Ratio between conventional and renewable generation
VGB PowerTech 8/2011 35
Ratio between conventional and renewable energy production in Germany with focus on 2020Christian Ziems, Harald Weber, Sebastian Meinke, Egon Hassel and Jürgen Nocke
Authors
Dipl.-Ing. Christian ZiemsProfessor Dr. Harald Weber University of Rostock Institute of Electrical Power Engineering Rostock/Germany
Dipl.-Ing. Sebastian MeinkeProfesssor Dr. Egon Hassel Dr. Jürgen Nocke University of Rostock Department of Technical Thermodynamics Rostock/Germany
Kurzfassung
Verhältnis zwischen konventioneller und regenerativer Erzeugung mit
Fokus auf das Jahr 2020
Der zunehmende Einfluss regenerativ einge-speister elektrischer Energie in das Energie-versorgungssystem, insbesondere in Deutsch-land, führt zunehmend zu einer Verdrängung konventioneller Kraftwerksleistung aus dem Netz.
Durch diese Reduzierung der rotierenden Mas-sen wird auch die Systemstabilität negativ be-einflusst. Es sind daher Untersuchungen zur maximal möglichen Integration regenerativer Erzeuger in das bestehende elektrische Ener-gieversorgungssystem notwendig. Darüber hi-naus müssen auch Untersuchungen zu ange-passten Fahrweisen konventioneller Kraftwer-ke und deren Auswirkungen auf die Lebens-dauer und Effizienz bestehender und neu zu errichtender Kraftwerksanlagen durchgeführt werden.
Der erfolgreiche Übergang in ein von regene-rativer Energie geprägtes Zeitalter wird aus diesem Grunde nur dann möglich sein, wenn die elektrische Energieversorgung als Ganzes an die neuen Anforderungen angepasst wer-den wird.
Wind power in Germany
Cur ren t s i t ua t ion and t r ends
In 2010 the wind power production in Ger-many amounted to about 37.3 TWh. In 2009 it still was about 38.75 TWh [12]. This reduction of wind energy feed-in in 2010 is the result of a meteorologically weak wind year. The fed-eral association of wind energy reported that the wind energy harvest had been below aver-age since the year 2000. Therefore, the wind turbines produced about 10 % less than it was expected [12].
Wind turbines in general are a type of power plant that uses intermittent, stochastic occur-ring energy depending on high and low pres-sure areas. Therefore, it is impossible to guar-antee the safety of supply from this kind of renewable energy for a longer time horizon. In the same way the last years were distinctly below-average this trend could change in the next years again to above-average. The achiev-able harvest of wind energy could then be much higher than today. Normally in Germany the annual injected wind energy averages to an equivalent of about 1,800 till 2,200 full-load hours for onshore wind sites. For offshore wind sites this value is much higher. For these turbines it is expected to reach up to 4,200 full-load hours as this is already the case in Denmark today. These offshore sites will mainly be built in the North Sea but there will be some wind farms in the Baltic Sea as well.
As reported by the Federal Association of Wind Energy in Germany in 2010, the installed wind capacity increased only by 1.55 GW instead of the expected value of 1.9 GW. Hence at the end of 2010 about 21,600 wind turbines with a to-tal installed capacity of about 27.2 GW were in operation. But the offshore part is still negli-gible with only 100 MW. In 2011 it is ex- pected to increase the offshore capacity up to 400 MW. In total the installed capacity of all wind turbines could reach up to 29 GW at the end of 2011 [12].
Until now the expansion of offshore wind power capacities has been delayed due to bad meteorological conditions and some technical initial problems with this new kind of power plant technology. Therefore, the predictions for the planned capacities in 2020 are updated continuously according to the actual technical
developments and improvements for offshore wind turbines. Today, latest predictions of the wind power industries are still very optimistic. At the moment it seems to be a realistic goal to reach up to 10 GW in the offshore sector until 2020 despite the DENA II study predict-ed up to 14 GW. With regard to different bot-tlenecks within the transmission line system and a very sluggish expansion of the existing transmission line capacities, it seems to be quite unrealistic to fulfil this ambitious goal.
