A Novel ARX-based Multi-scale Spatiotemporal Solar Power Forecast Model

Transcription

1 A Novel ARX-based Multi-scale Spatiotemporal Solar Power Forecast Model Abstract In this paper an autoregressive with exogenous input (ARX) based spatio-temporal solar forecast model is proposed. Compared with conventional temporal-only autoregressive models, the proposed formulation takes into account both spatial and temporal solar power correlations. The overall root mean squared error (RMSE) percentage can be reduced by.7% using spatio-temporal solar forecast compared with persistence forecast model for hour ahead intervals. Index Terms Spatio-temporal, Solar irradiance, Solar power forecast, Spatial correlation. Chen Yang, Student Member, IEEE, Le Xie, Member, IEEE Department of Electrical and Computer Engineering Texas A&M University, College Station, 7784, TX USA I. INTRODUCTION HOTOVOLTAIC (PV) generation is increasingly installed Pin power systems. As shown in Solar Technologies Market Report [], the global cumulative PV capacity in the United States of has added approximately 6.6 W, which is a 3% increase over the 7. W installed in 9. The potential barrier of integrating solar power into the existing power grid includes variability which is brought by the natural variation of solar irradiance and uncertainty caused by the forecast error of solar power []. Thus efficient use of the fluctuating solar power will benefit tremendously from forecast information on the expected power production [3]. This forecast information is also necessary for the management of the electricity grids and solar energy trading. The objective of this paper is to propose a multi-time scale forecast model performance evaluation from minutes ahead up to day ahead intervals. Overview of solar power forecast is presented in [4, 5], a physics-based numerical weather prediction (NWP) model with statistical adjustments like model output statistics (MOS) is proposed in [6] and several data-driven based forecast models are discussed in [7-9]. However, most of the existing literatures on short-term (hours ahead to minutes ahead) solar forecast uses temporal only models. Inspired by the recent work on spatio-temporal wind forecast models [, ], which leverage both spatial and temporal correlations of dispersed wind farms' output, we propose a spatio-temporal autoregressive with exogenous input (ARX) model for short-term solar power forecast. iven the fact that solar irradiance is primary affected by cloud coverage patterns, a solar forecast model will likely benefit from drawing spatial and temporal correlations among dispersed solar farms. This is becoming technically feasible driven by the technological advances in sensing communications and computation. In summary, the main contribution of this paper is two folds: ) We propose a spatio-temporal forecast model for solar generation in both hour ahead and day ahead levels. This forecast model takes into account historical data of both local and nearby solar sites. This model is tested with realistic solar data, and has shown improved forecast accuracy //$3. IEEE ) Based on the trade-off comparison between amount of information and forecast accuracy, the optimal spatial layer is suggested which provides even more accurate forecast and shows the potential to extend layer with more amount of information. This paper is organized as follows. Section II provides a comprehensive review of solar power forecast method of multitime intervals. Spatial correaltions of nearby solar farms are illustrated in Section III. In Section IV, we propose a detailed solar irradiance forecast method in which both spatial and temporal historical solar data is utilized to improve the forecast accuracy. Performance comparison between spatio-temporal and persistent forecast (PSS) model is provided in Section V, meanwhile the selection of optimal spatial layer is explained. Concluding remarks and future work are discussed in Section VI. II. OVERVIEW OF SOLAR POWER FORECAST METHOD There are three different approaches for solar power forecast. The first is the physics-based approach which requires large amount of data to accurately characterize the underlying weather model [5]. Another approach is the datadriven statistical approach such as ARX model [9] or computational intelligence tools like artificial neural networks (ANNs) []. The third approach is a hybrid one which combines the physics-based and data-driven model [3]. From a time-scale prospective, solar power forecast method can be classified from minutes ahead up to months ahead. For minutes ahead forecast, persistence, skycams, local irradiance trends are the major three tools to perform solar power forecast. iven the fact that rapid and erratic evolution of solar irradiance may not be observed by the existing solar irradiance sensors, it s very difficult to beat a persistence forecast in minutes ahead level. Some state-of-the-art forecast methods like the ANNs optimized by genetic algorithms which combined with the evolutionary non-integer order (ENIO) algorithm [7, 8] can achieve around 5% root mean squared error (RMSE) which slightly outperforms the persistence. However, the computational complexity is a major drawback due to fractional genetic algorithm plus ANN processing time. Also the increased sampling rate will make the persistence method more accurate. For hours ahead forecast, satellite-based cloud advection and physics-based NWP is mainly used in [5]. The NWP model explicitly predicts a time series of most atmospheric variables including solar irradiance at all grid points in the model domain. However, physics-based models require extensive experience to perform and a significant amount of time to optimize the model parameters. For days ahead forecast, NWP with statistical adjustments like MOS is widely used. In [6], MOS correction of global

