Power Plant Flexible Operation, focusing on

Steam Turbine Rotor Stress

Name: Federico Calzolari

Company: ANSALDO ENERGIA

Country: ITALY

Name: Paolo Levorato

Company: ANSALDO ENERGIA

Country: ITALY

Name: Carlo Bima

Company: ANSALDO ENERGIA

Country: ITALY

ABSTRACT

Nowadays the market requires flexible Power Plants in order to maximize the profits, for

example with two-shift operation. Moreover the customer requires faster start-ups: in

combined cycle power plants the steam turbine is often the limiting factor, due to rotor

thermal stress during speed and load transient.

AEN, as a turn-key power plant supplier, has the advantage to be able to optimize the whole

plant start-up, managing the GT and HRSG in order to minimize ST rotor thermal gradient;

the optimization of the start up / shut down phases is part of a general study for flexibilization.

Based on many years of experience in steam turbine design and service, AEN is studying a

new approach about stress monitoring and lifetime consumption calculation.

This paper describes the main aspects taken into account developing the new RSE and the

results expected by AEN.

In particular, the first step is the development of new detailed mathematical models, including

material data obtained from dedicated test.

AN INTRODUCTION TO EUROPEAN ELECTRICITY MARKETS

The implementation of the European Directive 96/92CE has led to the growth of several

electricity exchanges in the European Community, characterized by a complete liberalization

of the electricity market.

The main features underlined in the European Directive are the free competition aspect that

the electricity markets must have, the focus on environmental problems linked to power

generation, the institution of grid operators to guarantee the quality, the availability and

reliability of the electricity dispatching.

In the new electricity markets, power production and consumption quantities are exchanged

following the energy demand in a competitive environment, bringing to a floating production

demand and electricity prices. In the figures below it is shown how the electricity prices

hourly cost (the day ahead market outcome) follows the hourly energy demand (predicted by

the grid operator).

Energy demand provision (Jan 2009, 9th)

data from RWE Transportnetz Strom GmbH

15000

17000

19000

21000

23000

25000

27000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

hour

vo

lum

e [

MW

h]

Figure 1 – EEX spot hour contract chart for Jan 2009, 9th

and energy demand provision curve

from RWE data

Local energy exchanges are in example EEX (Germany, Austria and Switzerland), IPEX

(Italy), Powernext (France), Apx (Nederland), OMEL (Spain), UKPX (UK), etc.

The energy exchanges can be physical or financial.

A physical exchange (as OMEL and IPEX) is characterized mainly by a day ahead market,

based on hourly electricity prices, systems to solve congestions and a market for the

dispatching resources availability. There is a market administrator and a grid operator related

each other, volumes exchanged in the day head market are close to the physic electricity

transfers, the prices unpredictability is less than in financial exchanges.

Financial exchanges (as EEX, Powernext, Apx, UKPX) have as common features the

scheduling and management performed individually by the grid operator, the offering of

contract for base or peak power supply, supported by a market for the hourly negotiation (for

grid balancing), the provision of different price indexes to evaluate market trends. The success

indexes are the exchanged volumes and the products unpredictability. In a comparison to the

physical exchanges, the exchanged volumes are less and the prices unpredictability is more:

dealing with financial contract, it is not the case of generation capacity traded in the exchange

but of negotiated and exchanged electricity in different market conditions.

From the point of view of the European interconnected grid problematic, the implementation

of the directive 96/92CE has led to the development of UCTE (Union for the Coordination for

the Transmission of Electricity), specialized in the technical issues of the interconnected grid,

and ETSO (European Transmission System Operators), with the aim of international energy

exchanges compensation, congestions resolution in the interconnected lines, data exchange

for the system safety. Then the grid operator figure has appeared in the electricity generating,

transport and delivery area, whose main tasks are

To control the equilibrium between energy demand and offer and to generate the

transmission flow to assure the system safety,

To assure the development and maintenance of the grid,

To guarantee the access to the grid.

One of the major goal of interconnected operation in the electricity industry consists in

exchanging electrical energy among the interconnected partners maintaining at the same time

the security. If more energy flows across national or international interconnect lines into a

control zone than flows out of it, this difference constitutes the import of electrical energy.