But nevertheless this development shows the trend of renewable energy production in Ger-many towards the fertile offshore technology. Until 2020 there could be wind turbines with an installed capacity of up to 51 GW in opera-tion as shown in F i g u r e 1 which could feed in up to 63 % of today’s German peak load.
Feed- in cha rac t e r i s t i c s and fo recas t e r ro r s
At a first glance, the wind power feed-in char-acteristic for a longer time period, for example one year, seems to have a very high dynamic between low wind and high wind periods with very high power gradients. But if we take a more detailed look to a smaller time period, for example one or two days, the wind power profile is relatively smooth if it is averaged over Germany. Of course there are still high power gradients of up to several GW per hour, but with improved forecast models it is pos-sible to foresee the power feed-in with an as-tonishing accuracy. Therefore, power plant scheduling can be adjusted according to the forecast reports with a forerun of about 4 hours for intra-day corrections of conven-tional thermal power plants.
For example within the control area of 50 Hertz Transmission GmbH, one of the four German transmission system operators (TSOs) and which is the TSO with the highest installed wind power capacity of more than 11 GW (41 %), the power gradients in 2009 amounted to up to ±780 MW within a quarter hour pe-riod and up to ±1.7 GW within an one hour period. For a whole day the maximum power difference for the wind power feed-in was up to 7.7 GW.
The integration of such high amounts of wind power leads more frequently to situations where system stability, load flow restrictions and therefore the safety of supply have to be monitored critically by the TSO staff. In these
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cases, as occurred on the first weekend in Feb-ruary 2011, the transmission line system is characterised by a very high power exchange with the neighbouring transmission line sys-tems of other TSOs. This high load flow, among others through the German neighbour-ing countries, into the other German control areas is regulated by the so-called “horizontal wind compensation” within Germany and leads to periodically occurring load flows into the low wind feed-in areas in the South-West-ern part of Germany. The “horizontal wind compensation” arrange the wind power feed-in so that all control areas are involved in the wind integration issue according to the share of network load compared to the total German network load. In this context the schedules of all non-renewable power stations have to be adjusted according to wind power feed-in. At first this adjustment of schedules is based on the day-ahead wind forecasts which could have high forecast errors of several GW. Hence in the next step the schedules are adjusted ac-cording to the intra-day forecasts as well to minimise the remaining use of secondary and tertiary power reserves. If the TSO determines that there will be problems with the observ-ance of some load flow restrictions on single transmission lines, the so-called power plant re-dispatch is used to release a certain amount of power from these highly loaded transmis-sion lines by directly manipulating the power plant schedules in agreement with the power plant operators at the beginning and the end of these lines. Today, as reported by the TSOs, the re-dispatch costs are one of the main cost drivers for the transmission system operation charges.
But despite distinct improvements of the wind forecast models within the last years, a certain amount of wind power is determined not be-
fore a forerun of four hours. In these cases the only way to react to these forecast errors is the use of tertiary control reserves which are nor-mally held available by the on-line power plants or quick-start capable power stations like gas turbines or pumped storage power sta-tions. For the forecast errors that are deter-mined not before a quarter hour the primary and secondary control reserves have to be used.
Therefore, in the future it will be necessary that the wind turbines will be able to contrib-ute to the reserve power market to support the conventional power plants and to increase the safety of supply in high wind power periods.
Photovoltaic (PV) power feed-in in Germany
Cur ren t s i t ua t ion and t r ends fo r PV
In 2010 the photovoltaic sector experienced a real boom. Therefore, the installed capacity of photovoltaic systems was increased compared to the previous year by 80 %. The installed capacity was expanded by nearly 8 GW from 9.6 GW to more than 17 GW. The energy fed-in increased from 6.7 TWh in 2009 to 12 TWh in 2010 [13]. This means that in Germany about 900 full-load hours were reached aver-aged over all PV systems.
Although the legal refunds for PV energy were reduced continuously within the last years, to-day’s predictions for solar energy assume that up to 52 GW of PV systems will be installed until 2020. But with regard to the growth of 2010, the annual growth rates for the next years will be distinctly lower and could be in the region of 2 or 3 GW per year as shown in F i g u r e 2 .
