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The harmonics exacerbated by the integration of distributed energy such as wind power has been extensively studied. However, the interaction and propagation mechanism between harmonic sources in the hydro-wind complementary generation system are still not clear. To tackle this challenge, the presented study establishes the hydro-wind complementary generation system model and explores the harmonics propagation and interaction in all components. Then three operation mode of complementary system (scenario 1: stand-alone Hydroelectric Generating System, scenario 2: stand-alone Wind Farm (WF) and scenario 3: complementary generation system) are selected. The results demonstrate that the integration of HGS diminishes the harmonic at DFIG side but at the grid side. In complementary generation system, the THD

This study focuses on the start-up optimization strategies for a Hydroelectric Generating System (HGS). A mathematical model of HGS to describe the complex hydraulic coupling relationship, between the water diversion pipes, the hydro-turbine, the governor and the generator, is proposed. This allows to accurately describe the start-up process and identifying the effect of successive start-up time interval (ΔT) and the pipe structure on the water head and the rotational speed of HGS. The result shows that the successive start-up strategy with ΔT = 9s maximally reduces the water head fluctuation of units #1 and #2 by 30.94% and 25.77% compared with the simultaneous start-up strategy when the branch pipe is symmetric. For the asymmetric branch pipe, the unit behind branch B# starts up first is beneficial to reduce the water head fluctuation of the unit behind branch #A when the flow inertia time constant of branch #A is larger. Finally, the parameters of the start opening as well the PID governor parameters are optimized by a multi-objective particle swarm optimization for the asymmetric pipe in order to minimize the unit speed overshoot and the speed rise time. These results in this work provide a theoretical guidance for the selection of optimal start-up strategy in the case of symmetric and asymmetric HGS branch pipe structures.

With the increasing scale of wind energy being connected to the power grid, the system flexibility shows an increasingly important role in maintaining the power balance. This trend indicates that it requires a clearer understanding of how the flexibility resource provided by hydroelectric units affects the flexibility performance. It is a challenge for the flexibility assessment as one of the major reasons for the accurate quantification involves the randomness, volatility, and intermittency of wind power injected into the grid. To address this challenge, a mathematical model of a wind-hydro hybrid power system (WHHPS) is developed and verified. The flexibility indices, namely, the probability and expectation of upward/downward flexibility not supplied, are defined. Finally, the flexibility properties of different reserve ratios and line distances are quantitatively analyzed. One of the main results shows that both the upward and downward flexibility are improved with the reserve ratio increasing regardless of changes in wind speed types. The proposed methods and results provide a visualized reference for the dispatching department to evaluate the required flexibility for improving the utilization rate of wind energy.

A hydraulic generating system (HGS) may undergo Hopf bifurcations or limit point bifurcations before the occurrence of low-frequency oscillations (LFO). These oscillations severely limit the power transmission capacity and even threaten the stability of the power grid in some situations. Hence it is increasingly crucial to have a clear understanding of LFO in bifurcation scenarios. This problem becomes even more complicated with parametric uncertainties in power systems as it is always challenging to efficiently handle LFO under such conditions. To address this challenge, a mathematical model of a HGS is established which is then utilized to evaluate the sensitivity of state variables against parametric uncertainties. Subsequently, two bifurcation scenarios with variations in two sensitivity parameters (the proportional and integral adjustment coefficients) are analyzed to demonstrate the interactions between oscillation modes and bifurcations. Finally, the results are presented in terms of oscillation indicators of bifurcation scenarios. These indicators include the eigenvalue, frequency, damping and participation factor. One of the most important results shows that the governor provides positive damping to HGS and introduces ultra-low frequency oscillations to the system under certain conditions. The proposed approach and analytical results provide a useful tool for analyzing LFO in a HGS for bifurcation scenarios.

Performance evaluation of a hydropower generation system is a critical science and engineering problem, with ubiquitous presence in hydropower plant applications. This study aims at a nonlinear model of the hydropower generation system with multiple units, where a novel modeling methodology for the start-up transient process is presented. Experimental data from an existing hydropower station are considered to validate the established model. The numerical result obtains the effective intervals and possible optimal values of the critical system parameters to diminish the operating risk of hydropower stations. The result also shows the interaction effect of the multiple units and the vibration performance of the system in the start-up process. The implemented application has an interface with the effective evaluation for the safety strategy of the HGS in the actual transient operation, and the obtained results have good precision and are in agreement with theories and engineering applications.