Conversely, if more energy flows out of the control zone than into it, electrical energy is

exported.

Interconnection led to significant improvements. Several power plants operating in parallel

could back each other up in the event of power plant failures. The interconnection of the grids

also enabled power plants to be used more efficiently. The parallel connection of the

subsystems also improved security at several interconnection points in the extra-high-voltage

system. In the event of a particular line failure the electricity can be transmitted across the

remaining lines to the consumer.

Each control zone is lined up to the program value by means of load frequency control in

order to be able to specifically influence and control export/import even in a highly meshed

system. In its interaction with the primary-controlled power plants, load frequency control

also maintains the network frequency (typically 50 Hz).

Principal grid operator company are in example RWE Transportnetz Strom GmbH and E.ON

Netz GmbH in Germany, RTE EDF Transport S.A. in France, Terna S.p.A. in Italy, Red

Eléctrica de España S.A. in Spain, TenneT TSO B.V. in the Netherlands, etc.

PLANT OPERATIONAL STRATEGIES

The new features of the electricity markets have a strong impact on the operational modes of

power plants, above all because of the large variability of the hourly electric power price per

MWh versus a less variable fuel cost.

In particular a critical situation for a combined cycle power plant is the night time scenario,

when the energy power price per MWh is the lowest. There are two possible plant operating

modes:

a “two shift operation”, where the plant is at full load, or partial load depending on the

market requests, during the daytime and shutdowns every night and weekend

a “minimum load operation”, where the plant runs during the weekdays and

shutdowns only during weekend.

The first mode foresees a daily plant shut down during weekdays night period: after the

overnight shutdown, about eight hours, the plant will be still in condition to allow hot start-up.

The second operation mode foresees to operate at the environmental minimum load during the

night, preserving the plant from frequent heavy transients.

Evaluating the two possible solutions through a technical and economic analysis, estimating

gain and losses of the two possible operation modes in terms of fuel consumption, fuel costs,

power production and revenue in a variable energy market, it is evident that the better solution

is the two shift operation mode because the fuel consumption costs, running the plant at

minimum environmental load, overlook the power production gains because of the low power

price per MWh in the night period. In the two shift operation the only negative net is in the

start-up and shut-down intervals, as shown in the following charts.

hourly net in a summer weekminimum load operation during night

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

0 24 48 72 96 120

hours

€/h

net/h

mon tue wed thu fry

hourly net in a winter weekminimum load operation during night

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

0 24 48 72 96 120

hours

€/h

net/h

mon tue wed thu fry

hourly net in a summer weektwo shift operation

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

0 24 48 72 96 120

hours

€/h

net/h

mon tue wen thu fry

hourly net in a winter weektwo shift operation

-7000

-2000

3000

8000

13000

18000

23000

28000

33000

0 24 48 72 96 120

hours

€/h

net/h

mon tue wed thu fry

Figure 2 – Hourly net considering the two operational modes (shutdown during the weekend

and two shift operation) and the seasonal variation (summer and winter case)

The power generation trend follows the energy demand curve that could be provided by the

operator grid, considering to operate the plant at maximum load (taking into account the

primary frequency control reserve) in the peak hours, and varying the plant load as the

electricity demand. In both the operational mode, the plant is shut down during the weekend

and on Monday morning the plant operates a warm start-up.

No doubt that the two shift operation mode involves a major plant main components life

consumption, because they suffer most often thermal stresses for the frequent starts. Hence to

have a flexible power plant in order to stand this operational mode, some additional features

has to be implemented on plant components, which differentiate new plants from the previous

base load operated power plant.

FLEXIBLE COMBINED CYCLE POWER PLANTS

As consequences of a two shift operation, a flexible combined cycle power plant should have

cycling capability, reduced start-up times, reliable and iterative start-up/shut-down

procedures. This means particular characteristics of the main components in order to face the

stress due to the cycling operations, start-up times depend on material thermal stresses. The

most important and critical component is the Steam Turbine, as it needs careful metal heating

in the start up phase and the mechanical design provides limited clearances to increase the

efficiency. Other important parameters to be monitored are the HRSG drums temperature

gradient. Moreover vacuum achievement times have to be taken into account, depending on

the condenser typology.

