Analysis of RES production diagram, a comparison of different approaches

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1 POSTER 2015, PRAGUE MAY 14 1 Analysis of RES production diagram, a comparison of different approaches Michaela Hrochová 1 1 Dept. of Economics, Management and Humanities, Czech Technical University, Technická 2, Praha, Czech Republic Michaela.lachmanova@fel.cvut.cz Abstract. The integration of new renewable energy sources in large scale, especially intermittent ones, into the existing power grids has become nowadays one of the biggest challenges for the energy sector. The increasing electricity production from RES is causing significant problems within the power grid and several EU states have already introduced various restrictions on further intermittent RES development. These problems result mainly from the low predictability and high volatility of electricity production and they do not affect only the stability of power grid but also the price of electricity on the market as well as the needed amount of system and auxiliary services. Therefore future benefits from successful RES integration can be extensive. One promising way how to integrate and even promote RES and its future development is detailed analysis of production diagram and then the concept of virtual power plant. Keywords Renewable sources, production diagram, virtual power plant, statistical analysis 1. Introduction Due to the growth of energy consumption and also due to the decrease of fossil fuels reserves the increasing penetration of renewable energy sources (RES) can be observed. The benefits of this integration include the reduction of emissions in electricity generation, waste-free operation, reduction of the region's dependence on imported fuels and last but not least, preservation of the countryside. On the other hand due to the intermittency of these sources (mainly wind power and photovoltaic generation) the output is often quite impossible to be predicted accurately. Therefore it is necessary to cope with fluctuating production, which requires not only compensation of short-term variability but also plenty of backup power in case of long-term non-supply. One way to reduce the actual impacts of integration of renewables is to focus on the analysis of production from a given source, because only a thorough analysis of the diagram, the revelation of impacts influencing the shape of this diagram will help us to mitigate the negative impacts of integrating renewables. With the successful model the power production can be also better predicted and traded more profitably. It can be namely shown, that aggregation of production diagrams leads to reduction of total variability of whole portfolio of resources. This fact can result in decrease of RES integration negative impacts (as mentioned) and also in better economical profit for producer. Last, but not least, this portfolio can be optimized and used to cover an energy demand, which can be successfully used e.g. in case of island operation. This concept is known as virtual power plant (VPP). This paper compares different approaches to analyze a different types of renewable sources diagram and figures out contribution of possible aggregation. We had data of production of small hydro power plant, 17 photovoltaic panel sources and 3 wind turbines. 2. Methodology During the analysis of any production or consumption diagrams, we can identify many variables influencing final production. The behavior of these random variables can be described by various probabilistic models. For example the load can be typically expressed by a Gaussian process and it can be quite well predicted [1]. On the other hand the production from RES has mostly a random nature and therefore it is not suitable to be described with the help of standard statistic methods. So at first it is necessary to determine, whether a production of source is totally random in time, which would mean it cannot be satisfactorily modelled. If this hypothesis is rejected therefore data can be analyzed. So at the beginning we should observe data and if we suspect data to be random, this data should be tested to be random. One of way how to analyze the production diagram is the utilization of time series analysis. The aim of this approach is to decompose power production into deterministic and stochastic component. Then analyses and prediction of the stochastic component is provided.

