Hydroelectric Unit Research Articles

Research on Ultra-Low-Frequency Oscillation Suppression Method of High-Head, Large-Capacity Hydropower Units

Aiming at the problem of ultra-low-frequency oscillation (ULFO) caused by an irrational setting of governor parameters of high-head hydraulic turbine units, this paper proposes a method to optimize the additional damping control parameters of the governor to suppress ULFO. Firstly, the mechanism of ULFO is elaborated and the effect of system damping torque on ULFO is analyzed. Secondly, Hamilton’s theory is used to rank the magnitude of each unit’s contribution to the ULFO. Then, the parameters of the damping controller are optimized using the variational modal decomposition–Hilbert transform method and the Grey Wolf Optimization algorithm. It realizes the phase compensation of the hydroelectric unit governor and suppresses the ultra-low-frequency oscillation. Finally, the proposed method is validated using the simulation conducted in CloudPSS. The test results indicate that the proposed method can effectively suppress the ULFO caused by the high-head hydroelectric unit.

Fault Diagnosis in Hydroelectric Units in Small-Sample State Based on Wasserstein Generative Adversarial Network

In the practical production environment, the complexity and variability of hydroelectric units often result in a need for more fault data, leading to inadequate accuracy in fault identification for data-driven intelligent diagnostic models. To address this issue, this paper introduces a novel fault diagnosis method tailored for unbalanced small-sample states in hydroelectric units based on the Wasserstein generative adversarial network (W-GAN). Firstly, the fast Fourier transform is used to convert the signal from the time domain to the frequency domain to obtain the spectral data, and the W-GAN is trained to generate false spectral data with the same probability distribution as the real fault data, which are combined with the actual data and inputted into the 1D-CNN for feature extraction and fault diagnosis. In order to assess the effectiveness of the proposed model, a case study was conducted using actual data from a domestic hydropower plant, and the experimental results show that the sample features can be effectively enriched via data enhancement performed on small-sample data to improve the accuracy of fault diagnosis, which verifies the effectiveness of the method proposed in this paper.

Short-Term Hydro Scheduling considering Risk Aversion in a MINLP Approach

This paper presents an optimization model to help a hydro generating company to schedule its hydroelectric units in the short-term under a competitive environment. The hydro generating company considered has the ultimate goal of maximizing profits, taking also into account some risk aversion criterion. The problem is formulated as a mixed-integer nonlinear programming problem. An application to a real case study is presented. Conclusions are duly drawn.

Results of mathematical modelling of the cooling system for solar panels of a hybrid power plant based on solar and hydraulic energy

It should be noted that theoretical and experimental studies in the field of semiconductors have shown good prospects for creating matrix and multilateral photoelectric converters (MPCs) with vertical p-n junctions. Such PV have undeniable advantages in the tasks of generating high output voltages and converting concentrated solar radiation. In addition, the implementation of such PVs in a multi-sensitive design makes it possible to reduce the consumption of semiconductor silicon by up to three to four times.But, in conditions of a dry, hot, continental and dusty climate, for example, in the republics of Central Asia, their heating is observed when the FP operates. This problem can be solved by using it in conjunction with microhydroelectric power plants or additional cooling. The hybrid system developed by the authors includes a solar power plant, a counter-rotor hydraulic unit with a reactive and active impeller, a cooling system and an automatic control system. The characteristics of this system were studied on the basis of mathematical modeling in the “Comsol multiphysics 6.1” software environment.In the simulation, the solar panel was cooled with air and water using electricity from a hydroelectric unit. According to the calculation results, the heating of the solar panel without forced convection at an outside air temperature of 400-450C was 1080C. Water was supplied through an aluminum cover installed behind the solar panel and which had channels. The solar panel temperature was 49.2°C and the water temperature was 48.2°C.When cooled by ambient air, the temperature of the solar panel was 67.7°C. The cooling system efficiency was 74% when comparing the energy expended to cool a 2m2 solar panel and the power added when cooling the panel.

