Elsevier

Renewable Energy

Volume 145, January 2020, Pages 333-346
Renewable Energy

Novel stochastic methods to predict short-term solar radiation and photovoltaic power

https://doi.org/10.1016/j.renene.2019.05.073Get rights and content

Highlights

  • Short-term high-resolution probabilistic behavior of solar is investigated.

  • Two novel stochastic forecasting models are proposed for solar PV.

  • Forecasting of solar irradiance and PV power is provided.

  • The proposed algorithm performs better than traditional ARIMA model.

Abstract

Solar forecasting has evolved towards becoming a key component of economical realization of high penetration levels of photovoltaic (PV) systems. This paper presents two novel stochastic forecasting models for solar PV by utilizing historical measurement data to outline a short-term high-resolution probabilistic behavior of solar. First, an uncertain basis functions method is used to forecast both solar radiation and PV power. Three possible distributions are considered for the uncertain basis functions - Gaussian, Laplace, and Uniform distributions. Second, stochastic state-space models are applied to characterize the behaviors of solar radiation and PV power output. A filter-based expectation-maximization and Kalman filtering mechanism is employed to recursively estimate the system parameters and state variables. This enables the system to accurately forecast small as well as large fluctuations of the solar signals. The introduced forecasting models are suitable for real-time tertiary dispatch controllers and optimal power controllers. The PV forecasting models are tested using solar radiation and PV power measurement data collected from a 13.5 kW PV panel installed on the rooftop of our laboratory. The results are compared with standard time series forecasting mechanisms and show a substantial improvement in the forecasting accuracy of the total energy produced.

Introduction

Among different forms of clean energies, solar energy has attracted a lot of attention because it is sustainable and renewable, but the potential of using this form of renewable energy depends on its effective integration into power distribution systems without impacting voltage and frequency limits. However, the application of solar photovoltaic (PV) to the electric grid also has drawbacks, in particular the variability of power output adds stress and uncertainty to system. A major part of solar PV production is characterized by a large degree of intermittency driven by the natural variability of climate factors such as air temperature, wind velocity, precipitation, and evaporation [1]. The variable nature of solar PV could hamper further deployment due to the increase in reserves needed on the electric grid to compensate for fluctuations in the power output. Therefore, solar forecasting has evolved towards becoming a key component of economical realization of high penetration levels of PV systems [2].

Due to the intermittency of the power output of some renewable sources, micro-grid systems have become one of the main forms for the increasing share of distributed renewable systems [3]. As the amount of solar generation increases in relation to bulk generation, real-time controllers for dispatch will be needed to minimize the impact of short-term fluctuations in solar output. The performance of these real-time controllers will be improved by short-term solar output forecasting. Moreover, the recently opened Energy Imbalance Market (EIM) allows for generation and demand balancing across Balancing Authority Areas (BAA) on 15 min and 5 min timescales with California Independent System Operator (CAISO) oversight [4]. One of the main challenges is therefore to perform forecasts as accurately as possible to overcome potential variability and uncertainty of renewable energy generation [5,6].

This paper examines the stochastic modeling and short-term high-resolution forecasting of solar radiation and PV power output. We introduce two stochastic state-space models to characterize the behaviors of solar radiation and PV power output. The short-term high-resolution forecasting models are suitable for the development of optimal power controllers for PV sources. They can also be utilized for automatic generation control (AGC), better energy management system, unit commitment, power scheduling and dispatching [7,8].

Various algorithms have been introduced to forecast solar radiation and PV generation [9] reviewed the state-of-the-art methods for short term solar/PV forecasting. Solar radiation in spatially distributed locations can be forecasted using neighboring spatial location information. Sky camera and satellite data can help reveal spatio-temporal characteristics of the solar radiation. Solar forecasting with satellite imaging or sky cameras has become a hot topic recently for data acquisition and cloud movement [2,[10], [11], [12], [13], [14], [15]]. Analytical models have been developed for arbitrary cloud configuration and can also predict diffuse irradiance based on the information about cloud coverage [16]. Later, similar numerical solution has been extended to account for cloud movement [17].