2 2 ANALYSIS OF RES PRODUCTION DIAGRAM, A COMPARISON OF DIFFERENT APPROACHES, MICHAELA HROCHOVÁ Whether results from this analysis are not satisfactory, some other approach should be used. In the end we will aggregate diagrams to one portfolio diagram and contribution of aggregation will be evaluated. 2.1 Tests of randomness At first it is necessary to determine whether a production of a renewable resource is completely random in nature or whether we can observe some influences on the production. Let have hypothesis Test based on differences signs Test is based on number of positive differences (points of increase). Let V t be then expected mean of k (sum of points of increase) equals to 2.2 Time series analysis principle For the analysis of the power generation based on RES the method called time series additive decomposition was used. Here we used principles described e.q. in [2],[3],[4],[5] and [6]. Additive decomposition means that each value of the diagram y t can be expressed as the sum of the trend component T t, seasonal component S t and random component ε t: We consider that trend (T t) and seasonal (S t) component are deterministic and the last one (ε t) is random. The following characteristics are expected: and variance is given: Then test of H 0 is provided with rejection range (H 0 is rejected, if) Test based on turnings points Let r be sum of upper and lower turning points. Then expected mean of r and variance is given by formulas and test is provided with rejection range Test based on sum of iteration above and below median Let M be sample median of time observations. We have to construct a groups of observations disposed above (or below) median. Let u be number of these groups and m total sum of observations located above (or below) median. Test is then provided with rejection range We will proceed as follows: First we calculate the seasonal component by which data will be cleaned of. This gives a value consisting of trend and random components that we describe by linear regression. Trend is assumed to be constant (non-changing) in case small hydro diagram and also in case of PV plant diagram. From these data we calculate the trend components and determine the parameters of the random component. 2.3 Analysis of ideal curve residues In the case of small hydro power plant using of time series approach may be found to be quite suitable. We know that the same approach to individual output diagrams should be used for analysis of aggregated diagrams. Therefore at first we analyzed data by time series approach. Then it was released that this approach is not suitable for PV. Due to this fact the new idea of analysis was needed. So we proceeded to analyze PV output diagram in another way. The ideal curve of PV was modeled and subsequently characteristics of deviations were examined. Compared to previous approaches, when model was made by curve fitting existing data. Therefore now the ideal curve represents the model there. Thus the approach to prediction is the following: in the hour and the day will PV produce ideal power production which is reduced by the expected error. This errors (deviations from this ideal production) will certainly have an even greater variance but the overall prediction should be improved. The main aim of this approach is therefore only modelling of deviation values for each time moment. Obtaining an ideal curve Ideal curve was created in collaboration with publicly available programs PVGIS [7]. This software generates

3 POSTER 2015, PRAGUE MAY 14 3 approximate amount of electricity that the panels produced monthly (Wh). This amount is based on the geographical location of the plant, the installed capacity and position panels. The second type of information, provided by this software, was monthly average daily exposure curve in W/m2. So we have a monthly production for the plant in Wh, from which was necessary to obtain daily production. We therefore display the individual monthly values in columns and approximate them by curve, from which each day value of production was returned, as it can be seen in Fig.1. As it can be observed in the minor axis, calculations were provided on normalized values (divided by installed capacity). To get real production it is necessary to multiply all values by installed capacity. So daily production was available to be analyzed but we only had monthly average daily exposure curve. So this curve multiplied by the production gave us a single production for each hour. This is an ideal model from which residues (deviations) are calculated. where u 0,975 is quantile of the normal distribution and σ is standard deviation calculated from analyzed years. The occurrence of measured data in this band is estimated with 95% probability, which is ensured with above mentioned quantiles. The second way to create the reliability band is to simulate 39 simulations of development and for every moment to select the minimum and maximum value prediction. These values determine a band which would again contain predicted values with a 95% probability. But one of the most important testing of model is to compare model with simulations of whole model including random component. The plot of simulations and measured data is one of sufficient way to evaluate the model. The last one of method evaluating the model is the analysis of residues. The acceptable model should report the smallest value of average residue with the smallest variability. In case of indeflected model the residues should have character of normal distribution with N(0;s 2 ). 2.5 Aggregation of sources When we determine, which approach is suitable for analysis of given type of RES, we can aggregate given diagrams and analyze this aggregated diagram of portfolio. We assume that aggregation of differently variable sources decrease a total variability which will be tested by standard statistic methods. Fig. 1. Daily ideal production of electricity. Source PVGIS [7] The main aim of this approach is, as above mentioned, characterization of deviations from ideal diagram and modelling of these values. It can be shown that this idea, in modelling of PV output, brings more sufficient results then time series approach. 2.4 Model testing First approach to testing of model is only to plot tested data with model without random component. It shows a rough comparison of model with predicted data. The second approach is to create a reliability band, a determined interval where predicted values should be placed. It can be done by two method. First one uses quantiles of Gausses distribution and the second one uses simulations. While the first one determined the reliability band in the subsequent form: (13) 3. RES production analysis Data from production of small hydro power plant, photovoltaic panels and wind turbines were given and subsequently analyzed. 3.1 Case study Tři chaloupky, small hydro power plant Data for the creation of the model was given from the small hydroelectric power plant Tři chaloupky in the middle reaches of the Labe between Čelákovice and Lysá nad Labem. This source is a river flow plant with installed capacity of 1120 kw and an annual production of about MWh. This represents an annual maximum utilization of less than 6000 hours. Thus this resource would be characterized as a base source, so constant production with slight fluctuations can be assumed. The data set for analysis was very extensive; we had measurements for each 15 min for a period of four years ( ), so we processed this data to hourly averages. The model was created based on the analysis of the first three years and then tested for the fourth year. It should be mentioned that part of these results had been presented in [2].

