Assessing flexibility requirements in power systems

Transcription

1 Published in IET Generation, Transmission & Distribution Received on 10th October 2013 Revised on 3rd March 2014 Accepted on 3rd April 2014 ISSN Assessing flexibility requirements in power systems Yury Dvorkin, Daniel S. Kirschen, Miguel A. Ortega-Vazquez Department of Electrical Engineering, University of Washington, Seattle 98105, USA Abstract: This study proposes a methodology to assess the effect of wind power production on the flexibility requirements of a power system. First, the study describes the probabilistic characteristics of the intra-hour net load variability and demonstrates that they are best captured by non-parametric statistics. Then, this non-parametric approach is used to determine simultaneously the hourly flexibility requirements at a given probability level for large and small, continuous and discrete disturbances. This approach allocates the required flexibility among primary, secondary and tertiary regulation intervals. The usefulness of this method is then illustrated using actual 1 min resolution net load data, which has been clustered to take advantage of seasonal and daily differences in flexibility requirements. 1 Introduction Power production from renewable energy sources such as wind and solar is stochastic and thus contributes with random power injections to the net load profiles, that is, the difference between the load and the power produced by these sources. Alternatively, the net load can be defined as the part of load served by controllable generation resources and loads. Therefore, conventional generators are scheduled for a net load forecast and their outputs must be adjusted to compensate for unavoidable forecasting errors [1]. Although controllable loads are also able to compensate for these errors, so far the penetration of this technology remains modest [2]. While the uncertainty on net load can be reduced through the use of better forecasting methods [3] or the implementation of rolling scheduling [4], some residual mismatches between the actual and forecast net load will always remain. As the amount of installed stochastic generation increases, larger amounts of flexibility will thus be required to maintain the balance between load and generation [5, 6]. The term flexibility is used in this paper to denote the power system s ability to accommodate these net load changes by adjusting the output of generating units or the input of adjustable loads over the various regulation intervals. Flexible resources are expensive because they have higher investment costs and must be compensated for their lost opportunity cost or their lost utility. The amount of flexibility provided should therefore be minimised [7] through a careful matching with the actual requirements. In this paper, as in Makarov et al. [8], flexibility is characterised in terms of power capacity (MW), ramp rate (MW/min), that is, the ability to increase energy production with a certain rate, and ramp duration (min), that is, the ability to sustain ramping for a given duration. The importance of simultaneously assessing these three parameters instead of assessing only the capacity and ramp rate is demonstrated in [9] using an actual case study from Nevada. These data can then be processed to obtain the flexibility requirements in the primary, secondary and tertiary regulation intervals [10]. Seasonal fluctuations in renewable generation as well as daily and hourly load patterns have a significant effect on these requirements. Incorporating this information in the day-ahead generation scheduling process minimises the cost of providing flexibility. 1.1 Literature review The operation of power systems has always required the provision of flexibility, albeit under different labels. This flexibility has been assessed on an hourly basis. However, the need to minimise the cost of integrating highly intermittent stochastic renewable energy sources has led to the concept of intra-hour flexibility as a way of orchestrating the resources needed to deal with exogenous variability within a single operating hour. Ela and O Malley [11] apply a flexibility assessment tool that they proposed in [12] to determine the variability of stochastic generation over multiple timescales. Their model runs a day-ahead unit commitment and computes the absolute value of the real-time power imbalances for the entire day over different regulation intervals. While their model adequately assesses the absolute variability, it uses only four discrete intra-hour time horizons. Similarly, discrete timescales ranging from 15 min to 24 h in 15 min steps are used in [13]. These 15 min steps may not completely represent the variability on shorter timescales. Makarov et al. [8] use a data compression algorithm known as the swinging window [14] to find the turning points of the net load variability. These turning points are then processed to build a flying brick that determines the hourly requirements for capacity, ramping capability and ramping duration that meet the requirements at a given probability level [15]. The results of this processing are dependent on the degree of compression used when obtaining the turning 1

