**2. Concept of computational and experimental substantiation of hydropower plant safety**

Taking into account the consequences of accidents and disasters, hydropower plants with a capacity of 1000–5000 MW can be attributed to critical infrastructure objects. Hydropower plants with a capacity of more than 5000 MW can be considered as strategical objects of infrastructure. For such objects, along with the provision of generally accepted standards and requirements of strength, resource, and reliability, the problems of protection from severe accidents and disasters with survivability and risk analysis should be considered [4]. General requirements for ensuring the protection of hydropower plants from severe accidents were formulated in [5]. For water power plants, along with abidance of generally accepted requirements of technical regulations and standards, protection against the most severe catastrophes (design, beyond design and hypothetical) and terrorist impacts must be considered. When solving safety problems, the following should be analyzed:


The results of the investigation into the causes of the Sayano-Shushenskaya HPP catastrophe [2, 4, 5] indicate the need for conducting special studies of the causal

HPP with a capacity of 3840 MW, with a dam height of 105 m and a length of 1475 m; Bratskaya HPP with a capacity of 4500 MW, with a dam height of 124 m and a length of 924 m; and Boguchanskaya HPP with a capacity of 3000 MW, with a dam height of 96 m and a length of 2690 m (**Figure 1**). In the world, there are 7

In the presence of extensive national and international experience in the design, construction, and operation of large hydropower plants, accidents of various scales occur on them, including great economic losses and human losses. The largest in the history of hydropower is the Sayano-Shushenskaya HPP disaster, accompanied by the destruction and flooding of the machine room, damage to hydraulic units, and the death of people (**Figure 2**). In this regard, the development of measures and means to ensure the safety of hydropower facilities is of paramount importance.

*Sayano-Shushenskaya (a), Krasnoyarskaya (b), Ust-Ilimkaya (c), and Bratskaya (d) hydropower plants.*

large hydropower plants with capacity from 5000 to 14,000 MW.

*Probability, Combinatorics and Control*

**Figure 1.**

**Figure 2.**

**36**

*Disaster of Sayano-Shushenskaya HPP.*

complex of accidents at similar facilities to create scientifically based regulations of risk analysis, survivability, and safety criteria. These researches should include next computational and experimental works [5]:

10.Develop computational models of dams and computational technologies for analyzing the characteristics of their stress-strain state, taking into account the actual changes in the characteristics of concrete and the presence of cracks

11.Develop criteria for the performance of hydroelectric equipment based on the

12.Conduct model calculations of emergency situations and scenarios of their

13.Develop models and methods for assessing the social, environmental, and

To ensure the protection of hydropower plants from severe accidents and disasters, their design, construction, and operation should fully address traditional tasks:

• Conducting bench studies of hydrodynamic processes in the flow part of the

• Calculation and experimental analysis of hazardous mechanical and hydraulic processes in power systems of hydropower plants in regular and emergency

• Calculation and experimental analysis of the limiting states of critical elements

To solve these problems, it is necessary to develop fundamental research in the

modeling of mechanical, hydrodynamic, and electromagnetic processes that affect the conditions for the occurrence and development of severe accidents

• Development of new methods and means of prompt diagnosis of emergency

The scientific and methodological basis for ensuring the protection of hydropower plants from severe accidents and disasters is a risk analysis. Risk assessments

• Study of hazardous processes in the environment and technical systems of hydropower plants, taking into account the role of the human factor

• Development of methods and tools for mathematical (computational)

• Development of the theory and methods to ensure the protection of

hydropower stations from severe accidents and disasters

models of cavitation processes, fatigue, and corrosion damage.

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety…*

development for all existing hydropower plants of Russia.

economic consequences of accidents of hydropower plants.

• Carrying out normative calculations for static and cyclic strength

• Control and repair work on the damaged items of equipment

In addition to this, it is necessary to conduct:

for normal and extreme loads and impacts

and damage.

*DOI: http://dx.doi.org/10.5772/intechopen.88306*

hydroelectric station

situations

following areas:

and disasters

situations

**39**

can be performed in the classical form:


In order to form a general regulatory framework for the protection of hydropower plants, it is necessary to implement the following measures with the preparation of the relevant regulatory documents:


*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety… DOI: http://dx.doi.org/10.5772/intechopen.88306*


To ensure the protection of hydropower plants from severe accidents and disasters, their design, construction, and operation should fully address traditional tasks:


In addition to this, it is necessary to conduct:


To solve these problems, it is necessary to develop fundamental research in the following areas:


The scientific and methodological basis for ensuring the protection of hydropower plants from severe accidents and disasters is a risk analysis. Risk assessments can be performed in the classical form:

complex of accidents at similar facilities to create scientifically based regulations of risk analysis, survivability, and safety criteria. These researches should include next

