Smart Meter Based Short-Term Load Forecasting for Residential Customers

Transcription

1 Smart Meter Based Short-Term Load Forecasting for Residential Customers M. Ghofrani, SM IEEE, M. Hassanzadeh, SM IEEE, M. Etezadi-Amoli, life Sr. Member IEEE, M. S. Fadali, Sr. Member IEEE Department of Electrical and Biomedical Engineering University of Nevada, Reno Reno, Nevada Abstract This paper examines the potential impact of automatic meter reading (AMR) on short-term load forecasting for a residential customer. Real-time measurement data from customers' smart meters provided by a utility company is modeled as the sum of a deterministic component and a Gaussian noise signal. The shaping filter for the Gaussian noise is calculated using spectral analysis. Kalman filtering is then used for load prediction. The accuracy of the proposed method is evaluated for different sampling periods and planning horizons. The results show that the availability of more real-time measurement data improves the accuracy of the load forecast significantly. However, the improved prediction accuracy can come at a high computational cost. Our results qualitatively demonstrate that achieving the desired prediction accuracy while avoiding a high computational load requires limiting the volume of data used for prediction. Consequently, the measurement sampling rate must be carefully selected as a compromise between these two conflicting requirements. Index Terms -- smart meter, residential load, spectral analysis, shaping filter, Kalman filtering I. INTRODUCTION Short-term load forecast plays an important role in power system operation. An accurate load forecast benefits different electricity market parties and asset owners. Several methods for load prediction have been reported in the literatures [1]- [12]. [1] and [2] present a stochastic physically based model to predict the weather-dependent component of a residential load. The weather-independent component is modeled by an autoregressive (AR) model. A transformation technique with translation and reflection methods is utilized for regression based peak load forecasting [3]. Seasonal load change, annual load growth and latest daily load change are among the factors considered to forecast the load more precisely. [4] integrates artificial neural networks and fuzzy expert systems to form a hybrid model for short-term load prediction. Artificial neural networks provide the provisional forecasting in the first step, followed by a modification process by fuzzy expert systems in the second step. Comparing the forecast results of the hybrid model with those of the exponential smoothing method shows a better performance for the hybrid system. [5] presents three fuzzy-neural-network models for time-series forecasting of the electric load and their performance for load prediction. In [6], the authors proposes a new approach for short-term load forecasting that combines genetic algorithms and neural networks. The optimization capabilities of genetic algorithms improve the learning performance of the neural networks and decrease the probability of premature convergence. Also, the overall training time is reduced significantly. [7] calculates the load forecast directly from historical data as a local average of observed past loads. A multivariate product kernel is used to define the specific weights of the loads. A practical modeling approach for weekly load forecasting is given in [8] and its performance is verified using actual data. The approach is based on decomposing the electric load into weather-sensitive and non-weather-sensitive components. A non-linear regression technique incorporating the search algorithm proposed by Marquardt is used to model the load components. Development and implementation of a hybrid fuzzy neural based day-ahead load forecaster is discussed in [9]. The proposed approach is developed in three stages. In the first stage, the growth trend and the necessary compensation are used to update the historical load to the current load demand. The Kohonen self-organizing map is then used in the second stage to map the load profile. In the third stage, a neural network and a fuzzy parallel processor forecast the load for the current day using input variables such as day type, weather and holiday proximity. In [11], a short term load forecasting approach is developed which incorporates ARIMA time series modeling with the knowledge of expert operators. [12] proposes an ARMA model identification approach for shortterm load forecasting which is applicable to both Gaussian and non-gaussian processes. Advanced metering infrastructure (AMI) is the key element for transition of the existing electric grid to a smart grid. Smart meters are defined as advanced meters capable of two-way communication and real-time analysis of electricity consumption. Given the utility-scale smart meter deployments, plans and proposals in [13], a total of 59,940,150 meters will be installed and operable across the United States by This accounts for almost 47% of U.S. households according to EIA's (Energy information administration) forecast of