The existence of the gyroscopic effect has significant impact on the stability, dynamical behaviors and vibrational characteristics of the high-speed rotating systems. In this paper, the vibration characteristics of the hydro-turbine generator unit with the gyroscopic effect is analyzed. First, a novel nonlinear mathematical model of the hydro-turbine generator unit with consideration of the gyroscopic effect and multi-degree of freedom is established. Second, the vibration of the shaft system are investigated using time histories, phase trajectories and spectrograms based on an operation hydropower station. Some interesting phenomena are obtained by comparing the vibration laws of the hydraulic generator unit in the cases of both K = 0 (without gyroscopic effect) and K ≠ 0 (with gyroscopic effect). Those phenomena show that the effect of gyroscopic intensifies the vibration to some components of the hydraulic generator unit, and it has significant effect on the safe and stable operation of hydropower stations. Meanwhile, the proposed mathematical model can accurately reflect the influence of gyroscopic effect on the vibration characteristics of the hydro-turbine generator unit. The results of this study provides theoretical basis for the design and installation of hydraulic generator units and the optimal operation of hydropower stations.

In this paper, we pay attention to analyze the stochastic global stability and the bifurcation of the hydro-turbine generator. More specifically, the above research will be completed by introducing an analysis method of stochastic dynamics- stochastic averaging method. Initially, a mathematical model of the generator with a stochastic excitation will be established in Hamiltonian system. Then, utilizing the stochastic averaging method to derive the differential expression of the Hamiltonian function. Finally, the expression, whose physical meaning represent the mechanical energy, will be used to make a detailed analysis. The maximal Lyapunov exponent and stochastic bifurcation theory will respectively be adopted to research and discuss the stochastic global stability and the bifurcation. Research indicates that with the increasing of the rotation speed, the system will gradually change from absolute stability to absolute instability. Meanwhile, at a certainly interval of rotation angle, the probability of the generator being disturbed by stochastic factors will suddenly increase. All of the above, provides a novel perspective on the research of the hydropower stations stability, which is significant to the safety and stable operation of hydropower stations.

This paper investigates a backstepping sliding mode fault-tolerant tracking control problem for a hydro-turbine governing system with consideration of external disturbances, actuator faults and dead-zone input. To reduce the effects of the unknown random disturbances, the nonlinear disturbance observer is designed to identify and estimate the disturbance term. To drastically decrease the complexity of stability functions selection and controller design, the recursive processes of the backstepping technique are employed. Additionally, based on the nonlinear disturbance observer and the backstepping technique, the sliding mode fault-tolerant tracking control approach is developed for the hydro-turbine governing system (HTGS). The stability of HTGS is rigorously demonstrated through Lyapunov analysis which is capable to satisfy a tracking control performance. Finally, comprehensive simulation results are presented to illustrate the effectiveness and superiority of the proposed control scheme.

The output power of the hydro-turbine is a key component in precisely modeling the stability characteristics of a hydro-turbine governing system (HTGS), especially in working conditions that is far away the optimum operating condition. In this study, first, we formulate the energy losses of HTGS's components to present the hydro-turbine's output power and utilize it to establish a novel mathematical model of HTGS. Second, we perform global sensitivity analysis to extract sensitive parameters of the conversion efficiency, optimize the values of model parameters based sensitive results, and verify HTGS model to be effective in different working conditions by experimental data. Third, the distribution characteristics of energy losses are investigated with the increasing guide vane, and the corresponding stability regions are presented to predict the characteristics of transient stability trend. The obtained results could contribute to the optimization analysis and control of HTGS in working conditions that is far away the optimum operating condition.

This study focuses on the critical issue: whether uncertainties in parameters make a difference to transient characteristics. To solve this problem, a mathematical model is established for a multi-parallel hydropower system in the successive load rejection. It is validated against the operation data from Shitouxia Hydropower station located at the west of China. Moreover, we show how parametric uncertainty strongly affects the system output and how the closure law of the guide vane affects water hammer pressure, surge, and rotational speed in the successive load rejection. Results showed that there are nine parameters corresponding to the main effect and total effect exceeding other parameters, and effect level to main effect and total effect are same. In addition, the effect of the keen point on the water hammer pressure, surge, and rotational speed are investigated. Finally, all of these results provide a guidance in analyzing the stability of hydropower system with different layouts of hydraulic subsystems.

