Title Evaluating the Impact of Wind Power Uncertainty on Power System Adequacy Authors Esteban Gil Universidad T´ecnica Federico Santa Mar´ıa, Valpara´ıso, Chile Conference: 12th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2012), Istanbul, Turkey, Jun. 10-14, 2012. URL: – DOI: – Abstract This paper discusses how wind power uncertainty affects power system adequacy from an operational point of view. A method is presented to produce wind power generation simulated data to feed a Monte Carlo scheme. The Monte Carlo scheme randomly selects forced outage patterns for each conventional generator and wind power simulated patterns in order to evaluate how system adequacy metrics, such as Loss of Load Probability (LOLP) and Loss of Energy Expectation (LOEE) change with the introduction of wind power into the system. The method is tested on a model of the Chilean Northern Interconnected system. Results show how LOLP and LOEE change for different capacity reserve margin levels and different levels of wind penetration. Keywords Wind energy generation, power system reliability, power system adequacy, capacity value, Monte Carlo techniques, LOLP, LOEE (c) 2012 PMAPS.

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Evaluating the Impact of Wind Power Uncertainty on Power System Adequacy Esteban Gil Departamento de Ingeniería Eléctrica Universidad Técnica Federico Santa María Valparaíso, Chile [email protected] Abstract— This paper discusses how wind power uncertainty affects power system adequacy from an operational point of view. A method is presented to produce wind power generation simulated data to feed a Monte Carlo scheme. The Monte Carlo scheme randomly selects forced outage patterns for each conventional generator and wind power simulated patterns in order to evaluate how system adequacy metrics, such as Loss of Load Probability (LOLP) and Loss of Energy Expectation (LOEE) change with the introduction of wind power into the system. The method is tested on a model of the Chilean Northern Interconnected system. Results show how LOLP and LOEE change for different capacity reserve margin levels and different levels of wind penetration. Keywords- wind energy generation, power system reliability, power system adequacy, capacity value, Monte Carlo techniques, LOLP, LOEE

I.

INTRODUCTION

As wind generation technology matures and becomes more competitive with conventional generation technologies, its penetration and impacts on power systems will continue to grow. Therefore, system operators and regulatory bodies need to be prepared not only for wind power promised benefits but also for the novel operational and regulatory challenges that a larger wind power penetration will bring. Because of their different operational characteristics, wind energy generators can become a substantial challenge to incorporate in electricity grids long dominated by conventional thermal and hydro technologies. Depending on the scope of the beholder, the challenges brought by renewable technology integration will lie on one of these three categories: i) operational challenges, such as system transient stability problems caused by the low inertia of the wind farms, or additional operational burden due to the intermittent or undispatchable nature of wind power; ii) planning challenges, such as how much wind power can be accommodated into the market so as to maintain acceptable system reliability; and iii) regulatory changes, such as policy changes necessary in order to incentivize investments on renewable technologies and with the purpose of capitalizing on their perceived benefits. Of course, many of the integration issues brought by wind power also encompass complex modeling efforts in order to represent their particular characteristics and special operating regimes adequately into our existing models, and this has caused a boom of research efforts [1]-[2].

Many different studies have been conducted on integration of wind power into existing grids (see [3]-[5] for reviews and [6]-[11] for detailed studies). In particular, many of these studies deal with evaluating the impact that uncertainty in wind farm output has on power systems, generally with one or both of these objectives in mind: 1) To estimate the wind resource capacity value, that is, the contribution of each wind power generator to power system adequacy, and/or 2) To determine the additional amount of operational reserves that the system must carry to account for the uncertainty on wind power output. Hence, while the first objective is oriented to evaluating the contribution to reliability of the generator itself, the second objective attempts to evaluate the preventive actions that the system operator must take on face of the additional uncertainty such that system reliability remains within acceptable boundaries. Either of these objectives requires understanding of how power system adequacy, that is, the capacity of the system supply to meet its demand taking into account unexpected outages of generators or transmission infrastructure and possible constraints on the primary energy resource [12], changes under different operating conditions. The results presented in this paper correspond to a pilot study conducted to evaluate the impact on reliability that the possible incorporation of wind power into the Chilean Northern Interconnected System (Sistema Interconectado del Norte Grande, SING) might have. The SING is an almost purely thermoelectric system with about 3.7 GW installed generation capacity in 2010 and most of its load being industrial and relatively flat. Although the SING has not wind power installed so far, the Chilean market for renewable generation projects has accelerated its development over the last few years, mainly driven by the removal of barriers of entry and increasing electricity demand and prices. Recent changes to the regulatory framework seek to ensure that the characteristics of nonconventional renewable energy (NCRE) technologies are properly accounted for so that they can be effectively incorporated into the electricity market [13]. There are two main objectives for this study: 1) To develop and evaluate a method to produce wind power generation simulated data and 2) Use the simulated data in a Monte Carlo scheme that will allow a better understanding of how system adequacy metrics, such as Loss of Load Probability (LOLP) and Loss of Energy Expectation (LOEE) change with the introduction of wind. Section II of this paper will present the Monte Carlo scheme and discuss issues related to generation dispatch and

