Title Evaluating the capacity value of wind power considering transmission and operational constraints Authors Esteban Gil and Ignacio Aravena Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile Journal: Energy Conversion and Management, vol. 78, pp. 948-955, Feb. 2014. URL: http://www.sciencedirect.com/science/article/pii/S0196890413005906 DOI: 10.1016/j.enconman.2013.06.063. Abstract This paper presents a method for estimating the capacity value of wind considering transmission and operational constraints. The method starts by calculating a metric for system adequacy by repeatedly simulating market operations in a Monte Carlo scheme that accounts for forced generator outages, wind resource variability, and operational conditions. Then, a capacity value calculation that uses the simulation results is proposed, and its application to the Chilean Northern Interconnected System (SING) is discussed. A comparison of the capacity value for two different types of wind farms is performed using the proposed method, and the results are compared with the method currently used in Chile and the method recommended by the IEEE. The method proposed in the paper captures the contribution of the variable generation resources to power system adequacy more accurately than the method currently employed in the SING, and showed capable of taking into account transmission and operational constraints. Keywords Wind power, power system adequacy, capacity value, power system modeling (c) 2014 Elsevier. Personal use of this material is permitted. Permission from Elsevier must be obtained for all other uses.

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Published in Energy Conversion and Management, vol. 78, pp. 948-955, Feb. 2014.

Evaluating the capacity value of wind power considering transmission and operational constraints Esteban Gil, Ignacio Aravena Universidad T´ecnica Federico Santa Mar´ıa Valpara´ıso, Chile email: [email protected], [email protected]

Abstract This paper presents a method for estimating the capacity value of wind considering transmission and operational constraints. The method starts by calculating a metric for system adequacy by repeatedly simulating market operations in a Monte Carlo scheme that accounts for forced generator outages, wind resource variability, and operational conditions. Then, a capacity value calculation that uses the simulation results is proposed, and its application to the Chilean Northern Interconnected System (SING) is discussed. A comparison of the capacity value for two different types of wind farms is performed using the proposed method, and the results are compared with the method currently used in Chile and the method recommended by the IEEE. The method proposed in the paper captures the contribution of the variable generation resources to power system adequacy more accurately than the method currently employed in the SING, and showed capable of taking into account transmission and operational constraints. Keywords: wind power, power system adequacy, capacity value, power system modeling 1. Introduction Reliability in power systems is usually defined in terms of adequacy and security [1, 2]. While security refers to the system’s capacity of reaction and recovery to endure short term contingencies, adequacy refers to the capacity of the system supply to meet its demand, taking into account unexpected outages of generators or transmission lines and possible constraints on the DOI: 10.1016/j.enconman.2013.06.063 EC&M 2014 URL: http://www.sciencedirect.com/science/article/pii/S0196890413005906

primary energy resource (problems on the fossil fuel chain of supply, dry spells, lack of wind). The emphasis for this paper is on the adequacy aspect of power systems reliability, and for our purposes the terms adequacy and reliability will be used interchangeably. In a power system, loss-of-load (LOL) events refer to situations in which the system’s available generation and transmission capacity will not be able to supply all the demand. These events are generally limited to times with high demand or small capacity reserve margins and the occurrence of critical generators and/or transmission line outages. Different metrics for assessing system adequacy exist, based in evaluating either the probability and/or duration of loss of load events and/or the amount of unserved energy. Besides the assessment of system adequacy, it is relevant to ask for the specific contribution of each generator to it, which is usually measured by its capacity value. Capacity value, sometimes referred to as the generators’ firm power, firm capacity, or capacity credit, refers to the amount of generation which can be guaranteed to be available at a given time, and it is the most widely used metric for measuring the contribution of a particular generator to power system adequacy. The contribution to adequacy of variable generation such as wind and solar is an aspect on which there is a great deal of interest from regulators and generation companies. Before evaluating a wind farm capacity value, careful consideration of both the characteristics of the system and of the wind farms is required. On the one hand, system characteristics such as existence of hydro generation, level of wind penetration, flexibility of the thermal generators, reserve requirements, and transmission limitations, among others, can either facilitate or make more difficult the integration of new wind farms. On the other hand, wind farm capacity factors, location and access to transmission, correlation between wind and system demand can increase or decrease the reliability contribution of the wind farm. Since even conventional generators will not be able to provide their maximum power at all times (as a result of either maintenance or forced outages), a capacity metric should be suitable for generators with diverse operating regimes, be them baseload, intermediate, peaking or non-dispatchable generators. Hence, generators with a high forced outage rate (FOR) should be assigned a smaller capacity value than more reliable generators. This capacity metric should also take into account how much capacity a generator can make available at high risk periods [3, 4]. That is, when a generator is needed the most its contribution to system adequacy will be greater and should be 2