2 electricity customers in 2020 [14]. AMI makes it possible to obtain real-time measurement data from customers' smart meters whenever these data are needed. This feature provides an opportunity to forecast the load more accurately. However, the availability of massive amounts of data for use in forecasting will increase the computational cost of load prediction. Thus, an appropriate measurement sampling rate must be chosen so as to provide the desired prediction accuracy without excessive amounts of data. This paper examines smart meter-based short-term load forecasting for residential load prediction using a Kalman filter. In particular, it examines the effect of the measurement sampling rate on the forecasting error. The forecasting methodology based on the Kalman filter is explained in Section II. Spectral analysis is used to determine the shaping filter for the Gaussian noise. Section III gives the results of applying our methodology to data for a residence in Northern Nevada provided by NV Energy. Our conclusions are given in Section IV. II. FORECASTING METHODOLOGY The residential load is modeled as the sum of two individual components; the weather-dependent component and the lifestyle component. (1) The lifestyle component is the deterministic part of the load that is mostly dependent on individual energy consumption patterns. It is dominated by loads such as lighting, cooking, washers and dryers. The weather-dependent component is a Gaussian noise signal which primarily affects HVAC (heating, ventilation, and air conditioning) loads. The deterministic part of the residential load is subtracted from the measured consumption data leaving a zero-mean random signal from which we determine the shaping filter using spectral analysis. A. Spectral analysis The power spectral density function of the random component of the residential load data is obtained by using the least squares method (LSM) [15]. We fitted a Gauss-Markov process model to the random component of the residential load data. The spectral density function of the Gauss Markov process is: where α and β are constants. The shaping filter is the causal part of the spectral density function and its transfer function is: We obtain a state-space model for the process of (3) assuming unity white noise input. The state-space model is: (2) (3) (4) (5) Where U is the unity white noise input, X is the state variable, Y is the measurement, V is unity Gaussian white measurement noise. B. Kalman Filtering The dynamic behavior of a stochastic system is described by the simplified state vector and the output vector as follows: 1 (6) (7) where is the state-transition matrix calculated from the state matrix of the shaping filter [16]. The noise vectors and are independent zero-mean Gaussian and their covariance matrix is given by:,, (8) where, is the Kronecker delta, is the process noise covariance matrix, and R is the measurement noise covariance matrix. The Kalman filter is a recursive algorithm that is used in this paper for prediction. Given estimates of the initial state ˆX (0) and the initial error covariance matrix P (0), we use the measurement matrix C and the measurement noise covariance to calculate the Kalman gain. (9) The estimate is corrected with the measurement to obtain the a posteriori estimate (10) The error covariance matrix for the updated estimate is. (11) The next state is predicted using the state equation as follows: 1 (12) and the error covariance matrix for the predicted state is: 1 (13) The correction and prediction cycle is repeated to yield a sequence of state estimates. III. RESULTS AND DISCUSSION The performance of the proposed method is evaluated for short-term load forecasting through the residential load data provided by NV Energy. Fig. 1 illustrates the 15 minutes

3 interval load profile of a residential customer on March 30, The load data is considered as the sum of a deterministic part and a random component. A 10th order polynomial is used to fit the load profile. The fitted curve for the given load data with a sampling period of 15 minutes for a 24 hour period is shown in Fig. 1. Figure 1. Measured residential load data and polynomial fit (3/30/2011) The weather-dependent component of the residential load is obtained by subtracting the polynomial fit from the measured load. Power spectral estimation is then used to obtain the shaping filter from the weather-dependent component. The parameters of the power spectral density of a Gauss-Markov process are calculated by minimizing the least-squares error. Fig. 2 shows the power spectral density of the random component of the load data together with that of the Gauss- Markov process for a sampling period of 15 minutes. Figure 3. Residential load prediction for a 15 minute sampling period and a 15 minute forecasting horizon (4/1/2011) The communication capability of the smart meters makes it possible to obtain the real-time measurement data whenever the data are needed. This feature provides an opportunity to evaluate the performance of the proposed forecasting method for different sampling periods and forecasting horizons. Since the load data are provided in 15 minutes interval, larger sampling periods of 30 minutes and one hour are considered along with 15 minutes sampling period for different cases. Fig. 4 and 5 illustrate the residential load prediction for sampling periods of 30 minutes and one hour, respectively. These predictions correspond to forecasting horizons of 30 minutes and one hour, respectively. Figure 4. Residential load prediction for a 30 minute sampling period and a 30 minute forecasting horizon (4/1/2011) Figure 2. Spectral density of noise and fitted Gauss-Markov The shaping filter of (3) obtained with the residential load data for March 30, 2011 was used to design a Kalman filter and predict the load for April 1, Note that, the day that is considered for prediction purposes must have similar climatic characteristics to the day for which the shaping filter was obtained. The residential load prediction for a sampling period of 15 minutes and a forecasting horizon of 15 minutes is shown in Fig. 3. Figure 5. Residential load prediction for a 1 hour sampling period and a 1 hour forecasting horizon (4/1/2011)