Feed- in cha rac t e r i s t i c s and fo recas t qua l i t y
By nature the feed-in characteristic of PV is generally more foreseeable than the wind power because the solar power feed-in nor-mally correlates to the angle of incidence over the day. Hence on a sunny day with less cloud-iness, the maximum power feed-in is reached at noon. Due to the change of the angles of incidence over the year, the efficiency of the PV systems is higher in the summer period. But nevertheless the solar power feed-in is re-lated to forecast errors, too. In the case of increasing cloudiness, the efficiency of the PV systems is reduced intensively because the
Wind onshore Wind offshore
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Figure 1. Future trend of the installed wind turbine capacities in Germany until 2025 (own expectation with reference value for 2020 according to the DENA II study [11]).
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Figure 2. Future trend of the installed photovoltaic capacities in Germany until 2025 (own expec-tation with reference value for 2020 according to the prediction of the German TSOs).
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VGB PowerTech 8/2011 37
photovoltaic cells primarily use direct solar radiation while solar thermal systems can use the diffuse radiation as well. In the case of a very sunny cold winter period, the PV effi-ciency and power feed-in can be almost as efficient as in the summer because the level of efficiency of the photovoltaic cells, which consist of a semi-conducting material, is high-er at colder conditions.
Thus, despite the lower quantity of sunshine hours in winter, the power feed-in can reach up to more than 70 % of the installed capacity as occurred in Germany on May 7, 2011. On
that day, the midday PV peak amounted to 12 GW. On such a sunny day, the feed-in char-acteristics are similar to a half sine oscillation. Therefore, the ramping rates of the PV are similar to the derivatives of a sine function which means that the highest ramping rates occur between 8 and 10 o’clock in the morn-ing and between 2 and 4 o’clock in the after-noon.
The forecast models for solar power feed-in are still developing and so today forecast er-rors of several GW are still possible if the me-teorological conditions are changing quickly.
Therefore, at the moment an estimation of the forecast errors of solar power is hardly appre-ciable.
Correlation between wind, PV and the network load
Cor re l a t ion be tween wind and PV
Basically over the year there are seasonal dif-ferences for wind and solar power feed-in. As expected, the majority of solar energy is in-jected within the summer period whereas the majority of wind energy is injected in the au-tumn and winter period as well as at the begin-ning of the spring period. But nevertheless fi-nally there is no guarantee for a foreseeable long-term safety of supply by intermittent re-newable energy sources without having suffi-cient storage capacities. Therefore, there will occur periods even for several weeks or in the worst case several months in the future where almost the whole network load has to be cov-ered by conventional power plants. This could change earliest if several new storage systems will be installed with storage capacities of sev-eral TWh. But even with these storage capaci-ties a substantial shutdown of several conven-tional power plants will be possible only if there will be enormous excess capacities for wind and solar energy to fill the storages when the intermittent power supply is high for a short time to store this excess power under consideration of the enormous storing losses.
As the solar and wind power production is naturally a stochastic occurring process it is absolutely possible that high wind and high solar power feed-in are occurring on the one hand at the time and on the other hand both energy sources contribute nearly nothing to cover the network load. For example at the be-ginning of 2011 a very long period of several weeks with very low wind power production occurred in Germany with power values below 1 GW.
To illustrate some worst case scenarios that could threat the network stability in terms of controller stability and enough reserved con-ventional power capacities in F i g u r e s 3 , 4 , 5 , 6 and 7 some of these inconvenient com-binations of high wind and photovoltaic power at low network load periods were picked out.
Cor re l a t ion be tween so la r r ad ia t ion and ne twork load
The network load normally increases drasti-cally between 6 and 10 o’clock in the morning and reaches its peak load at high noon. At the same time, the PV power production increases on a sunny day. Hence this correlation reduces the dynamics of residual load that has to be covered by conventional power plants. But in contrast to the morning, in the early evening the solar power production does not correlate
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38 VGB PowerTech 8/2011
to the network load at all. In this case the net-work load does not decrease until 8 pm while the photovoltaic power decreases massively between 2 and 6 pm.