2 points, and therefore some data might be lost. Also, this flying brick couples the secondary and tertiary regulation intervals and therefore treats extreme disturbances at each regulation interval unequally. As a result, while the requirement might be fulfilled at a given probability level, some hazardous disturbances in each regulation interval might be missed. Finally, the position of this flying brick in the probability space of the turning points is not optimised. Therefore the enforced flexibility requirements may lead to over or under estimation of the actual flexibility requirements. Nazir and Bouffard [16] establishes that the representation of the net load variability in the frequency domain fits an exponential function of the form a f b (with a = and b = 2.4 for the data they used). The authors of this paper also analysed the variability of the net load on different timescales and determined that they can be described using the Skew-Laplace probability density function (PDF). Lee and Baldick [17] argue that parametric PSD estimation methods have a higher accuracy and the PSD function can be modelled as a set of affine functions. The common thread of [16 18] is that in the future the PSD estimation of wind variability could be converted into flexibility requirements in the time domain, which could then be enforced in the decision-making mechanisms used to draw the generations schedule. However, all these papers describe such formulations as topics for future research. The flexibility requirements are set separately for the primary, secondary and tertiary intervals [10]. The flexibility in the primary regulation interval (also known as frequency response or contingency reserve [19]) is provided by synchronised generators that respond automatically to sudden changes in the net load. These are typically caused by substantial generation outages or load disconnections, and are handled using the droop characteristic of the generating units. Flexibility in the secondary regulation interval (also known as regulation reserve [19, 20]) is provided by synchronised generators to accommodate continuous changes in the net load. The participation of each generating unit that provides secondary reserve is dictated by their participation factor [20]. Flexibility in the tertiary regulation interval (also known as load following or replacement reserve [19]) can be provided by synchronised or non-synchronised generators. Its purpose is to replace the already deployed primary and secondary flexibility and its deployment is performed manually and usually based on a cost minimisation analysis [10]. The data used to characterise the variability of the net demand plays a major role in setting the flexibility requirements. Makarov et al. [8, 15], Ela and O Malley [11], Nazir and Bouffard [16] and Bouffard and Ortega-Vazquez [18] use data with a 5 min resolution and therefore do not capture faster disturbances. Lee and Baldick [17] use data with a 1 min resolution but focus on modelling wind generation rather than the net load and thus do not capture other disturbances (e.g. conventional generation outages and deviations between forecast and actual loads) that may require the deployment of flexibility. (2) It argues that these intra-hour deviations are best represented using non-parametric statistics. (3) Using this non-parametric statistical representation of the need for intra-hour flexibility, it formulates an optimisation problem to simultaneously evaluate the day-ahead flexibility requirements for primary, secondary and tertiary regulation intervals at a given probability level. 2 Methodology 2.1 Characterising the deviations in net load Since different types of events lead to deviations between the forecast and actual values of the net load and thus require the deployment of flexibility resources, it is useful to develop a systematic way of categorising these deviations according to their most salient features. As explained in [8], any deviation with index k can be described by its magnitude, ΔP, ramp rate, ΔR, and ramp duration, ΔT z k W { } DP k, DR k, DT k The parameters of deviations that occur in a given system can be obtained for each operating interval by analysing historical data. This paper focuses on estimating the flexibility requirements for the day-ahead schedule. The proposed method schedules the flexibility in 24 intervals of 1 h to mirror the current practice of system operators [21]. However, the proposed method does not prevent from the use of shorter intervals. To capture the whole range of deviations, data with a 1 min resolution (or higher) should be used. First, the difference between the actual metered net load, Pm met, at every minute m of every operating hour and the hourly forecast value, P f is calculated, as illustrated in Fig. 1a (1) P d m = P met m P f (2) The actual metered net load, P met m, represents the net load profile after accounting for the flexibility obtained from adjusting controllable loads and renewable curtailments. The resulting hourly profile of deviations in net load, Pm,is d then analysed at different timescales, ΔT, to capture and characterise the deviations at each of these timescales with their magnitudes