Besides using ground-based images, there also exist approaches that only rely on a sensor network. For instance Ref. [18], established intra-hour forecasts using a network of 80 rooftop PV systems spread over a large area. More sensor network based forecasting methods have been proposed in Refs. [[19], [20], [21]], which rely on information from a collection of neighboring sites. Very short-term sub-5-min forecasting has been conducted in Ref. [12] using emerging sky camera technology.

Similarly, multiple linear regression methods including support vector machine (SVM) [22] were used to study the solar power output characteristics, combined with weather data and solar radiation data. Moreover, hybrid forecasting techniques have been investigated recently, including k-means algorithm [23], Artificial Neural Networks (ANNs) model [5], k-nearest neighbors (kNN) [24], as well as SVM with Wavelet Transform (WT) algorithm [25,26], to increase the forecast accuracy. However, most of the aforementioned methods required large amount of data samples, and the fitting results were sensitive to pathological data [27]. Besides many assumptions, such as linear cloud edge, that have to be made, various types of error will be embedded in different phases of such methods, especially during the conversion from cloud condition to ground-level radiation [28].

The solar/PV forecasts have attracted substantial attention from stochastic modeling and forecasting studies. The works in Refs. [[29], [30], [31]] represent solar radiation using hidden Markov models (HMMs). The works in Refs. [[32], [33], [34]] represent solar radiation using autoregressive integrated moving average (ARIMA) model. Lastly, the work in Ref. [35] presents a stochastic solar radiation forecasting framework based on conditional random fields (CRFs). These works provide accurate models and forecasting that capture the hourly, daily, and seasonal solar PV trends. However, they lack accurate high-resolution modeling and forecasting of fast and large fluctuations of solar radiation/PV power that often occur as illustrated in Fig. 1 for a typical summer day.

Moreover, a method based on a combination of an ARMA model and a Kalman filter has been introduced for the scope of solar radiation and temperature forecasting. The ARMA model is built with a high order parameters (p,q) in order to retrieve the state-space parameters needed to run the Kalman filter. [36] has presented a work which extends previous studies [37,38], to solve the problem of bias removal from the Kalman forecasts.

The closest related prior work to the present paper is the state-space modeling framework recently published in Ref. [39], where the linear Kalman filter is used to perform forecasting for different time horizons, between one minute and one hour ahead. They considered two sets of inputs, one that consisted only of past PV measurements and another which also incorporated cloud cover and air temperature values from a nearby meteorological station. They used a Kalman filter, where parameter tuning was addressed via two methods: an AR model and an expectation maximization (EM) algorithm.

Most of the aforementioned techniques require additional measurements or sensor networks other than purely local solar radiation/PV power generation as in our paper. This increases the deployment complexity in both hardware and software, not to mention some unrealistic assumptions, such as linear cloud edge and various types of error embedded in different phases of these methods [28]. The advantage of our algorithm is that it is ‘data-driven in real-time and adaptive’, i.e., directly uses the collected data from local interested site to generate solar forecasting. While the methods mentioned above are offline needing training sets and cross validation on the top of using more information. This motivates us to develop novel low data demanding algorithms to improve the efficiency and accuracy of short-term high-resolution solar radiation/PV power forecasting. A new data-driven stochastic framework for short-term forecasting of solar radiation and PV production is laid out.

In this paper, we focus on designing a robust stochastic forecasting model which can accommodate the factors affecting PV output for higher forecast accuracy. In order to avoid requiring exogenous influential features namely the cloud cover and the temperature, we introduce a unique stochastic framework to forecast the solar radiation and the PV production. For this scope, a methodology based on statistical inference techniques is built, specifically, the uncertain basis functions method and Kalman filtering based EM algorithm. Both of the two introduced algorithms work adaptively and recursively to track the latest dynamics of the solar radiation and PV generation.

We begin with the uncertain basis functions technique, which takes into account the uncertain physical properties of the system of solar and PV power. In contrast with traditional works, where basis functions (e.g., radial basis function [40], and wavelets [41]) are fixed, we assume that the basis functions are random, according to three different probability distributions, i.e., Uniform, Gaussian and Laplace distributions.