With the actually installed capacities for PV, the solar power acts like a peak shaver for re-sidual load. Therefore, at the time of the peak load, the demand for peak load power plants is reduced. Basically this is a positive effect but to increase the solar energy fraction from to-day 2.3 % in Germany to more than 10 % in 2020, additional high PV power capacities have to be installed within the next 20 years. So in the future there will be new peaks in the residual load created by the PV, one in the morning and one in the evening. In addition to these new peaks, the high PV power produc-tion will force conventional power plants to operate in lower partial loads or even shut-down for several hours every day. This chang-ing power demand could then lead to a demand of up to 30 GW for flexible conventional pow-er on each high PV day.
Long-term integration of wind and solar power into the network
operation strategies
Bas ic r equ i r emen t : Gr id expans ion
As reported by the DENA II study, a massive expansion of the existing grid by more than 3,000 kilometres is instantly needed to inte-grate the planned high renewable power pro-duction into the electrical energy supply sys-tems on the transmission and distribution sys-tem levels.
But until now, the grid expansion is making only very low progress in Germany. These de-lays in grid expansion are the reason for ongo-ing and increasing problems with wind and PV power feed-in because the existing grid hits its technical limitations with increasing frequency in terms of transmission line limita-tions and transformer full load capacities. Es-pecially the distribution systems are striking their maximum capabilities in periods with
very high wind power feed-in already today. In these cases, the wind power feed-in has to be limited by the TSOs and distribution system operators (DSOs) which mean to shut down wind turbines. In the future, the offshore wind farms in the North will exacerbate this prob-lem because the majority of power has to be transmitted to the Southern part of Germany with its big urban areas.
Fu tu re need o f s to rage sys t ems
Today, only pumped storage power stations (PSPS) are available to store excess energy for a longer period on a larger scale. But these storage capacities will not be sufficient to solve the bottleneck problem of the power grid in Germany in periods of high intermittent re-newable energy production because the total storage capacity is limited to about 40 GWh only and an installed power of about 7.1 GW in pump and turbine mode today.
Besides the question of sufficient storage ca-pabilities and the financial consequences due to this expensive technologies with regard to the electrical energy price, it is not sure to which extent the grid expansion, that has been identified to be necessary, will be realisable at all. In this context the collision of interests within the society plays an important role, too. Accelerated grid expansion requires under-standing by German people. But even if all
these obstacles can be overcome in the near future, there will remain some fundamental questions regarding some single lines. On the one hand there are enormous costs for new transmission lines with regard to occupancy rates and on the other hand there are the enor-mous costs and storage losses for centralised or decentralised storage systems to avoid transportation over long distances. Therefore, the production of synthetic natural gas (SNG) and other chemical compounds like methyl alcohol by the use of renewable energy or the decentralised storage of electrical energy in car batteries could be the more economical alternative compared to the expansion of some transmission lines. This problem is similar to the expansion of highway systems to holiday areas which will probably only be used to ca-pacity in the vacation periods. Here it is the question how often occurs a high renewable power load flow and is it worthwhile the long-term investment?
Investigation of the power plant and grid operation
Methods and a s sumpt ions fo r t he power p l an t s chedu l ing s imula t ion
To analyse power plant operation, a detailed power plant scheduling model for almost all German power plants with more than 120 MW of rated power was developed within the VGB research projects 283 [9] and 333. This sched-uling model enables a detailed investigation of the operation strategies of single power plants under consideration of primary and secondary reserve power. In addition, the basic technical limitations of common fossil and nuclear pow-er plants are considered like minimum power output, minimum up- and downtimes, ramp-ing rates and start-up and shutdown limita-tions [8]. For more realistic assumptions, the simplified losses of the level of efficiency at part load operation are considered as well. The model was formulated as a mixed-integer lin-ear minimisation problem commonly known as the unit commitment problem. For simplifi-
Figure 6. High PV feed-in summer 2020 (May): eight days with low load on an extended holiday week-end and nuclear phase-out with import/export capability.
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VGB PowerTech 8/2011 39
cation the pumped storage power capacities are simulated by a summarised single storage power station.
To generate the residual power for power plant scheduling, the renewable power production from wind and photovoltaics as well as the run-of-river (RoR) power and combined heat and power fraction (CHP) are assumed as non-dispatchable. To simulate the characteristic of CHP production this fraction was assumed to correlate to the seasonal outside temperatures which have an assumed simplified cosine character over the year. The CHP fraction as well as the whole power plant scheduling process has a resolution of hourly steps with a time horizon of 36 steps for each single opti-misation step. A more detailed analysis of the CHP fraction is still under development and therefore it is not possible to allocate the CHP production to single power plants until now.