and ramp rate parameters, as illustrated in Figs. 1b and c for some typical timescales. The process of obtaining these parameters is illustrated in Fig. 2a. First, the difference between the net load at the beginning and the end of the time interval ΔT gives the magnitude of the deviation, ΔP, as follows DP = P d m+dt Pd m (3) 1.2 Contributions This paper makes the following contributions: (1) It proposes a systematic method for characterising intra-hour net load deviations from the operating plan that require the deployment of flexibility resources. If this value is positive, this deviation requires up flexibility, that is, the ability of generators to pick up load or the ability of adjustable loads to reduce their consumption. On the other hand, a negative value means that down flexibility must be deployed, that is, controllable generators must reduce their output or adjustable loads must increase their consumption. Since the duration of this deviation is defined as ΔT, its 2

3 Fig. 1 Characterising the deviations in net load a Actual metered net load data and its forecasted value for three operating hours b Magnitude of deviations for the selected timescales within one operating hour c Ramp rate of deviations for the selected timescales within one operating hour Data: ERCOT net load data ramp rate, ΔR, can be calculated as follows DR = DP DT As illustrated in Fig. 2b, the characteristics of the deviations are calculated over each interval ΔT of the hour under consideration. The process starts at the beginning of each operating hour, when load and generation are assumed to be balanced, with ΔT = 1 min and is repeated for ΔT =2, 3,, 60 min. The number of intra-hour deviations considered at each hour obviously varies with the timescale considered. For example, 60 deviations are characterised at the 1 min timescale, but only 20 at the 3 min timescale. For some timescales, an integer number of intervals cannot be fitted (4) in 1 h. In this case, the last step is truncated at the end of hour, as shown in Fig. 2c. For instance, there is one deviation for the 45 min timescale and only one such timescale can fitted in the hourly interval. The variability during the remaining 15 min is accounted for on the 15 min timescale. Therefore the hourly deviation for any timescale larger than 30 min is represented by a combination of two events with respect to the top of the operating hour. Although, the capacity and ramp rate parameters of net load deviations in (3) and (4) have been similarly defined in other studies, the methodology of this study assumes that higher resolution data are available and takes the top of each operating hour, when load and generation are assumed to be balanced, as a reference. This makes it possible to characterise net load deviations ranging from 1 to 60 min with 1 min steps. Thus, this approach captures net load deviations that occur over an interval of time smaller than the incremental step used in [13] and the ramp duration time used in [8]. 2.2 Gooess of fit of net load variability to standard probability distribution functions Previous studies have proposed to use the normal [6], skew-laplace [16], a particular case of generalised extreme value (GEV), extreme value (EV) and Cauchy PDFs [22] to fit capacity parameters of wind and net load variability. These PDFs are assumed to be used to account for wind forecast errors in scheduling tools. However, references do not provide rigorous analytical proof of the gooess of fit of these parameters to the PDFs. The data points, representing the deviations in the net load data, are obtained in accordance with the methodology presented in Section 2.1. Next, the obtained data points have been distributed based on their ramp rate parameters, calculated as explained in (4), in buckets with the a 5 MW/ min step. A few points have been assigned to the buckets with a ramp rate of 350 MW/min or larger. Therefore these have been merged in one bucket with the total number of 189 data points. Then, the capacity parameters of the data points in each bucket have been fitted to the standard PDFs. The best-fit parameters are obtained for each bucket by Fig. 2 Characteristics over interval ΔT a Schematic representation of the magnitude, ramp and ramp duration characteristics of a flexibility event at the timescale ΔT b Obtaining all flexibility events for a given timescale, ΔT c Assessing net load variability for the timescales which do not fit an integer number of intervals in one operating hour 3