2 horizontal irradiance (HI) forecasts from three operational NWP models are evaluated. It turns out that MOS application to the NWP irradiance output is successful in minimizing bias and reducing RMSE. However, due to the complex cloud microphysics and limitations in spatial resolution, clouds and their radiative properties are difficult to predict in numerical models. Consequently, NWP models are expected to show inherent regional or global biases limiting forecast accuracy. For weeks ahead up to months ahead forecast, climatology and climate trends [5] are utilized to forecast long term characteristics of solar resources by time of day and day of year. While most of the aforementioned forecast models are based on local measurement only, recent study shows the potential spatial correlations among geographically dispersed solar farms. In the next section, we will briefly discuss the possibility of leveraging spatial correlations among different solar farms for enhanced forecast of solar power. III. SPATIAL CORRELATIONS OF SOLAR FARMS A. Spatial correlation Solar data from spatial neighborhoods is very useful for solar power forecast. Also the cloud coverage is included because the variability of solar irradiance is mainly caused by the rapid change of cloud cover percentage. Meanwhile, the cloud usually covers a large area which means the cloud coverage remains unchanged within a large area. Taking account of the local topographic information into solar irradiance forecast is also highly beneficial. Simulation result in [4] shows ramping at a single site can be severe, but diversity between sites can mitigate ramps when the data of several locations are aggregated. Also [5] points out that correlation decreases rapidly with distance, significant benefit from spatial averaging should occur even below 5 m in their case of Renewable Energy Laboratory (NREL) Oahu measurement site. B. Solar Power versus Solar Irradiance It is of interest to power system operators to get high confidence forecast of solar power output. However, most of the measurements are directly related with solar irradiance. In this subsection, we briefly review the relationship between solar power and solar irradiance. The variables and constants in this section are defined in Table. Symbols V oc I l I TABLE NOTATIONS Description Open circuit terminal voltage Photon-generated current component Cell reverse saturation current Solar irradiance W / m S η Solar panel size Conversion efficiency including ratio of the electric power output to the light power input and power efficiency of inverter As insolation drops, short-circuit current drops in direct proportion. Decreasing insolation also reducesv oc, but it does so following a logarithmic relationship that results in modest changes inv oc. Meanwhile current-voltage characteristic curve [6] shows the voltage in the maximum power point tracking (MPPT) curve is almost unchanged when the temperature is constant. The current-voltage relationship for the ideal PV cell is given by ( qv / kt I = I ) l I e () where kt / q = 5.7mV at a temperature of 5 C. More specifically, the photocurrent is related to sunlight intensity by the relationship Il = Il( ) () It is reasonable to assume a linear relationship between PV generations output and solar irradiance, and it is suitable to link solar irradiance with PV generation with the panel size and efficiency at a given materiel. Thus, the following equation can be used to calculate the electric power of PV generation: P = S η (3) IV. PROPOSED SOLAR IRRADIANCE FORECAST MODEL In this section, we focus on solar irradiance forecast, which is a challenging topic due to the variability casued by cloud coverage and haze, dust and smoke particles. A. Model Formulation The standard equation of ARX model is as follows: yt () + ayt ( ) + ayt ( ) + + ayt n ( n) = b u( t d) + b u( t d ) + + b ( ) u u m u t d m + u (4) + + b u ( ) ( ) u i t di + b u i u i t di i + + b u ( t d m + ) + ε ( t) mu i i i i where yt ( ) is output at time t, n is number of poles, mi is the number of poles plus and d i is number of input u i samples that occur before the input affects the output. For conventional ARX model, the exogenous input is usually not the same data category as that of output. Also there exist several input samples that occur before the input affects the output. However, in the ARX based spatio-temporal forecast model, exogenous inputs are historical values of solar irradiance at neighbor sites and cloud cover percentage rather than utilizing the temporal only based auto regression (AR) model. B. Model Implementation We take into consideration that the input and output measurement data should be synchronized. Thus we use the arx (namely n=, m=, d = ) in our simulation model. It has high accuracy and no time delay between output and exogenous inputs, historical values with up to ten steps before are included. The objective is to forecast the solar irradiance at base location in various time scales varies from 5 minutes up to day head. In order to determine the optimal amount of information for spatio-temporal model, the performance indices of all five