A detailed description of the power plant scheduling model and all assumptions as well as the final results and conclusions will be presented in the final report of the research project 333 which probably will be published at the end of 2011.
Fi r s t s imu la t ions fo r s e l ec t ed scena r ios
To illustrate the influence of wind and photo-voltaic power production onto the power plant operation Figures 3, 4 and 5 shows an 8-day winter period for February 2010, 2017 and 2020. In the selected time period, both high wind and low wind power periods occur. The PV power feed-in varies significantly between low and medium values. The period includes a weekend with typical low network load. Each Figure shows an 8-day power plant scheduling simulation which consists of eight single opti-misation steps where each has a 36 hour hori-zon which means there is a overlapping of 12 hours between consecutive days. All sce-narios show an assumed nuclear phase-out until 2022. Therefore, only one nuclear power plant remains in the scenario for 2020. The as-sumptions for the network load are based on the public data available at the ENTSO-E homepage. These time series were scaled to certain annual energy consumption values for each year. For the scenarios shown here, an annual reduction of about 0.35 % was assumed for electrical energy consumption.
The energy values stated on the right in each Figure show the energy feed-in for the select-ed time period sub-divided by the different types of power plants.
The wind power time series used in Figures 3, 4 and 5 were created by an own wind model whereas the time series in Figures 6 and 7 come from the DENA II study [11]. The CHP fraction was assumed to increase from about 12 % in 2010 to about 22 % in 2020 with re-gard to the total electrical net energy con-
sumption. The installed capacities for wind and PV were assumed according to the values in Figures 1 and 2. The time series are based on measurements from 2007 and 2008 and were scaled according to the installed capaci-ties with certain assumption for the full-load hours, the capacity credit and simultaneity factors for the onshore, offshore and PV power feed-in.
The simulations in Figures 3, 4 and 5 show only very slight renewable excess power be-cause these scenarios are not the worst case for the combination of renewable power pro-duction and the network load. In contrast Fig-ures 6 and 7 show a time period with a very inconvenient combination of power produc-tion and consumption for winter and summer. In these scenarios, the renewable excess power increases up to 25 GW. This excess power has to be exported from Germany, or if there is not sufficient transmission line capacity available, it should be stored in large storage systems. Otherwise the renewable production facilities have to be shutdown to guarantee the safety of supply.
Until now no investigations were made con-cerning the system stability for the scenarios shown here with regard to the remaining iner-tia of conventional online power plants. The remaining conventional power plants that are shown in the periods of renewable excess pow-er are used to allocate the total primary and secondary control reserves. This leads to cer-tain fraction of conventional “Must-Run” power. For the scenarios in Figures 3, 4 and 5, it was assumed that the flexibility of hard coal power plants is better with regard to the mini-mum power output limitations and the ability to provide reserve power from low partial loads. Therefore, the remaining power plants are hard coal power plants in these scenarios.
Reduc t ion o f i ne r t i a and s t ab i l i t y o f t he p r imar y con t ro l
For 2020 it is expected to have something around 50 GW of wind power and again about 50 GW of photovoltaic installed in Germany. On days with high wind and solar power feed-in theoretically the whole peak network load of about 80 GW could be cover by renewable energy. However, a certain number of conven-tional power plants have to be online and syn-chronised to the grid in order to have enough primary and secondary control reserves avail-able at any time. If it is assumed that in special situations only 30 % of the network load is contributed by conventional power plants the network time constant TG is reduced by 2/3 as well according to
PG · TATG = ––––––– PN
because the wind turbines and photovoltaic systems do not contribute to the system inertia until now. In this equation PG is the power of the conventional online power plants, TA the
average acceleration time constant and PN the total network load.