given more weight. In consequence, the capacity value of a generator able to inject energy into the system during the periods of high system risk (usually the periods of high demand) should be higher than the capacity value of a generator unable to do so. Techniques for estimating capacity value for variable generators should be based in probabilistic analyses and should also consider the particular characteristics and operating regimes of each generator and how they contribute to improving system adequacy, especially during high risk periods. This paper is an extended and revised version of the paper presented in [5]. The paper presents a Monte Carlo based method for estimating the capacity value of wind farms in the Chilean Northern Interconnected System (SING). Although there are currently no wind farms installed in the SING, there are several projects in different stages of development. Thus, there is a great deal of interest on evaluating how wind power will be impacting system operation and what capacity value should wind farms be assigned in order to allocate the capacity payments. In the SING, the effects of transmission constraints and of a relatively inflexible thermal generation park with many time-coupling constraints suggest the use of a simulation-based approach instead of the IEEE-recommended method [6] for calculating capacity value of wind power. This paper is structured as follows: section 2 discusses different approaches for determining the capacity value of wind; section 3 discusses the method currently employed in Chile and then presents an alternative methodology for determining the capacity factor of generating units; section 4 presents simulation results and compares the different methods for calculating the capacity value. Finally, section 5 presents the main conclusions of this work. 2. Methodologies for calculating the capacity value of wind International practices for the calculation of the capacity value of variable generation such as wind and solar can vary considerably [4, 6, 7]. A number of approximation methods have been employed for calculation of the capacity value of wind, such as [8, 9]. Because of their easy implementation, not requiring simulation over a large number of samples, and only requiring historical data for their use, many systems use some variation of the approximation methods based on some statistic (either average or quantile) for the generation capacity factors during peak demand periods. In general, although 3

these approximate methods can be useful as quick screening methods, their use is not recommended as they are incapable of fully capturing the wind resource variability or the correlation of wind generation and load [6]. Besides their inability of modeling complex power system operational aspects, approximation methods can be inadequate in certain power systems such as the SING as they are incapable to consider risk properly, as shown in Figure 1. This figure shows how the risk is distributed over time for the SING. For example, we can say that the top 5% of the periods concentrate only about 25% of the risk, and the top 10% of the periods concentrate only about 43% of the risk. Thus, averaging generation values over a limited number of periods would leave an important proportion of the risk without being addressed. In conclusion, approximation methods based on peak load informtion are better suited for systems where the risk concentrates in a small number of periods, which in light of Figure 1 is not the case for the SING. The Effective Load Carrying Capability (ELCC) approach consists on evaluating the additional demand that the system is able to handle while preserving the same system adequacy, given the addition of the generator being studied. This general idea, introduced by Garver in 1966 [10], has been successfully applied for decades to conventional generators and it is certainly valuable when dealing with variable generators. Despite ample acceptance of these ideas, there are quite a lot of dissimilarities in terms of their implementation [11]. When evaluating the contribution to adequacy (capacity value) of variable generators, the analysis has to take into the account that a unit with higher output during high risk periods should be assigned a higher capacity value that a unit with the same capacity factor but available more during periods of low system risk. Thus, correlation between Loss of Load Probability (LOLP) (seen as a metric of system adequacy) and generation output should play a fundamental role in any method. Following this principle, the IEEE Power and Energy Society Task Force on the Capacity Value of Wind Power has proposed a procedure to treat wind generation in the traditional (ELCC) calculation method [6] which has been applied successfully to, for example, the Irish Power System [7]. The IEEE-recommended method starts by calculating the hourly system LOLP by convolution for different levels of demand. Then, an iterative process is followed (to be described in more detail in Section 3.2) to determine the additional load that the system is capable of carrying with the addition of the wind farms so that the Loss of Load Expectation (LOLE) in hours/year remains the same that without the wind farms. 4