1.Develop a fundamentally new methodology for assessing and improving the protection of hydropower plants, as critical facilities, from severe disasters

2.Conduct a computational modeling and experimental analysis of the new parameters of the resource, survivability, safety, and risks in the conditions of

hydrodynamics, and aerodynamics of the occurrence and development of a

automated protection of hydro turbines and hydroelectric power plants in the

In order to form a general regulatory framework for the protection of hydropower plants, it is necessary to implement the following measures with the prepa-

1.Develop standards and carry out categorization of hydropower plants as critically and strategically important infrastructure facilities according to the

2.Develop a nomenclature of emergency and catastrophic situations at

3.Build scenarios for the development of severe disasters; identify the damaging factors and the degree of vulnerability of hydropower stations in severe

4.Develop a methodology for assessing the strategic risks of severe disasters at

5.Develop principles, methods, and systems for protecting hydropower plants

hydropower plants, taking into account all stages of the life cycle.

6.Develop the diagnostic methods of hydropower plants and automated protection systems in the event of emergency and catastrophic situations.

7.Determine the role of human factors and responsibility at the stages of decision making, project implementation, and operation of hydropower

8.Perform the complex computational and experimental studies'survivability, safety, and protection of hydropower plants from severe disasters on models

9.Develop safety criteria for hydraulic engineering dams and methods for

3.Develop a methodology for refined estimation of the dynamics,

4.Develop a methodology for constructing a special control system and

transition from standard to emergency and catastrophic situations.

computational and experimental works [5]:

a severe disaster of hydroelectric power plants.

severe catastrophe on typical hydraulic units.

risk levels of national, regional, and local disasters.

hydropower plants and levels of protection from them.

ration of the relevant regulatory documents:

from accidents and disasters.

plants to prevent severe disasters.

assessing actual safety factors.

accidents.

and objects.

**38**

according to risk criteria.

*Probability, Combinatorics and Control*

$$R\_{\Sigma}(t) = \sum\_{i} R\_{i}(t), \tag{1}$$

*l t*ðÞ¼ *Fl Q t*ð Þ*; l*0*; Ne* f g *;*Δ*K* (8) *N l*ðÞ¼ *FNl Q t*ð Þ*; Ne; l*0*; lc* f g *;*Δ*K* (9)

where Δ*K* is the magnitude of the stress intensity factor.

scenarios of possible accidents of hydro turbines.

• Emergency situations (extreme loads)

• Overflow over the dam 10<sup>8</sup>

following accident probability values:

*DOI: http://dx.doi.org/10.5772/intechopen.88306*

The estimation of probabilities *Pi*(*t*) is carried out taking into account Eqs. (3)–(9) under the assumption that the form of the probability functions *FP*, *FQ*, *Fσ*, *FN*, *Fl*, and *FNl* and their parameters is defined. Damage assessment *Ui*(*t* + *τ*) is performed by actual losses or calculated by economic methods for the considered

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety…*

tures of hydropower plants in accordance with the above principles gave the

• Normal working conditions of hydropower plant (regulatory loads)

The calculated estimates of the probability of damages to equipment and struc-

*Pi* <sup>¼</sup> <sup>2</sup>*:*<sup>2</sup> � <sup>10</sup>�<sup>4</sup> � <sup>1</sup>*:*<sup>5</sup> � <sup>10</sup>�<sup>3</sup>

*Pi* <sup>¼</sup> <sup>6</sup>*:*<sup>0</sup> � <sup>10</sup>�<sup>3</sup> � <sup>3</sup>*:*<sup>1</sup> � <sup>10</sup>�<sup>2</sup>

*Pi* ≥0*:*1

of hydropower plants were given the following values (in rubles):

• Destruction (flooding) of hydropower plant 10<sup>9</sup>

Angaro-Yenisei cascade of Russia were obtained:

• Risk of destruction of hydropower plant

• Risk of breaking the pressure front

• Risk of terrorist threat

give probabilities *Pi* = 3.3 � <sup>10</sup>�<sup>2</sup>

**41**

–10<sup>9</sup>

• The destruction of the dam (breakthrough of the pressure front) 10<sup>9</sup>

Taking into account the indicated probabilities and damages, the following generalized risk assessments (in \$) of accidents for hydropower plants of the

*<sup>R</sup>*<sup>Σ</sup> <sup>¼</sup> <sup>3</sup>*:*<sup>6</sup> � <sup>10</sup><sup>5</sup> � <sup>2</sup>*:*<sup>5</sup> � <sup>10</sup><sup>6</sup>