pre-dispatch under uncertainty while Section III will discuss the generation of simulated wind data. Section IV will describe the test system and present preliminary simulation results. II.

METHODOLOGY

A. Overview Evaluating the impact of a particular generator on power system adequacy is usually performed by using the Effective Load Carrying Capability (ELCC) approach. The ELCC approach consists on evaluating the additional amount of 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 [14], has been successfully applied for decades to conventional generators and it may certainly prove valuable when dealing with intermittent generators such as wind. For example, the reliability equalization technique, based on ELCC principles, replaces the generator of interest by some benchmark generation unit of a variable capacity, and then varies its capacity until some system adequacy metric (e.g. LOLP) is the same than with the generator being evaluated. Despite ample acceptance of these ideas, there are quite a lot of dissimilarities in terms of their implementation. For example, no clear rules exist regarding the type of benchmark generator to use when doing reliability equalization, or about the most appropriate system adequacy metric to use (LOLP, LOLE, LOEE, etc.)[15]. Traditionally, ELCC-based ideas have been implemented by applying convolution to the probability distributions of the generators’ availability and the demand [16]-[17]. This method does not need simulation and works well if the variables are independent. But since availability of wind is usually correlated to system demand, simulation methods should be used instead. The Monte Carlo simulation scheme presented in this paper can be summarized as follows: Using a forecast of wind power for the following day, a detailed hourly unit commitment is obtained for each day. Then, the unit commitment decisions are fixed and a Monte Carlo simulation is applied to the economic load dispatch in order to obtain LOLP and LOEE versus capacity reserve margin. The Monte Carlo sampling is done to randomly determine forced outage patterns for each conventional generator, and to randomly select a wind power simulated pattern that preserves the correlation between load and wind power generation. Considering that having un-served energy is a rare event, the process usually requires a large number of simulation samples as it tries to make estimations about the tail of the probability distribution of the balance between demand and supply. B. Pre-dispatch To model realistically how pre-dispatch decisions are made, on the Unit Commitment (UC) algorithm the generators are scheduled to operate or not based on a prediction of demand and wind output for the next 24 hours, considering a hard operating reserve requirement to account for unexpected outages and errors in the load and wind forecasts. Because most of the generating units in the SING are large inflexible coal and gas-fired units, most on-off decisions need to be modeled as integers and the unit commitment becomes a

relatively large Mixed Linear Integer Program to solve. Although some authors have suggested the use of stochastic programming [18]-[22] for this type of problems, its use would increase substantially simulation time and thus it is considered to be out of the scope of this preliminary study. Once a solution has been obtained, the algorithm then fixes the UC decisions of the most inflexible conventional generators and passes them down to the Economic Load Dispatch (ELD) algorithm. C. Load dispatch using Monte Carlo The UC decisions from the previous stage are fixed for the inflexible units, and load dispatch is conducted for different Monte Carlo samples. In this stage only peaking and fast intermediate generation units can change their commitment decision, thus the mathematical optimization problem is considerably faster to solve. The Monte Carlo sampling randomly selects forced outage patterns for each conventional generator, and also randomly selects a wind power simulated pattern created as per described in Section III. The Monte Carlo simulation results can then be used to obtain various power system adequacy metrics. In this case we selected a capacity adequacy metric (LOLP) and an energy adequacy metric (LOEE). It must be observed that different periods carry different risk, as the balance between demand and supply is not always the same. Thus, the focus of this paper will be on obtaining a relationship between the reserve capacity margin and the power system adequacy metric of choice. Notice that the capacity reserve margin varies through the year as a result of load variation, scheduled outages of generators and transmission lines, and as a result of the connection of new power plants. In this preliminary stage of the study 200 Monte-Carlo samples per case are being considered. However, based on uncertainty estimates of the adequacy metrics, over 1000 samples may be necessary in later stages in order to reduce the uncertainty of the estimates, especially in low-risk/high capacity reserve margin periods. III.