Since only conventional power plants provide primary control reserve, in the primary con-trol loop in F i g u r e 8 the acceleration time constant is reduced if the number of remaining online power plants is reduced in periods with high renewable power generation. This reduc-tion of the time constant has the same effect as an increased gain of the control loop of the primary control. In F i g u r e s 9 a and 9 b the network frequency and the provided power of primary control is shown for the case of a net-work time constant of 10s in the first simula-tion and for the case of 10/3s in the second simulation. As illustrated by this simple model of primary control, the reaction of primary control is influenced negatively with regard to controller stability. The system looses its damping because the compensation process accelerates and the overshoot increases. The model used here to show the effect of reduced inertia is only a simplification to show the trend. For more accurate analysis of the sys-tem behaviour under the influence of high re-newable power feed-in, it is necessary to use detailed models of real network control loops as well as an accurate reproduction of the be-haviour of power plants in Germany. It seems to be reasonable to draw the first conclusion after initial considerations, i.e. the intermittent resources contribute to the system inertia to stabilise the system and primary controller stability. In the same way this holds true for the inadvertent exchange power with other countries because an unstable primary control affects this behaviour negatively, too.
Lifetime consumption and improvements of conventional
fossil power plants
In a future power grid with high renewable power feed-in, especially from wind power, it becomes more important as well as economi-cally beneficial for conventional power plants to be able to adjust production in order to bal-ance renewable energies. But due to the long lifetime, the majority of current power plants have been designed decades ago mainly for steady-state operation. Consequently, the fo-cus was put more on reliability and preserva-tive operation than on high dynamics.
The recent and ongoing changes in the energy market in Germany will lead to an increased number of start-ups and load changes, which cause additional lifetime consumption. Im-provements of the existing technologies are required to enable higher dynamics at limited additional stress during transient operation.
This is especially true for coal-fired power plants because of fuel pulverisation in coal mills. These mills have a slow and often un-
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40 VGB PowerTech 8/2011
known dynamic and limit the ramping rates of coal-fired units. Additionally, the boiler itself shows a slow transient response due to its big metal and water masses as well as uncertain-
ties like degradation of the heat transfer due to ash build up on the heating surfaces. To over-come this, the ramping rates are made suffi-ciently slow.
Improvements to this conservative approach could be achieved by the use of advanced control systems, e.g. state observers and model-based control systems or additional
Figure 8. Control-oriented scheme of the primary control referred to the total network to simulate a decreased network time constant TG due to reduced inertia.
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Figure 9a. TG = 10 s, ∆pGv = 1 %, frequency deviation (left), primary control power (center), f-p-locus (right).
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Figure 9b: TG = 10/3 s, ∆pGv = 1 %, frequency deviation (left), primary control power (center), f-p-locus (right).
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VGB PowerTech 8/2011 41
sensors, like for example coal dust measure-ment [1].
For the evaluation of such optimisations of the process and the control system, computer aided simulation of the power plant process could be a powerful tool.
Me thods fo r s imula t ion
In order to judge the expected impacts of a more dynamic power plant operation, a de-tailed, transient model consisting of one-di-mensional or lumped interlinked sub-models, based on thermodynamic fundamental equa-tions, has been created. A 550 MW hard coal power plant, that started its operation in 1994, has been used as reference. This power plant represents the state of the art and is due to its long residual lifetime heavily affected by future changes of the energy market.
The focus of the investigation has been put on the water/steam cycle, the combustion cham-ber of the steam generator and the fresh air passage with coal mills, as well as their dy-namics and the influence of different opera-tion modes on distinct devices e.g. thick-walled headers and turbine shafts.
A simplified schematic of the model is shown in F i g u r e 1 0 . Indicated are the feed water
pumps, high-pressure preheaters (HPP), steam generator, different turbine stages, as well as forced draft and mill fan, air preheater and coal mills. The low-pressure preheaters (LPP) are not part of the power plant model, since they are not highly stressed, due to their low temperature level.
For making simulation-based statements about the influence of different power plant opera-tion modes, the thermodynamical model is coupled to a reduced copy of the power plant control system.
Modelica, which is a modular concept, uses the simulator Dymola® [2, 3] for modelling.
Methods fo r eva lua t ion o f l i f e t ime consumpt ion
With this model it is possible to predict tem-peratures and temperature gradients at points which are inaccessible to measurements like wall temperatures of highly-stressed compo-nents.
