Impact of wind generation on the operation and development of the UK electricity systems

Electric Power Systems Research 77 (2007) 1214–1227

Impact of wind generation on the operation and development of the UK electricity systems Goran Strbac a,∗ , Anser Shakoor a , Mary Black b , Danny Pudjianto a , Thomas Bopp c a

Imperial College London, London, United Kingdom b CE Electric UK, Newcastle, United Kingdom c Siemens, Erlangen, Germany Available online 17 October 2006

Abstract Although penetration of wind generation may displace a significant amount of energy produced by large conventional plant, there are issues associated with the extent to which wind generation will be able to replace the capacity and flexibility of conventional generating plant. This is important since wind power is variable, so it will be necessary to retain a significant proportion of conventional plant to ensure security of supply especially under conditions of high demand and low wind. Hence, the capacity value of wind generation will be limited as it will not be possible to displace conventional generation capacity on a “megawatt for megawatt” basis. Wind power is variable and not easy to predict, hence various forms of additional reserves will be needed to maintain the balance between supply and demand at all times. Additionally, if the majority of wind generation plant is located in Scotland and the North of England, reinforcement of the transmission network will be needed to accommodate the increases in the north-south flow of electricity. In this paper an assessment of the costs and benefits of wind generation on the UK electricity system is carried out, assuming different levels of wind power capacity. Overall, it is concluded that the system will be able to accommodate significant increases in wind power generation with relatively small increases in overall costs of supply, about 5% of the current domestic electricity price in case of 20% energy produced by wind power. © 2006 Elsevier B.V. All rights reserved. Keywords: Wind generation; Energy; Electricity system

1. Introduction The UK Government has set a target for the connection of major volumes of renewable generation sources so that 15% of the overall electricity consumption is supplied from renewable sources by 2015. The aspiration of the Government, as set out in the Energy White Paper, is that this trend continues and 20% of energy is provided from renewable sources by 2020. Various renewable technologies will contribute to this goal. Given the vast wind resource available and its leading competitive position among renewable technologies, wind generation will be a major contributor to achieving this target. Assuming a wind capacity utilisation factor of 35%, 26 GW of wind generation will produce 80 TWh, which is about 20% of the overall annual UK electricity consumption.

∗

Corresponding author. Tel.: +44 207 5946169; fax: +44 207 5946282. E-mail address: [email protected] (G. Strbac).

0378-7796/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2006.08.014

Integration of wind generation in the operation and development of the electricity system is associated with both benefits and costs. For example, the investment cost of wind generation is greater than that of conventional gas or coal plant. On the other hand, generation of energy from wind saves fuel and hence reduces the cost of system operation. There are a number of issues associated with integration of wind power in system operation and development. Although penetration of wind generation may displace significant amount of energy produced by large conventional plant, concerns over system operation costs are focussed on whether wind generation will be able to replace the capacity and flexibility of conventional generating plant. Furthermore, the location of these new sources will be of considerable importance in assessing the impacts on the transmission and distribution network infrastructure. Given that wind is intermittent, it will be necessary to retain a significant proportion of conventional plant to ensure security of supply especially under conditions of high demand and low wind. Clearly, the capacity value of wind generation will be limited as it will not be possible to displace conventional generation

G. Strbac et al. / Electric Power Systems Research 77 (2007) 1214–1227

capacity on a “megawatt for megawatt” basis. Given that wind power is variable and not easy to predict, various forms of additional reserves will need to be made available to maintain the balance between supply and demand at all times. If the significant on and offshore wind resources in the UK are exploited for generation, an adequate transmission network will become critically important. This will open the question as to what reinforcement of the existing transmission network would be needed in order for this power to be transported to load centres. Wind turbines are generally not able to provide the range of system support services (e.g. voltage and frequency regulation) that are provided by conventional thermal and hydro plant. At relatively low levels of penetration this can usually be tolerated, but at the higher levels indicated by the target it will require systematic solutions in order to maintain stability and integrity of the transmission system. This paper explores the technical and economic issues associated with the integration of wind generation in the operation and development of the future GB electricity system. We have identified and made quantitative estimates of ranges of costs and benefits associated with the integration of wind generation. The costs of the following are considered: • Wind generation (off and on shore), including installation and operation. • Additional cost of balancing the system. • Additional network connection and reinforcement costs. The benefits quantified include: • Displaced fuel costs. • Displaced conventional generation capacity and operation costs. 2. Cost of installation and operation of wind generation The present-day installed cost for onshore wind in the UK is about £650/kW, and for offshore around £1000/kW. The installation costs of wind energy have reduced significantly over the last decade and this trend is likely to continue. A number of recent studies have suggested that the corresponding wind generation installation costs in 2020, onshore, will lie between 55% and 70% of the present level, while offshore costs may be in the range between 40% and 70% of present costs. Operation and maintenance costs for wind plant vary. Onshore values tend to be in a range between £10/kW/yr and £20/kW/yr, while for very large offshore farms values are estimated to fall in the range between £20/kW/yr and £25/kW/yr. In our analysis we will assume equal share of onshore and offshore connections [1]. Given the uncertainty over the future cost of wind energy, we will work with a range of possible costs. One extreme (maximum cost) is determined by assuming no further reduction in cost of wind generation (installation and operating cost), while assuming a 40% decrease in cost at 2020 will be used as the other, minimum cost extreme. We will assume this cost reduction is achieved over the time in a linear fashion.

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Table 1 Estimated range of installation and operation costs of wind generation for various levels of wind penetration Installed wind capacity (GW)