MODELING OF THE WIND

A. Modeling issues In general, generators such as thermal plants burning fossil fuels, thermonuclear plants, or hydroelectric plants can be considered to be available as long as the unit is not on maintenance or an unexpected outage occurs. In contrast, wind generation output depends on meteorological factors outside direct operator control. The following will discuss different aspects and challenges related to the operation and integration of wind generation, and will indicate certain guidelines that need to be followed to properly simulate the effect that wind generation uncertainty will have on UC and ELD decisions. 1) Dispatchability Dispatchability of a generation unit refers to the ability of the system operator to program or decide (dispatch) in advance if and how much a unit will be generating within a specified timeframe. In the formulation of the mathematical problem, dispatchability of a unit refers to the suitability of the unit generation in a given period to become a decision variable in the UC and the ELD optimization problems. Since the

operational costs of wind power tend to be small or negligible compared to the operational costs of conventional thermal power plants, there are no transmission or unit commitment constraints, wind generation will only be limited by the availability of the renewable resource. However, due to the intermittent nature of the wind resource, wind generation is treated not as a decision variable (either generated deterministically or stochastically) but as an input of the optimization problems. 2) Average capacity factor and seasonal patterns The average capacity factor of wind generation changes over time as a result of cyclic behaviors of the weather (e.g. day and night; Winter and Summer). As the load also manifests such cyclic behavior, it is important to represent these cycles in the modeling since the correlation between load and wind power output may play a very significant role in evaluating its contribution to power system adequacy. 3) Correlation between load and wind output Evaluating the impact of wind power on system adequacy must take into account how much capacity the generator can make available at high system risk periods [5]-[23]. That is, when a generator is needed the most its contribution to system adequacy will be greater. 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) will be higher than the capacity value of a generator unable to do so. 4) Variability and Predictability Variability of a generator refers to the extent to which its output can exhibit undesired or uncontrolled changes [24]. Thus, a metric for variability will describe how far the generator’s output lies from its average generation. Obviously, the variance or standard deviation of a generator’s output is a metric for the generator’s variability. Although all types of generation are subject to some variability as a result of unexpected outages, in wind generators this characteristic is more accentuated. For example, wind speeds, and therefore wind power output, can be highly variable at different timescales: hourly, daily and seasonally.

2.

Simulated wind data should be a good representation of historical wind data: Seasonal patterns in the data should be reproduced, and each simulated data pattern should have autocorrelation and partial autocorrelation functions similar to the ones of the historical data.

3.

Correlation between wind power availability and load should be preserved, as wind power capacity value can be very dependent on this correlation.

4.

Uncertainty in the first few periods of the forecast should be smaller than in later periods: Wind power can be predicted reasonably accurately for the next few hours, but not very accurately for periods far-ahead. This should be reflected in that the simulated data for the Monte Carlo simulation should increase its variance as time progresses.

C. Modeling of wind power uncertainty For the purposes of this work two types of wind data will be needed. First, we need a time series corresponding to the forecast of the wind for the next 24 hours for use in the UC algorithm. Second, we need a set of time series of simulated wind power data for use in the Monte Carlo simulations. The historical wind data is from 20 months of generation data from a 62MW wind farm relatively close but not connected to the SING. The data was normalized to values between 0 and 1 to allow later resizing. All statistical analyses of the data were conducted in R [25]. 1) Removing seasonal variations Despite not having enough historical wind power data to properly identify yearly seasonal patterns, their existence is strongly suggested by the analysis of historical wind speed data, and as a boxplot indicating the 25, 50, and 75 percentiles of hourly wind generation of the wind farm for each month illustrates in Figure 1. It is observed that during the first half of the year the wind farm capacity factor remains relatively low and then increases with the Spring, peaking in September. Thus, to account for this seasonal variation a linear model of the wind generation data using the month as a factor was fitted.

