A Mathematical Model and Its Application for Hydro Power Units under Different Operating Conditions

Yang, Weijia; Yang, Jiandong; Guo, Wencheng; Zeng, Wei; Wang, Chao; Saarinen, Linn; Norrlund, Per

doi:10.3390/en80910260

Cited by 82 publications

(30 citation statements)

References 16 publications

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“…When the hydro-turbine generator unit operates under small fluctuation conditions, the transfer coefficients of the hydro-turbine are usually calculated by the constant transfer coefficient method [31], the simple linear method [26], or the external characteristic method [32]. However, the simple linear method and the constant transfer coefficient method only apply to the small fluctuation condition.…”

Section: Nonlinear Expressions Of the Hydro-turbine Transfer Coefficimentioning

confidence: 99%

Nonlinear Modeling and Dynamic Analyses of the Hydro–Turbine Governing System in the Load Shedding Transient Regime

2018

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Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro-turbine governing system. In order to study the dynamic characteristics of the hydro-turbine governing system during the load shedding process, a novel nonlinear mathematical model of the hydro-turbine governing system is established considering the hydro-turbine system, the generator system and the governor system. In particular, a novel nonlinear mathematical model of the six hydro-turbine transfer coefficients is presented based on the definitions and hydro-turbine internal characteristics. After that, from the viewpoint of nonlinear dynamics and the practical engineering, the dynamic characteristics of the hydro-turbine governing system are investigated utilizing bifurcation diagrams, time series, Poincare maps, power spectrums and phase planes. Some meaningful results are found. The advantages of the novel nonlinear mathematical model are illustrated and commented in detail in comparison with the previous model. Finally, these models and analysis results will provide some theoretical references for the operation of hydropower stations in the load shedding transient.Energies 2018, 11, 1244 2 of 17 to optimizing the control of the HTGS. Based on the polynomial robust H ∞ optimization method, Eker [16] presented a robust single-input multi-output design approach for governors for speed control of hydro-turbines. Khodabakhshian and Hooshmand [17] put forward a new robust proportionalintegral-derivative (PID) controller for automatic generation control of hydro-turbine power systems, which is designed mainly based on a maximum peak resonance specification. Ren et al. [18] proposed an improved cascade control strategy for hydro-turbine speed governors, which can effectively decrease fluctuations of the rotational speed under non-Gaussian disturbance conditions in practical hydropower plants. Chen et al. [19] focused on designing the fractional-order PID controller using a chaotic non-dominated sorting genetic algorithm II for the HTGS, which has a better performance than traditional integer PID controllers. Zhang et al.[20] created a brand new non-linear predictive control method using the Takagi-Sugeno (T-S) fuzzy method and the generalized predictive control, which can govern a non-linear system more effectively. Chen et al.[21] established a new nonlinear mathematical model of the HTGS with a surge tank, and then, the nonlinear dynamical behaviors of the system in small fluctuation process were studied in detail. Guo et al. [22] studied the stability of the HTGS of the hydropower station with sloping ceiling tailrace tunnel utilizing the Hopf bifurcation theory, and also got the algebraic criterion of the occurrence of Hopf bifurcation. Xu et al. [23] built the Hamiltonian mathematical model of the multi-hydro-turbine governing system with a sharing common penstock under the excitation of stochastic and shock load, and then, discussed the stability of the system by comparing ...

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Section: Nonlinear Expressions Of the Hydro-turbine Transfer Coefficimentioning

confidence: 99%

Nonlinear Modeling and Dynamic Analyses of the Hydro–Turbine Governing System in the Load Shedding Transient Regime

2018

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“…As this paper is the study of the start-up process simulations, it does not consider units with load situations, that is, the unit load M g is 0. The following formula is the synchronous generator model [20]:…”

Section: Generator and Load Modelmentioning

confidence: 99%

Multi-Objective Optimization of Start-up Strategy for Pumped Storage Units

Hou

Tian

et al. 2018

Energies

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This paper proposes a multi-objective optimization method for the start-up strategy of pumped storage units (PSU) for the first time. In the multi-objective optimization method, the speed rise time and the overshoot during the process of the start-up are taken as the objectives. A precise simulation platform is built for simulating the transient process of start-up, and for calculating the objectives based on the process. The Multi-objective Particle Swarm Optimization algorithm (MOPSO) is adopted to optimize the widely applied start-up strategies based on one-stage direct guide vane control (DGVC), and two-stage DGVC. Based on the Pareto Front obtained, a multi-objective decision-making method based on the relative objective proximity is used to sort the solutions in the Pareto Front. Start-up strategy optimization for a PSU of a pumped storage power station in Jiangxi Province in China is conducted in experiments. The results show that: (1) compared with the single objective optimization, the proposed multi-objective optimization of start-up strategy not only greatly shortens the speed rise time and the speed overshoot, but also makes the speed curve quickly stabilize; (2) multi-objective optimization of strategy based on two-stage DGVC achieves better solution for a quick and smooth start-up of PSU than that of the strategy based on one-stage DGVC.

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“…where r 1 is the rotor radius; µ 0 is the air permeability; k j is the air gap flux potential; i is the generator excitation current; l is the generator rotor length. Apart from the above, there are four meaningless intermediate variables (Λ 0 , Λ 1 , Λ 2 , and Λ 3 ) calculated in reference [14].…”

Section: Unbalanced Magnetic Pull Modelmentioning

confidence: 99%

“…Therefore, hydropower stations have become an important part of public utilities and infrastructure [4][5][6][7][8][9][10]. Recently, with the rapid development of manufacturing and energy industry, the hydropower stations have been developing towards higher rotational speeds, larger capacity and more complex operation conditions [11][12][13][14]. For for the HGSS, it is essential to establish a mathematical model on hydraulic instability to study the influences of the hydraulic instability.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analyses of the Hydro-Turbine Generator Shafting System Considering the Hydraulic Instability

Zhuang

Gao

et al. 2018

Energies

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Hydraulic instability is a complex factor causing the vibration of hydro-turbine generator shafting system (HGSS), and the mechanism is the uneven distribution of flow along the circumference. The common reasons for this phenomenon include the inconsistency of the blade exit flow angle, the relay stroke and the guide vane opening. This paper mainly focuses on the research of the hydraulic instability caused by the inconsistency of the blade exit flow angle. Firstly, based on the Kutta-Joukowski theorem, the hydraulic unbalance force model is firstly presented. Then, considering the chain reaction among the hydraulic, mechanical and electrical instability, a combined nonlinear mathematical model of the HGSS is established. Finally, by using numerical simulation, the dynamic characteristics of the HGSS with the changing of the deviation of the blade exit flow angle, the blade exit diameter and the guide vane opening angle are analyzed. Moreover, it is found that the hydraulic instability determines the overall changing trend of the shafting dynamic behaviors. In addition, some stable ranges of the HGSS are distinguished. But above all, these results can efficiently provide a reference for the design and manufacture of hydro-turbine blades and the operation of hydropower stations.

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A Mathematical Model and Its Application for Hydro Power Units under Different Operating Conditions

Cited by 82 publications

References 16 publications

Nonlinear Modeling and Dynamic Analyses of the Hydro–Turbine Governing System in the Load Shedding Transient Regime

Nonlinear Modeling and Dynamic Analyses of the Hydro–Turbine Governing System in the Load Shedding Transient Regime

Multi-Objective Optimization of Start-up Strategy for Pumped Storage Units

Dynamic Analyses of the Hydro-Turbine Generator Shafting System Considering the Hydraulic Instability

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