Ranges of cost of wind energy (p/kWh) Expected minimum

Expected maximum

5 10 15 20 25

0.11 0.20 0.28 0.35 0.40

0.11 0.21 0.32 0.42 0.53

Given the assumptions made, the range of values of wind generation costs is estimated for various levels of penetration. All cost components are first annualised and then divided by the total annual energy consumption (400 TWh). Table 1 hence presents installation and operation costs with installed capacity expressed as a contribution to unit electricity price. Thus, the costs and benefits quantified will hence be expressed in terms of p/kWh, which can then be related directly to unit electricity prices. In this context, it is useful to note that the domestic electricity prices currently average about 6 p/kWh in the UK. 3. Cost of real time balancing Generation and demand in an electricity system must be balanced at all times. Traditionally, the balance between demand and supply is managed by flexible generation. Historically, demand is largely uncontrollable although some segments of demand side may be price sensitive. In real time, the output of large conventional generators would generally be adjusted to match any changes in demand. In order to deal with unpredicted variations in demand and generation, the system operator requires appropriate automatic response, to neutralise rapid variations from a few seconds to a few minutes, and reserves to deal with slow variations over time horizons from several minutes to several hours. On average, the system operator commits about 600 MW of dynamic frequency control, while about 2400 MW of various types of reserve is required to manage the uncertainty over time horizons of the order of 3–4 h. These values could be significantly changed in the future considering that wind generation is both variable and unpredictable. 3.1. Variability and predictability of wind power The inherent variability of wind generation will require more resources to be made available in order to manage short-term balancing between demand and supply. However, the amount of additional resource required for managing the unscheduled wind power will not be on a megawatt for megawatt basis. The key factor here is the phenomenon of geographic diversity of individual outputs of wind farms. The output of individual wind turbines is generally not highly correlated, particularly when wind farms are located in different regions. Hence, system operators need to deal with the variability of the net aggregated output of a large group of wind farms, rather than with the variations in the output of individual wind farms.

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Fig. 1. Frequency distribution of changes in wind generation output over 0.5-h and 4-h time horizons.

The magnitude of wind output fluctuations will also strongly depend upon the time horizon considered. Clearly, the magnitude of wind fluctuations increases as the time horizon under consideration becomes longer. Statistical analysis of the fluctuations of wind output (for an assumed annual wind generation profile) over the various time horizons can be performed to characterise the variability in wind output. The fluctuations of wind power output, as a percentage of wind capacity installed, over 0.5-h and 4-h time horizons are shown in Fig. 1. Standard deviations of the change in wind output over these time horizons were found to be 1.4% and 9.3% of the total installed wind capacity, respectively. If, for example, the installed capacity of wind generation is 10 GW (given likely locations of wind generation), standard deviations of the change in wind generation outputs were estimated to be 140 MW and 930 MW over the 0.5-h and 4-h time horizons, respectively. This means that the range of possible changes in wind output in the 0.5-h time horizon would be about ±420 MW and for time horizon of 4 h about ±2790 MW. The results obtained broadly agree with earlier studies [2–4]. However, the predictability of wind variations in managing demand and generation balance is very important. If the fluctuations of wind were perfectly predictable, the additional cost of operating the system with a large penetration of wind power would not be very significant provided that there is sufficient flexibility in conventional plant to manage the changes in wind. Clearly, the present system can deal with very large predictable variation in demand (changes in demand of 12,000 MW over the morning demand build-up are routinely managed). For short-term wind forecasts, up to several hours ahead, persistence-based techniques are generally used, while for longer horizons, forecasts based on meteorological information are frequently applied.1 Standard deviations of wind forecast error should be combined with the standard deviations of demand/generation forecast errors to determine the level of the overall mismatch (error) that need to be managed. This is calculated following the standard statistical approach of combining the independent (uncorrelated) errors (the mean square error of the combination is the sum of the mean square errors). Assuming that the standard devia1

There is considerable activity in the area of wind prediction and although significant developments have been lately made with wind energy forecasting tools, further improvements in the accuracy of wind prediction are expected.

tion of the forecast error of changes in demand (and conventional generation output) over the time horizon of a 0.5-h is 340 MW and that the standard deviation of change of wind output over the same time horizon is 140 MW (for 10 GW of installed capacity) the resulting standard deviation of the  mismatch between demand and generation is 368 MW (= 3402 + 1402 ). This also shows that adding 10 GW of wind capacity only marginally increases the standard deviation of the overall forecasting error in the time horizon of 0.5-h (from 340 MW to 368 MW). The reserve and regulation capacity needed to deal with the uncertainty (given the lead time) is usually defined as the variation contained within three standard deviations of the overall system forecasting error. This amount of capacity committed to provide reserves will contain 99% of the possible mismatches between demand and supply in the characteristic time horizons (Fig. 1). For the example discussed above, the system would need be able to absorb fluctuations of ±3 × 368 MW = 1143 MW, in the time horizon of a 0.5-h. 3.2. Need for additional reserve and cost estimates Penetration of wind generation will impose additional requirements on the remaining large conventional plant to deliver both the flexibility and reserve necessary to maintain the continuous balance between load and generation, which will inevitably have cost implications. When analysing the need for additional continuous response and reserve requirements time horizons of 0.5-h and of 4-h, respectively, are normally considered [5]. The reserve requirements are driven by the assumption that time horizons larger than 4 h will be managed by starting up additional units, which should be within the dynamic capabilities of gas fired technologies. Over that time horizon, the maximum change in wind output could be about 25% to 30% of the installed wind capacity. Consequently corresponding amounts of reserve will need to be made available to accommodate these changes [5]. The second and third columns of Table 2 present estimated amounts of additional reserve required to accommodate changes in wind output for various levels of penetration, considering a 4 h time horizon. When providing continuous spinning reserve a synchronised plant must run part loaded. Hence the direct costs of its provision Table 2 Reserve requirements and cost Installed wind capacity (GW)

0 5 10 15 20 25

Additional reserve requirements (MW)

Range of cost of additional reserve (p/kWh)

Expected minimum

Expected maximum

Expected minimum

Expected maximum

0 340 1172 2241 3414 4640

0 526 1716 3163 4706 6300

0.000 0.002 0.008 0.015 0.022 0.030

0.000 0.005 0.015 0.027 0.041 0.055

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Fig. 2. Marginal cost of electricity and increase in CO2 emissions.

Fig. 3. Allocation of reserve between synchronised and standing.

are driven by fuel cost, the efficiency of plant when operating part loaded, and the operation and maintenance cost due to additional wear and tear. Coal and gas units operate less efficiently when part loaded, with an efficiency loss of about 20% (losses in efficiency of coal plant are generally lower, while these could be higher in case of new gas plant). As a consequence, the unit cost of electricity production is higher at minimum stable generation compared to full load operation. A linear relationship between cost of electricity and loading level is assumed in this paper, as shown in Fig. 2. The marginal cost of electricity at MSG is assumed to be 20% more expensive than that at full load. Similarly, the CO2 emissions will also increase. A linear relationship is assumed and shown in Fig. 2. At MSG the CO2 emissions are assumed to be 0.72 t/MWh and at full load 0.6 t/MWh. For the evaluation of the cost of reserve two scenarios are investigated, with fuel cost of £10/MWh and £20/MWh. The results are presented in the last two columns of Table 2. The cost is obtained by assuming that the cost of holding synchronised reserve will be, on average, between £2/MW/h and £4/MW/h, for fuel cost of £10/MWh and £20/MWh, respectively, given the assumptions of efficiency losses of about 20% and that all wind power output can be absorbed by the system. As we will show, for relatively high penetration of wind power (above 20%) in systems with the conventional generation dominated by plant of low flexibility (such as nuclear), it may not be possible to absorb all wind power generated. In such a system, reserve provided by standing plant (OCGT or storage) will increase the capability of the system to incorporate wind power.