U susret revitalizaciji turbina HE Đerdap 2: Merenje rasporeda vektora brzina na ulazima turbina

The continuous flow measurement on hydroelectric turbine units is conventionally carried out using the relative methods (mostly Winter-Kennedy), where the complex velocity field in flow cross section is replaced by a single measured quantity. On a physical model, mapping parameters are determined. The Winter-Kennedy method is most used, where this relative (index) flow quantity is obtained by measuring differential pressure. The measurement uncertainty of the determined flow using this method is usually significantly higher than the uncertainty of other relevant quantities for determining the optimal turbine operating conditions. To reduce the flow uncertainty, it is necessary to perform "absolute measurements" of the entire velocity field and determine the necessary corrections to the index method under real operating conditions. This is especially true for plants where disposition is different from one used on physical model, which is the case of “Đerdap 2” and recognized problem of skewed inflow. With the aim of better assessing the hydraulic efficiency of turbines and to collect data on the actual operating velocity distribution in the inlet section in front of trash-rack needed for planned revitalization works, an innovative system for absolute flow measurement has been designed and implemented. The moving frame was designed and installed at the turbine inlet, upstream from the trash-rack. The 15 electromagnetic (EM) sensors and two redundant acoustic Doppler sensors were installed on horizontal bar. Each sensor measures all three velocity components. The frame moves by lifting along the entire height of the flow section, allowing the entire velocity field to be scanned. The position of the frame is tracked by two encoders, while two pressure sensors are used to measure the water depth. Measurements are synchronized with the local SCADA system, so appropriate turbine operation data are also used. Considering the specificities of the measurement system itself with newly developed EM sensors, as well as hydraulic conditions, an adequate procedure has been developed to assess the uncertainty of the measured flow. This paper presents the measurement method and provides some measurement results on the units of the “Đerdap 2” hydroelectric power plant.

ACOUSTIC OSCILLATIONS IN A DEEP WELLBORE GENERATED BY ITS ELASTIC DEFORMATIONS IN THE FIELD OF SEISMIC WAVES FROM A REMOTE SOURCE*2

This paper analyzes the possibilities of an original approach to constructing a distributed seismic monitoring system based on a stationary seismoacoustic propagation path of a sounding signal. Such a stationary path can be formed by a powerful source of low-frequency vibration oscillations located on the earth's surface, and a signal recording point located tens (or more) kilometers away from it. It is proposed to use hydroelectric power station units as a powerful vibration source, which have a typical mass of several hundred tons and create vibration signals in the environment of the earth's rocks with characteristic frequencies from a few to one to two tens of Hz (including harmonics), and as a registration point – deep well equipped with the necessary measuring instruments. To record low-frequency longitudinal waves in the thickness of the earth's rocks surrounding the well, a fairly simple and effective method is proposed, based on the use of an extended wellbore as a distributed seismic antenna and a microphone installed on the upper section of the well. The work shows that stresses in the field of a longitudinal seismic wave, acting on the wellbore, cause a change in its diameter, which in turn leads to the occurrence of oscillations of the column of liquid filling the wellbore at the frequencies of the seismic waves determined by the source. A specific scheme for implementing the discussed approach is considered using the example of the Nizhny Novgorod hydroelectric station and the Vorotilovskaya deep well located at a distance of about 40 km. Quantitative estimates and experimental data demonstrating the possibilities of using the corresponding stationary route are presented.

Ozone Transport in 311 MVA Hydrogenerator: Computational Fluid Dynamics Modelling of Three-Dimensional Electric Machine

In this paper, a three-dimensional turbulent fluid dynamics numerical model of a 311 MVA full hydroelectric power plant unit is made, using the finite element method, to study and understand the ozone transport mechanisms inside the enclosured electric machine structure. In the real world, ozone is produced by partial discharges related to faults on stator bars. In order to analyse ozone transport from localised sources, a 3D fluid dynamic model of a complete hydrogenerator in operation is developed and presented for the first time. The model has a high level of geometric detail. Furthermore, a new proposal to simplify the modelling of radiators is implemented and validated. The modelled structure is based on a Campos Novos hydrogenerator electric machine and it consists of 378 coil-type stator bars made of copper covered by mica and, more externally, by a semiconductor coating layer. Other parts are also represented, including the stator core and air directors made of stainless steel, copper radiators, the rotor with its epoxy surface, and the concrete floor and concrete external walls. In the fluid dynamics model, a finite element mesh was designed to represent the air regions inside the hydrogenerator and the material surfaces that react with ozone (with their respective reaction rates), where the airflow and ozone transport are modelled using the Navier–Stokes equations and the mass conservation law. Partial discharge sources are represented by ozone sources with prismatic shapes, placed on surfaces of stator bars. Ozone concentrations have been calculated inside and around the generator machine. The rotor radius is 3.8075 m and its rotation frequency is 200 RPM. Radial air velocity due to interpole ventilation is also considered (2.2 m/s, as experimentally verified in loco. The radial velocity in the vicinity of the radiators is 3 m/s. It has been concluded that the ozone transport profile is influenced by the source positioning on the stator bars in such a way that source pinpointing is possible and it depends on determining the local and global maxima areas of ozone concentration at the radiators.