4 means of the maximum likelihood estimation. The only exception is the standard deviation for the normal distribution, which is calculated using the square root of the unbiased estimate of the variance. Next, these estimated best-fit parameters are used to calculate the value of PDFs for the capacity parameters of data points in each bucket. Next, the obtained PDFs are used to obtain cumulative density functions (CDFs) for each bucket. Then, the Kolmogorov Smirnov (K S) test [23] is used to determine whether these distributions fit the net load variability data. The K S test is applied to the CDF obtained from a given PDF in every bucket with the empirical CDF (ECDF) for the same bucket. The ECDF is a staircase function that increases by 1/n at each of the n data points in the dataset. The output of the K S test determines whether the null hypothesis should be accepted or rejected for each bucket at a given significance level, α. If the K S test rejects the null hypothesis for a particular bucket, the gooess of fit of the probability distribution is acceptable. On the other hand, if it accepts the null hypothesis, the gooess of fit of this distribution is not acceptable. The gooess of fit of a distribution for each bucket can thus be estimated by applying the K S test to each of them. The advantage of the K S test is that no assumption regarding the origin of the sampled distribution is needed and all the aforementioned standard distribution functions are thus treated equally. To treat all CDFs in the tail regions equally, the tail of each of the analytical distribution has been truncated at the maximum and minimum value of the capacity parameters in each bucket. Table 1 shows the results of the K S test applied to the net load variability obtained from the Electric Reliability Council of Texas (ERCOT) net load data in the period from September 2008 to August The quality of fit in Table 1 represents the ratio of the sum of the data points in all the buckets where an analytical PDF passed the K S test successfully to the total number of data points. These analytical PDFs have a limited capability of fitting a given percentage of the data points. For instance, the normal distribution has the best performance and successfully fits capacity parameters of deviations with ramp parameters up to 45 MW/min (79.2% of the data points). In terms of the K S procedure explained above, it means that K S rejects the null hypothesis for the buckets with ramps <45 MW/min. Similarly, the Cauchy distribution passes the K S test for ramp parameters up to 25 MW/min (72.1% of disturbances). However, the GEV and EV PDFs fail to fit deviations with ramp parameters larger than 5 MW/ min and thus adequately represent the least amount of disturbances 54.1%. If the desired percentage of captured data points is set at the 95th percentile (as suggested in [15]) or 98.8th percentile (as practiced in ERCOT [24]), respectively, none of the PDFs can comply with these requirements. On the other hand, the non-parametric approach makes no assumption about an empirical distribution. Instead, this approach captures a user-specified amount of samples of deviations of the net load. Therefore, the flexibility requirements obtained with a non-parametric representation estimates flexibility requirements more accurately as compared with standard probability distributions. 2.3 Determination of the day-ahead flexibility requirements As suggested in [8] and illustrated in Fig. 3, each deviation in the net load can be represented by a point in a three-dimensional space where the coordinates are the magnitude, ramp rate and ramp duration of the deviation. This cloud of points, ζ k, represents the deviations that have been observed for a particular operating hour. In this three-dimensional space, three boxes or rectangular parallelepipeds (one for each regulation interval) can be sized and positioned to capture the most probable deviations. The most distant points captured by each box define the flexibility requirements for the corresponding regulation interval in terms of positive or negative magnitude, up and down ramp rate and ramp duration. Therefore, if the boxes enclose a data point, then the flexibility requirements enforced by the day-ahead generation scheduling process will provide enough resources to accommodate that particular event. The size of the box for each regulation interval can be set to capture a fraction ω of the deviations in net load. This parameter ω should be chosen large enough to protect the system against most unforeseen deviations. However, some of these deviations have a low probability of occurrence and scheduling resources to protect against them on the day-ahead stage would be unjustified in economic terms. Such rare events would then be handled by deploying the flexibility resources from the real-time market via re-dispatching synchronised generators and committing additional flexible generators. However, the accurate assessment of day-ahead flexibility requirements enables co-optimisation of energy and reserve procurement to minimise the need in real-time corrective actions [10]. Selecting the size and position of these boxes is formulated as an optimisation problem, which assesses the sum of the normalised dimensions of each box and captures a given percentage of data points. This normalisation of dimensions is based on the range of deviations observed over a sufficiently long period of time (ΔP max/min, ΔR max/min and ΔT max/min ) and enables simultaneous optimisation of decision variables in capacity, ramp rate and ramp duration units. When reducing the dimension of the boxes in the capacity direction, the optimisation problem minimises the Table 1 Results of the K S test PDF Quality of fit, % Maximum ramp rate bucket successfully fit, MW/min normal Cauchy GEV EV Fig. 3 Optimising flexibility requirements over a set of net load deviations on the primary (I), secondary (II) and tertiary (III) regulation intervals 4