The vertical line in Fig. 3 shows a possible split between synchronised and standing reserve. Synchronised reserve will be used to accommodate relatively frequent but comparatively small imbalances between generation and demand while standing reserve will be used for absorbing less frequent but relatively large reductions in wind power. Assuming a flexible generation system, the allocation of reserve between synchronised and standing plant will be a trade-off between the cost of efficiency losses of part-loaded synchronised plant providing synchronised reserve (plant with relatively low marginal cost but running at all times) and the cost of operating less efficient standing plant providing standing reserve (plant with relatively high marginal cost but running only occasionally). Application of standing reserve could also increase the amount of wind power that can be absorbed as fewer generating units will be scheduled to operate, leaving more room for wind. This is particularly relevant for relatively large penetration of wind, when high wind conditions coincide with low demand in systems with relatively inflexible conventional generation. We have therefore studied the behaviour of three generating systems of different flexibilities, for the level of wind power penetration of 20%. Among dynamic parameters of generating units considered, the ability of plant to be turned on and off and the ability to run at low levels of output (minimum stable generation) were found to play a critical role. On the other hand, ramp rates were not found to be particularly important, as long as the maximum rate of change of output of plant that provides synchronised reserve was above 5 MW/min, which is well within existing gas and coal technologies. The characteristics of the systems studied are presented in Table 3. The key differences between these systems are in their ability to absorb wind power. The so-called base load segment of the generation mix considered consists of generally inflexible plant that runs at full output and cannot be turned on and off frequently (such as nuclear). We have also incorporated a segment of the generation mix that includes plant that is only moderately flexible, that can be turned on and off but with somewhat limited ability to run part loaded, i.e. with relatively high minimum stable generation, and a segment of very flexible plant. Due to the inability of the low flexibility system to substantially reduce the output from synchronised conventional generation, it will not be able to absorb the entire production of wind generation and the excess of wind power will be wasted if some form of stor-

3.3. Allocation of synchronised and standing reserves In addition to the synchronised reserve, the balancing task can be supported by flexible standing reserve, which is supplied by higher fuel cost plant, such as open cycle gas turbines (OCGTs) and storage facilities. Application of standing reserve could in principle improve the system performance through reduction of the fuel cost associated with system balancing. This is achieved by reducing the amount of synchronised reserve committed. This increases the efficiency of system operation by reducing the number of part-loaded generators. This also reduces the amount of CO2 produced by reserve plant, thereby increasing the benefit of wind energy in terms of emissions reductions.

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Table 3 Characteristics of generation systems considered Generation system

Parameters (%)a

Inflexible generation

Generation of moderate flexibility

Flexible generation

Low flexibility (LF) generation system

MSG Capacity installed (GW)

100 8.4

77 26

50 >25.6

Medium flexibility (MF) generation system

MSG (%) Capacity installed (GW)

100 8.4

62 26

50 >25.6

High flexibility (HF) generation system

MSG (%) Capacity installed (GW)

N/A 0

N/A 0

45 >60

a

MSG stands for minimum stable generation and is expressed as percentage of the maximum generator capacity.

age is not used. We have assumed the fuel cost of moderately flexible and flexible generation to be £20/MWh. The cost of inflexible generation has no impact on the value of storage given that it must run in both systems with and without storage. CO2 emissions for the moderately flexible and flexible generation are assumed to be 0.4 t/MWh. Storage plant is assumed to be 70% efficient. In order to study the performance of these different generation systems, in contrast to the above analytical approach to estimating the cost of reserve, we have developed a significantly more detailed simulation model to analyse, hour by hour, a year round operation of the system with taking into consideration daily and seasonal demand variations and variations in wind output. One of the key advantages of this approach is the ability to optimise more precisely the amount of synchronised reserve required (in each hour) as a function of wind output forecasts and the amount of standing reserve available. This was shown to be an important advantage of the simulation approach over the statistical assessment employed in earlier studies, particularly in the context of the accuracy of the quantification of the cost of operation, the value of storage and its additional value when compared with OCGT plant.2 The simulation model is run for a time horizon of 1 year and the following information is obtained: • annual energy produced by conventional plant; • annual generation cost including cost associated with carrying spinning reserve; • annual energy not supplied (due to insufficient reserves and constraints on ramp rates); • annual wind generation curtailed (due to minimum stable generation constraints and constraints on ramp rates); • annual charge and discharge energies (when a storage system is used); • annual energy produced by OCGTs (when OCGT plant is used); • annual CO2 emissions. 2

The model employed does not explicitly consider start-up cost and hence the potential benefits arising from reducing the number of start-ups of generating units as a result of the application of flexible storage or OCGTs are not included. We however do not expect this approximation to make a significant impact on the relative competitiveness of storage over OCGT plant, given that the number of start-ups is expected not to be very sensitive with the choice of the form of standing reserve used (OCGT or storage technology).

Comparing the results of the individual studies the following key outputs are obtained: (i) The value of standing reserve (for both forms—storage and OCGT plant) is quantified by evaluating the difference in the fuel cost (and CO2 emissions) when intermittency is managed via synchronised reserve only, against the performance of the system with various amounts of standing reserve. (ii) The relative competitiveness of storage against OCGT technology is then evaluated as the difference in savings in fuel cost delivered by storage versus OCGT plant. 3.4. Storage versus OCGT Standing reserve can be provided by conventional flexible plant and storage. Energy storage systems appear to be an obvious solution to dealing with the intermittency of renewable sources: during the periods when wind generation exceeds the demand, the surplus could be stored and then used to cover periods when the load is greater than the generation. However, it is important to remember that bulk energy storage is only one of the options available for managing intermittency. In this context OCGT technology can be considered as a principal competitor to storage (assuming similar levels of plant reliability). Storage is generally more valuable than OCGT plant when providing standing reserve, particularly in generation systems with low flexibility (e.g. with significant proportion of inflexible nuclear generation). The following factors will determine the relative competitiveness of storage- and OCGT-based standing reserve: (i) Storage can provide both upward (“positive”) and downward (“negative”) reserve whilst an OCGT plant can provide only upward regulation. In the case where generation is lower than demand, storage is discharged, whereas when demand is lower than generation then storage can be charged to balance the system. The ability of storage to provide this “negative” reserve will be of critical importance when low demand conditions coincide with a high level of output of wind generation. The actual magnitude of this inherent benefit will be driven by the amount of wind installed and the flexibility of the generation system. (ii) The cost of running storage will be driven by its efficiency and the cost of base load generation, while the cost of run-