A Multistep Prediction Model for the Vibration Trends of Hydroelectric Generator Units Based on Variational Mode Decomposition and Stochastic Configuration Networks.

Accurately predicting the changes in turbine vibration trends is a key part of the operational condition maintenance of hydropower units, which is of great significance for improving both the operational condition and operational efficiency of hydropower plants. In this paper, we propose a multistep prediction model for the vibration trend of a hydropower unit. This model is based on the theoretical principles of signal processing and machine learning, incorporating variational mode decomposition (VMD), stochastic configuration networks (SCNs), and the recursive strategy. Firstly, in view of the severe fluctuations of the vibration signal of the unit, this paper decomposes the unit vibration data into intrinsic mode function (IMF) components of different frequencies by VMD, which effectively alleviates the instability of the vibration trend. Secondly, an SCN model is used to predict different IMF components. Then, the predicted values of all the IMF components are superimposed to form the prediction results. Finally, according to the recursive strategy, a multistep prediction model of the HGU's vibration trends is constructed by adding new input variables to the prediction results. This model is applied to the prediction of vibration data from different components of a unit, and the experimental results show that the proposed multistep prediction model can accurately predict the vibration trend of the unit. The proposed multistep prediction model of the vibration trends of hydropower units is of great significance in guiding power plants to adjust their control strategies to reach optimal operating efficiency.

Application of data science in the prediction of solar energy for the Amazon basin: a study case

Abstract The need for renewable energy sources has challenged most countries to comply with environmental protection actions and to handle climate change. Solar energy figures as a natural option, despite its intermittence. Brazil has a green energy matrix with significant expansion of solar form in recent years. To preserve the Amazon basin, the use of solar energy can help communities and cities improve their living standards without new hydroelectric units or even to burn biomass, avoiding harsh environmental consequences. The novelty of this work is using data science with machine-learning tools to predict the solar incidence (W.h/m²) in four cities in Amazonas state (north-west Brazil), using data from NASA satellites within the period of 2013–22. Decision-tree-based models and vector autoregressive (time-series) models were used with three time aggregations: day, week and month. The predictor model can aid in the economic assessment of solar energy in the Amazon basin and the use of satellite data was encouraged by the lack of data from ground stations. The mean absolute error was selected as the output indicator, with the lowest values obtained close to 0.20, from the adaptive boosting and light gradient boosting algorithms, in the same order of magnitude of similar references.

Assessment of the operational flexibility of virtual power plants to facilitate the integration of distributed energy resources and decision-making under uncertainty

Distributed energy resources (DERs) are elements that actively participate in the supply of renewable energy and contribute to the decarbonization of the power system. However, they lack two factors necessary to take advantage of their operational flexibility: observability and controllability. In this sense, Virtual Power Plants (VPPs) are a feasible alternative to provide the necessary requirements for the optimal management of a set of distributed units. Therefore, knowledge of the technical and energy characteristics of each unit that makes up the VPP is a necessary condition for the effective integration of DERs into the power system. This paper proposes a methodology to graphically represent, quantify and exploit the aggregate operational flexibility of a set of units. The proposed methodology is based on five metrics related to active and reactive power, which serve as a tool to facilitate the VPP Operator's decision-making under uncertainty. Consequently, achieving the coordinated operation of several distributed units makes it possible to achieve common objectives. For instance, frequency and voltage regulation, compliance with a planned power curve, or dealing with the variability of renewable energies. The proposal is applied to a theoretical case study and through real operational tests between a hydroelectric unit and a photovoltaic plant. Finally, it is shown that the results obtained are a useful tool in real-time.