For the first 90 minutes of a soft start, the oc-curring wall temperatures of the superheater 2 outlet header are displayed in F i g u r e 1 1 . Obviously the metal temperature at the outside of the wall follows the inner temperature with a certain delay and its amplitudes are consid-
erably smaller. This effect can be explained with time specifics of the heat conduction. The noticeable phase shift of the temperatures leads to relative high temperature differences between the inner and outer phase in case of sharp edged changes in evaporator heating or cooling.
Different controller parameter sets can be benchmarked with a view to preserving opera-tion at concurrently high load dynamics thanks to the evaluation of metal temperatures.
Quantification of the effects of thermal stress on the different components of a plant is a challenging task as the processes of fatigue are complex and highly statistical. For this reason, the results of a fatigue prediction in this context can only be of qualitative nature and should be understood as a trend indicator that is capable of identifying the most stressed components and predict possible side effects of innovative control strategies on this com-plex system. For a detailed investigation of certain components, a FEM analysis consider-ing the installation situation (and with it pos-sible pretensions in the component) and the exact geometry should be taken into account.
However, for a first estimation of the effects of future more dynamic plant operation two dif-ferent approaches are used and should be dis-cussed in the following:
The guidelines of the Deutsche Dampfkesse-lausschuss (2000) TRD 301 and 508 [4, 5] give directives for the estimation of fatigue of thick-walled boiler components under smoul-dering pressure and temperature due to start-up processes.
For this purpose an effective stress range is evaluated with a Wöhler-diagram for crack initiation. The following equation gives the law for calculating the stress range ∆σ.
dm βLϑEϑ∆σi = αm ––– ∆ρ + αϑ –––––– ∆θ (1) ∙ 2sb
∙
∙ 1 – ν ∙
Herein αm, αϑ, dm, βLϑ, Eϑ, ν, ∆ρ and ∆θ denote for mechanical and thermal correction factor for stress super-elevation at branches, mean diameter, mean wall thickness, linear expansion coefficient, Young’s modulus, Pois-
Freshair
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Reheater 2Superheater 4Superheater 2Superheater 1
Cyclone
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Figure 10. Structure of power plant model.
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Figure 11. Metal temperatures in the SH 2 outlet header.
Sa (log)
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Figure 12. Principle of evaluation of component stress for cyclic loading.
Ratio between conventional and renewable generation
42 VGB PowerTech 8/2011
son’s ratio and the range of pressure and tem-perature difference during load change, re-spectively. F i g u r e 1 2 shows qualitatively the evaluation of the working stress during load change. The maximum number of load changes comparable to the actual one is gener-ated from the Wöhler-curve. The percentile fatigue of the actual load change is then:
1e = –– 100 (2) N
This estimation leads to conservative results in order to handle the numerous uncertainties in calculation of working stresses at complex components and material properties.
This method allows to benchmark different and possible future operation modes in terms of their level of deterioration to different com-ponents. In F i g u r e 1 3 is the fatigue of a warm start and several load changes plotted for the in- and outlet headers of the super- and reheaters. It should be stated, that currently normal operation is between 50 % and 100 % load with a ramping rate of 2 % per minute, so the shown load change of higher then 60 % as well as the load gradients of 4 % per minute could be considered as an unconventional op-eration. These load changes corresponds to a possible future operation with a lowered mini-mum load of for instance 35 % and a doubled load gradient.
It could be obtained, that the outlet header of super heater three and four are affected the most, whereas the headers of the reheaters are not or low stressed. Furthermore it could be derived, that conventional load changes less the 50 % barely cause any fatigue, because the stress levels are below the endurance strength.
Considering the flaw growth of pre-damaged component gives a far more sensitive view on the operation mode. The Forschungskuratori-
um Maschinenbau [6] gives guidelines for the calculation of crack progress. F i g u r e 1 4 gives a general overview on crack propagation rate as function of the range of stress intensity factor.
There is a certain load that does not lead to crack propagation (∆K ≤ ∆Kth). In region I to III there is a stable propagation to be expected (∆Kth ≤ ∆K ≤ ∆Kc) which can be conserva-tively estimated by the law of Paris and Er-dogan:
da––– C∆Km (3) dN
Where a, N, C, m denotes for crack length, number of cycles, a case-specific factor and a load specific exponent, respectively.
