0.8052 | 1.0132 | Risk |

1.5024 | 1.1784 | 0.8017 | 1.0139 | Risk |

1.4709 | 1.1656 | 0.8082 | 1.0122 | Risk |

1.4928 | 1.1607 | 0.8862 | 1.0091 | Risk |

1.4613 | 1.2062 | 0.9873 | 1.0065 | Risk |

Predictive data of a nonlinear HGS for the load rejection transient process.

The training data of HGS in Table

Based on Table

Dynamic safety assessment results of the predictive HGS during the load rejection transient process.

Figure

Moreover, we report the dynamic statistical ratios of the HGS for the four safety levels, as shown in the bar chart of Figure

Based on the pipe water pressure testing of the studied HGS presented in [

In this paper, we have presented a dynamic framework of safety assessment of HGSs in transient processes. To achieve this, we consider a nonlinear HGS for the load rejection transient process from an existing hydropower station, and the critical system variables are extracted. Then, we have assessed the safety of the HGS using the Fisher discriminant method. The dynamic safety evolution process has been studied, and the safety level has also been determined during this transient process. The result demonstrates that the nonlinear HGS studied in this paper has a better stability because it is in the Safety and Tolerable levels about the probability of 76.2% during the load rejection transient. Meanwhile, there is no Risk level for this HGS. It also reveals that the HGS achieves the perfect performance of antidisturbance and the harmonious operation of its different parts. However, the Fisher discriminant method is a linear projection approach, which may not better reflect some uncertainties existing in the HGS. Therefore, future work will explore a more rigorous evaluation method to improve the reliability of the assessment result.

To date, not many studies pay attention to assessing the safety level of the HGS in large fluctuation transient processes. To overcome this limitation, this work presents a new framework for the dynamic safety assessment of transient HGSs. This not only provides the operation guidance of HGSs, but also gives the design standard for the safe operation of hydropower stations. Furthermore, although the proposed Fisher discriminant method can realize the dimensionality reduction of the multidimension variables for the transient HGS, some drawbacks may not be ignored. For instance, the linear discriminant function (as mentioned in (

Sectional area of the upstream pipe,

Water hammer wave speed, m/s

Sectional area of the downstream pipe,

Positive characteristic line

Negative characteristic line

Intermediate variables

Diameter of penstock, m

Darcy-Weisbach resistance coefficient

Hydroturbine speed, rad/s

Piezometric head of penstock, m

Pressure of the penstock

Gravitational acceleration, m/

Mechanical torque of the hydroturbine, N·m

Guide vane opening, rad

Hydroturbine flow,

Flow of the penstock

Transient time, s

Linear discriminant coefficient

Linear discriminant function

Flow velocity, m/s

Displacement along penstock direction, m

Angle between penstock and horizontal direction, rad

Guide vane opening, %

Hydroturbine efficiency, %

Mean matrix

Objective function

Covariance matrix

Number of training groups

Value at the arbitrary time

The authors declare that they have no conflicts of interest.

This study was supported by the National Natural Science Foundation of China (71573256) and the National Key Research and Development Plan of China (2017YFC0804408).