Ensuring the safe operation of hydropower stations is one of the key challenges for electric generation. Clearly the safe operation of such systems can only be archived with proper and effective maintenance scheduling. The objective of this study is to analyze, rank and prioritize the risk factors responsible for equipment failures of a hydraulic turbine generator unit (HTGU) based on operating data and expert elicitation. Here a simple qualitative risk evaluation model is proposed able to consider seven typical failures in HTGU. The proposed tool is applied for the risk prioritization of equipment failures, e.g. shaft torsion, misalignment, rotating fault, axis bend, runner fault, water guide, and wicket gate of a hydropower station in China. The obtained results have been compared against the actual statistics of equipment failures of a hydropower station in China, considered showing good agreement. All of these results provide theoretical guidance for digitalization realization of equipment failures.

Global primary energy consumption will continue to increase with a high rate to 2050, which will be a big challenge for countries to meet both global and regional energy demand. Pumped storage stations (PSS) integrated to a hybrid power system (HPS) with solar and wind power for China are under construction to tussle with this challenge. Historically, modeling of a PSS integrated HPS has been ignored the interaction effect between the shaft vibration and the governing strategies, which will increase the dynamic risk of PSS disconnected immediately to HPS. Here we unify the models of the hydro-turbine governing system and hydro-turbine generator units with a novel expression of hydraulic forces. We quantize all the parameter’s interaction contributions of PSS integration to HPS and validate this model with the existing models. Finally, we show the feasibility of PSS’s model in integrating of a HPS under steady and fault scenarios.

This study focuses the energy distribution of a hydroelectric generating system. Understanding the way energy distribution is important for researchers because it determines many of the macroscopic attributes, such as conversion efficiency, dynamic characteristics, et al. Historically, energy modeling has been split into two directions, focusing on stability analysis and its control, and has not yet been studied from the viewpoint for the stochastic turbine flow. Here we established a novel stochastic model to analyze the energy distribution of the hydroelectric generating system. We verified this model with the monitored data from Nazixia hydropower station of China. We also show how the stochastic turbine flow affects the energy losses of the system. The result shows that the one with the highest influence is the hydraulic impact losses in spiral case (more than 60%), and the hydraulic friction loss first keeps 19% as the stochastic intensity changes from 0.01 to 0.5, then increases to 20% when the stochastic intensity reaches 0.6.

This paper focuses on the safety analysis of a nonlinear hydro-generating unit (HGU) running under different loads. For this purpose, a dynamic balance experiment implemented on an existing hydropower station in China is considered, to qualitatively investigate the stability of the system and to obtain the necessary indices for safety assessment. The experimental data are collected from four on-load units operating at different working heads including 431 m, 434 m, 437 m, and 440 m. A quantitative analysis on the safety performance of the four units was carried out by employing an integration of entropy weights method with grey correlation analysis. This assisted in obtaining the safety degree of each unit, providing the risk prompt to the operation of nonlinear hydro-generating units. The results confirm that unit 4 has the highest level of safety while unit 3 operates with the lowest safety condition. This provides the optimal operational schedule of HGUs to cope with the fluctuations of electricity demand in the studied station. The proposed methodology in this paper is not only applicable to the HGUs in the studied station but could also be adopted to assess the safety degree of any hydropower facility.

Shaft mis-alignment is one of the most common faults in rotating machineries. Most existing approaches that establish mathematical models address the complex forces acting on the shafting of the hydraulic turbine generating system, and fail to comprehensively consider the impact of the coupling hydro-mechanical-electrical factors on the vibration of the shafting. In this paper, a novel model is developed, considering the coupling relationship of the penstock (hydraulic system), the power grid (electrical system) and the guide vane device (mechanical system). Global sensitivity analysis is performed to investigate the effect of parametric uncertainty on the shaft vibration, and the novel model is verified compared with the numerical results of the FEW model and measured data from monitoring system of Nazixia hydropower station. Furthermore, the effects of the coupling hydro-mechanical-electrical factors are analyzed in detail when the mis-alignment distance is set as different values. The results show the synchronous dynamic evolutions of the hydraulic turbine flow, the guide vane opening, the rotational speed and the amplitudes of the shafting centroid. Moreover, the relationship between the mis-alignment distance and centroid amplitudes is investigated, and a stable operation interval is obtained regarding the coupling mis-alignment distance on the basis of the criteria of the coupling mis-alignment in rotating machineries. Finally, these results offer a useful insight into the vibration diagnosis of hydropower stations.