Intelligent fault diagnosis of hydroelectric units based on radar maps and improved GoogleNet by depthwise separate convolution

Abstract Fault diagnosis plays an essential role in maintaining the safe and stable operation of hydroelectric units. In this paper, an intelligent fault diagnosis method based on radar maps and improved GoogleNet by depthwise separate convolution (DSC) is proposed to address the problems of low recognition accuracy and weak computing speed of fault diagnosis models in the field of hydroelectric unit fault diagnosis at present. Firstly, a one-dimensional signal sequence is obtained and denoised. Secondly, five time-domain features are extracted and radar maps are plotted. Then, an improved GoogleNet intelligent fault diagnosis model based on DSC (DSC-GoogLeNet) is constructed for training and validation. To assess the effectiveness of the proposed model, two case studies are conducted using the simulated dataset of the rotor experimental bench and the actual measured dataset of a domestic hydroelectric power plant. The results demonstrate that the average recognition accuracy of the fault diagnosis method proposed in this paper is as high as 99.04% on the simulated dataset, and even though the recognition accuracy decreases on the actually measurement dataset, it still has a recognition rate of 98.79%. The fault diagnosis performance is better than the other types of comparison models. The results demonstrate that the proposed fault diagnosis method holds significant engineering applicability in the domain of safe operation of hydroelectric units. It effectively addresses the existing challenges in fault diagnosis within this field with accuracy, stability, and efficiency.

Intelligent decision-making support system for the commissioning of a small hydroelectric power plant in the Republic of Tyva

This paper investigates the cutting forces arising when using a single abrasive grain. Analytical studies were carried out using a model of a single abrasive grain in the form of a rod with a radiused apex acting on the workpiece material. The slip-line method (method of characteristics) was used to calculate the deformation intensity of a plastically edged workpiece material under the action of a single grain. Mathematical models were developed for the following factors: plastic deformation of the material, edging of the stagnated zone and its friction against the grain surface when moved upwards in the form of chippings, grain friction against the plastically deformed material, and the action of the dynamic component of plastic deformation. The significance of the dynamic component in the overall balance of forces related to plastic deformation was established by determining the ratio of dynamic stress on the break line and shear yield point. This dependence calculated for D16T and 30HGSA materials showed the feasibility of accounting for the dynamic component system based on a small hydropower station located in the Todzhinsky district of the Republic of Tyva. For an adequate assessment of the operational reliability of hydropower units, a logical and probabilistic method based on the kinetic theory of fault tree was used. The method allows the failures of the used equipment, as well as unplanned shutdowns of units due to a shortage of water resources in the Great Yenisey (low water, overdrying, and frozen frost), to be taken into account. The development of a generation system based on a small hydroelectric power plant for the settlements in the Todzhinsky district of the Republic of Tyva offers a load of up to 2,500 kW, which helps to reduce the cost of purchasing, delivering, and storing diesel fuel, while diesel generators can be used as backup power sources. 3 scenarios of structuring a small hydroelectric power plant were considered that involved various numbers and total capacity of hydrogenating units: 5x500 kW, 4x630 kW, and 3x800 kW. Therefore, by using the multi-criteria optimization method, the optimal structure of the generating system based on a small hydroelectric power plant having three hydroelectric units (each characterized by a capacity of 800 kW) was selected from the three proposed options, taking into account the reliability and uncertainty of the initial information.

Graph attention-based U-net conditional generative adversarial networks for the identification of synchronous generation unit parameters

After generation units are connected to the power grid, electrical parameters such as generation unit output voltage, current and power need to be monitored for the safe and reliable function of grids. Obtaining accurate parameters of synchronous generation units (SGUs) is normally the basic requirement for grid stability analysis and control. To improve the accuracy of identifying SGU parameters, this study proposes graph attention-based U-Net conditional generative adversarial networks (GAUCGANs) for the identification of SGU parameters. The mapping between real and generated samples is modeled by applying conditional generative adversarial networks (CGANs). The CGANs of the GAUCGANs proposed in this study consist of U-Nets-based generators, fully convolutional networks-based discriminators, and graph attention networks (GATs). The U-Nets of the GAUCGANs enhance the ability of generators to generate generative samples that are infinitely close to real samples. The U-Nets-based generators of the GAUCGANs are responsible for generating the SGU parameters; the fully convolutional networks-based discriminators of the GAUCGANs determine whether data is from the generator or the real data. In addition, the classification loss and sample labels are derived from the GATs. The addition of GATs will further enhance the ability of the generators to remove adversarial disturbances. In this study, the proposed GAUCGAN for parameter identification is compared with the traditional parameter identification algorithms. The comparison algorithms are applied to the Simulink standard SGU, hydroelectric unit No. 6 of the waterfall gorge hydropower plant, and the generation unit at the 18th bus of the IEEE 36-bus power system. The numerical simulation results from the GAUCGANs verify that the GAUCGAN can more accurately identify SGU parameters than the traditional parameter identification algorithms. The GAUCGANs improve the accuracy by at least 61.60% on average over the other methods by comparing the RMSE, MAE, MAPE, and SMAPE under three cases comprehensively.