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ning OCGTs will depend on fuel used and the efficiency of the technology employed. The overall effect of the above factors on the relative performance of storage versus OCGT plant will be system specific and will depend on the amount of standing reserve utilised. Clearly, the impact of (i) will depend on the amount of wind installed and the flexibility of the generation system, while the importance of (ii) will be increasing with the increase in utilisation of standing reserve. The value of storage in providing standing reserve by storage is calculated by evaluating the difference in the performance of the system when intermittency is managed via synchronised reserve only, against the performance of the system with storage facilities used to provide standing reserve. We have calculated the total annual reductions in fuel cost that is attributable to storage. We have also calculated equivalent capital values of these savings in annual fuel cost using a rate of 10% over a 25-year time period. This information represents the capital value of storage, as a function of the capacity installed, representing the maximum allowed revenue that storage developers may expect. In order for storage technologies to be competitive, the manufacturing cost must be below its value. Reductions in fuel utilisation in the system with storage are directly reflected in the improvement of CO2 performance of the system and are system specific. Therefore, we have also calculated the amount of CO2 that can be saved by storage. Finally, we quantify the savings in wind energy curtailed by using storage. By applying storage, the amount of synchronised reserve committed can be reduced and this leads to an increase in the amount of wind power that can be absorbed. This is a consequence of operating fewer conventional generating units and hence reducing the amount of wind that has to be rejected when high wind conditions coincide with low demand. Any remaining surplus of wind can be absorbed by charging the storage facilities. Within our methodology we calculate the amount of wind that would need to be curtailed in order to maintain a stable operation of the system. However, the value of wind curtailed cannot be used to directly measure the benefits of storage because the storage efficiency is a key factor here. For example, having a very large but very inefficient storage facility could reduce the amount of wind curtailed (as all surplus can be stored) but very little of the wind stored would be actually saved. Therefore, reductions by storage in the amount of energy produced by conventional plant are used to measure the net effect of wind energy saved. In effect this reduction in energy comprises the utilisation of wind, as shown by the reduction in wind curtailment, but with the deduction of energy lost due to storage efficiency losses. The annual reduction of fuel cost obtained from the application of storage is shown in Fig. 4. The value of storage is higher in the system with less flexible generation and reduces with the increase in storage capacity installed. Fig. 5 presents the capital value of storage capacity as a function of installed capacity. The CO2 savings, shown in Fig. 6, are higher in systems with less flexible generation and increase with the increase in storage

Fig. 4. Reduction of fuel cost with energy storage.

Fig. 5. Capitalised value of reduction of fuel cost with energy storage.

capacity installed (the latter is specific to the system studied and the range of capacities applied in this work). For example, a storage system of 3 GW installed in a generation system of medium flexibility (MF case), would save 3.2 million tonnes of CO2 per annum. This amount of CO2 saved, would be emitted by a conventional plant of more than 900 MW running at full output for a year. Fig. 7 shows the net reduction in energy produced by conventional plant. For the LF case, benefits of storage are significant. The reduction of the output of conventional plant is between 8.9 TWh/p.a. and 12.3 TWh/p.a., depending on the size of storage capacity installed. The contribution to savings of wind energy is significant as the reduction in output from conventional plant is more than 10% of the total wind contribution. More flexible systems can absorb more wind and the benefits

Fig. 6. Benefits of storage: reduction in CO2 emissions.

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However, for flexible generation systems (of dynamic characteristics similar to those of today’s CCGT and OCGT technologies), and for wind power penetration levels in the order of 20%, OCGT technology is likely to continue to be more competitive for system balancing purposes. More work is however required to understand the implications of significantly higher levels of wind penetrations and the role that storage could play in these circumstances. 3.5. Impact of wind generation on frequency response

Fig. 7. Benefits of storage: reduction in energy provided by conventional generation.

in terms of reduction in output from conventional plant reduce. For the HF case; however, the reduction in wind curtailment due to the presence of storage is relatively small, as the system is highly flexible. For large storage capacity, a significant amount of reserve is provided by storage and the increased utilisation of storage will lead to an increase in energy produced by conventional plant necessary to charge storage. However, note that although in the HF system supported by storage, more energy is produced by conventional plant (to cover losses in storage plant), the production cost is lower. For 5 GW of storage, the total amount of energy produced by conventional plant is increased by 219 GWh/p.a. (Fig. 7), while simultaneously, the cost of production has reduced by £99 m/p.a. (Fig. 4), and the amount of CO2 emitted is reduced by 1.9 million tonnes (Fig. 6). The system with storage can clearly run more efficiently, because storage, as a standing reserve provider, reduces the amount of part-loaded plant. If the future UK generation mix consist of inflexible base load plant, accompanied with moderately flexible plant that can be turned on and off but with somewhat limited ability to run part loaded (with relatively high minimum stable generation), and for wind power penetrations levels in the order of 20% and above, storage could play a useful role in improving the ability of the system to absorb wind generation. The main benefits of storage over conventional forms of standing reserve will be in its ability to store wind during low demand and high wind conditions, when inflexible plant is required to continue running. Part of the energy from wind that is being saved (depending on efficiency) can be made available subsequently.