*<sup>R</sup>*<sup>Σ</sup> <sup>¼</sup> <sup>1</sup>*:*<sup>0</sup> � <sup>10</sup><sup>6</sup> � <sup>5</sup>*:*<sup>0</sup> � 106

*<sup>R</sup>*<sup>Σ</sup> <sup>≤</sup>5*:*<sup>1</sup> � <sup>10</sup><sup>4</sup>

The aggregated statistical estimates of major accidents of hydropower plants

–2.3 � <sup>10</sup>�<sup>3</sup>

reach 5 � <sup>10</sup><sup>9</sup> \$, and indirect damages are (1.8–2.5) � <sup>10</sup><sup>10</sup> \$.

Qualitative estimates of potential damage for the enlarged scenarios of accidents

–1010

. Direct damages from such accidents

–10<sup>11</sup>

• Violation of normal operating conditions of hydropower plant (increased loads)

$$R\_i(\mathbf{t}) = P\_i(\mathbf{t}) \times U\_i(\mathbf{t} + \mathbf{r}) \tag{2}$$

where *Pi*(*t*) is the probability of reaching the *i*th limiting state leading to disaster with damage *Ui*(*t* + *τ*) and *τ* is discounting time.

The probability *Pi*(*t*) is determined by the given criteria of the limiting state for the most critical zones of highly loaded elements of hydraulic equipment structures:

$$P\_i(t) = F\_p\{\sigma\_\varepsilon, e\_\varepsilon, d\_\varepsilon, l\_\varepsilon, t\} \tag{3}$$

The values of critical stresses *σc*, deformations *ec*, damage *dc*, and size of crack-like defects *lc* depend on the complex of operating technological and operational loads:

$$Q(t) = F\_Q\{Q\_M(t), Q\_H(t), Q\_E(t), Q\_V(t), Q\_S(t)\}\tag{4}$$

where *Q <sup>M</sup>* is mechanical loads from the weight and installation and welding of elements and from the rotation of the hydraulic turbine; *Q <sup>H</sup>* is hydrodynamic loads from pressure and pressure of water, water hammer, and pressure pulsation; *Q <sup>E</sup>* is electromagnetic load from the interaction of the rotor and the stator of the turbine; *QV* is vibration loads; and *QS* is seismic loads.

The components of stresses *σ* and deformations *e*, which characterize the stress-strain state of the structure, are determined by calculation and experimental methods according to the values of the indicated loads:

$$\{\sigma, \varepsilon\} = F\_{\sigma} \{Q(t), a\_{\sigma}, E, \mu, m, A, W\} \tag{5}$$

where *E*, *μ*, and *m* are modulus of elasticity, Poisson's ratio, and strain hardening coefficient, *A* and *W* are sectional areas and moments of resistance of the considered elements of hydro turbines, and *ασ* is stress concentration factors.

Characteristics *E*, *μ*, and *m* of the mechanical properties of materials are determined by laboratory testing and full-scale sample testing. The stress concentration coefficient *ασ* is determined experimentally or by calculation methods.

Based on Eq. (5), the characteristics of cyclic loading of hydro turbine elements are determined: stress amplitudes *σ<sup>a</sup>* and deformations *ea*, mean stresses *σ<sup>m</sup>* and deformations *em*, and cycle asymmetry coefficients *r* = *σmin*/*σmax*. Next, determine the number of loading cycles to failure:

$$N\_{\mathfrak{c}} = F\_N\{\sigma\_a, e\_a, \sigma\_m, e\_m, r, \mathbf{S}\_{\mathfrak{c}}, \boldsymbol{\upmu}\_{\mathfrak{c}}, \sigma\_{-1}, m\_N, m\_{\sigma}, \boldsymbol{\alpha}\}\tag{6}$$

where *Sc* and *ψ<sup>c</sup>* are tensile strength and ultimate plasticity of the material, *σ*�*<sup>1</sup>* is material fatigue limit, *mN* and *m<sup>σ</sup>* are the characteristics of the sensitivity of materials to cyclic loading, and *ω* is the loading frequency.

The ratio of actual *Ne* to critical *Nc* loading cycles establishes damage level:

$$\begin{split}d(N,t) &= \sum\_{i} d\_{i}(N,t), d\_{i}(N,t) \\ &= N\_{\epsilon}^{(i)} / N\_{\epsilon}^{(i)}\end{split} \tag{7}$$

If there are crack-like defects in the structural elements, the resources *l*(*t*) or *N*(*l*) are determined at the crack growth stage from initial *l*<sup>0</sup> to critical *lc* sizes:

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety… DOI: http://dx.doi.org/10.5772/intechopen.88306*

$$l(t) = F\_I\{Q(t), l\_0, N\_\epsilon, \Delta K\}\tag{8}$$

$$N(l) = F\_{\rm Nl} \{ Q(t), N\_c, l\_0, l\_c, \Delta K \} \tag{9}$$

where Δ*K* is the magnitude of the stress intensity factor.