Hence possible interventions to increase plant cycling capacity are the following:

The use of an auxiliary boiler or the check of the existing auxiliary steam system to

feed ST sealing system

A new HRSGs specific design

The use of cycling skilled materials in the thermal cycle lines penalized by thermal

stress

Moreover possible interventions to allow frequent plant start-ups are:

Steam turbine Rotor Stress Evaluator (RSE) software oriented to increase plant

flexibility

An auxiliary boiler to maintain performed vacuum

A Sparging System for the initial stage of HRSG pressurisation

Desuperheaters (SH and RH outlets) to disengage GT load operations

A well installed fully automatic start-up system

Performed field test and dynamic simulator test

In this paper, features concerning power plant flexible operation, focusing on steam turbine

rotor stress are inspected to improve plant flexibility and permit a full automatic plant start-

up.

Concerning the frequency control, this issue depends on the national grid codes. However, it

is natural that this problematic involves above all the turbomachinery. An efficient contribute

to frequency control can arise from the steam turbine when the plant is running at high

percentage of load. Hence, flexibility studies for the steam turbine involve also the contribute

to the participation to the frequency control.

STEAM TURBINE OPERATION IN FLEXIBLE COMBINED CYCLE

The steam turbine installed in a combined cycle can operate in “two shift operation” or

“minimum load operation”; in any case the turbine has to be able to perform several start-up

without relevant stress; for example: 50 cold start-up, 1300 warm start-up, 5200 hot start-up

considering a plant total life of 25 years. This result is possible with a correct plant

management and suitable turbine design.

In two-shift operation mode, the turbine generator load follows the actual power demand

during the day. However, at night and during weekends, the turbine generator will be shut

down. In accordance with the operational mode, a base load design machine is mainly

subjected to constant high temperature loading, i.e. the lifetime is consumed by creep damage.

The damage due to starts and load changes is correspondingly low. The lifetime expenditure

of a two shift machine is mainly determined by the number of starts. The transient, thermal

stresses provoke a high influence of low cycle fatigue against the low creep damage.

Steam turbine start-up curves selection

Turbine start-ups can be classified into various categories according to the thermal condition

of the turbine at the start-up time. The true ruling criteria are the thermal temperatures to

which the various components (such as the HP and IP inner casings) have cooled. The typical

start-up categories are: cold, warm and hot. For each start-up category there is a curve for

turbine speed and turbine loading related to main steam pressure and temperature.

The steam turbine supplier has to provide more flexible start up parameters (such as greater

steam turbine temperature mismatch) while maintaining reasonable constant life consumption.

Start-up times and start-up curves configuration are selected in order to maintain steady

thermal stresses and not exceed admissible limits.

Such start-up times and curves shapes for the start-up procedure depend on the live steam and

reheat steam temperatures. If these temperatures change otherwise than as in the following

diagrams, the start-up and loading curves must be adjusted.

To optimize the turbine start-up time Ansaldo has introduced four steam turbine thermal state:

hot, warm, warm-cold and cold instead of the classic three: hot, warm, cold. The attached

curves are an example. In this case after 8 hours of shutdown time the steam turbine can start-

up in hot condition, while after 48 hours it can start-up in warm condition. If for any reason

the plant can start after 48 hours but later, the steam turbine can accelerate according to

“warm-cold” instead of “cold” condition, saving 60 minutes.

Figure 3 – Cold

Figure 4 – Cold-Warm

Figure 5 – Warm

Figure 6 – Hot

Steam turbine start-up curves analysis

The inlet steam temperatures in HP and IP turbine sections have to follow the expected curves

within tolerance of ±10°C. Otherwise the “Rotor stress evaluator” will start to reduce the

steam flow through a limitation on turbine valves opening to reduce the stress on the turbine;

this action produces a variation of the generated electric load; this event is not acceptable in

the energy free market where the sold electric power and the foreseen availability of power in

time should be fulfilled.