3 layers are compared. Based on the trade-off between amount of information and forecast accuracy of different layers, the optimal spatial and temporal line for ARX based spatiotemporal forecast can be found. V. PERFORMANCE EVALUATION A. Performance Indices In the simulation of validating the effectiveness of the two models, three major performance indices are used. Following common practice for the evaluation of solar power predictions [5], we use the mean absolute errors (MAE) as the main score. MAE = N forecasted, i measured, i (5) N i = where N is the total number of simulation step, forecasted, i is the forecasted solar irradiance while measured, i is the value from solar irradiance measurement. As additional scores, we use the root mean square error RMSE = ( ) n forecasted, i measured, i (6) N i = and FIT index which is defined as follows: forecasted measured FIT = ( ) mean( ) measured measured Typically, for RMSE and MAE percentage, smaller values represents better forecast performance, while for FIT the higher the score, the better forecast result is. B. Solar Data Source In our case, we illustrate in detail with a solar irradiance dataset from five locations in Colorado of the United States. All the data are realistic historical data from NREL website [7]. Note that the solar irradiance data is available for the whole year except the data at Sun Spot One only contains up to Nov.8, [8], thus the whole year dataset is used to train the forecast model along with the validation of the effectiveness of the model. ) Data Filtering Since the solar irradiance before sunrise and sunset is negligible, the data before a.m. and after p.m. are deleted for hour interval. For minute interval measured dataset, only solar irradiance between a.m. and :5 p.m. are included in the analysis. Based on the explanation of the measured data and instrument [7], negative values in cloud coverage and solar irradiance data set in the given time period above are reset to zero. ) Site Information Table shows the geographic distance of five locations. TABLE EORAPHIC INFORMATION OF FIVE SOLAR SITES Site Location Distance to BMS(mile) BMS olden, Colorado LRSS Watkins, Colorado 44 SPMD South Park, Colorado 75 XECS Pueblo, Colorado 6 (7) Solar irradiance at these five locations are correlated with each other, thus spatial correlation should be included in additional to correlation with solar irradiance of itself. Figure shows the auto-correlations and cross-correlations of five locations up to time lag hours in. The auto-correlation coefficients at each location are larger than up to hours lag. And cross-correlation coefficients are also significantly large. BMS Time lag hour Time lag hour SPMD BMS vs XECS Time lag hour LRSS Time lag hour BMS vs SPMD Time lag hour Time lag hour Figure. and cross-correlations of hour solar irradiance at BMS, LRSS, SPMD, XECS, SS Furthermore, the cross correlation between BMS and four neighbor sites are shown in Figure 3. Cross correlation coefficients Time lag hour Figure 3. of hour solar irradiance between BMS and other four sites C. Case studies Based on the aforementioned dataset, the future solar irradiance is forecasted with two models: a PSS model and an ARX based spatio-temporal forecast model which includes information from neighbor sites. And then solar irradiance forecasts are converted into solar power with a certain power curve. PSS is usually taken as a reference and an advanced forecast model is thought to be good if it outperforms PSS. PSS assumes the future solar irradiance is the same as the current one. For example, if t is the solar irradiance at time t in olden (Colorado), then k minute future solar irradiance is predicted as ˆt+ k= t. In the simulation, performance evaluation is based on the comparison between the spatio-temporal model and the PSS SS BMS vs LRSS XECS Time lag hour Cross correaltion between five locations BMS vs SS Time lag hour BMS vs LRSS BMS vs SPMD BMS vs XECS BMS vs SS Time lag