The transient process of hydropower generation system (HGS) frequently appears when the unit operates, which is the result of the interaction between the subsystems, contains abundant information. Researches on the transient process usually simplify the coupling relationship between subsystems. However, the coupling between the subsystems during the transient process is unknown. Here we show that the coupling of the two sub-information systems is represented by the information flow between the intuitive parameters of the two systems in the transient process. And what we found is the coupling between systems is bidirectional. Furthermore, we found that the information flow path and direction of the system will not change with the change of load. The most strongly coupled part of the information is the two sets of parameters at the end of the path rather than the beginning of the path, which is the response components of the unit represented by the guide vane that could change the dynamic characteristics of HGS. Our results demonstrate how information, matter, and energy cooperate in the load rejection process of HGS. The analysis methods presented here could be direct and efficient approaches for further research and engineering applications in system information mining.

In recent years, ground source heat pump systems are recognized as effective renewable energy heating, ventilation and air-conditioning systems. In ground source heat pump systems, ground heat exchangers serve as heat-conducting medium with vertical distribution or horizontal distribution. Many remarkable studies were carried out in the past few years. However, most of the existing reviews mainly contributed to vertical ground heat exchangers research along with design, performance, and applications. A systematic summary on analyzing thermodynamic performance of horizontal ground heat exchangers in ground source heat pump systems is essential. Therefore, this review aims to summary the optimal thermodynamics analysis on horizontal ground heat exchangers in ground source heat pump systems. According to the analytical solutions, numerical simulations and experimental measurements, the reviewed research articles are classified into four sub-categories: linear-loops, slinky-coils, helical-coils and others. The optimal thermodynamic performance for each study is illustrated and discussed. Furthermore, assessments and comparisons among different horizontal ground heat exchangers are summarized. In the end, future development suggestions and research direction recommendations related to ground source heat pump systems with horizontal heat exchangers are given.

This paper reports on fast-slow dynamical analysis of a typical complex engineering system coupling with hydraulic-mechanical-electric power. Here, we find a high-dimensional hydropower generation system that fast-slow effect manifesting as spiking states and quiescent states exists by means of multi-time-scale structure mining. In our experimental analysis, we extract critical fast-slow variant parameters used to further study the behaviors of the presented system. Our results reveal that the change of fast-slow variant parameters has remarkable impact on the fluctuation interval of spiking states and quiescent states, which provides guidance for system parameter setting; meanwhile, we experimentally demonstrate that multi-time-scale physical phenomena reflect the stability and operational feature of the complex hydropower generation system. This work, combined with multi-scale dynamic analysis and a snapshot of macro-significance of engineering, enables us to develop a novel framework for investigating instability of complex engineering systems.

This paper brings attention to the dynamic characteristics of a hydro-turbine governing system with viscoelastic materials. Fractional calculus is introduced to established a diversified nonlinear mathematical model of a hydro-turbine governing system, considering the memory characteristic of the viscoelastic materials of the hydraulic servo system. Furthermore, the effect of different fractional orders on the generator speed is studied by analysis of fractional bifurcation diagrams, time waveforms, phase orbits, Poincare maps, power spectrums and spectrograms. Fortunately, some motion laws of the bifurcation points and chaotic regions with the increase of fractional order α are obtained, and the safe range of k d with different fraction order is presented. All of the above results provide a sound theoretical basis for designing and running of the hydro-turbine governing system.

Multi-time scales modeling of hydro-turbine governing system is crucial in precise modeling of hydropower plant and provides support for the stability analysis of the system. Considering the inertia and response time of the hydraulic servo system, the hydro-turbine governing system is transformed into the fast-slow hydro-turbine governing system. The effects of the time-scale on the dynamical behavior of the system are analyzed and the fast-slow dynamical behaviors of the system are investigated with different time-scale. Furthermore, the theoretical analysis of the stable regions is presented. The influences of the time-scale on the stable region are analyzed by simulation. The simulation results prove the correctness of the theoretical analysis. More importantly, the methods and results of this paper provide a perspective to multi-time scales modeling of hydro-turbine governing system and contribute to the optimization analysis and control of the system.