As will be discussed below, the penetration of intermittent wind generation will increase the need for continuous frequency regulation (due to a reduction in the accuracy of dispatch instructions). Wind generation could also increase the need for frequency response, although this depends upon the extent to which wind generation will be able to satisfy future Grid Code requirements. The effect of rapid variations in the output of individual wind generators will be relatively minor, as the level of correlation between the fluctuations of the individual wind farms will be small in the time horizon considered (several seconds to a minute). It follows that the direct impact of wind generation on dynamic frequency control service may be small. However, as the volume of wind generation increases, the error in the forecast of its aggregate output will also increase. This will increase dispatch errors, which will be neutralised by automatic governor actions, placing additional requirements on continuous frequency response. Estimates for the continuous response service requirement with respect to wind power capacity installed are as presented in Table 4. We can observe that the increase in demand for continuous frequency regulation will be relatively small for modest increases in wind power connected. However, at the level of 25 GW of wind, the requirement for additional continuous frequency regulation is likely to double. The expected minimum figures correspond to a highly diversified wind output. Given the current expected distribution of wind farms in the UK, with large concentrations in The Wash, Thames Estuary, North West England and Scotland, the need for continuous frequency response is likely to be closer to the expected maximum. In line with the above discussion we assumed that the average fuel cost of holding response is between £2/MW/h and £4/MW/h

Table 4 Additional requirements for continuous frequency response and cost Installed wind capacity (GW)

Required additional continuous frequency response (MW)

Range of additional cost of continuous response (p/kWh)

Expected minimum

Expected maximum

Expected minimum

Expected maximum

0 5 10 15 20 25

0 34 126 257 413 585

0 54 192 382 596 827

0.0000 0.0004 0.0017 0.0034 0.0054 0.0077

0.0000 0.0009 0.0034 0.0067 0.0104 0.0145

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(driven by fuel cost and losses in efficiency), and that the delivery of 1 MW of dynamic response requires about 2 MW of de-load. The last two columns of Table 4 summarise these additional response costs. It is important to mention that demand currently makes a significant contribution to providing non-dynamic response and that the role of demand could increase which would reduce the cost of both reserve and response. 4. Value of fault ride through capability Fig. 8. Frequency regulation services (from NGT SYS).

The design characteristics of conventional synchronous thermal and hydro generators enable the plant to contribute to the provision of system support services (dynamic voltage and frequency regulation) that are critical for the stable operation of the system. Wind generation uses different technology from conventional plant and generally, at the moment, may not able to provide a similar range of support services to the system. At relatively low levels of penetration this can usually be tolerated. However, operating the system with large amounts of such plant could pose major challenges in terms of sustaining system integrity. Hence, a number of transmission network operators have recently set out proposals that specify requirements for the connection of wind generation equipment to the transmission network. In a number of countries, Grid Codes have been reviewed to reflect the trend of increased levels of penetration of wind generation. In addition to frequency and voltage control, communication, dispatch, etc., one of the key issues is associated with the ability of this plant to maintain stable operation during faults on the transmission network, in order to avoid widespread tripping of wind generation and loss of substantial amounts of active power generation. This is known as fault ride through capability.3 The primary objective of this investigation was to estimate the order of magnitude of additional system cost that would need to be incurred, in order to accommodate wind generation of varying degrees of the capability to withstand faults on the UK transmission network. In cases where wind generation is not immune to faults, the system will need to deal with losses of wind generation in addition to losses of conventional plant. This will increase the demand for frequency regulation services. As discussed above, in order for conventional plant to provide frequency response it must run part loaded. Thermal units operate less efficiently when part loaded, with an efficiency loss of between 10% and 20%. The cost of additional frequency regulation services therefore can be used as measure of the value of fault ride through capability.

3 For the duration of a fault on the transmission network, the voltage on the faulted phases is assumed to be zero at the point of fault. Considering relatively low transmission circuit impedances, such fault conditions can cause a large transient voltage depression across wide network areas. Conventional synchronous generators are expected to trip only if a permanent fault occurs on the circuit they are directly connected to. However, other electrically nearby generators that are connected to healthy circuits will remain connected and stable after the faulted circuits are disconnected.

For this purpose, we have developed a generic dynamic generation system model to examine technical, economic and environmental performance of the UK system operating with a significant amount of wind generation (10 GW). This includes implicit modelling of different degrees of ability of wind turbine generators to ride through to faults. In the UK frequency is managed by a combination of (a) continuous and (b) occasional response services. These two services are illustrated in Fig. 8. Continuous response is provided by generation equipped with appropriate governing systems that control their outputs to neutralise the frequency fluctuations that may arise from relatively modest changes in demand and generation. Traditionally, large synchronised generators, instructed to operate in frequency sensitive mode, have provided this service. The objective of occasional response is to contain significant and abnormal frequency excursions caused by sudden mismatches in the generation/demand balance, e.g. loss of generation. Primary frequency response requires the most rapid generator response. The generators must be capable of increasing their active power output within 10 s of predefined system frequency excursions, and be capable of maintaining this response for a further 20 s. Generators that provide secondary frequency response services must be capable of increasing their active power output within 30 s of predefined system frequency excursions, and be able to maintain this response for a further 30 min [6]. The system frequency drops sharply following a sudden loss of generation, as illustrated in Fig. 8. The rate of change of the frequency deviation following the loss of generation is proportional to the magnitude of the loss and inversely proportional to the kinetic energy stored in the power system. This initial rate of frequency change df/dt can be calculated in accordance to Eq. (1) (P denotes the amount of generation lost and Ekinetic stands for the stored kinetic energy of the power system considering generation and demand side):  dfpu  P = (1) dt t=0 2 × Ekinetic Given that the kinetic energy stored in the system is proportional to the amount of rotating machines on the system, the most critical condition will be at times of low demand. Assuming the existing limit of 1320 MW for the maximum credible

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Fig. 9. Generic system to model primary frequency response.

loss of generation and assuming an average inertia constant of H = 6 s, the maximum initial rate of the frequency drop, observed during minimum load conditions (e.g. 20 GW), would amount to 0.275 Hz/s. Clearly, by increasing the loss of generation, the rate of change of the frequency deviation will increase; and the time available for frequency response to develop and to contain the frequency drop will reduce. Generators operating in frequency sensitive mode (including load disconnections triggered by low frequency relays) would need to react sufficiently fast not to allow the frequency to drop below 49.2 Hz (see Fig. 8). On the other hand, inertial effect decelerates the rate of change of the frequency fall. As, currently, doubly fed induction generation based wind turbines do not produce inertial effects, this will have an adverse impact on the system frequency performance and increase the need for frequency response services. 4.1. Description of the model To study the performance of the UK generation system, we developed a generic model of the system primary response characteristics. The model is used to estimate the maximum loss that the system can withstand and the corresponding response requirement. The single busbar governor-turbine-power system model shown in Fig. 9 is used. All generators are modelled as one lumped generator and the loss of generation is modelled as a superimposed load change. Following a sudden loss of generation, the frequency will start falling (f), and the rate of change of frequency will be determined by the system’s inertia. We also included the positive effects of frequency sensitive load (D). The droop settings (Req ) of the governors will dictate the need for the increase in the generators’ active power output. However, the speed of the reaction of the governor and turbine will be driven by the values of their respective time constants (T). The value of these time constants will drive the delay in the response of the generators. Finally, the increase in generators active power output will not only reduce the rate of change of the frequency drop but will contain the frequency fall and eventually increase the system frequency.