The steam temperature control can be obtained by modulating the gas turbine load which

produces the hot burnt gases to HRSG or by steam final desuperheaters, located between the

HRSG and the steam turbine.

The first solution forces the gas turbine to work at reduced load to decrease the temperature of

burnt gases to HRSG (see the attached typical trend) when the steam turbine is under start-up

condition, the second solution allows an independent gas turbine start-up from the steam

turbine start-up because the steam temperature form HRSG is controlled by the

desuperheaters, so the plant is more flexible.

As mentioned before, the steam turbine rotor hot parts are under low cycle fatigue stress and

creep. The fatigue is generated by the steam temperature variations with relevant steam flow,

as during start-up phase or very high load variations (more than 50%). The creep occurs in

components subjected to high temperature stresses (typically more than 500°C). The creep

normally is not the most important factor.

The life consumption for each turbine component is obtained by the sum of both fatigue and

creep: when the 100% load is reached, some fractures can be attended on rotor surfaces,

which means that rotors have to be repaired or substituted.

In case of steam turbine in combined cycle the most important factor is done by low cycle

fatigue because the request start-ups during the operation is very high; even for this reason is

very important to follow the foreseen start-up curves.

Till now the start-up phase has been analyzed but now it is necessary to analyze the shut-

down phase to limit the rotor stress and increase the flexibility.

Both in “two shift operation” or “minimum load operation” is important to maintain the heat

during the shut-down phase, in this way the turbine can restart in hot conditions (night

standstill) or warm condition (weekend standstill); this is important to reduce start-up time

and limit the related fatigue stress.

Figure 7 – GT diffuser outlet temperature and mass flow vs. power output

Figure 8 – Cooling curves for steam turbine

The best solution is to reduce the steam flow (maximum 10%/minute) by closing the turbine

valves while the gas turbine still produces hot burnt gases, maintaining the vacuum in the

condenser and in the gland steam after turbine trip; hence it is possible to reduce the heat lost

by the IP rotor to the condenser, see attached diagram.

Steam turbine mechanical features for operating combined cycle

The steam turbine is subjected to many hot and warm start-up; each start-up produces a

fatigue stress, and after some years could damage the rotor.

The target is to design the turbine in order to limit the low cycle fatigue and to reduce the

start-up time.

The solutions may be:

Suitable materials to reduce the creep and fatigue.

Inner casing without big flanges but jointed with shrinking rings (see attached

drawing) to reduce strains/forces due to asymmetrical thermal expansion.

The inner connection for the steam is symmetrical and distributes flow at the complete

radial section of the turbine.

The steam turbine is working in sliding pressure mode, with all valves laminating the

steam in full arc admission; this avoid parts of turbine not involved in steam flow.

Figure 9 – ST mechanical features

HHPP

Steam turbine functional features for operating combined cycle

The experience of many steam turbine applied in combined cycles suggests to adopt some

technical features in order to optimize the operation of the rotating machine. The steam

turbine start up flexibility and commissioning time have played an important role in the start

up of the whole combined cycle plant. Heavy penalties for failing to bring the unit on line as

scheduled on predicted start up time. In addition, due to the higher fuel costs and increased

reserve margins, combined cycles are being dispatched as intermediate duty units rather than

base load, as originally foreseen. Achieving the aim of a fast and reliable start up requires a

careful design and integration of the steam turbine and balance of plant requirements.

Steam turbine automatic start-up

Due to the strict requirements of the national dispatcher to the power plant managers for

respecting the declared start-up times and due to reduced personnel involved in the normal

operation of a combined cycle unit (typically one technician in control room and another one

around the machinery), it is strongly recommended to have automatic start-up and shut-down

sequences for the steam turbine.

To operate in automatic mode, the control functions related to the process systems of the

steam turbine (lube oil system, jacking oil and turning gear system, drain valves, gland

sealing steam to the sleeves to prevent air or steam leaking into or out of the turbine,

condenser vacuum, control oil system, turbine reset, turbine speed run up, turbine loading) are

divided in hierarchically way. Coming from the top to the bottom, the following levels are

foreseen:

Turbine Run up (TRU) is the general sequence that manages the start up and shut

down of the machine.