4 model. We plot the forecast values versus the actual measured solar irradiance, thus the more data concentrated in the narrow band, the better performance of corresponding forecast model is. ) 5-minute-ahead forecast For 5-minute-ahead forecast, the MAE and RMSE percentage of more than consecutive 5 minutes ahead simulation results are used as benchmarks for performance evaluation. Note the 5 minutes ahead forecast is composed of 5 consecutive -minute ahead forecasts which are updated with the most recent actual measured solar irradiance. Table 3 shows the data period for training the spatiotemporal model and validation process for four cases. The four cases correspond to four seasons in a year. TABLE 3 MODEL TRAININ AND VALIDATION PERIOD FOR FIVE MINUTES AHEAD FORECAST Case Number Training Period Validation period Jan.~Feb.8 March.~ March.3 Apr.~May.3 June.~June.3 3 July.~Aug.3 Sep.~Sep.3 4 Sep.~Oct.3 Nov.~Nov.3 It turns out the persistence outperforms ARX based spatiotemporal model at this time scale partially due to the fact that inter-temporal variation of solar power output does not have too much dramatic changes during few minutes time period. ) 5-minutes-ahead forecast While for 5-minutes-ahead forecast, the MAE and RMSE percentage of more than 3 consecutive 5 minutes ahead simulation results are calculated as benchmarks to compare the performance. The 5 minute forecast is composed of 3 consecutive 5 minute ahead forecasts which are updated with actual measured solar irradiance. Moreover, the simulation model training and validation period is the same as 5 minutes ahead forecast as shown in Table 3. The PSS model performs better than the ARX based spatiotemporal model due to the solar irradiance seldom has dramatic changes between two consecutive time steps. 3) -hour-ahead forecast For hour ahead forecast, the MAE and RMSE percentage of more than 5 consecutive hour ahead simulation results are used as benchmarks to compare the performance. The simulation model training and validation period is the same as shown in Table 3. The performance evaluation of case 3 is illustrated in Figures 4 and 5. Figure 4 is the spatio-temporal forecasted value versus actual measured value while persistence forecasted value versus measured value is shown in Figure 5. As shown in Figure 4, the data is more concentrate in the narrow band than that of in Figure 5. The MAE percentage of spatio-temporal forecast model is 6.3% lower than that of PSS model while RMSE percentage reduced by 7.5% when compared with PSS model. According to [5], monthly MAE percentage can be around.7% from a.m. to 3 p.m. of a 5MW solar facility in central California. Also based on hour ahead forecast of Merced test bed in California by the state-of-the-art ENIO method [8], the RMSE percentage is around 8.9%. Forecasted Solar Irradiance W/m Figure 4. Spatio-temporal model performance of case3 for hour ahead forecast Forecasted Solar Irradiance W/m Measured Solar Irradiance W/m FIT=3.73 MAE=6.49% RMSE=.66% FIT=-.7 MAE=3.8% RMSE=9.% Case 3 Spatio-temporal forecast model Case 3 Persistent model Measured Solar Irradiance W/m Figure 5. Persistence model performance of case3 for hour ahead forecast The average MAE percentage for hour ahead forecast of our spatio-temporal model can be as little as 8.7% while the RMSE percentage is %. Thus it surpasses other forecast methods of similar complexity. The performance summary of all four cases is shown in Table 4. TABLE 4 PERFORMANCE EVALUATION FOR HOUR AHEAD FORECAST Case Case Index Spatio-temporal PSS Spatio-temporal PSS MAE% RMSE% FIT Case3 Case4 Spatio-temporal PSS Spatio-temporal PSS MAE% RMSE% FIT ) -day-ahead forecast For day ahead forecast, the MAE and RMSE percentage of more than 3 consecutive day ahead simulation results are used as benchmarks to compare the performance. Case uses data set from January till the end of March for training and validate the effectiveness of the model with the data in April. Case selects from May till the end of July in training period and August as validation period. Case 3 chooses from September till the end of Octomber and validates the model with the data in November.

5 We use case as an example to illustrate the performance evaluation of two models which is shown in Figures 6 and 7. Figure 6. Spatio-temporal model performance of case for day ahead forecast Figure 7. Persistence model performance of case for day ahead forecast As shown in Figure 6 and Figure 7, the dot of persistence is relatively sparse when compared with spatio-temporal model. The MAE percentage of spatio-temporal forecast model decreases by 4% as of PSS model. According to the result analysis mentioned in [5], the RMSE percentage for day ahead forecast is around % in AWST s IEA Project Day-Ahead Experiments for three locations in Penn State, PA, Desert Rock, NV and oodwin Creek, MS. The average MAE percentage of our model for day ahead forecast is as small as 5% while for RMSE is %. Detailed performance index comparison is shown in Table 5. In all three cases, the spatio-temporal model outperforms persistence model in all three indices. Index Forecasted Solar Irradiance W/m Forecasted Solar Irradiance W/m Measured Solar Irradiance W/m TABLE 5 PERFORMANCE EVALUATION FOR DAY AHEAD FORECAST FIT=-.63 MAE=7.73% RMSE=.% FIT=-6.4 MAE=.7% RMSE=8.