Maximum credible loss is modelled as the sum of the maximum expected loss of conventional generation4 and a certain amount of wind generation. The latter is modelled as the product of the actual wind output at the particular 0.5-h and the wind power loss factor (WPLF). The WPLF defines the proportion of wind generation that could be lost as a result of a critical fault on the transmission system. The WPLF will be driven by the location of wind farms and the degree of fault ride through capability. For example, a WPLF of 10% represents a scenario in which up to 10% of the actual wind generation output in the particular 0.5-h could be lost due to a fault at a critical location. A WPLF of 0% represents the situation where wind generation is a fully compliant with the proposed grid code. The simulations were carried out for two generation systems of different levels of flexibility: a high flexibility system (optimistic scenario) in which all generators could provide frequency response, and a low flexibility system (pessimistic scenario) in which only half of the total number of generators take part in providing the service. Based on the developed dynamic response model shown in Fig. 9, we simulated year round operation of the system. A number of case studies were performed to analyse the cost implications of the potential need to deal with the increased magnitude of generation losses in the UK system, including different magnitudes of conventional generation losses and different systems flexibility maximum. For each of the scenarios analysed, WPLFs were varied between 0% and 30%. The resultant additional annual primary response costs5 and the corresponding capitalised value (obtained by using conventional net present value calculation) are presented in Tables 5 and 6, respectively. For this purpose we used a discount rate of 7% and duration of 20 years and a total installed wind power capacity of 10 GW. We observe that the additional annual response costs increase with increasing WPLF. Clearly, the ability of wind generators to withstand faults is a major driver of the additional response cost.

4

In the simulations, 1000 MW and 1320 MW were used. Using our model we estimated the base level annual cost of response to be in order of £65m per year (for MCL of 1320 MW). 5

G. Strbac et al. / Electric Power Systems Research 77 (2007) 1214–1227 Table 5 Annual cost WPLF (%)

Minimum

Maximum

Unit

30 20 10 5 0

106.1 63.7 24.7 14.3 0.0

154.6 95.5 45.7 21.4 0.0

m£ p.a. m£ p.a. m£ p.a. m£ p.a. m£ p.a.

Table 6 Capitalised cost/additional cost of fault ride through capability WPLF (%)

Minimum

Maximum

Unit

30 20 10 5 0

112.4 67.5 26.2 15.1 0.0

163.8 101.2 48.4 22.7 0.0

£/kW £/kW £/kW £/kW £/kW

The capitalised additional response costs given in Table 6 correspond to the value of fault ride through capability. In other words, the additional investment in improving the fault ride through capability would be economical, provided the cost of equipping wind turbine generators to enable fault ride through is less than the value given in the table. The results of a survey presented in the Grid Code consultation paper suggest that the cost of equipment associated with providing fault ride through capability is in the order of 1% up to 3% of the wind turbine cost. This indicates that the cost of providing fault ride through capability is lower than the associated value quantified in this study, particularly for high WPLFs. This suggests that it would be cost efficient to invest in equipment and solutions necessary to enable wind turbine generators to ride through faults. However, for low WPLF the cost seems to be similar to the value of fault ride through capability. Furthermore, the benefit of wind generation providing inertial effects was estimated. Across the various cases considered, it was found that the primary response cost could be reduced by 10–30% of the corresponding base case cost. This is considered to be significant and this question should be investigated further. It should be noted however that the proposed Grid Code does not address plant inertia and that there is no incentive for its provision. 5. Capacity benefits of wind generation In order to maintain the risk of system security at appropriately low levels, the installed capacity of generation is greater than the peak demand. This is necessary to deal with failures of generators and uncertainty in demand. Prior to privatisation and deregulation of the industry in 1990, the former Central Electricity Generating Board (CEGB) worked on the assumption that only about 85% of the total installed generating capacity would be available during winter peak demand periods. In other words, it was necessary to meet 100% of demand with only 85% of installed generation capacity. Furthermore, additional generating capacity was required to cover the risk that the weather

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might be colder than expected and hence that peak demand may increase. As a result, while planning their generation system, the CEGB required a 24% capacity margin to deal with such eventualities. This capacity margin of generating plant over peak demand has been necessary for achieving the desired level of security of electricity supply and should not be considered as surplus in generation capacity. This level of generation margin was economically justified by balancing the cost of this capacity margin against the cost incurred by consumers of electricity (society) in cases of interruptions caused by shortages in generation. In market-based operation of the electricity system, there is no set standard for the generation planning margin and the need for new plant is determined by market forces. Although the amount of generation available to meet expected demand at any point in time is to be determined by market forces, it is important to consider how a power system with a large penetration of renewable energy sources would deal with large seasonal and daily variations in demand and how a sufficient amount of capacity margin will be maintained. Clearly, wind generation is considerably more variable than conventional generation and the capacity value of wind generation plant is limited. The last security standard employed in the UK by the CEGB is taken here as indicative of the degree of security required and this was used to evaluate the need for conventional generation capacity in the future, given various levels of penetration of wind power. The reliability index called loss of load probability (LOLP) was formerly used to measure the adequacy of the generation system and determine the amount of plant necessary to meet the demand at an adequate level of security. This index quantifies the probability of peak load exceeding available generation (i.e. probability of a shortage). A capacity margin of 24% equates to a LOLP value of 0.09 (9%). The method requires relatively simple input. The conventional units are characterised by their long-term behaviour in terms of their average failure and repair cycles and this defines their average availabilities. For this paper a simplified conventional system with identical thermal units of generic capacity 500 MW each, characterized by plant outage rate of 15% (availability 85%) is assumed. A standard two state operation model was applied to simulate the behaviour of conventional generating units: unit fully available with a probability of 0.85 and hence unit unavailable with a probability of 0.15. The total wind capacity is represented in the system as a multistate unit. The intermittent behaviour of wind is statistically assessed from the frequency distribution of wind generation (Fig. 10), obtained from the annual 0.5-hourly profiles of various wind farms, based on a sample of historic wind generation data. For the calculation of the capacity value of wind, profiles with two different diversity factors were created. Fig. 11 shows the results of analysis carried out for a range of wind penetrations to examine the generating capacity of conventional plant that can be displaced by wind while maintaining the risk of loss of supply at the historical level of 9%. The expected level of conventional plant that can be displaced by wind in the UK is presented in Table 7. We can observe that

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Fig. 10. Frequency distribution of the normalized annual wind output.