Functional group (FG). The functional group put together open and close loop

belonging to the same auxiliary process system. Automatic complex controllers as

turbine run up and turbine loading could be considered at the same level. The

functional group purpose is to command and monitor the subordinated loops and to

interface with the higher level and the operator.

Drive control level has the task to manage the single loop concerning the drive

interlocks and the drive interface with the field, the operator and the higher levels.

A great importance assumes the coordination of all the components essential to start up of the

whole plant, such as Gas turbine, Heat Recovery Steam Generator, Steam turbine, main steam

and hot reheat steam Desuperheaters, Auxiliary boiler, etc. In this way it is allowed to have

repeatable start up of the combined-cycle power plant in the shortest possible time without

violating permitted thermal stress limits for thick-walled components, such as drums and

headers.

Participation of steam turbine in grid frequency control

Power stations foreseen to support grid frequency must be able to operate in the part-load

range so that they can supply the required power reserves. They must also be able to respond

quickly within a few seconds after a collapse in grid frequency. Due to the required quick

response time, only gas turbines are typically used for this purpose. The steam turbine works

in natural sliding pressure mode having the valves fully opened to generate the maximum load

possible at the higher efficiency. In other words the steam turbine only reacts passively to

load changes in the gas turbine. The rapid load changes required for frequency support cannot

be achieved for this reason

An important improvement to be evaluated in the management of a combined cycle is the

opportunity to integrate the steam turbine in the control of the grid frequency.

The implementation of a logic coordinated with gas turbine and HRSG permits to react to a

frequency variation with a parallel contribution of power generated by the gas turbine and by

the steam turbine. It is very helpful where dynamic processes are involved. In this way of

operation the steam turbine control valves work partially closed to modulate the steam flow

into the turbine to have the possibility to control the grid frequency according to the selected

droop (from 2% to 8%), but obviously at a reduced load.

Steam turbine with “minimum load operation”

Considering the “minimum load operation” the load variations during the night has not to

generate a decreasing of steam temperature at plant low load; it is important to modulate the

steam flow in the turbine with nominal temperature so no fatigue stress is created.

The HRSG produces steam at nominal temperature still the gas turbine has a load upper 40%

so the steam turbine produce a power output of 50%, because the steam flow form the boiler

is decreased. The minimum plant load will be around 45%.

In these conditions the low cycle fatigue will be reduced. The load variation will follow the

curves indicated in the hot start-up.

In case to further reduction on the minimum gas turbine load, with increase of NOx and CO,

the steam temperature decreases and the steam turbine will be subjected to thermal stress

during next start-up phase.

Anyway there are some experiences showing that the minimum load operation can be reduced

acting on the steam turbine. It is possible to operate the steam turbine not in natural sliding

pressure, but in different ways as in load control loop. Consequently, the control valves can be

partially closed reducing the load produced by the steam turbine and by the whole combined

cycle. The steam produced by HRSG and not used by the steam turbine is diverted to the

condenser through the by-pass systems. In this operating mode it can be selected the

possibility to insert the frequency control on the steam turbine leaving the gas turbine working

at its minimum load without the “disturbances” generated by the grid.

ST STRESS MONITORING AND LIFETIME CONSUMPTION

Ansaldo Energia is carrying out a R&D project to develop a tool, that could optimize the start-

up time of the steam turbines installed in the power plants designed for two-shift operation.

The activity in the first phase is oriented towards the realization of an “off-line” design tool,

that is able to optimize the steam turbine start-up time taking into account the lifetime

consumption.

The tool is based on a finite element model of the steam turbine rotor for calculating thermal

and stresses distribution during transients, used for the definition of stresses and lifetime

consumption in the critical points of the rotor.

Two operating modes are foreseen:

Calculation of stress and lifetime consumption based on user defined start-up (steam

conditions, speed and load variation vs. time)

Calculation of optimal start-up parameters based on target lifetime consumption

This will make it possible to have an optimization of the start-up based on the total number of

the expected start-ups.

The tool will also take into account the lifetime consumption due to creep, calculated at each

different critical location.