КОМБІНОВАНЕ РЕГУЛЮВАННЯ КОМУТОВАНИМИ КОНДЕНСАТОРАМИ Й ВЕНТИЛЬНИМ ПЕРЕТВОРЮВАЧЕМ НАПРУГИ АСИНХРОННОГО ГЕНЕРАТОРА АВТОНОМНО ПРАЦЮЮЧОЇ МІНІ-ГЕС

The principles of operation and a static simulation model of the power-generating equipment of the autonomous power supply source based on a hydroelectric unit with a 275 kVA induction generator and a combined capacitor-inverter excitation system supplying a symmetrical passive load have been developed. The initial excitation of the generator is carried out by a bank of capacitors of the initial excitation. During low power demand the generator voltage is kept constant by adjusting the reactive power of the semiconductor converter, and at high loads, the voltage is adjusted as a result of the switching of additional capacitor banks. The developed methodology for performance analysis the pro-posed power supply source is based on the IG equivalent circuit. Computations of the static characteristics of the gen-erator operating with a constant rotor speed were carried out and the obtained static characteristics were analyzed for two set values of the load power factor. Ref. 5, fig. 4, table.

Evaluation Method of the Incremental Power Supply Capability Brought by Distributed Generation

More and more distributed generation (DG) and energy storage (ES) devices are being connected to the distribution network (DN). They have the potential of maintaining a stable supply load during failure periods when using islanding operations. Therefore, DG and ES have capacity value, i.e., improving the power supply capability of the system. However, there are strong fluctuations in DG outputs, and the operations of ES devices have sequential characteristics. The same capacity of DG has different load-bearing capabilities compared to conventional thermal or hydroelectric units. This paper proposes a method for evaluation of power supply capability improvement in DNs. First, the temporal fluctuation in both power source and load demand during fault periods is considered. A DN island partition model considering the secondary power outage constraint is established. Then, a modified genetic algorithm is designed. The complex island partition model is solved to achieve accurate power supply reliability evaluation. And the incremental power supply capability associated to DG and ES devices is calculated. Finally, a case study is conducted on the PG&E 69-bus system to verify the effectiveness of the proposed method. It is found that with a 20% configuration ratio of ES devices, the power supply capability improvement brought about by 6 MW DG can reach about 773 kW.

Analisis Potensi Daya Pada Pembangkit Unit 7 PLTA Tes

Currently the need for electrical energy is increasing both for industrial and household needs, but until now a lot of electrical energy has been replaced by non-renewable resources (coal), which will run out if it continues to be used. Tes Hydroelectric Power Plant is one of the electrical energy generators that can be renewable. Among the several generating units in Tes Hydroelectric Power Plant, Tes’s hydroelectric power plant unit 7 is the most recent, having been inaugurated for the first time in 2014. The power potential that can be projected from this hydroelectric power plant unit 7 still needs to be looked at further. Therefore, this study aims to analyze the potential for electric power from the Tes’s hydroelectric power plant unit 7 from 01 July 2022 to 03 July 2022.
 In making observations about the analysis of the power potential at the Tes’s hydroelectric power plant unit 7, several methods are used. Such as observation of data for 3 days of operation from 01 July 2022 to 03 July 2022, literature study and several interview methods with field consultants. The value of the air discharge obtained from the use of air volume per day at the Tes’s hydroelectric power plant unit 7. On three days of observation, the Tes’s hydroelectric power plant unit 7 were able to produce the highest electrical energy on 03 July 2022, namely 100,722 kWh and the lowest was 99,808 kWh on 02 July 2022. In three days, the electric power that paid for the Tes’s hydroelectric power plant unit 7 reached 4173, 40 kW. The Tes’s hydroelectric power plant unit 7 can generate a daily net income of Rp. 105,689,588, - with a perkWh price of Rp. 1300, - and reduced by the basic cost of Rp. 244.81, -, from the sale of electrical energy.

Research on Denoising Method for Hydroelectric Unit Vibration Signal Based on ICEEMDAN-PE-SVD.