Fig. 11. Conventional capacity displacement by diverse and non-diverse wind resource.

wind generation only displaces a relatively modest amount of conventional plant, as expected. In order to maintain the same level of security, a significant capacity of conventional plant will be required to be connected. Much of the conventional plant on the system will only operate at low load factors because wind generation displaces much more energy than capacity. Under the present market arrangements in the UK there are no explicit capacity payments, and so the energy prices (in combination with any ancillary services income) received need to be high enough to cover the fixed cost of the plant through these occasional runs. We also note that the capacity credit of wind (the ratio between the capacities of conventional generation displaced and wind installed) reduces with the level of penetration. Table 7 Displaced conventional plant, wind capacity credit and benefit Installed wind capacity (GW)

Displaced conventional generation (GW)

Capacity credit of wind generation

Capacity benefit (p/kWh)

0 5 10 15 20 25

0 1.7 3 3.9 4.7 5

n.a. 0.34 0.30 0.26 0.23 0.20

0.000 0.026 0.045 0.059 0.071 0.075

Assuming that the cost of conventional plant is about £400/kW, with a £20/kW/yr operation and maintenance cost, the benefit from wind generation in this context can be computed. The ranges of possible value of the capacity benefits are given in the last column of Table 7 for various levels of wind power penetration. It is important to observe that the above-mentioned approach, used for assessing the required plant margin, quantifies the probability that peak demand will exceed available generation. However, this approach neither gives any indication of the frequency of the occurrences of insufficient capacity conditions, nor the duration for which they are likely to exist. Furthermore, the severity of shortages, in terms of power and energy is not quantified (only the probability of a single shortage occurring). The information about the frequency, duration and magnitudes of various potential deficits is necessary to establish if bulk energy storage facilities or demand side management options are to be considered as an alternative to conventional plants backup for renewables. In order to determine the risk of supply interruptions at various levels of wind penetration, the frequency and duration method was applied. This technique was first presented by Halperin and Adler in 1958 [7] and later on presented in various formulations by other authors for various applications in power systems. Ringlee and co-workers [8,9] and later Billinton and Allan [10] derived the recursive relations for computerbased algorithms to calculate the probability, frequency and outage duration of reserve capacity states. So far the technique was primarily implemented for conventional technologies, however, in this analysis this technique is applied for systems having both conventional and intermittent generation sources. The generation system model considered in this approach is based upon a Markov chain model and assumes statistically independent, stationary, exponential distribution of available and repair times for each generating unit. In addition to the unit availability levels the transition rates and frequencies of departures for each state of all units are also required. Wind is again modelled as a multi-state unit. The number of transitions among various generation bands of wind power are computed using a Markov chain model [11]. For the analytical treatment of loads within a Markov framework, loads are represented by daily peak and off conditions. The application of such models is also supported by other authors [5,12,13]. All generation capacity states are combined with the load statistics to compute data on the probability and frequency of occurrence of various system reserve capacity conditions known as the reserve margin states. A negative margin, therefore, represents a state in which the system load exceeds the available capacity and depicts a system failure situation. The mean cycle time, i.e. the time elapsed between two successive deficits of same magnitudes and mean duration; the time for which a capacity shortage situation lasts, are calculated for both individual as well as cumulative margin states. By applying the FDM approach we have investigated how various extents of wind penetration affect the frequency and duration of potential capacity deficits. A comparison of this is

G. Strbac et al. / Electric Power Systems Research 77 (2007) 1214–1227

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cycle. The saturation in additional capacity requirement was observed beyond 5 critical days due to the relatively low load levels appearing on next days. 5.1. Possible backup options for intermittent sources

Fig. 12. Frequency of interruptions at various magnitudes of shortages with systems with and without wind.

made with a system having no intermittent source. The results are presented in Fig. 12. The above analysis was based on a 1-year time series of wind generation data and so extreme conditions of the coincidence of very high demand and little or no wind may not be captured. A popular question that often arises in the debate on reliability of intermittent resources, for wind in particular is: “what happens if the wind stops blowing?” Given that comprehensive data sets required for a rigorous analysis is not available, this issue has been explored here with the worst-case scenario approach. We have performed an analysis considering a range of frequency of extreme conditions (no wind for 1–5 days) as well as for varying degrees of wind generation availability (0–75% of wind capacity installed) during peak load periods of the year. The corresponding impacts are analysed for various levels of wind penetration during no or low wind availability conditions. A considerable reduction in the capacity credit of wind was observed due to no or very low availability levels of wind output (Fig. 13). It can be seen from the results that a single day of no wind generation availability across the entire wind source can result in 20% reduction in the capacity credit of wind. It must be emphasized here that the additional capacity requirements depend heavily on the peak load levels existing during no/low wind days. An assumption was made here that the highest of the annual peak loads persists for 5 days during the daily peak

The issue of backup for intermittent renewable sources arises from the fact that this generation has relatively low capacity value (Fig. 11) and hence can only make a limited contribution to generation security. It is important to examine the opportunities for alternatives, such as storage and demand side management in providing system security. Having the quantitative assessment of the extent of possible supply shortage levels against various levels of wind penetration it becomes possible to compare various backup options for supporting the renewable generation. The magnitude of the generation shortages combined with their cycle times and the duration of their existence provide the technical input to system planners in performing cost–benefit analysis for the selection of the most appropriate backup option. Although intermittent generation will displace the energy produced by large conventional plant it has only limited capacity value. In order to maintain system security and flexibility, there is a need for the presence of a significant capacity of conventional plant. However, a considerable proportion of such plant will operate with lower load factors. This has an important impact on the economics of conventional plant. Alternatively, backup capacity could be provided by demand side management to enhance the capacity value of intermittent resources. Results from the frequency and duration analysis of capacity deficits for various generation scenarios can be used to establish the technical as well as economic feasibility of the DSM preference over other alternatives. Altering this natural diversity may result in subsequent peak demands, which could be higher than the ones to be smoothed. It can be a good option for relatively small to intermediate levels of expected shortages that are not very frequent. Large industrial customers can provide backup for occasional deficits of large magnitudes that last for shorter period of time against privileged tariffs. The domestic sector could be more flexible if equipped with more sophisticated controlling devices. The capacity contribution, given the size of bulk storage facilities required (both power and energy), is relatively modest. The alternatives to storage-based solutions of providing capacity are conventional generators and demand side management, and the value of storage in this context will be determined by the cost of these alternatives. Depending on the particular storage technology used, storage-based backup solutions may be superior in providing greater flexibility for balancing than conventional generation and demand side management. On the other hand, the efficiency of storage plant will be critical for the competitiveness of the technology. 6. Fuel savings and network costs

Fig. 13. Capacity credit reductions during no/low wind days in the peak demand period.