In the second phase of the project the results of the “off-line” tool will be used to optimize

steam turbine start-up time, developing a simplified model to be implemented in the

automation system, that could calculate “on-line” the rotor lifetime consumption.

Materials

It is really important, to obtain reliable results from the calculation tool, to be able to rely on

the material data. Hence it is foreseen, in order to increase the knowledge of the material

properties and consequently reduce the safety margin to be applied in the FEM computation,

to execute a test campaign on materials used by Ansaldo Energia to manufacture steam

turbines. The more relevant data to be obtained by the test are LCF and stabilized cyclic

stress-strain curve at different temperatures. Particular attention will be paid on materials used

at critical points in terms of thermal stress.

Thermomechanical analysis of the rotor

Figure 10 shows the general approach followed for the thermomechanical analysis. Input used

in thermomechanical analysis are rotor geometry, Heat Transfer Coefficient (HTC) & bulk

temperature (Tbulk).

Definition of: ST configuration, transient operating cycle

Cycle

Thermodynamic

data

Heat transfer

coefficients and

bulk temperature

calculation

FE Model

Material data

(Young’s modulus,

Density, Thermal

Conductivity, …..)

CAD drawings

Thermal transient

analysis

Transient stress

analysis

Loads (centrifugal

force) and boundary

conditions

(mechanical)

Critical Zone

Detection

Figure 10 – Thermomechanical analysis

Steps involved in thermomechanical analysis are the following:

Heat transfer coefficient (HTC) and bulk temperature (Tbulk) information is obtained

using calculations from the turbine thermodynamic data.

Finite element model of the rotor geometry is prepared after cleaning the geometry

and applying suitable mesh density in critical locations.

After FE model preparation, transient heat transfer analysis is conducted to obtain the

rotor metal temperatures.

These temperatures along with centrifugal load are applied on the rotor and stress

analysis for the transient condition is conducted. As effect of pressure in rotor stresses

in transient condition is very small so pressure loads are neglected. Centrifugal load

due to rotor and rotor blades is considered in the analysis and the blade centrifugal

load is applied at the contact face of the rotor grove as a distributed pressure load.

At the end of the thermo mechanical analysis stress and temperature history at various

critical locations of the rotor is obtained for use in life consumption calculations.

LCF approach

Figure 11 shows a typical flow chart for life consumption calculation at any typical location in

the rotor. Using the stress components at the location, an equivalent stress history is obtained,

using von Mises stress. Major and minor stress cycles are obtained using rainflow counting

method. For each stress cycle elasto plastic strain range is obtained by using Neuber

correction. Corresponding to this strain range life is obtained using Coffin-Manson strain life

relation.

Equivalent Stress

Calculation

Material data (LCF

and Creep)

Critical Zone Stress

Data (from

Thermomechanical

Analysis)

Cycles Identification

Total Damage

Rain-Flow Method

LCF Cycles

Neuber’s CorrectionCoffin-Manson

Method

Miner’s Rule

Figure 11 – Life Consumption Calculations

Inputs for LCF Calculation

In order to compute low cycle fatigue life, critical locations are identified on the rotor

components. Following inputs are required at each critical location for LCF calculations.

Stress history and metal temperature history for the start up – base load – shut down

mission. This is obtained at the critical locations from FE stress analysis. All the stress

components, principal stresses, equivalent stress and temperature for a critical location

are used.

Iso-thermal stabilized cyclic stress strain curve in the form of Ramberg Osgood curve.

Cyclic Young’s modulus E.

Iso-thermal low cycle fatigue material data for strain life relation (this is combination

of Basquin’s equation and Coffin-Manson’s equation).

Major and minor cycles identification

The rainflow counting method is used in the analysis of fatigue data in order to reduce a

spectrum of varying stress into a set of simple stress reversals. Its importance is that it allows

the application of Miner's rule in order to assess the fatigue life of a structure subject to

complex loading.

Procedure for applying rainflow counting method is the following:

Depict the loading or stress or strain sequence as a function of time

o This is obtained from the stress analysis for transient conditions.

o Start with largest maximum or smallest minimum.

o Use straight lines between (local) minima and maxima.