4 The forecasting accuracy is determined by calculating the mean absolute percentage errors (MAPE) [17]. The average percentage error (APE) is given by: 100 (14) MAPE is then calculated by: (15) Table I gives the MAPE calculated for different sampling periods and forecasting horizons. TABLE I. CALCULATED MAPE (%) FOR DIFFERENT SAMPLING PERIODS AND FORECASTING HORIZONS hour minutes minutes 15 minutes minutes hour Prediction results show an inaccurate load forecast with MAPE of % for a sampling period and forecasting horizon both equal to one hour. Shorter time intervals between receiving real-time measurement data from the customers' smart meter improves the accuracy of the proposed method and decreases the MAPE. The MAPE is reduced to % and % for 30 minutes and 15 minutes sampling periods, respectively. However, the increasing amounts of measurement data used for load forecasting with shorter sampling periods (15 and 30 minutes) will increase the computational load of the forecast. Considering sampling periods of 1 minute and less, the performance accuracy of the proposed method will improve significantly while the computational burden will increase substantially. Consequently, the choice of measurement sampling rate must be a trade-off between the accuracy and computational load. MAPE (%) MAPE (%) Computational Load (min) Sampling Period (min) Figure 6. Effect of measurement sampling rate on prediction accuracy and computational load for a distribution feeder with 500 residences Computational Load (min) The effect of measurement sampling rate on prediction accuracy and computational load for a distribution feeder with 500 residences is illustrated in Fig. 6. The computational load is the total time required to process the 500 measurement data sequentially. Fig. 6 provides a qualitative representation of the compromise between prediction accuracy and computational load. IV. CONCLUSION Short-term load forecasting for residential customers is becoming a reality with the availability of smart meters. Using data provided by a utility company, we show how a residential load can be represented as the sum of a deterministic component and a random Gaussian perturbation. Kalman filter is then used to predict the residential load for different sampling periods and forecasting horizons. The accuracy of the load predictions for different sampling periods and forecasting horizons is evaluated. Our results demonstrate that while a faster sampling rate providing more real-time measurement data substantially improves the accuracy of the load forecast, the additional computational cost can be quite high. Thus, achieving the desired prediction accuracy while limiting the volume of data used for prediction requires careful selection of the sampling rate. Our results demonstrate that the sampling rate selected must provide the best compromise between prediction accuracy and computational load. V. ACKNOWLEDGMENT We would like to thank NV Energy of Reno Nevada for the support of this project. Special thanks to Gary Smith, Carlos Saldona, Alberto Godoy and Stephen Tam for their time and support. REFERENCES [1] I. C. Schick, P. B. Usoro, M. F. Ruane, and F. C. Schewppe, Modeling and weather-normalization of whole-house metered data for residential end-use load shape estimation, IEEE Trans. Power Syst., vol. 3, no. 1, pp , Feb [2] A. H. Noureddine, A. T. Alouani, and A. Chandrasekaran, A new technique for short-term residential electric load forecasting including weather and lifestyle influences, Proc. of the 35th MIdwest Symposium on Circuits and Systems, vol. 2, pp , Aug [3] T. Haida and S. Muto, Regression based peak load forecasting using a transformation technique, IEEE Trans. Power Syst., vol. 9, pp , Nov [4] K. H. Kim, J. K. Park, K. J. Hwang, and S. H. Kim, Implementation of hybrid short-term load forecasting system using artificial neural networks and fuzzy expert systems, IEEE Trans. Power Syst., vol. 10 pp , Aug [5] P. K. Dash, G. Ramakrishna, A. C. Liew, and S. Rahman, Fuzzy neural networks for time-series forecasting of electric load, Proc. Inst. Elect. Eng. Gen., Transm. Dist., vol. 142, pp , Sept [6] S. J. Huang and C. L. Huang, Genetic-Based multi-layered perceptions for taiwan power system short-term load forecasting, Int. J. Elect. Power Syst. Res., vol. 38, no. 3, pp , July 1996.

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