% Case Spatio-temporal forecast model Measured Solar Irradiance W/m Case Case Case 3 PSS Case Persistent model PSS Spatiotemporal Spatiotemporal Spatiotemporal PSS MAE% RMSE% To summarize, for minutes ahead forecast like 5 minutes ahead and 5 minutes, PSS model shows better performance spatio-temporal model. However, for hour ahead or day ahead forecast, the advantage of spatio-temporal model outperforms PSS models. D. Optimal Solar Power Forecast Method One important practical issue for implementing spatiotemporal forecast is to optimally determine layers of communications among different solar farms. In the subsection, we address the problem by investigating the optimal layer of communication. The index to determine the optimal layer is based on the MAE percentage improvement which is called accuracy improvement versus information layer (AIVIL). ( MAEi+ MAEi)/ MAEi AIVIL =, i =,,3, 4 (8) ( Ii+ Ii)/ Ii where MAEi the mean absolute error (MAE) percentage at layer i, I i indicates the amount of information needed for the proposed forecast model to work at layer i. Thus the higher the AIVIL score, the more accuracy improvement corresponding to the same added information is achieved. However, as AIVIL score is calculated from Layer, there is an exception that if Layer has the most accuracy it would be the optimal layer since it requires the least information. Based on the descending sequence of cross-correlation between the base solar site and information layer in Figure 3, the simulation results of various layers using spatio-temporal forecast model are shown in this part. ) Optimal hour ahead forecast Case 3 Forecast Accuracy versus Information Layer for hour ahead forecast.4 MAE percentage of Spatio-temporal Model Layer Figure 8. Forecast accuracy versus information layer of case3 for hour ahead spatio-temporal forecast Figure 8 shows a clear gradually decreasing MAE percentage as the layer added. Layer 4 of case 3 which is the largest layer has the best result. TABLE 6 CASE 3 PERFORMANCE COMPARISONS OF FOUR LAYERS Index Layer Layer Layer 3 Layer 4 MAE (%) Improvement (%) NA AIVIL NA It turns out that the biggest layer (Layer 5 or Layer 4) performs better than others in the hour ahead forecast model of all four cases. Please note that as SS does not have data after the end of October, thus case 3 and case 4 only includes other three solar site information and cloud coverage. Thus, more layers of communications yield better forecast results for hour ahead forecast. Based on the four simulation cases, the optimal layer of spatio-temporal model should

6 include all the related information in the layer to achieve the best forecast result. ) Optimal day ahead forecast Figure shows the tendency of forecast accuracy as the layer increased. Case Forecast Accuracy versus Information Layer for day ahead forecast.5 MAE percentage of Spatio-temporal Model Layer Figure. Forecast accuracy versus information layer of case for day ahead spatio-temporal forecast The MAE percentage increases as the layer adds in the day ahead intervals, it may partially be caused by not including weather information in the spatio-temporal model. TABLE 7 CASE PERFORMANCE COMPARISONS OF FIVE LAYERS Index Layer Layer Layer 3 Layer 4 Layer 5 MAE (%) Improvement (%) NA AIVIL NA From Table 7, though Layer 5 has the highest AIVIL score, the optimal layer for day ahead spatio-temporal forecast model is Layer which includes the least information. Layer only includes solar irradiance at LRSS and has the least MAE percentage among the five layers. The results of all three cases show that the smallest layers which include the nearest site information would be most likely to achieve the best forecast performance for days ahead forecast. Both optimal time interval and optimal spatial layer are proposed in this forecast model which yield an optimal solution from both time and spatial prospective. VI. CONCLUSION AND FUTURE WORK In this paper, we propose an ARX based spatio-temporal model for solar power forecast. Compared with conventional temporal-only solar irradiance forecast models such as the PSS model, the ARX based spatio-temporal model considers both the local and geographically correlated solar irradiance for solar forecast. In hour ahead and day ahead solar irradiance forecast, the proposed ARX based spatio-temporal model outperforms PSS model in all aspects, and the optimal spatial layer is also suggested to help obtain more accurate forecast. In future work, we plan to perform a probabilistic distribution of forecast errors and also investigate the impact of the proposed forecast model on power system operations. Another important direction research is to analyze the trade-off between communication/computation burden and the improved economic benefits by incorporating more spatially correlated solar data into power system dispatch models. VII. REFERENCES [] NREL. (November ). Solar Technologies Market Report. Available: [] D. A. Halamay, T. K. A. Brekken, A. Simmons, and S. McArthur, "Reserve Requirement Impacts of Large-Scale Integration of Wind, Solar, and Ocean Wave Power eneration," Sustainable Energy, IEEE Transactions on, vol., pp. 3-38,. [3] E. Lorenz, J. Hurka, D. Heinemann, and H.. Beyer, "Irradiance Forecasting for the Power Prediction of rid-connected Photovoltaic Systems," Selected Topics in Applied Earth Observations and Remote Sensing, IEEE Journal of, vol., pp. -, 9. [4] Mark Ahlstrom and J. A. Kankiewicz. 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