5 amount of capacity to be scheduled on the day ahead. As explained in [5, 6, 25], if the capacity requirements for flexibility are reduced, a lower cost schedule can be obtained. If the boxes are compressed in the ramp direction, coal-fired and nuclear generation with relatively low ramp rates and marginal costs can be committed to provide flexibility. As shown in [5, 25], this commitment also reduces the operating cost, since this type of flexibility requirements avoids committing expensive flexible generation. On the other hand, a larger ramp duration requirement enables relatively slow base-load generators to provide flexibility, which also reduces the operating cost [25]. Therefore the objective function of this optimisation problem combines two conflicting objectives. When it determines the shape and size of the flexibility boxes in the three-dimensional space, it aims to reduce the capacity and ramp rate requirements and increase the ramp duration requirements. This objective function is linear and thus can be formulated in mixed-integer linear programming for each regulation interval as follows min [ ] p req up p req treq up + t req DP max up DP min + rreq up r req DR max up DR min DT max up + DT min The decision variables of this problem, p req up(), rreq up(), treq up() represent dimensions of the box in the probability space of Fig. 3. These variables are discrete, that is, whether a particular deviation (represented as a point in Fig. 3) should be included in the box for one of the regulation intervals. Since deviations can be positive or negative, two binary variables, u up and u, are associated with each i th and j th data point in the up and down direction, respectively. If these binary variables are non-zero for a given data point, this data point determines the up or down corner of a box, which enforces either an up or down flexibility requirement. Since a single data point must enforce power capacity, ramp rate and ramp duration requirements, only one element in each of these two binary vectors is allowed to be non-zero N up i=1 u up i = 1, N j=1 (5) u j = 1 (6) Since the box at each regulation interval must capture at least the ω percentage of all data points N, the following constraint is enforced N up i=1 u up i d up i + N j=1 u j d j v 100 N (7) Since only one binary variable u is allowed to be non-zero in each direction, (7) has only two non-zero terms. The parameter d represents how many data points are closer to the origin than the data point under consideration. Thus, the two non-zero terms represent the total sum of data points captured by the box if the flexibility requirements would have been enforced at that particular data points. By varying parameter ω, the system operator can change the proportion of points to be captured, and therefore regulate its reliability preferences by tightening or relaxing constraint (7). According to (6), (7), the binary variables u up or u are non-zero exclusively for the data points, which should be taken as the flexibility requirements. Thus, these requirements can be calculated as follows p req up u up i DP up i, p req u j DPj (8) r req up t req up u up i u up i DR up i, r req u j DR j (9) DT up i, t req u j DTj (10) If a binary variable in (8), (9) is non-zero, then the up () flexibility requirements are not lesser (greater) than a corresponding data point. The interplay between the objective function (5) and the constraints (7) (9) determines the flexibility requirements that capture the desired fraction of the recorded deviations while minimising the size of the boxes. The optimisation problem (5) (10) is formulated and solved for each regulation interval separately. Technically, a joint optimisation could be formulated for all regulation intervals simultaneously. In that case, constraints (6) (10) would be enforced for each regulation interval separately and the objective function would contain terms for all three regulation intervals. However, such a formulation would increase the number of decision variables in the optimisation problem and increases the computational burden. Inspired by Makarov et al. [8], this formulation explicitly models and optimises over three decisions variables p req up(), rreq up() and treq up(). This generic formulation could be reduced to a model with two decision variables and infer the third variable using (4). However, such a two-variable formulation would neglect the correlation between all three decision variables and would require linearisation to incorporate the proposed formulation in a scheduling tool. As a result, the two-variable formulation would increase the computational burden and achieve a lower accuracy. 