Surge tank is an essential device to control hydraulic transient of a Hydroelectric Gnerating Systems (HGS)s. However, various types of surge tanks differently reflect in reducing water hammer and improve performance of HGS. This study aims to analyze the different performance of Air Chamber Tank (ACT) and Orifice Surge Tank (OST) during the successive load rejection process (SULRP). In this study, the mathematical model of the ACT is established and use to analysing the replacement the existing OST in Shitouxia Hydropower station consisting in three parallel unit system. A modified NSGA-II algorithm is used to perform multiple objective optimization ACT properties and to minimize pressure head in ACT and water head at the inlet of units. The optimization result indicates that the proper selection of initial indoor air height and delay time lead to the decrease maximum water head and fluctuation period in surge tank and falls in overspeed and pressure head at inlet of unit. The results show that, the diameter of ACT can be 2 m smaller than the existing OST and it can decrease the fluctuation period from 130 s to 110.7 s while slightly increasing the overspeed in the last unit. The increasing delay time of the closing guide vane of last unit decreases the water fluctuation in ACT and OST and the maximum water fluctuation in OST and ACT reduce with slope −6.2% and −15% when ΔTd is in range of [14] , [25] seconds. Finally, the optimized dimension of ACT and OST provides essential guidance for decision-makers to deal with hydraulic transient in SULRP.

The research object of the article is a similar model of a naval ship with an integrated sandwich composite superstructure. The similarity model of this naval ship is based on the similarity theory, which is obtained by scaling down the actual naval ship. Based on the theoretical guidance of the double-beam method, by using the static loading test of the four-point bending method, the article analyzes the magnitude and trend of the strain, stress, and deformation of the measuring points on the naval ship model under different load cases. The main measuring points of the similar naval ship model are located in the typical cross-sections, each deck, and the interface between the steel main hull and the integrated sandwich composite superstructure. The article mainly explores the changes of longitudinal strain and stress of the measuring points with height on three typical cross-sections, and the changes of longitudinal strain and stress with the ship's length on the interface, and the deformation of the top deck of the superstructure. Combining with the results of finite element numerical simulation, the complicated mechanical properties of the naval ship model with an integrated sandwich composite superstructure are explored by mutual verification with the experiments. Some valuable conclusions are obtained for the construction and design of the naval ship with an integrated sandwich composite superstructure.

This paper focus on a Hamiltonian mathematical modeling for a hydro-turbine governing system including fractional item and time-lag. With regards to hydraulic pressure servo system, a universal dynamical model is proposed, taking into account the viscoelastic properties and low-temperature impact toughness of constitutive materials as well as the occurrence of time-lag in the signal transmissions. The Hamiltonian model of the hydro-turbine governing system is presented using the method of orthogonal decomposition. Furthermore, a novel Hamiltonian function that provides more detailed energy information is presented, since the choice of the Hamiltonian function is the key issue by putting the whole dynamical system to the theory framework of the generalized Hamiltonian system. From the numerical experiments based on a real large hydropower station, we prove that the Hamiltonian function can describe the energy variation of the hydro-turbine suitably during operation. Moreover, the effect of the fractional α and the time-lag τ on the dynamic variables of the hydro-turbine governing system are explored and their change laws identified, respectively. The physical meaning between fractional calculus and time-lag are also discussed in nature. All of the above theories and numerical results are expected to provide a robust background for the safe operation and control of large hydropower stations.

There is a region of pump-turbine operation, often called the S-shaped region, in which one unit rotational speed corresponds to three unit flows or torques. In this paper, the dynamic model of the pump-turbine in S-shaped regions is established by introducing the nonlinear piecewise function of relative parameters. Then, the global bifurcation diagrams of the pump-turbine are presented to analyze its dynamic characteristics in the S-shaped regions. Meanwhile, a stability criterion of runaway point is given based on the established theoretical model. The numerical experiments are conducted on the model and the results are in good agreement with the theoretical analysis. Furthermore, the effects of the characteristic curve slopes on the stability of the pump-turbine are studied by an innovative use of the three-dimensional bifurcation diagrams. Finally, the factors influencing the runaway stability of pump-turbines are also discussed, based on the dynamic analysis.

This paper addresses the Hamiltonian mathematical modeling and dynamic analysis of a hydro-energy generation system in the transient of sudden load increasing. First, six dynamic transfer coefficients of the hydro-turbine for the transient of sudden load increasing are innovatively introduced into the hydro-energy generation system. Considering the elastic water-hammer model of the penstock and third-order model of the generator, we established a dynamic mathematical model of the hydro-energy generation system in the transient of sudden load increasing. Moreover, from the point of view of the transmission and dissipation of energy of the system, we propose the hydro-energy generation system into the theory frame of the generalized Hamiltonian system. A novel Hamiltonian model of the hydro-energy generation system is established utilizing the method of orthogonal decomposition. Finally, based on the data of a real hydropower plant, numerical simulations and physical experiment are carried out, and the results indicates that the Hamiltonian system can reflect the essence of the nonlinearity of the hydro-energy generation system in the transient of sudden load increasing. More importantly, these methods and results will supply theoretical basis for designing and running a hydropower plant.