4 4 ANALYSIS OF RES PRODUCTION DIAGRAM, A COMPARISON OF DIFFERENT APPROACHES, MICHAELA HROCHOVÁ Fig. 2. All fifteen minutes measurements 2008, small hydro Fig. 5 Testing of model, band reliability with quantiles Fig. 3. Processed data, daily averages At first we decided to test data for randomness, but we observe that small hydro production shows repeated regular influences, so data were not tested. For analysis a time series approach had been used, a model without random component has been created and subsequently tested (as described in part 2.2. and 2.2.1) and results can be seen in Fig. 4., 5, 6, 7. Fig. 6 Testing of model, band reliability with simulations Fig. 4 Model of small hydro diagram, without random component Fig. 7 Testing of model with simulations on values of year 2011 We used time series approach and results are quite satisfactory. The reason is that small hydro power plant diagram is quite stable and well-predictable. We will see that this approach is in case of photovoltaic production or wind turbine production inappropriate.

5 POSTER 2015, PRAGUE MAY Case study photovoltaic sources For further analysis data from 17 PV plants have been used to develop the model. PV plants have an installed capacity of between 200 kw and 2000 kw and all of them are located in North Moravia and installed on the ground on the pillars. It was fifteen-minute measurement from one year, so hourly average values were created. At first we decided to test data for randomness, but we observe that photovoltaic production shows repeated strongly regular influences (e.g. null production in night), so data were not tested. At first we used time series approach, which mean that model without random component was created and compared with real PVE output. Subsequently random component was for each moment generated and then compared with real PVE output. Results can be observed in Fig. 9. and Fig. 10. Fig. 11 Model 3 ideal curve residues, without random component, plotted with measured values Fig. 14 Model 2 - plotted with simulations Fig. 9. Model 1 - time series approach without random component We can observe by comparing Fig. 10 and Fig 14, the ideal curve residues approach is quite suitable than time series approach. Simulated production better fits to real PVE output. 3.3 Case study wind turbines sources For further analysis we had fifteen minutes data of production of 3 wind turbines from years These data were plotted and observed and expected to be even more random than in case of photovoltaic production. Fig. 10 Model 1 compared with simulations It can be observed, that this approach is not as suitable as in case of small hydro due to high variability of photovoltaic source. So we used another approach, we modelled ideal curve, as mentioned above, and for each time moment residues were analyzed and these residues were modelled and predicted. Results are plotted in Fig. 11 and 12. Fig. 12 Wind turbine production January 2011