2.4 Net load clustering The variability of net load over the secondary and tertiary regulation intervals depends to a large extent on the season, the day of the week and the time of the day. It is therefore desirable to adjust the flexibility requirements to reflect these factors. To this end, the available historical data must be divided into clusters of periods having similar characteristics in terms of net load variability. These clusters can be generated using a recursive hierarchal algorithm as described in [26]. This algorithm distributes net load variability profiles into a given number of subsets in such a way that profiles in each subset are similar. Since the objective is to minimise the difference between profiles in each cluster, the metric used for clustering is the volume of the flexibility parallelepiped, as illustrated in Fig. 3. The edges of this parallelepiped are equal to the 95th percentile of magnitude, ramp and ramp duration distributions for each operating hour. The hierarchal clustering algorithm first divides the set of daily net load profiles in two sets to account for the hourly difference in daily patterns. Next, it divides each of these clusters in two clusters to account for seasonal variations. At this stage, the difference among daily profiles of different weeks is estimated. The outcome of the method is thus four clusters; each of which contains daily net load variability profiles, exhibiting similar features. A detailed description of this method can be found in [26]. Since the seasons and days are clustered in terms of the net load variability, the net load profiles belonging to 5

6 the same cluster may not exactly match calendar seasons. In this paper, season 1 and season 2 refer to the higher and lower net load variability periods of the year, respectively. Similarly, days 1 and 2 refer to days with higher and lower net load variability, respectively. After the clustered population is created, the corresponding net load profiles are grouped with the net load variability profiles accordingly. 3 Case study 3.1 Data preparation This case study is based on net load data from ERCOT, metered with a 1 min resolution from September 2008 to August Sixteen daily profiles that exhibit drastic changes in the metered variables, and are thus likely associated with metering errors, were discarded. Among the remaining days, some isolated data points were manually assessed to be bad data and were substituted by the average of the neighbouring values. The high resolution of these data ensure that it captures all disturbances that operators of that system handled using primary, secondary and tertiary regulation, regardless of their magnitudes or whether they were sudden or progressive. Since the data for wind spillage and flexibility provided by controllable loads are not available, this case study assumes (in line with other studies, e.g. [8, 13, 16]) that no wind power generation was curtailed and that no controllable loads contributed to flexibility during the period considered. In addition, the geographical distribution of wind farms is ignored and the aggregated wind generation is assumed to be connected at a single node with sufficient transmission capacity. Since wind spillage is an almost instantaneous dispatch resource, which does not require procurement in advance, this flexibility can be extracted in real-time and does not necessarily require a day-ahead procurement studied in this paper. The available data were first clustered to reflect the effect of the season and the day of the week on the net load variability. Table 2 shows the distribution of daily net load profiles among clusters. The net load profiles included in each cluster were then processed as described in Section 2.1 to generate the set of triads representing the deviations ζ k. 3.2 Determination of flexibility requirements Data: Deviations from the schedule in the primary regulation interval are supposed to be handled by units providing a speed-governor response. The droop settings of these units are set for a long time period and thus cannot be adjusted to reflect daily or even seasonal variations in the statistics of net load fluctuations. Therefore, for the primary regulation interval, deviations identified with ΔT = 1 min are extracted and the percentage captured, ω, is set at 99.7%. On the other hand, the secondary and tertiary flexibility requirements can be procured on a much shorter basis. Clusters of net load variations can therefore be used to Table 2 Population of clusters Season Day Number of daily net load profiles determine seasonal and daily adjustments to the flexibility requirements. The secondary regulation interval includes deviations with ramps with durations of 2 5 min. The tertiary regulation interval includes deviations with ramps that have a duration longer than 5 min. For both the secondary and the tertiary regulation interval, the percentage of deviations captured is set at 98.8% as practiced by at least one ISO [24]. 3.3 Primary regulation interval Equation (4) links the magnitude and ramp rate of each deviation with its duration, which is 1 min for the primary regulation interval. Thus, the magnitude and ramp rate are numerically equal in this regulation interval. Because more down deviations (61% against 39%) were observed during the period under study, the optimisation yields an up requirement of MW and a down requirement of MW. These optimised primary requirements are thus 8.7 and 15.8% larger, respectively, than the size of the largest unit in the ERCOT interconnection (1150 MW) [24]. 