Wind energy will reduce the amount of fuel burnt in gas and coal power stations. For a given capacity of wind generation installed, the amount of fuel saved will be driven by the load fac-

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tor (utilisation). Similar to other studies we assumed an average load factor of 35% and a fuel cost in the range of £10–20/MWh to calculate the level of savings for 25 GW of installed wind capacity. 6.1. Network cost When connecting wind farms at various location across the country the transmission reinforcement cost needs to be considered. This includes a detailed assessment of the impact of the locations of new conventional plant and decommissioning of existing generation. Depending on the development scenario considered, the range of costs was found to be between £65/kW and £125/kW of wind generation capacity [2]. Lower values correspond to scenarios with dispersed wind generation connections, with significant proportions of offshore wind around the England and Wales coast, while the higher values correspond to the scenarios with considerable amount of wind being installed in Scotland and North of England. Incorporating these estimates of cost of infrastructure reinforcement we evaluated the network cost for 25 GW of installed wind capacity. 7. Summary of overall additional cost and benefits of wind power The expectation is that in the UK, a large proportion of wind power will be installed in order to respond to the climate change challenge. This generation will displace the energy produced by large conventional plant, raising questions about the ability of such a system to manage the balance between supply and demand, and hence, to maintain the security of the electricity supply system. Clearly, meeting variable demand with intermittent, and/or uncontrolled and/or inflexible generation will be a major challenge for secure operation of sustainable electricity systems of the future. The analysis demonstrated that in order to accommodate intermittent generation it may be necessary to retain a significant proportion of conventional plant to ensure security of supply (e.g. under conditions of high demand and low wind). Hence, the capacity value of intermittent generation will be limited as it will not be possible to displace conventional generation capacity on a “megawatt for megawatt” basis. Also, intermittent generation is not easy to predict, hence various forms of additional reserves will be needed to maintain the balance between supply and demand at all times. An assessment of the costs and benefits of wind generation on the GB electricity system, assuming different levels of wind power capacity, has been made in this paper. Overall, it is concluded that the system will be able to accommodate significant increases in intermittent power generation with relatively small increases in overall costs of supply. These additional costs will be primarily driven by the capital cost of wind generation while the benefits in terms of the cost of fuel saved will be directly influenced by fuel prices. The average values of the various components of additional costs and benefits of integrating 25 GW of wind in the GB electricity system are summarised in Table 8.

Table 8 Estimates of additional cost (positive values) and benefits (negative values) of integrating 25 GW of wind in GB system Component Fuel cost savings Capacity benefits Cost of wind generation Balancing cost Network cost Overall

p/kWh −0.288 −0.038 0.465 0.054 0.094 0.28

The net additional costs (i.e. costs less benefits) amount to around 0.28 p/kWh which is 5% of the current domestic electricity price. These costs should also be viewed in the context of the recent impact of gas price rises on the cost of electricity. It should be noted that the additional operating cost associated with accommodating the variable and unpredictable output of wind power represents a relatively small proportion of the total. We found that the application of storage for providing standing reserve could contribute to a cost effective integration of significant amount of wind power particularly in generating systems with limited flexibility. Other factors, such as the amount of storage installed, and wind capacity installed were also found to have potentially large impact on the value of storage. The analysis suggests that in generation systems of limited flexibility and with significant penetration of wind generation the value of storage was found to be about £800/kW and £470/kW for the low and medium flexibility systems with 3 GW of storage installed. We have also carried out an investigation to estimate the order of magnitude of additional system cost that would need to be incurred in order to accommodate wind generation of varying degree of the capability to withstand faults on the UK transmission network. The work carried out clearly demonstrates that, if a significant amount of wind generation with relatively low robustness is to be installed this would lead to a considerable increase in system costs. These additional costs would be significantly higher than the expected cost of engineering necessary to provide fault ride through capability. The results of the studies performed suggest that requiring sufficient fault ride through capability for large wind farms (new Grid Codes) would be economically efficient. References [1] L. Dale, D. Milborrow, R. Slark, G. Strbac, Total cost estimates for large-scale wind scenarios in UK, Energy Policy 32 (2004) 1949–1956, http://www.elsevier.com/locate/enpolicy. [2] Energy Policy Review, Supplementary Submission from National Grid, 2001, http://www.cabinet-office.gov.uk/innovation/. [3] Short-Term Power Fluctuation of Wind Turbines: Analysing Data from German 250 MW Measurement Program from the Ancillary Services Viewpoint, NREL, 1999. [4] Eric Hirst, Interaction of Wind Farms with Bulk-Power Operations and markets, Project for Sustainable FERC Energy Policy, 2001. [5] ILEX Energy Consulting and Goran Strbac, UMIST Quantifying the System Costs of Additional Renewables in 2020 (SCAR Study), DTI, 2002, http://www2.dti.gov.uk/energy/developer/support.html.

G. Strbac et al. / Electric Power Systems Research 77 (2007) 1214–1227 [6] Johnson, NGC GC (1998) 2004. [7] H. Halperin, H.A. Adler, Determination of reserve generating capability, AIEE Trans. Power Apparatus Syst. 77 (1958). [8] J.D. Hall, R.J. Ringlee, A.J. Wood, Frequency and duration methods for power system reliability calculations. Part I. Generation system model, IEEE Trans Power Apparatus Syst. PAS-87 (9) (1968). [9] J.D. Hall, R.J. Ringlee, A.J. Wood, Frequency and duration methods for power system reliability calculations. Part II. Demand model and capacity reserve model, IEEE Trans. Power Apparatus Syst. PAS-88 (4) (1968).

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[10] R. Billinton, R.N. Allan, Reliability Evaluation of Power Systems, Plenum Press, 1984. [11] L. Masters, J. Mutale, G. Strbac, S. Curcic, N. Jenkins, Statistical evaluation of voltages in distribution systems with embedded wind generation, IEE Proc. Gen. Trans. Distrib. 147 (4) (2000) 207–212. [12] M.J. Grubb, The integration of renewable electricity resources, Energy Policy (1991). [13] J. Nahman, M. Graovac, Load modelling for generating system capacity reliability evaluation using the frequency and duration method, IEE Proc. 139 (6) (1992).