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.

This paper focuses on the stability of a hydropower station. First, we established a novel nonlinear mathematical model of a Francis hydro-turbine governing system considering both fractional-order derivative and time delay. The fractional-order α , which is introduced into the penstock system, in the range from 0.82 to 1.00 is on the left side of the model in a incommensurate manner in increment of 0.03 to provide an adjustable degree of system memory. The time delay τ , which exists between the signal and response in the hydraulic servo system, in the range from 0 s to 0.26 s is inserted on the right side of the model in increment of 0.04 s . Utilizing the principle of statistical physics, we respectively explored the effects of the fractional-order α and the time delay τ on the stable region of the system. Furthermore, we exhaustively investigated the nonlinear dynamic behaviors of the system with different governor parameters by using bifurcation diagrams, time waveforms and power spectrums, finding that only under the condition of reasonable collocation of governor parameters the system can maintain stable operation. Finally, all of the above numerical experiments supply new methods for studying the stability of a hydropower station.

Pumped storage plants (PSP) are operated under transient processes frequently in the case of the intermittent and unpredictable renewable energy. When PSPs are working in the load rejection process, the serious accident may be caused by the significant fluctuations of rotating speed and pressure. Seeking an appropriate law of guide vane movement in load rejection process is an approach to improve operating stability of PSP. This paper focuses on the optimization of self-adaptive closure law of pump turbine model for one Chinese PSP, based on sliding mesh technique and current closure law. Variations of speed and pressure are regarded as judgment functions. Meanwhile, detached eddy simulation(DES) is adopted to characterize internal flow field of pump turbine(PT) with adaptation of the optimized closure law. Not only the distribution of pressure and the turbulence kinetic energy in flow domains is analyzed details, but also the fluid evolution in passage is investigated. As a result, the optimized closure law is beneficial to impair the fluctuating rates of speed and pressure in transient process. It is illustrated that both the rotor-rotor and rotor-stator interaction in vaneless spaces are the sources of increased fluid instability in pump turbine. Note that the unstable flow regime emerges at the same moment in the inlet and outlet conduits, whereas their locations are opposite to the unit.

Life cycle assessment (LCA) has been an emerging feature of modern structural health monitoring techniques that aims at evaluating equipment degradation process and it can be used for development of dynamic maintenance plans. A novel framework based on LCA is proposed in this paper for dynamic maintenance planning of hydro-turbines. Using a Hidden Markov Model (HMM) and the inspection data of hydro-turbine runner cracks from actual operations, the transition probability matrix and sojourn time of different crack states are obtained. This is utilized for predicting the expected remaining useful life (RUL) and the formulation of maintenance intervals. Moreover, maintenance plans are developed from the influence of cracks in different states leading to critical conditions. The proposed method, as demonstrated in the case study, efficiently updates the maintenance intervals and reduces the likelihood of failure events. The results of this paper provide a valid maintenance framework for achieving higher operational safety of hydropower stations with minimal resource losses.

Increasing the efficiency of an electric power system with cleaner productions is important for the fastest growing power industries. In this paper, hydro and wind renewable energy sources are considered to determine the optimal coordinated generation mode with high energy efficiency. In the proposed approach, the power efficiency is studied based on the quantification of economic benefits in the generation process. The economic benefit evaluating method is calculated by considering necessary items such as the regular operational cost, hydro regulation cost, power loss cost, plant investment and generation profit. From the operator's viewpoint, the mathematical expression of the hydro regulation cost is innovatively presented in the proposed method. To achieve the efficiency analysis, a new hydro-wind hybrid model is established using MATLAB/Simulink, which overcomes the previous limitation on data dependencies. Three real operating challenges, including the fluctuation of wind speed, the price volatility in market, and the influence of wind power permeation, are considered to reflect the relationship between the uncertain operating condition and optimal coordinated generation mode. Simulation results highlight the impact of real operating challenges on the hydro regulation cost, generation benefit and energy efficiency in the hybrid power system. The proposed model and method will result in a system with high efficiency and improved financial condition. Meanwhile, it will also benefit the policy development of renewable energy-based power industries.