3.4 Secondary regulation interval Figs. 4 and 5 show the optimised flexibility requirements for the secondary regulation interval during seasons 1 and 2, respectively. Table 3 summarises the key characteristics of these requirements for each operating hour of the different clusters: the maximum power capacity (P max, MW), ramp rate (R max, MW/min) and ramp duration (T max, min) requirements; operating hours (OH) when these extreme requirements are needed; the average power capacity (P ave, MW), ramp rate (R ave, MW/min) and ramp duration (T ave, min) requirements; and the number of rating hours when the requirements exceed the average level (N ave ). The maximum and average up and down requirements for day 1 and season 1 are larger than those for day 2 and season 2, respectively. Furthermore, the periods of the day when the maximum up requirements are observed vary for season 1 (afternoon ramping and evening drop, 15:00 and 19:00) and season 2 (morning ramp, 11:00). The maximum down requirements appear during the night hours (23:00 and 1:00), except for day 1 of season 2 (12:00). It is also important to note that the average up and down requirements are not sufficient during 5 14 operating hours depending on the cluster. For example, the up average requirement for day 1 of season 1 is as much as 5.3 times less than the hourly requirement for 19:00. If the flexibility requirements were set uniformly for all seasons and days at the average calculated over all the data points, 39% of the deviations during the 19:00 operating hour would not be covered. The average up and down ramp rate requirements are also larger for season 1 and day 1 than for season 2 and day 2. Similarly, these requirements are insufficient for some operating hours. Most importantly, larger hourly ramp rate requirements are not necessarily observed at operating hours with larger power capacity requirements. For instance, the hourly ramp rate at 09:00 and 10:00 for day 2 of season 1 are essentially the same; however, the capacity requirement at 10:00 is 2.3 times larger. This effect is due to the longer ramp durations (5 min as compared with 2 min) expected at 10:00. However, the secondary regulation interval is intended to handle deviations lasting up to 5 min. During some operating hours, ramping periods of such duration do not occur. However, during these hours faster response should be procured. This faster response is then 6

7 Fig. 4 Secondary flexibility requirements for season 1 a Power capacity requirements b Ramp rate requirements c Ramp duration requirements Fig. 5 Secondary flexibility requirements for season 2 a Power capacity requirements b Ramp rate requirements c Ramp duration requirements 7

8 Table 3 Key characteristics of flexibility requirements for the secondary regulation interval Secondary power capacity summary (MW) P max OH P ave N ave P max OH P ave N ave Secondary ramp rate summary (MW/min) R max OH R ave N ave R max OH R ave N ave Secondary ramp duration summary T max OH T ave N ave T max OH T ave N ave able to cover smaller and slower deviations. For example, the up requirements at 4:00 of day 1 of season 1 are MW, 87.7 MW/min and 2 min, which also cover the data point with coordinates MW, 28.8 MW/min and 5 min. 3.5 Tertiary regulation interval Figs. 6 and 7 illustrate flexibility requirements in the tertiary regulation interval. Table 4 summarises key statistics of these requirements using the same notations as in Table 3. As with the secondary regulation interval, the tertiary up and down capacity requirements are larger for day 1 and season 1 than those for day 2 and season 2, respectively. Similarly, the maximum power capacity and ramp rate requirements are all observed at different operating hours and periods of the day. The average requirements are insufficient to cope with deviations during approximately half the operating hours. During some operating hours, the tertiary requirements are negligibly small and the expected deviations might be handled with secondary reserve. For example, the up power capacity requirement is minimal between 21:00 and 04:00 and between 17:00 and 05:00 for seasons 1 and 2, respectively. Similarly, the down power capacity requirements are minimum from 05:00 to 08:00 and from 06:00 to 16:00 for seasons 1 and 2, respectively. The maximum tertiary power capacity and ramp rate requirements are usually observed at different operating hours. For example, the maximum power capacity and ramp rate requirements for day 1 of season 1 are observed at 08:00 and 19:00, respectively. Compared with the secondary regulation interval, tertiary flexibility requires more capacity but smaller ramp rates and therefore longer ramp durations. Furthermore, the maximum requirements in the secondary and tertiary regulation intervals do not occur at the same operating hours. For example, on day 1 of season 1, the maximum secondary and tertiary power capacity requirements occur at 08:00 and 19:00 for the morning and evening peaks, respectively. The tertiary ramp duration requirements also exhibit strong hourly differences and vary from 6 to 58 min, which indicates whether a power system should be secured against deviations with longer durations. Otherwise, tertiary capacity requirements are more relaxed. Also, these longer lasting deviations require the highest ramp rates. 