However, the IEEE-recommended method [6] may not be entirely appropriate for the SING as it does not allow to directly take into account operational aspects such as transmission constraints and generation time-coupling constraints, which play an important role in this system. When interested in evaluating the system risk considering operational issues, a production model to properly assess the system risk under different operating conditions may need to be used [12, 13]. Monte Carlo simulation using synthetic wind time series to estimate capacity value has previously been proposed in [14, 15]. In this paper we have implemented a Monte Carlo scheme that repeatedly runs a SING production model randomly sampling synthetic wind generation time series and thermal generator outages. Therefore, the LOLP values obtained by this method are aiming to combine the probability of having energy not served in the system (an operational LOLP ) and the more traditional definition of LOLP found on the reliability literature. From an adequacy point of view, the LOLP depends of the capacity reserve margin (available capacity minus the load), and one should see it to increase as the load increases and the capacity reserve margin decreases. If instead of using the traditional adequacy-based definition of LOLP we define an operational LOLP as the probability of having energy not served for certain operating conditions, we can add an operational dimension to the analysis. Of course, if we also want to consider transmission constraints and losses, and chronological constraints of generating units such as minimum up and down times or loading ramps (which appear as generating units try to follow demand and/or wind generation changes), a purely analytical approach may underestimate the system risk, raising the need for using system-simulation approaches as the one proposed in this paper. 3. Evaluating the capacity value 3.1. Chilean context The Chilean law, according to the supreme decree 327 (Procedures of the General Law of Electric Services, DFL 1), understands for firm capacity of a generator ‘the maximum power that a generator can inject to and transport on the transmission system during the peak hours of the system, considering its probable unavailability’. The definition of firm capacity (capacity value) given in the Chilean Law can certainly suit well conventional generators who got a relatively constant unavailability rate. However, in the case of variable generation their availability will depend on the availability of the 5

primary energy source, be it wind, solar radiation or other. Naturally, variable generators contribution to adequacy can be quite different depending on the correlation between the system’s risk (usually also correlated with the system’s demand) and the availability of the primary energy resource. In the case of wind farms, another aspect worth considering is that since they only seldom generate at maximum capacity, the transmission lines where they will connect to the system may not be designed for injection at full capacity of the plant under all possible transmission power flows, so their contribution during peak times may be limited by transmission constraints. In the previous definition the contribution to system adequacy is implicit in its reference to peak hours. Although the regulation includes in the calculation of firm power not only the contribution to power system adequacy but also some aspects more closely related to power system security [17], it is currently being revised to isolate the adequacy contributions into the capacity value (potencia de suficiencia) and leave the security aspects confined to the ancillary services market. Henceforth we will talk about capacity value to refer to the firm power ignoring any system security aspects that may currently appear on the Chilean regulation. The Chilean Northern Interconnected System (SING) is an almost entirely thermal system with about 3.7 GW installed generation capacity serving about 90% industrial (mining) loads and only about 10% residential load. Electric energy supply comes mainly from coal-fired units with relatively inflexible operating regimes (69.2% of total generation in 2011), some newer combined-cycle and open-cycle gas-fired units (25.8%), some fuel-oil and diesel peaking plants (3.9%), and a small amount of hydro generation (0.5%) [18]. Despite the system having relatively large capacity reserve margins, due to an inflexible generator mix coupled with a number of transmission constraints loss of load events are not uncommon. rapidly growing (5.5% load growth in 2012) In general, unless there are binding transmission constraints, wind capacity value should be calculated for all wind farms in the system to account for the resource diversity. However, the SING is a system with currently no wind power installed, so the subsequent analyses will evaluate the capacity value of two wind farm projects together and separately (as at this point it is not clear whether both projects will materialize). Naturally, the situation is different for systems with plenty of incumbent variable generation.

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3.2. IEEE recommended method With the objective of providing clarity on the calculation of the capacity value of wind power, the IEEE Power and Energy Society proposed a Task Force on the Capacity Value of Wind Power , which recommended the procedure described in [6]. The method, grounded on ELCC principles, relies on the calculation of the Loss of Load Expectation (LOLE) of the system and starts by calculating the systems’ Capacity Outage Probability Table (COPT) [2]. The COPT for the total system capacity Csys is obtained by convolving the discrete probability distributions of the available capacity Ci of individual generators, as equations (1)-(3) show:  0 p = FORi (1) Ci = max p = 1 − FORi Ci X Csys = Ci ∼ (C1 ∗ C2 . . . Ci . . . CN −1 ∗ CN ) (2) i∈I

Then, the LOLP for a certain system demand Dsys can be calculated directly from the COPT as: LOLP = P[Dsys > Csys ]

(3)

Thus, the COPT is used with the hourly load time series to calculate hourly LOLPs, which in turn allow the calculation of the annual LOLE with no wind (LOLEnowind ). Then the process is repeated using instead the net load (load minus wind generation) and a new LOLE is calculated (LOLEwithwind ≤ LOLEnowind ). Then, through an iterative process an additional load across all hours is added to the net load and the LOLE recalculated until its value reaches LOLEnowind . The IEEE method is described and discussed in more detail in [6] and then contrasted against other methods found in the literature. The authors of the paper stress that the key factor in any methodology should be to capture the relationship between wind generation and load. We would go farther to pinpoint that any method should be able to capture the relationship between wind generation and system risk, although it is certainly true that in many systems load and system risk are highly correlated. However, there are systems such as the SING where most of the risk is not caused by the lack of generation capacity, but by transmission bottlenecks and operational constraints. Furthermore, the load in the SING is very flat (it is 90% industrial load), and large portions of the system risk are not in the periods of higher demand, as Figure 1 shows. 7