Multi-energy integrated sources are increasingly being used as the bundling-sale for electric systems. Estimating the power supply reliability and regulation performance of the fixed-speed Pumped-Storage Generation Systems (PSGSs) in suppressing power fluctuations of intermittent energy is essential to the operational safety and reliability of a system. However, the regulation process relates to the coupling fluctuations of hydraulic-mechanical-electrical factors, leading to a multiple time-scale effect to the whole hybrid power system. This makes the PSGS’s power response lagging behind the wind power fluctuation and further impacts the power supply reliability of the hybrid power system. To enable the analysis, a numerical model which describes operating states of the presented integrated system, including wind energy and PSGS, is developed in MATLAB/Simulink. Then, ten wind scenarios are selected to study complementation and regulation ability of the PSGS based on a framework of evaluation indicators. The results show that longer power response delay and larger guide vane distance opening result in weaker complementary response of PSGS to wind disturbances. It is also shown that the PSGS provides good complementary capability at lower random wind standard deviation (0.5 vs 1.5), larger wind speed mean value (15 m/s vs 13 m/s) and lower wind speed deviation (5 m/s vs 12 m/s). Furthermore, an unexpected regulation behavior is demonstrated: fast settling and peak times coincide with large variation in overshoot, undershoot and peak value of the power response. This presents a challenge in assessing performance of the integrated generation system. The proposed evaluation method and presented results are important steps to increasing the national power grid capability to accept high integration of multiple energy sources.

In this paper, we investigate the existence and uniqueness of the solution to a class of nonlinear fractional order system with delay. The estimate value of the above solution is also obtained by using the generalized Gronwall inequality.

This paper focuses on the Hamiltonian mathematical modeling and dynamic characteristics of multi-hydro-turbine governing systems with sharing common penstock under the excitation of stochastic and shock load. Considering the hydraulic-coupling problem in the common penstock, we propose a universal dynamic mathematical model of the multi-hydro-turbine governing system. Then, the proposed model is fitted into the theoretical framework of the generalized Hamiltonian system, utilizing the method of orthogonal decomposition. The dissipation energy, the produced energy and the energy supplied from the external sources are derived from the Hamiltonian model and compared with the physical energy flow. Furthermore, numerical experiments based on a real hydropower station demonstrate that the Hamiltonian function can describe accurately the energy variation of the hydro-turbine system in the transient process and in the stable process. Moreover, in order to deal with the randomness and mutability of the electrical load, we introduce a Gaussian function and a jump function to the control signal of the PID controller to analyze the dynamic characteristics. In addition, the intensity of the shock load is discussed when the system loses its stability. The proposed approach can be used for improving the stability of hydropower stations.

The modeling of traditional shafting systems mainly pays attention to the running states in the small fluctuations. However, the dynamic behaviors of the shafting system for a water jet mixed-flow pump in the transient states play a key role in maintaining safety and stability. In this paper, a dynamic mathematical model of the shafting system for a water jet mixed-flow pump during the startup process is established considering fractional-order damping forces, rub-impact forces and misalignment faults. Furthermore, we analyzed the characteristics of the above system during the startup process with different impact forces through the above fractional-order mathematical model. Moreover, the effect of the fractional-order on the startup process is also studied by bifurcation diagrams, time waveforms and phase orbits. Fortunately, some laws are found from the numerical simulation results. Finally, compared with the physical experimental data, the fractional-order model of the shafting system for the water jet mixed-flow pump has certain advantage and effectiveness.

In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

Pumped storage generating system contains twenty-four transition processes, stability performance of these transition processes determine power system quality and unit vibration. This paper focuses on the stability performance of pumped storage generation system during the transition from condenser mode to generating mode. The physical feature of condenser mode is extensively analyzed, and a mathematical model that describes the dynamic transition process of PSGS is therefore built. As two typical factors related to transition process, the switching points (27 s,30 s and 33 s) and guide vane laws (exponential type and linear type) are selected and further performed to compare stability performance of PSGS. Based on this, numerical results indicate that delayed switching point results in system oscillations and exponential law of guide vane is benefit for quicker loading. This model and analysis method successfully express the transient characteristic of PSGS from condenser mode to generating mode, as well as effectively predict the dynamic response of system parameters.