Predictability of a generator refers to the extent to which the output of the generator can be inferred in advance (for the next hour, day, week, month or year) [24]. Intermittent generators’ predictability is directly related to the autocorrelation and seasonal patterns present in the time series of its output. For example, while wind farm production in the short term (a few hours ahead) can be predicted with some precision, it is not possible to do so on the long term (at least hourly) because of the chaotic nature of the weather. B. Guidelines for generating simulated wind data Based on the previous discussion, a set of guidelines for generating simulated wind data is suggested: 1.

Wind generation must not be treated as a decision variable. Instead, wind generation patterns must be created externally (preferably stochastically) and fed to the UC and ELD problems.

Figure 1. Boxplot of wind generation versus month

algorithm outlined in [26] and implemented in R´s forecast package. Using this procedure, the best model turned out to be a SARIMA(1,0,1)x(1,0,0){24} model with parameters outlined in Table I. The diagnostics for the model fitting of the remainder can be seen in Figure 4. The model is considered to satisfactorily represent the data, as the autocorrelation function of the SARIMA model residuals is very flat and the p-values of the Lung-Box statistic are all small. TABLE I.

PARAMETERS OF THE SARIMA(1,0,1)X(1,0,0) {24} MODEL ar1

ma1

sar1

0.9306 0.1536 0.0645 coefficient 0.0033 0.0088 0.0085 standard error sigma^2 estimated as 0.005761: log likelihood=16138.04 AIC=-32266.09 AICc=-32266.09 BIC=-32228.38

intercept 0.0000 0.0114

Figure 2. Boxplot of wind generation versus hour

A boxplot of the data using the hour of the day as a factor is shown in Figure 2. The boxplot suggests a strong daily seasonal pattern, as a result of predictable weather variations between night and day. In order to get rid of the daily seasonal pattern, we applied a local polynomial regression fitting procedure to the residuals of the previously fitted linear model. The residuals of the new model are shown in Figure 3.

Figure 4. Diagnostic of the fitted SARIMA(1,0,1)x(1,0,0)[24] model

3) Using the fitted model to produce forecasted and simulated data For each day, a forecast and a set of simulated data are produced using the previous values of the time series, the parameters of the SARIMA(1,0,1)x(1,0,0){24} model, and the seasonal patterns identified earlier. Figure 3. Time series of the residuals after removing the yearly and daily seasonal effects

2) SARIMA model fitting According to the partial autocorrelation function of the residuals, there is strong evidence of an implicit autoregressive process and a remaining seasonal autoregressive process. The autocorrelation function also shows the signature of a moving average process. Based on a KPSS test, we identified no need for first-differencing, and based on a CH test we identified no need for season-differencing. In order to determine the order of the most adequate Seasonal Autoregressive Integrative Moving Average (SARIMA) model, we conducted a recursive search using the

While for the 24-hour ahead forecast the model error is assumed to be zero and the predicted values are simply a linear function of the previous values, the simulated data series errors are generated by randomly sampling from a normal distribution with zero mean and variance as given by Table I. After applying the SARIMA model to the data and the randomly generated errors, simulated wind generation patterns are then reconstructed by summing up the seasonal components. IV.

SIMULATION RESULTS

A. Test system The test system is the Chilean Northern Interconnected System (Sistema Interconnectado del Norte Grande, SING).

The energy 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 ancillary services and is able to perform stochastic simulations [28]. Once PLEXOS formulates the mathematical program, it is solved using Xpress [29]. The CDEC-SING, the SING independent system operator (ISO), provides on their website a PLEXOS database of their system for purposes of their weekly generation programming containing detailed production and network data. For this work, the collection of databases for a whole year (Nov. 2010 to Oct. 2011) were merged, tested, and adapted to suit the purposes of this study. The outputs of the simulations were benchmarked against actual system outputs to check for correctness and consistency. Then, by using Monte Carlo simulation following the procedure outlined in Section II, system adequacy metrics (LOLP and LOEE) for the system at different capacity reserve margins were obtained. B. Results Results for LOEE versus capacity reserve margin for different-sized wind farms are shown in Figure 5. LOLP results are shown in Figure 6. Both LOLP and LOEE are observed to decrease exponentially as the mismatch between available capacity and peak load (capacity reserve margin) increases.