3.3. Monte Carlo method for calculating the operational LOLP In this paper, instead of using a traditional LOLP calculation as the one in equations (1)-(3), we instead propose the use of an operational LOLP (understood as the probability of having energy not served anywhere in the system). This operational LOLP is obtained by using a stochastic production cost model with detailed DC power flow and unit commitment. Thus, the operational LOLP is obtained using a Monte Carlo scheme that accounts for: (i) limited amount of historical wind time series, (ii) generator outages, (iii) transmission constraints, and (iv) generation time coupling constraints. The procedure is as follows: Step 1. Using a forecast of demand and wind power, a detailed hourly unit commitment is obtained for each day of a whole year. Step 2. A synthetic wind generation time series is randomly selected. Step 3. An outage pattern for each thermal generator is randomly sampled using the each generator Forced Outage Rate (FOR) and time-torepair. Step 4. Using the unit commitment decisions from the first step and the randomly sampled wind time series and thermal generators outages, the production model runs an economic load dispatch with DC power flow. Step 5. Any loss of load events occurring in the previous step is recorded and used to recalculate the LOLP versus demand curve. Step 6. Go back to step 2 until an arbitrary number of iterations is reached or there are no significant changes in the LOLP versus demand curve. The Monte Carlo scheme uses synthetic time series due to the limited availability of historical wind time series (as in [14], [15]). The synthetic wind time series are generated by means of a SARIMA model trying to preserve the autocorrelation and shape of the historical wind data and, more importantly, the relationship between wind availability and load. The synthetic wind data was generated by means of a SARIMA model as in [23]. Notice that by simulating a full year using historical load participation factors for each bus, we were able to capture 8760 different dispatch conditions, which allowed us to account for transmission congestion. Besides, the unit commitment in step 1 and economic load dispatch in step 4 allowed us to also account for generator’s time coupling constraints. The market simulations were conducted using PLEXOS. PLEXOS is a Mixed Integer Linear Programming (MILP) based electricity market simulation and optimization software. PLEXOS co-optimizes thermal, hydro, and 8

ancillary services and is able to perform Monte Carlo simulations [19]. Once PLEXOS formulates the mathematical program, it is solved using Xpress [20]. The CDEC-SING, the SING independent system operator (ISO), provides on their website PLEXOS databases of their system for purposes of their generation programming containing detailed production and network data, which were adapted for the purposes of this work. The outputs of the simulations were benchmarked against actual system outputs to check for correctness and consistency. In order to obtain a smoother LOLP versus demand curve an aggregation is carried out (after the simulation, so that the effect of transmission constraints has already been captured) to get 20 blocks of demand of approximately 40MW each. The LOLP of each block is then calculated by counting all the loss of load events in that block. The process is illustrated in Figure 5 for the case with no wind farms. In the simulations it is desirable to use a high-demand profile (such as a 10% probability of exceedance load profile) instead of an average demand scenario in order to obtain a more complete representation of the LOLP versus demand curve. This improves the estimation of the capacity value for generating units that may not be dispatched that much under an average demand scenario, but that might be contributing to system adequacy in extreme cases. 3.4. Capacity value calculation method employed in Chile The methodology currently in place for firm power in Chile (omitting the security aspects) is based on the LOLP and considers that every component of the system makes a contribution to its reliability depending both on its capacity and availability, and that such contribution can be valued in terms of a comparison with and without the component. For example, the addition of a new generator to the system would imply that, for each level of demand, the system risk would in general be smaller or equal than in the original system. Considering this criterion, the current methodology for the SING can be summarized in 3 steps, given by the relationships (4), (5), and (6): 1. The initial power Piini is calculated as the net power for the worst possible availability of the primary energy resource. 2. The initial power is weighted by the unit availability αi and by the relative decrease of the LOLP evaluated for the maximum demand of the period (LOLPi corresponds to the system’s LOLP without unit i). In this way the preliminary capacity value (P CVi ) is obtained.