Start from the top and let a “drop” start from every maximum and minimum. A drop

stops if:

o it starts from a maximum and passes a larger or equal maximum.

o it starts from minimum and passes a larger or equal minimum.

o it reaches the run of another drop.

Identify closed loops by joining drops

Figure 12 – Example of rainflow counting method

Neuber’s Correction

Finite element stress analysis performed is an elastic stress analysis. Hence the elastic stress

strain range has to be converted into elasto-plastic stress strain range. Elasto-plastic strain

range is obtained by Neuber’s correction. Elastic-Plastic strain and stress are obtained from

the intersection point of the Neuber’s hyperbola passing through the linear elastic stress-strain

curve and the stabilized cyclic stress-strain curve. The stabilized cyclic stress-strain relation

can be expressed by Ramberg-Osgood curve.

Ramberg-Osgood equation for cyclic stress strain curve is given by

'

1

'

n

KE

Ramberg-Osgood equation for hysteresis curve

'

1

'22

n

KE

Neuber’s correction is applied on the Linear elastic stress cycle obtained from the rainflow

counting method to predict:

elasto – plastic strain range.

Maximum and minimum stress of hysteresis loop.

Mean stress of the hysteresis loop.

LCF Life Analysis

Strain-life method is one of the most common life prediction methods. It is also called the

local strain approach, the crack initiation method, and the strain-life approach. The method

used to calculate life is based on Basquin, Coffin and Manson method. Basquin showed that

for LCF, fatigue life has a power law relationship with elastic strain range or amplitude.

Coffin and Manson showed that for LCF, fatigue life has a power law relationship with plastic

strain range or amplitude. Addition of elastic and plastic strain parts yield total strain life

relationship covering low and high cycle regimes.

Figure 13 – Basquin, Coffin and Manson curve

Miner’s Rule to estimate total damage due to variable amplitude loading

Rainflow counting provides the major and minor cycles in the stress history. Total damage

due to all the cycles, major or minor, is given by Miner’s rule.

According to Miner’s rule failure occurs when:

1i i

i

N

n

Life

Str

ain

/Str

ess A

mp

litu

de

N1 N2

2

1

n1 n2

Figure 14 – Calculation of total damage due in stress history

Let us assume there are n1 cycles with 1 strain amplitude and n2 cycles with 2 strain

amplitude:

Number of cycles undergone with strain amplitude 1 = n1

Number of cycles to failure with strain amplitude 1 = N1

Number of cycles undergone with strain amplitude 2 = n2

Number of cycles to failure with strain amplitude 2 = N2

Then,

Damage due to cycle 1 is given by ΔD1 = n1 / N1

Damage due to cycle 2 is given by ΔD2 = n2 / N2

Total Damage, D = (ΔDn) = (ni / Ni)

CONCLUSIONS

Over its many years of experience in the power plant business, Ansaldo Energia has kept pace

with the new demands for involving the generating units in the flexible behaviour requested

by the market.

A flexible steam turbine can help us to approach the most strict requirements of the combined

cycle in terms of frequent and fast start up operation and for the grid frequency control.

The complexity of a power plant offers a wide variety of approaches for improving the

operating mode in terms of frequency control, but there are physical limits, which

nevertheless must be kept in mind. Our company sees special customer as a challenge and at

the same time an opportunity to expand our realm of experience. In the future, the need to

maintain a defined power control reserve within electrical grids will grow in importance.

The best solution is to manage the combined cycle in “two shift operation” philosophy; the

more start-up foreseen will not cause damages for thermal fatigue if the plant, if the steam

turbine will follow the start-up curves; in this case the total life expected will be more than 25

years as in the minimum environmental load operation. The economic evaluation advantages

the two shift operation.

In case of “minimum environmental load operation” the steam turbine stress will be lower

than in “two shift operation”, only when the steam temperature is maintained about at nominal

value; if in the future the minimum environmental load during the night will decrease and

consequently the steam temperature will be lower, the thermal fatigue on steam turbine

increase to a situation similar to the “two shift operation”.