6 6 ANALYSIS OF RES PRODUCTION DIAGRAM, A COMPARISON OF DIFFERENT APPROACHES, MICHAELA HROCHOVÁ So H 0 was set (we expect data from wind turbine totally random): and tests of randomness with following results were provided: Test based on differences signs k Test value -23,5483 Critical value 1, Hypothesis was rejected Test based on turnings points r Test value 124,1531 Critical value 1, Hypothesis was rejected Test based on sum of iteration above and below median u 755,5 m Test value -179,059 Critical value 1, Hypothesis was rejected Tab. 1: Testing of randomness of wind turbine production So we analyzed data and hypothesis of randomness was rejected by all used tests. That shows that production of wind turbines is not absolutely random and we can expect that we can create a model. As we realized, time series is not suitable and appropriate for analysis of wind turbine production. Idea of ideal curve for wind turbines is not usable at all. In following research we will use another approaches (autocorrelation analysis, method combining time series principle and random component generator related to weather prediction ) and we will set another appropriate approach. 4. Aggregation of diagrams As appropriate models were set, we determined aggregated portfolio of sources (17 PVE and one wind turbines). Values were analyzed in relative form by dividing by installed capacity, so following results are calculated in nkw. We provided a following basic statistical analysis: Relation mean Relation standard deviation Wind turbine 1 0,2391 0,2976 Photovoltaic source 0,1242 0,2110 Portfolio of 17 PVE 0,1208 0,2057 Portfolio of 17 PVE and wind turbine 0,1364 0,1757 Tab. 2: Statistical analysis of aggregated diagram As it can be observed, only simple aggregation of 17 photovoltaic sources decrease standard deviation from 0,211 to 0,2057. This decrease is even much significant, if we add a wind turbine to the portfolio. Than only by simple aggregation relative standard deviation decrease to value 0,1757, which shows at least 15% of reduced variability. This hypothesis will be in following research evaluated. Combination of intermittent sources power diagrams added with one wind turbine source is only the first step to create a complex portfolio of energy sources with decreased total variability and more sufficient predictability. Question of aggregated of portfolio of sources leads to many questions to solve. Which model is appropriate to use to portfolio analysis? Which composition of portfolio is optimal to operate? Which conventional source to smooth aggregated diagram and decrease total variability is ideal to use? Some sources were suggested (biomass, combined steam-gas plant, ) and will be analyzed. But last and not least, for real operation of virtual power plant is necessary to link the operation of VPP to prices on electricity market. It will be also part of following research. 5. Conclusion In this paper some possible approaches for RES diagram analyses were presented. Using of time series approach has been proved suitable for sources with small variability as a small hydro plant. Sources depending on more stochastic parameters (e.q. variable sunlight) requires other approach. We suggested modelling of deviation from ideal curve, which is quite satisfactory for photovoltaic sources. Also we realized that time series approach neither ideal curve residues approach is not suitable for wind turbine production analysis, so one of our goals in following research is to find out appropriate approach to analyze wind turbines diagram. The aggregated portfolio was then analyzed and the decrease of total variability was proved by simple basic statistical analysis. In further research we will focus more on detail analysis of portfolio and we would like to suggest some approach to determination of ideal portfolio structure. This optimization should concentrate on advantages of

7 POSTER 2015, PRAGUE MAY 14 7 aggregation of different RES combinations. The final goal is then to create a model of virtual power plant with optimal shares of different types of sources and with minimized and best predicted variability. Acknowledgements Research described in the paper was supervised by doc. Ing. Jaroslav Knápek, CSc., Department of Economy, Management and Humanities, FEE CTU in Prague and supported by the Student Grant Competition under grant No. SGS14/139/OHK5/2T/13. References [1] Malahat Peik-Herfeh, H. Seifi, M.K. Sheikh-El-Eslami, Decision making of a virtual power plant under uncertainties for bidding in a day-ahead market using point estimate method, International Journal of Electrical Power & Energy Systems, Volume 44, Issue 1, January 2013, Pages 88-98, ISSN , ( 66) [2] LACHMANOVÁ, Michaela. Analysis of power sources variability. Praha, Diploma thesis. Czech Technical University Faculty of Electrical Engineering. [3] CIPRA, Tomáš. Finanční ekonometrie. (Financial Econometry)1. Print Ekopress:, 2008, 538 s. ISBN [4] Male vodni elektrarny (Small hydropower plants). 1. print Bratislava: Jaga, 2003, 175 s. ISBN [5] RNDr. KATEŘINA HELISOVÁ, PH.D. ČVUT, FEL. Mathematics for Economy: Materials for the course [online] [cit ]. Available from: < zapisky.pdf> [6] GABRIEL, Pavel. Male vodni elektrarny (Small hydropower plants). Vyd. 1. Praha: ČVUT, 1998,321 s. ISBN [7] PVGIS. PVGIS: photovoltaic software [online]. [cit ]. Available from: pe About Authors... Author is PhD student at Department of Economics, Management and Humanities, Faculty of Electrical Engineering, Czech Technical University. The aim of her PhD research is to deal with a RES integration by RES diagram analysis.