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3. Finally, the capacity value of each unit CVi is calculated by scaling up the preliminary capacity value in such a way that the sum of the capacity value of every generator in the system is equal to the maximum demand of the period. Piini ≤ Pimax − Piaux 1 − LOLPi D=Dmax −P ini P CVi = · αi Piini 1 − LOLP

(4) (5)

D=Dmax

Dmax CVi = P CVi · PK j=1 P CVj

(6)

This methodology penalizes hard the variable generation units, because their availability is arbitrarily considered to be low. Thus, by receiving almost no capacity payments (representing about 20% of the conventional generators’ income), the entry of new wind and solar capacity in the systems is disencouraged. 3.5. Proposed method for capacity value calculation An alternative procedure consists in considering the capacity made available by the generator in relation to the total system demand only during the periods when it is required to operate. Therefore, the data of interest will t be a set of pairs (Dt , Pav i ) ∀t ∈ {1, 2, . . . , N }, where N corresponds to the number of time blocks. Next, the capacity made available by the generator (if dispatched) is evaluated for different tranches of the total demand curve, procedure from which representative values of the generator available capacity Pil for each representative value of the demand Dl , l ∈ {1, 2, . . . , L << N } are obtained. These L pairs correspond to the effective capacity of each unit for each level of demand. To obtain the capacity value, it is proposed to calculate the weighted average of these values of available capacity Pil , where the weights χli are related to the contribution that each Pil makes to the adequacy of the system (see equation (7)). A way of calculating these weights is considering them proportional to the difference between LOLP and LOLPi , based on equations (8) and (9), so that those tranches of Pil that increase reliability the most are more important in the sum.

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L X

χli Pil

(7)

∆LOLPli = LOLPi D=Dl − LOLP D=Dl

(8)

P CVi =

l=1

∆LOLPli χli = PL j j=1 ∆LOLPi

(9)

The steps of the procedure are schematically presented in Figure 2. In order to obtain a measure comparable to the current procedure, the capacity values obtained by the proposed procedure must be scaled up or down so that the capacity values for each generator sum up to the maximum demand, as indicated in (6). 3.6. Impact of the proposed method It is convenient to discuss the impact of the proposed method on different types of power plants. For conventional baseload generators, most of their capacity is available (and required) most of the time (discounting planned or forced outage periods), so its preliminary capacity value will be relatively independent of the weights χli and will be approximately equal to αi Pimax . Peaking units are only required to operate during periods of high demand, and since their maintenance usually occur during periods when they are not required to operate, their availability is only hindered by forced outages. Consequently, as their weights χli are zero for low demand values and then increase with the demand, the preliminary capacity value of a peaking plant will be approximately Pimax . In the case of non-dispatchable units such as wind and solar, leaving aside maintenance and forced outages, their capacity value will depend strongly of the correlation between demand and the availability of the primary energy resource, as the weights χli increase with the total demand. The implication is that if the available generation has a positive correlation with the demand/risk, the weights will be higher when generation is higher, giving a higher capacity value. If the correlation is negative, the opposite is true and the capacity value will be lower. Furthermore, as we as using an operational LOLP instead of the traditional LOLP calculated by convolution, other factors such as location in the transmission system and operational constraints are also playing a role in the calculation. 11

4. Results 4.1. Demand and wind power generation The SING market was simulated for the year 2015 based on National Commission of Energy (Comisi´on Nacional de Energ´ıa, CNE) projections [21] and considers two potential wind farms in 2 different locations, each one of 200MW. Wind data was obtained from two onshore wind speed monitoring stations (Escondida and Estanque de Agua) installed by the Chilean Department of Energy (Ministerio de Energ´ıa [22]. The first station (Wind Coast) is in the lowlands near Antofagasta, while the second one (Wind Interior) is located uplands near Calama. The datasets contain wind speed measurements taken at a height of 20 and 80 meters every 10 minutes since 2009. Wind speed data was then converted into generation using generic wind farm efficiency curves [24, 25]. Figure 4 compares the wind generation variability during the day (for a full year of data) against how the system risk is distributed in different hours of the day. The wind generation variability during the day is illustrated using box-and-whiskers plots. The boxes show the lower, median, and upper quartiles, the whiskers show the maximum and minimum values of the data (excluding possible outliers), and the dots represent possible outliers (values more or less than 3/2 of the upper and lower quartiles, respectively). The line in 4 shows the system risk at different hours of the day as measured by the percentage of the total loss-of-load (LOL) instances obtained in the Monte Carlo model (for the case with no wind). Table 1 shows the capacity factor and the correlation of generation and total demand for both wind farms estimated for 1 year of data, and Figure 3 shows the correlation between wind and load by vigiciles (20-quantiles). Although correlation coefficients only can provide limited information, in general a high positive correlation coefficient between load and wind implies a better chance for wind generation to meet the demand. The data shows that Wind Coast, despite having a lower capacity factor than Wind Interior, has a higher correlation with the load (Figure 3) and generates more when the system risk is high (Figure 4). 4.2. Operational LOLP versus demand curves Considering that having unserved energy is a rare event, obtaining the curves usually requires a large number of simulation samples. First, 100 Monte Carlo samples are used to estimate the number of loss-of-load instances for each of the 8760 hours in a year (giving us 876,000 data points). As we are 12