The state-space model is dedicated to describing the system with all the parameters needed to capture the statistical properties and system dynamics. Thereafter, as a second phase, we talk about the methodology to estimate the needed parameters which quantify the dynamics of system. A filter-based EM mechanism is employed to estimate the parameters and state variables in the state-space model. The mechanism results in a finite dimensional filter which only uses the first and second order statistics. As mentioned in Ref. [39], the advantage of using linear discrete-time Kalman filter is mainly related to its ability to do future forecasting in real-time online in a memory-less way.

With both the uncertain basis and state-space model approaches, we can build a model from which we derive (estimate) an a priori unknown hidden signal and re-utilize it for forecasting w.r.t. the measured data. This mechanism is recursive, which allows the solar radiation and PV power to be forecasted online from measurements. Preliminary results based on this idea were initially presented in Refs. [42,43]. However, this paper includes more derivation details and case studies, which provide a concrete solar forecasting framework. Moreover, both Laplace distribution uncertain basis functions and Prediction Error Minimization (PEM) algorithm are presented for the first time.

To demonstrate the effectiveness of the introduced approach, simulation-based experimental analysis is carried out based on a set of PV generation data collected from PV cells located on the rooftop of the Distributed Energy Communication & Control (DECC) laboratory at Oak Ridge National Laboratory (ORNL) for the year of 2015. Although preliminary study for solar forecasting using uncertain basis functions has been investigated in Ref. [42], we will compare it with the stochastic state-space method as well as the traditional time series techniques.

The modeling and forecasting strategy of this paper starts in Section 2 with the uncertain basis algorithm to forecast solar radiation and solar power generation. A stochastic state-space algorithm is then presented in Section 3, based on Kalman filter and EM. A revisit to traditional time series technique is cast in Section 4, which is well-suited to forecast the solar radiation/PV generation. In Section 5, we present the simulation study regarding the forecasting performance using the introduced algorithms, and provide a comparison with time series methods, which act as a benchmark. Conclusions are provided in Section 6.

Section snippets

Modeling and prediction with uncertain basis functions

In this section, we introduce the uncertain basis functions technique employed to model and forecast solar radiation/PV power. The modeling and forecasting of signals using uncertain basis functions were proposed recently in Ref. [44]. Since the traditional ARIMA method is unable to yield good performance under highly dynamic and uncertain disturbances, the uncertain basis function technique has been utilized in forecasting frequency fluctuations in power grid [45,46]. Considering the uncertain

Stochastic state-space model

The state-space model has been widely employed in control systems and signal processing since it can be used online and updated after receiving the most recent observation. It consists of a state (or system) equation (11) and a measurement (or output) equation (12). yk denotes the solar radiation/PV power measurement at time k. The state-space equation in discrete time can be written in the following form:xk+1=Akxk+Bkwkyk=Ckxk+Dkvkwhere xkRn (Rn denotes the space of real vectors of dimension n

Comparable forecasting methods - time series forecasting

Time series forecasting has been applied for different applications with higher degree of success since the last decade. A time series is a collection of time ordered observations xt, each one being recorded at a specific time t (period) [54]. Time series can appear in a wide set of domains such as finance, production or control, just to name a few. As a first approximation, a time series model (xˆt) assumes that past patterns will occur in the future. In fact, a time series model could be used

Numerical studies and discussion

To illustrate the effectiveness of the introduced solar PV power forecasting techniques, we evaluate their performances for different scenarios in this section. According to a set of solar radiation/power data from our local PV panel, both the state-space model and uncertain basis functions model are applied. For the state-space model, any initial values can be chosen since all these values will converge. For the basis-functions model, we chose to get a tradeoff between the computations while

Conclusions

In this paper, we have considered the modeling and forecasting of short-term high-resolution solar radiation and PV power output using two stochastic methodologies. We validated the stochastic models using real measurement data. Given total solar PV generation measurements, the introduced methodologies can forecast short-term high-resolution trends of solar PV power with different time horizons. The uncertain basis model provides an excellent method for forecasting solar PV power. Since the

Acknowledgment

This material is based upon work supported by the U.S. Department of En-ergy, Office of Energy Efficiency and Renewable Energy under contract number DE-AC05-00OR22725..

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    This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan http://energy.gov/downloads/doe-public-access-plan.

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