3.6 Validation of results The flexibility requirements, obtained with the proposed method and the data for the year from September 2008 to August 2009, have been tested against the net load data for the year from September 2009 to August The performance of these requirements has been compared with the current ERCOT method for determining ancillary service requirements [24]. These methods are compared in terms of operating hours when day-ahead flexibility requirements are not sufficient and additional flexibility must be obtained from the real-time or balancing markets to meet net load realisations. For the primary regulation interval, both methods produce flexibility requirements that are sufficient to cope with all disturbances in this regulation interval. Table 5 compares the performance of both methods for the secondary and tertiary regulation interval in terms of the number of operating hours, N t, when real-time corrective actions are required and the expected hourly amount of energy of these corrective actions, E t (MWh). For each regulation interval, the expected hourly amount of energy of these corrective actions is itemised for shortages caused by a lack of capacity, ramp rate or ramp rate duration requirements. The proposed method, denoted as optimal in Table 5, outperforms the existing method, 8

9 Fig. 6 Tertiary flexibility requirements for season 1 a Power capacity requirements b Ramp rate requirements c Ramp duration requirements denoted as current in Table 5, in terms of the number of shortage occurrences as well as the expected amount of energy that must be procured to compensate for these imbalances. 4 Conclusion This paper proposes a technique to quantify rigorously the needs for operational flexibility. Deviations between the Fig. 7 Tertiary flexibility requirements for season 2 a Power capacity requirements b Ramp rate requirements c Ramp duration requirements 9

10 Table 4 Key characteristics of flexibility requirements for the tertiary regulation interval Tertiary power capacity summary (MW) P max OH P ave N ave P max OH P ave N ave Tertiary ramp rate summary (MW/min) R max OH R ave N ave R max OH R ave N ave Tertiary ramp duration summary (min) T max OH T ave N ave T max OH T ave N ave Table 5 Comparison of performance of different reserve requirement methodologies Regulation interval Method Capacity Ramp rate Ramp Duration N t E t N t E t N t E t secondary optimal current tertiary optimal current scheduled and actual values of this net load are defined by their magnitude, ramp rate and duration. This methodology relies on high resolution, historical data about variations in the net load and thus makes possible a more precise assessment of variability than the techniques proposed in [8, 9, 11, 13, 15, 16], which account for net load variability on a limited set of discrete timescales. In addition, this paper enrols a hierarchal clustering approach to show that this variability and thus flexibility requirements depend on the season, day of the week and time of the day. Based on this definition, the paper also proposes a non-parametric method for optimising the flexibility requirements over the primary, secondary and tertiary regulation intervals. This method fits the net load variability better than the parametric PDFs used in [6, 16, 22] and thus assesses the flexibility requirements more accurately. In addition, the proposed MIP formulation optimises the position of the flexibility parallelepiped in the probability space as well as its dimensions and thus the flexibility requirements are optimal compared with the results presented in [8]. Finally, the paper shows that these requirements depend on the season, day of the week and time of the day and describes a method for clustering the data needed to characterise these requirements. Future work will also explore the trading of flexibility products, namely capacity and ramps, in a market environment and the relationship with existing products in the form of reserve in different regulation intervals. 5 References 1 Wood, A.J., Wollenberg, B.F.: Power generation, operation, and control (Wiley, 1984) NERC State of Reliability Report. Available at: com/files/2012_sor.pdf 3 Lew, D., Milligan, M.: The value of wind power forecasting. Proc. 91st American Meteorological Society Annual Meeting, the Second Conf. Weather, Climate, and the New Energy Economy, Washington, DC, Tuohy, A., Denny, E., O Malley, M.: Rolling unit commitment for systems with significant installed wind capacity. Proc IEEE Power Tech, Lausanne, Conejo, A.J.: Scheduling energy and reserve in systems with high wind penetration. Proc. IEEE Power and Energy Society General Meeting, San Diego, Ortega-Vazquez, M.A., Kirschen, D.S.: Assessing the impact of wind power generation on operating costs, IEEE Trans. Smart Grid, 2010, 1, (3), pp Ma, J., Silva, V., Ochoa, L., Kirschen, D.S., Belhomme, R.: Evaluating power system flexibility. Proc Power & Energy Society General Meeting, San Diego, Makarov, Y.V., Loutan, C., Jian, M., de Mello, P.: Operational impacts of wind generation on California power systems, IEEE Trans. Power Syst., 2009, 24, (2), pp

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