Vibration monitoring and analysis play a crucial role in the fault diagnosis of hydroelectric units. However, accurate extraction and identification of fault features from vibration signals are challenging because of noise interference. To address this issue, this study proposes a novel denoising method for vibration signals based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), permutation entropy (PE), and singular value decomposition (SVD). The proposed method is applied for the analysis of hydroelectric unit sway monitoring. Firstly, the ICEEMDAN method is employed to process the signal and obtain several intrinsic mode functions (IMFs), and then the PE values of each IMF are calculated. Subsequently, based on a predefined threshold of PE, appropriate IMFs are selected for reconstruction, achieving the first denoising effect. Then, the SVD is applied to the signal after the first denoising effect, resulting in the SVD spectrum. Finally, according to the principle of the SVD spectrum and the variation in the singular value and its energy value, the signal is reconstructed by choosing the appropriate reconstruction order to achieve the secondary noise reduction effect. In the simulation and case analysis, the method is better than the commonly used wavelet threshold, SVD, CEEMDAN-PE, and ICEEMDAN-PE, with a signal-to-noise ratio (SNR) improvement of 6.9870 dB, 4.6789 dB, 8.9871 dB, and 4.3762 dB, respectively, and where the root-mean-square error (RMSE) is reduced by 0.1426, 0.0824, 0.2093 and 0.0756, respectively, meaning that our method has a better denoising effect and provides a new way for denoising the vibration signal of hydropower units.

Intelligent Analysis of Vibration Faults in Hydroelectric Generating Units Based on Empirical Mode Decomposition

Implementing intelligent identification of faults in hydroelectric units helps in the timely detection of faults and taking measures to minimize economic losses. Therefore, improving the accuracy of fault signal recognition has always been a research focus. This study is based on the improved empirical mode decomposition (EMD) theory to study the denoising and feature extraction of vibration signals of hydroelectric units and uses the backpropagation neural network (BPNN) to establish corresponding connections between signal features and vibration fault states. The improved EMD in this study can improve the performance of noise reduction processing and contribute to the accurate identification of vibration faults. The vibration fault identification criteria can adopt three dimensionless feature parameters: peak skewness coefficient, valley skewness coefficient, and kurtosis coefficient of the second- and third-order components of the signal, with recognition rates and accuracy reaching 90.6% and 96.2%, respectively. This paper’s area under the curve (AUC) values were 0.7365, 0.7335, 0.9232, and 0.9141 for abnormal sound detection of the fan, water pump, slide, and valve, respectively, with an average AUC value of 0.8268. This paper’s accuracy is 90.1%, and the loss function value is 0.27. The validation results demonstrate that this paper’s method has high intelligent fault analysis capabilities. The experimental results confirm that this method can effectively detect vibration signals in hydroelectric units and perform effective noise reduction processing, thereby improving the diagnostic accuracy of fault signals. Therefore, this method can be effectively applied to the detection of vibration faults in hydroelectric units.

Presence of crack due the constant exploitation of turbine shaft

Designing, constructing and putting into operation a hydroelectric power plant includes complex tasks. Stresses of turbine and hydromechanical equipment of hydro power plants arise during the production of parts and assembly of equipment (residual stresses), in the process of performing functional requirements in exploitation and in the disturbed process of exploitation. After several decades of constant exploitation of the horizontal bulb turbine, which is an integral part of the hydroelectric power unit, empirically, the formation of a crack occurs in the turbine shaft due to the influence of corrosion, erosion and cavitation. Through experimental tests and calculations it has been determined that values of bending stresses of the turbine, which occur due to the action of fatigue and corrosion, as well as stress concentration, are bigger than 25 MPa for flanges exposed to water, and in other case bigger than 40 MPa for flanges exposed to `corrosive water` and can cause the occurrence of surface cracks on the transition radius between the cylindrical part of the shaft and the flange. It has been determined that stress values in the zone under the influence of bending stresses were bigger than allowable values, which led to the occurrence of many cracks due to fatigue corrosion. One of those cracks caused the failure of the shaft and of the whole turbine. Key words: crack, turbine shaft, fatigue, stress concentration

Simplifying capacity planning for electricity systems with hydroelectric and renewable generation

This work investigates approaches to simplify capacity planning for electricity systems with hydroelectric and renewable generators with three specific foci. First, we examine approaches to represent the efficiency of hydroelectric units. Next, we explore the effects of water-travel times and the representation of run-of-river units within cascaded hydroelectric systems. Third, we analyze the use of representative operating periods to capture electricity-system operations. We conduct these analyses using an archetypal planning models that is applied to the Columbia River system in the northwestern United States of America. We demonstrate that planning models can be simplified significantly, which improves model tractability with little loss of fidelity.