The stress intensity factor has to be calculated depending on the flaw’s geometry and size and its position within the component. With this tool it is possible to detect the most strained components by comparing the crack growth over a certain reference time period.
In an analogue manner as in Figure 13 the flaw propagation is shown for thick-walled headers in F i g u r e 1 5 .
In contrast to the fatigue also low stress levels of small load changes cause impairment and consequently with this estimation a method is given to evaluate the deterioration potential of load changes during normal operation.
In this way, future demands on power plants which might become necessary in order to re-alize wind integration successfully at control-lable costs can be benchmarked. Since the detailed manner of the plant model does not allow long term simulation over years or even weeks due to high computing time, fatigue has to be extrapolated by decomposing long-term load schedules to base operation scenarios and adding the individual fatigues and crack
growths under the assumption of linear dam-age accumulation. In co-operation with the power plant scheduling model, it is possible to evaluate such long-term load profiles for e.g. a heavy wind month.
This aspect of power plant operation manage-ment will probably become more important due to highly increasing wind power produc-tion and its fluctuating characteristic.
Furthermore the modular structure of the model allows the easy replacement of single components, e.g. life steam temperature con-trol, which enables for example the benchmark of advanced control systems or the implemen-tation of different or additional hardware for different operation scenarios.
References
[ 1] Dahl-Soerensen, M.J., and Solberg, B.: Pul-verized Fuel Control using Biased Flow Measurements. In: IFAC Symposium on Power Plants and Power Systems Control, Tampere (2009).
[ 2] Casella, F. and Leva, A.: Object-Oriented Modelling and Simulation of Power Plants with Modelica. In: proceedings of 44th IEEE Conference on Decision and Control, and the European Control Conference, Sevilla (2005).
[ 3] Casella, C. and Leva, A.: Open Library for Power Plant Simulation: Design and Experi-mental Validation. In: proceedings of 3rd. In-ternational Modelica Conference, Linköping (2003).
[ 4] Deutscher Dampfkesselausschuss: Technische Regeln für Dampfkessel (TRD) 301 Berech-nung auf Wechselbeanpruchung durch schwel-lenden Innendruck bzw. durch kombinierte Innendruck- und Temperaturänderungen. Carl Heymanns Verlag KG (2000).
[ 5] Deutscher Dampfkesselausschuss: Techni-sche Regeln für Dampfkessel (TRD) 508 Zu-sätzliche Prüfungen an Bauteilen berechnet mit zeitabhängigen Festigkeitswerten Carl Heymanns Verlag KG (2000).
[ 6] Forschungskuratorium Maschinenbau: Bruchmechanischer Festigkeitsnachweis für Maschinenbauteile, VDMA-Verlag (2001).
[ 7] VDI/VDE 3508: Blockregelung von Wärme-kraftwerken. Verein deutscher Ingenieure und Verband der Elektrotechnik Elektronik Infor-mationstechnik, Düsseldorf 2003.
[ 8] Carrión, M., and Arroyo, J. M.: A computa-tionally efficient mixed integer linear formu-lation for the thermal unit commitment prob-lem, IEEE Trans. Power Syst., vol. 21, no. 3, pp. 1371-1378, Aug. 2006.
[ 9] Gottelt, F., Ziems, C., Meinke, S., Haase, T., Nocke, J., Weber, H., and Hassel, E.: Auswir-kungen von fluktuierender Windenergieein-speisung auf das regel- und thermodynami-sche Betriebsverhalten konventioneller Kraft-werke in Deutschland, Universität Rostock, Studie, 21. Oktober 2009.
[10] Neise, F.: Risk Management in Stochastic In-teger Programming With Application to Dis-persed Power Generation, Vieweg + Teubner Research, 2008.
[11] dena-Netzstudie II – Integration erneuerbarer Energien in die deutsche Stromversorgung im Zeitraum 2015-2020 mit Ausblick auf 2025 (http://www.dena.de/themen/thema-esd/projekte/projekt/netzstudie-ii/).
[12] strom-magazin.de: Artikel vom 26.01.2011 „Windbranche verfehlt eigene Ausbauziele deutlich“.
[13] strom-magazin.de: Artikel vom 31.01.2011 „Photovoltaik legte 2010 über 80 % zu“. □
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