Table 1: Characteristics of the wind farms. Correlation coeff. of wind Capacity generation and load Wind farm factor [%] Data aggregated Hourly data by vigicile Wind Coast 42 0.16 0.87 Wind Interior 53 -0.14 -0.95 Both wind farms 48 0.03 0.30

running a full unit commitment algorithm for each day and for each iteration, the simulation scheme is also capable of capturing some other effects that are important in the SING, such as loss-of-load instances caused by time-coupling constraints of some thermal units (min up time, min down time, and loading ramps). As Figure 5 shows, the operational LOLP grows approximately exponentially with the demand, although there are some hours with lower total system demand and higher LOLP. This is because we use different load profiles for each bus, so some distributions of the total load among the buses may carry more risk than others due to transmission constraints. Figure 5 also shows how the demand and the loss-of-load instances (over 100 runs) are distributed in each of the 20 demand blocks. Notice that this aggregation of loss-of-load instances by load blocks occurs after the simulations have been conducted, so the effects of transmission constraints in the LOLP have already been captured. This is different than aggregating the load before the simulation, in which case the effects of transmission bottlenecks on loss-of-load events would be lost. Finally, the resulting operational LOLP versus demand curve is obtained by dividing the number of loss-of-load instances by the number of hours on each block, and by the number of simulation samples. The resulting curve is plotted on logarithmic scale at the bottom of Figure 5. 4.3. Assessing the impact of the wind farms The resulting operational LOLP versus demand curves considering Wind Coast, Wind Interior, and both wind farms are presented in Figure 6. Figure 6 shows how wind generation improves system adequacy by reducing the operational LOLP, although the improvement varies with the demand level depending on the wind pattern. While Wind Interior seems to simply shift the LOLP curve to the right (from the No Wind case), Wind Coast distorts

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the curve making the system more reliable at high demands as a result of having a higher correlation with the load. By reviewing the simulation results from the production model, we could also assess the impact of including transmission and operational constraints into the analysis. In the SING, most large thermal power plants are located in the coast (because of the access to water), while most industrial loads are located inlands. On the one hand, the Wind Interior farm would be located next to one of the largest mining loads (Chuquicamata), therefore relaxing transmission congestion in the area. On the other hand, Wind Coast would be located in the O’Higgins bus from where it can directly supply Escondida, Zaldivar , and other mining loads through the O’Higgins-Domeyko transmission corridor. Furthermore, Wind Coast location close to one of the largest non-industrial loads (the city of Antofagasta) and its high correlation with the load also causes the thermal power plants in the area to see a flatter net load (load minus wind), which has a positive impact on reliability by relaxing some of the generator time-coupling constraints. In this way, the proposed method based on system-simulation allows to incorporate some of the operational benefits of the potential wind farms to the capacity value calculation. 4.4. Calculation of the capacity value Both the current Chilean method and the proposed method require the LOLPi curves (Figure 6) for each generator.The LOLPi curves for 2 thermal generators were also obtained (Figure 7): U14 (coal-fired, baseload unit) and U11 (diesel-fired, peaking unit). For the rest of the generators the LOLP curves were estimated by shifting the system LOLP curve to the left, procedure suitable for conventional generators, as Figure 7 shows. In a system with other wind farms installed, the capacity value calculation would need to be performed for all wind farms. However, as in the SING there are currently no wind farms installed, the analysis is also conducted for each one individually. Table 2 shows the capacity values obtained by each methodology and are compared against capacity values obtained by the IEEE-recommended method. For the current method, the initial power Piini for the wind farms is chosen as the power that the units are able to deliver the 70% of the time. Table 2 shows that while capacity value of the thermal units do not vary much between the current and the proposed methodologies, the capacity values of the wind generators with the proposed method increase considerably. 14

Table 2: Capacity values calculated using different methods. Current Method Proposed Method IEEE Generator Pmax P CV CV P CV CV CV [MW] [MW] [MW] [MW] [MW] U14 136 130 101 115 93 U11 38 33 26 26 21 Wind Coast 200 0 0 120 97 Wind Interior 200 38 29 85 69 Both wind farms 400 132 100 195 158