100%

LOLP (%)

The SING is an almost entirely thermal system with about 3.7 GW installed generation capacity serving mainly flat industrial loads (mining) and a small percentage of residential loads (about 10%). It has several old baseload coal units with relatively inflexible operating regimes (57.8% of total generation in 2010), some newer combined-cycle and opencycle gas-fired units (26.8%), some fuel-oil and diesel-based peaking plants (15%), and a small amount of hydro generation (0.4%) [27]. Despite the system having relatively large capacity reserve margins (over 70%), an inflexible generator mix coupled with a number of transmission constraints cause many instances of unserved energy to occur.

10%

1% 40

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Capacity reserve margin (%) No Wind

Wind 100MW

Wind 2x100MW

Wind 200MW

Expon. (No Wind)

Expon. (Wind 100MW)

Expon. (Wind 2x100MW)

Expon. (Wind 200MW)

Figure 6. System LOLP versus capacity reserve margin for wind farms of different size

The results in Figures 5 and Figure 6 show that system adequacy is reduced (as LOLP and LOEE increased) when wind farms are introduced to the system. This decline in adequacy will eventually need to be compensated by increasing the operational reserves carried by the system, in order to restore adequacy to acceptable levels. Table II shows LOEE values in MWh for different capacity reserve margin levels. At the lowest capacity reserve margin (80%), the introduction of 100MW of wind increases the LOEE by about 4 MWh, while at higher capacity reserve margins the impact of wind power uncertainty on system adequacy is reduced. TABLE II.

SYSTEM LOEE (MWH) VERSUS CAPACITY RESERVE MARGIN Capacity reserve margin 80% 100% 120% 11.6 6.6 3.8 15.6 8.9 5.1 19.8 11.3 6.5 20.2 11.5 6.6

No Wind Wind 100MW Wind 2x100MW Wind 200MW

LOEE (MWh)

100

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120

140

160

180

200

Capacity reserve margin (%) No Wind

Wind 100MW

Wind 2x100MW

Wind 200MW

Expon. (No Wind)

Expon. (Wind 100MW)

Expon. (Wind 2x100MW)

Expon. (Wind 200MW)

Figure 5. System LOEE versus capacity reserve margin for wind farms of different size

As the wind farm size increased, adequacy with respect to the ‘no wind’ case decreased. Additionally, we tried to compare if wind resource diversity played an important role for this particular system by comparing the performance of a single 200 MW capacity wind farm against 2x100 MW wind farms, but our results were inconclusive. Since unserved energy events are of rare occurrence, a large number of simulations might be necessary in order to properly estimate if the system adequacy metrics are significantly different for both cases. V.

CONCLUSIONS

Numerical results show that system adequacy, as measured by both LOLP and LOEE, decreases exponentially as the capacity reserve margin for the system is reduced. Our preliminary results for the SING showed that at the lower capacity reserve margin every 100 MW of wind generation added to the system increased the LOEE by about 4 MWh as a result of wind power uncertainty. This constitutes a clear signal

to the ISO about how much additional operational reserve to carry in order to keep system adequacy at its original level. On subsequent simulations we have observed the impact of wind uncertainty on power system adequacy to be quite dependent on specific characteristics of the system, such as generation technology mix, load shape, operational reserve carried, transmission conditions, and ramping characteristics of the thermal units. The statistical properties of the wind power time series data are also very relevant in this type of analysis. As shown in Figure 2, the wind data we used for this study has a very strong daily pattern, which makes its uncertainty to be less troubling than simulated data generated from different wind data sets. A follow-up study will evaluate the additional operational reserves that this system will need to carry per each MW of wind power installed using additional wind data. We also expect to elucidate if wind resource diversity will play a significant role in the impact that wind power uncertainty has on power system adequacy. ACKNOWLEDGEMENTS The author acknowledges the support of the Chilean National Commission for Scientific and Technological Research (CONICYT) under grant Fondecyt 11110502. REFERENCES [1] [2]

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