The estimation of probabilities *Pi*(*t*) is carried out taking into account Eqs. (3)–(9) under the assumption that the form of the probability functions *FP*, *FQ*, *Fσ*, *FN*, *Fl*, and *FNl* and their parameters is defined. Damage assessment *Ui*(*t* + *τ*) is performed by actual losses or calculated by economic methods for the considered scenarios of possible accidents of hydro turbines.

The calculated estimates of the probability of damages to equipment and structures of hydropower plants in accordance with the above principles gave the following accident probability values:

• Normal working conditions of hydropower plant (regulatory loads)

$$P\_i = 2.2 \times 10^{-4} - 1.5 \times 10^{-3}$$

• Violation of normal operating conditions of hydropower plant (increased loads)

$$P\_i = \mathbf{6.0} \times \mathbf{10^{-3}} - \mathbf{3.1} \times \mathbf{10^{-2}}$$

• Emergency situations (extreme loads)

*Pi* ≥0*:*1

Qualitative estimates of potential damage for the enlarged scenarios of accidents of hydropower plants were given the following values (in rubles):


Taking into account the indicated probabilities and damages, the following generalized risk assessments (in \$) of accidents for hydropower plants of the Angaro-Yenisei cascade of Russia were obtained:

• Risk of breaking the pressure front

$$R\_{\Sigma} = \mathbf{3.6} \times \mathbf{10^5} - 2.5 \times \mathbf{10^6}$$

• Risk of destruction of hydropower plant

$$R\_{\Sigma} = \mathbf{1.0} \times \mathbf{10^6} - \mathbf{5.0} \times \mathbf{10^6}$$

• Risk of terrorist threat

$$R\_{\Sigma} \le 5.1 \times 10^4$$

The aggregated statistical estimates of major accidents of hydropower plants give probabilities *Pi* = 3.3 � <sup>10</sup>�<sup>2</sup> –2.3 � <sup>10</sup>�<sup>3</sup> . Direct damages from such accidents reach 5 � <sup>10</sup><sup>9</sup> \$, and indirect damages are (1.8–2.5) � <sup>10</sup><sup>10</sup> \$.

*<sup>R</sup>*ΣðÞ¼ *<sup>t</sup>* <sup>X</sup>

The values of critical stresses *σc*, deformations *ec*, damage *dc*, and size of crack-like defects *lc* depend on the complex of operating technological and

with damage *Ui*(*t* + *τ*) and *τ* is discounting time.

*Probability, Combinatorics and Control*

*QV* is vibration loads; and *QS* is seismic loads.

the number of loading cycles to failure:

**40**

rials to cyclic loading, and *ω* is the loading frequency.

methods according to the values of the indicated loads:

operational loads:

*i*

where *Pi*(*t*) is the probability of reaching the *i*th limiting state leading to disaster

The probability *Pi*(*t*) is determined by the given criteria of the limiting state for the most critical zones of highly loaded elements of hydraulic equipment structures:

where *Q <sup>M</sup>* is mechanical loads from the weight and installation and welding of elements and from the rotation of the hydraulic turbine; *Q <sup>H</sup>* is hydrodynamic loads from pressure and pressure of water, water hammer, and pressure pulsation; *Q <sup>E</sup>* is electromagnetic load from the interaction of the rotor and the stator of the turbine;

where *E*, *μ*, and *m* are modulus of elasticity, Poisson's ratio, and strain hardening coefficient, *A* and *W* are sectional areas and moments of resistance of the consid-

Characteristics *E*, *μ*, and *m* of the mechanical properties of materials are determined by laboratory testing and full-scale sample testing. The stress concentration

Based on Eq. (5), the characteristics of cyclic loading of hydro turbine elements are determined: stress amplitudes *σ<sup>a</sup>* and deformations *ea*, mean stresses *σ<sup>m</sup>* and deformations *em*, and cycle asymmetry coefficients *r* = *σmin*/*σmax*. Next, determine

where *Sc* and *ψ<sup>c</sup>* are tensile strength and ultimate plasticity of the material, *σ*�*<sup>1</sup>* is material fatigue limit, *mN* and *m<sup>σ</sup>* are the characteristics of the sensitivity of mate-

The ratio of actual *Ne* to critical *Nc* loading cycles establishes damage level:

If there are crack-like defects in the structural elements, the resources *l*(*t*) or *N*(*l*) are determined at the crack growth stage from initial *l*<sup>0</sup> to critical *lc* sizes:

*i*

<sup>¼</sup> *<sup>N</sup>*ð Þ*<sup>i</sup> <sup>e</sup> =N*ð Þ*<sup>i</sup> c*

*d N*ð Þ¼ *; <sup>t</sup>* <sup>X</sup>

*Nc* ¼ *FN σa;ea; σm;em;r; Sc; ψ<sup>c</sup>* f g *; σ*�<sup>1</sup>*; mN; mσ;ω* (6)

*di*ð Þ *N; t , di*ð Þ *N; t*

(7)

The components of stresses *σ* and deformations *e*, which characterize the stress-strain state of the structure, are determined by calculation and experimental

ered elements of hydro turbines, and *ασ* is stress concentration factors.

coefficient *ασ* is determined experimentally or by calculation methods.

*Ri*ð Þ*t ,* (1)

*Ri*ðÞ¼ *t Pi*ðÞ�*t Ui*ð Þ *t* þ *τ* (2)

*Pi*ðÞ¼ *t Fp σc;ec; dc; lc* f g *; t* (3)

*Q t*ðÞ¼ *FQ QM*ð Þ*t ; QH*ð Þ*t ; QE*ð Þ*t ; QV*ð Þ*t ; QS* f g ð Þ*t* (4)

f g *σ;e* ¼ *Fσ*f g *Q t*ð Þ*; ασ; E; μ; m; A;W* (5)

It should be emphasized that the approach outlined requires statistical information on all parameters, which is included in the calculations. Particular attention should be paid to characteristics of mechanical properties, parameters of stressstrain states, and structural damage. Such information can be obtained by conducting large volumes of tests and experimental studies. At the same time, the most preferable are methods and means allowing to evaluate the determining parameters (stresses, deformations, sizes of defects), taking into account the peculiarities of the micro- and macrostructure of structural materials.

due to the interaction between the stator and the rotor at the blade frequency, as well as the loads caused by Karman vortices. Special attention should be paid to resonance phenomena, when the proximity of the natural frequencies of the elements of hydro turbines and the frequencies of external influences occurs.

*Laboratory, Bench, and Full-Scale Researches of Strength, Reliability, and Safety…*

failure at a given operating time.

*DOI: http://dx.doi.org/10.5772/intechopen.88306*

assessment of the resource

and loading conditions

the resource

**43**

during the diagnostics [9].

estimation [8].

The level of resource exhaustion is determined by the results of special calculations. These calculations consist in determining the time *t* or the number of loading cycles *N* as a function of amplitudes *σ<sup>a</sup>* and average values *σ<sup>m</sup>* of the loading cycle, defect sizes *l*, characteristics of the mechanical properties of materials (conditional yield strength *σ*0.2, temporary fracture resistance *σb*, fatigue limit *σ*1, destructive deformations *εf*), and safety factors for stresses *nσ*, for a number of cycles *nN* and for size of defects *nl*. The results of the calculations usually defined the fatigue diagrams of the main elements of hydro turbines, the residual resource, and the probability of

The main elements of hydraulic turbines requiring the design justification of the resource are an impeller, a turbine shaft, a turbine cover with fastening elements, a shoulder blade of guide, and other elements. Calculation justification is carried out on the basis of data on operating modes, acting loads, defects, and damages detected

One of the main stages of resource assessment is the determination of external loads for equipment components and the corresponding internal stresses. Despite the great interest of this topic and the significant achievements of recent years, the problem of correctly describing the dynamic behavior of hydro turbine under partial power conditions and during transients has not been fully resolved. With this in mind, it is becoming a more common method of computational modeling [10]. These methods are based on mathematical models that include three main elements: geometric model, model of external loads, and model of boundary conditions. The accuracy of each model can have a decisive influence on the results of numerical experiments, including the issues of resource

The main problems of estimate resource for hydro turbines today are:

• The complexity of accounting technological and operational defects, stress concentration, residual stresses in welded joints, and heat-affected zones

• The poverty of database on the characteristics of materials for a reliable

of external loads and non-design modes of operation

the present stage are characterized by the following circumstances:

emergence of new technical capabilities

stages the assessment of hydro turbine resource

• The complexity of the damage summation mechanism in condition uncertainty

• The difficulty of predicting crack growth under the conditions of actual spectra

The trends in the development of hydro turbine resource assessment methods at

1. Increasing interest for the problem resource assessment in connection with

2.The desire to increase the reliability and accuracy of solving problems at all

3.The need to take into account the non-project operation condition influence on