Method [MW] 69 58 127

Furthermore, the results obtained with the proposed method are also better aligned with the capacity values obtained with the IEEE method, as both methods can capture the fact that Wind Coast generation has a higher correlation with the demand than Wind Interior, despite the second one having a higher capacity factor (it generates 12% more energy per year). This illustrates the importance of properly adressing the relationship between system risk and load in the calculations. 5. Conclusions The measure of the adequacy contribution of a generator (its capacity value) can vary strongly depending on the method used for calculating it, and will privilege some generators over others. Therefore, choosing a methodology that is both rooted on solid theoretical foundations and that takes into account the system characteristics is vital to allow a reliable system operation and to provide the right incentives for entry of new capacity in the medium and long term. The simulation-based method to evaluate the system risk allowed to consider transmission and operational constraints, so the capacity value of the wind farms could factor in the positive and/or negative effects that the wind farm may have on the operation of the system. This can provide a signal regarding the location of future wind farms that existing methods do not have. The methodology proposed in this paper for calculating the capacity value is basically a weighted average of the power made available by that generator (with the weights proportional to the contribution to operational LOLP reduction) and represents the contribution that the unit makes to system adequacy, taking into account some operational effects. The method proved 15

capable of capturing the contribution of wind farms to power system adequacy discriminating the periods of higher risk, and its results were better aligned with the results from the IEEE-recommended method than the current method. Because of the direct relationship between demand and system risk, a positive correlation between available generation capacity and system load is awarded while a negative correlation is penalized. 6. Acknowledgments The authors acknowledge the support of the Chilean National Commission for Scientific and Technological Research (CONICYT) under grant Fondecyt 11110502. 7. References [1] NERC Board of Trustees, Glossary of Terms Used in NERC Reliability Standards, Technical Report, North American Electric Reliability Corporation, 2012. [2] R. Billinton, R. Allan, Reliability Evaluation of Power Systems, Plenum Press, New York, NY, USA, 2nd. edition, 1996. ISBN: 978-0-306-452598. [3] M. Milligan, P. Donohoo, D. Lew, E. Ela, B. Kirby, H. Holttinen, E. Lannoye, D. Flynn, M. O’Malley, N. Miller, Operating reserves and wind power integration: An international comparison, in: 9th International Workshop on Large-Scale Integration of Wind Power into Power Systems as well as on Transmission Networks of Offshore Wind Farms, pp. 18–19. [4] M. Milligan, K. Porter, The capacity value of wind in the United States: Methods and implementation, The Electricity Journal 19 (2006) 91–99. [5] E. Gil, I. Aravena, A LOLP-based method to evaluate the contribution of wind generation to power system adequacy, in: Proc. of Fourth International Renewable Energy Congress (IREC2012), Sousse, Tunisia, dec. 2012, pp. 125–131. [6] A. Keane, M. Milligan, C. Dent, B. Hashe, C. D’Annunzio, K. Dragoon, H. Holttinen, N. Saaman, L. S¨oder, M. O’Malley, Capacity value of wind power, IEEE Transactions on Power Systems 26 (2011) 564–572. 16

[7] B. Hashe, A. Keane, M. O’Malley, Capacity value of wind power, calculation, and data requirements: The Irish power system case, IEEE Transactions on Power Systems 26 (2011) 420–430. [8] K. Dragoon, V. Dvortsov, Z-method for power system resource adequacy applications, IEEE Transactions on Power Systems 21 (2006) 982–988. [9] C. D’Annunzio, S. Santoso, Analysis of a wind farm’s capacity value using a non-iterative method, in: 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, pp. 1–8. [10] L. Garver, Effective load carrying capability of generating units, IEEE Transactions on Power Apparatus and Systems PAS-85 (1966) 910–919. [11] P. Aguirre, C. Dent, G. Harrison, J. Bialek, Realistic calculation of wind generation capacity credits, in: 2009 CIGRE/IEEE PES Joint Symposium on Integration of Wide-Scale Renewable Resources Into the Power Delivery System, pp. 1–8. [12] B. Cummings, M. Lauby, J. Seelke Justification for a NERC resource adequacy assessment model: A NERC staff white paper, Technical Report, NERC, 2007. [13] J. Fazio, A probabilistic method to assess power supply adequacy for the pacific northwest, Northwest Power and Conservation Council, Technical Report, 2011. [14] W. Wangdee,R. Billinton, Considering load-carrying capability and wind speed correlation of WECS in generation adequacy assessment, IEEE Transactions on Energy Conversion, 21, 3, 734–741, 2006. [15] R. Billinton, Y. Gao, R. Karki, Composite system adequacy assessment incorporating large-scale wind energy conversion systems considering wind speed correlation, IEEE Transactions on Power Systems, 24, 3, 1375–1382, 2009. [16] E. Gil, I. Aravena, Evaluating the contribution of intermittent generation to power system adequacy at different demand levels, to be presented at 2013 IEEE Power & Energy Society General Meeting, Vancouver, Canada. 17

[17] Manual de Procedimiento N◦ 23: C´alculo de Potencia Firme y determinaci´on del Balance entre Generadores, Direcci´on de Operaci´on CDECSING, 2009. [18] CDEC-SING, 2011 Annual Report: Statistics and Operation, Technical Report, CDEC-SING, Santiago, Chile, 2012. [19] Energy Exemplar, PLEXOS for Power Systems–Power Market Simulation and Analysis Software [computer software], 2013. URL http://www.energyexemplar.com/. [20] B. Daniel, Xpress-Optimizer Reference Manual, Fair Isaac Corporation, Leamington Spa, Warwickshire, UK, 2009. [21] Comisi´on Nacional de Energ´ıa, Fijaci´on de Precios de Nudo Abril de 2012, Sistema Intercontectado Norte Grande (SING): Informe T´ecnico Definitivo, Technical Report, CNE, Santiago, Chile, 2012. [22] Ministerio de Energ´ıa, Campa˜ na de Prospecci´on E´olica en el Norte de Chile, Technical Report, Santiago, Chile, 2010. [23] E. Gil, Evaluating the impact of wind power uncertainty in power system adequacy, in: Proceedings of IEEE 12th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2012), Istanbul, Turkey, pp. 664–669. [24] J. McLean, Equivalent Wind Power Curves, Tech. Rep. for TradeWind Consortium, jul, 2008. [25] P. Nørgaard, H. Holttinen, A Multi-Turbine Power Curve Approach, , 2004, Gothenburg, Sweden.

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100% 90% Proportion of risk (%)

80% 70% 60% 50% 40% 30% 20% 10%

0% 0%

20%

40% 60% Proportion of time (%)

80%

100%

Figure 1: Proportion of risk versus proportion of time in the SING.

19

Pi

(a) Pil

×

×

×

×

×

×

× D

LOLP

LOLPi LOLP

(b) ∆LOLPli

D

weights χi

(c)

× χli

×

D1

×

D2

×

D3

×

×

× ···

Dl

· · · DL−2 DL−1 DL

D

Figure 2: Representative generation for different demand tranches, contribution to LOLP reduction, and weights for calculating capacity value with the proposed method

20

0.7

Percentage of Rated Capacity

0.6 0.5 0.4 0.3 0.2 0.1 0 0.7

0.75

Wind Interior

0.8 0.85 0.9 Percentage of Peak Load Wind Coast

0.95

1

Both wind farms

Figure 3: Correlation between wind and load based on vigiciles.

21

0

0.0

2

0.2

4

0.4

6

0.6

8

0.8

Wind Interior Generation [pu]

10

1.0 2 4 6 8 10

2 4 6 8 10

Hour

Hour 14

16 18 20 22 24

12

14

16 18 20 22 24

22 Loss-of-load instances [%]

12

Figure 4: Wind generation box-and-whiskers plot and percentage of loss-of-load instances per hour [16]. 2

0.2

4

0.4

6

0.6

8

0.8

10

1.0

Loss-of-load instances [%]

0

0.0

Wind Coast Generation [pu]

23 2575 2616 2657

2616 2657

2616

2657

2534

2493

2453

2412

2371

2330

2289

2248

2208

2167

2126

2085

2044

2004

1963

1922

1881

2575

1.E-04

2575

1.E-03

2534

1.E-02

2534

1.E-01 2493

0

2493

1000

2453

2000

2453

3000

2412

4000

2412

5000

2371

2330

2289

2248

2208

2167

2126

2085

2044

2004

1963

1922

1881

Number of loss-of-load instances 6000

2371

2330

2289

2248

2208

2167

2126

2085

2044

2003

1963

1922

1881

Operational LOLP

Number of hours

2657

2616

2575

2534

2493

2453

2412

2371

2330

2289

2248

2208

2167

2126

2085

2044

2003

1963

1922

1881

Operational LOLP 0.35

0.4

0.25

0.3

0.15

0.2

0.05 0.1

0

800

700

600

500

400

300

200

100

0

Demand [MW]

Figure 5: Construction of operational LOLP versus demand curve for the No Wind case.

1e+00 1e-01 1e-02 1e-03 1e-04

Operational LOLP [-]

Base case (all units) Wind Coast only Wind Int. only No Wind

1900

2100

2300

2500

2700

Demand [MW] Figure 6: Operational LOLP versus demand curves with and without wind.

24

1e+00 1e-01 1e-02 1e-03 1e-04

Operational LOLP [-]

Base case (all units) Without thermal unit U11 Without thermal unit U14

1900

2100

2300

2500

2700

Demand [MW] Figure 7: Operational LOLP versus demand curves with and without thermal plants U11 and U14.

25