R studio Machine learning

CHAPTER 16

Predictive Analytics for Comprehensive Energy Systems State Estimation

Yingchen Zhang*, Rui Yang*, Jie Zhang†, Yang Weng‡, Bri-Mathias Hodge* *National Renewable Energy Laboratory, Golden, CO, United States, †University of Texas at Dallas, Richardson, TX, United States, ‡Arizona State University, Tempe, AZ, United States

OVERVIEW CHAPTER

Energy sustainability is a subject of concern to many nations in the modern world. It is critical for

electric power systems to diversify energy supply to include systems with different physical charac- teristics, such as wind energy, solar energy, electrochemical energy storage, thermal storage, bio-

energy systems, geothermal, and ocean energy. Each system has its own range of control variables

and targets. To be able to operate such a complex energy system, big-data analytics become critical to achieve the goal of predicting energy supplies and consumption patterns, assessing system opera-

tion conditions, and estimating system states—all providing situational awareness to power system

operators. This chapter presents data analytics and machine learning-based approaches to enable

predictive situational awareness of the power systems.

343

1 INTRODUCTION

Historically, the power system has been designed with dispatchable generation

providing enough electricity to meet demand and additional reserves to meet

contingencies. With the increase in wind and solar integration, better methods to forecast grid conditions will be needed to accommodate high penetrations

of these variable and uncertain clean energy technologies. Another challenge

with future grids is the ability to account for distributed energy resources (DER) that may not be under the operational control of the utility. Electricity

end users increasingly actively participate in power system operations by provid-

ing energy or demand services, such as distributed photovoltaic (PV) or demand response (DR). System operators need to dramatically enhance their capability in

monitoring, estimating, and predicting resource adequacy, demand fluctuations,

as well as system health to be able to address the ever-changing grid challenges.

New sensing and monitoring capabilities provide power system operators with

new opportunities to understand and predict the system conditions at all levels. At the transmission level, deployment of phasor measurement units (PMUs)

has provided new capabilities in most major interconnections. In distribution

Big Data Application in Power Systems. https://doi.org/10.1016/B978-0-12-811968-6.00016-4

Copyright © 2018 Elsevier Inc. All rights reserved.

NWP

Persistence

ARMA

ANN

SVM

Box-Jenkins

Kalman filter

Markov chain

Resource forecasting

Persistence

Regression

Kalman filter

ANN

Time series

Load forecasting

State estimation

SVR

Gaussian process

Measurements SCADA, PMU

Weighted least squares

PMU-based linear SE

Forecasting- aided SE

Predictive SE

Dynamic SE

PG PL

FIG. 1

Overview.

344 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

systems, smart meter-based advanced metering infrastructure has enabled two-

way communication between system operators and customers. The adoption of

solar and wind generators have created the need for power system operators to have better awareness of macro and microclimate conditions, such as irradi-

ance and wind speeds. Smart devices such as inverters and electrical vehicle

charging stations possess self-awareness and monitoring capabilities that can be used for centralized controls. When all of these new sensing technologies

are adopted in large numbers, it creates an enormous amount of data at finer

geographic and temporal scales than power system operators are used to han- dling. Therefore, big data analytics can play an increasingly important role in

the modern power system operations in terms of estimation and prediction

of comprehensive system conditions.

In this chapter, various methods to forecast the output of variable renewable

energy resources, such as wind and solar are first reviewed. Then, different load forecasting methods are discussed. Finally, how to estimate and forecast grid

states is explained. Fig. 1 gives an overview of the topics covered in this chapter.

2 RESOURCE FORECASTING

2.1 Renewable Forecasting

Renewable energy resources, particularly wind and solar energy, have become a

primary focus in government policies, academic research, and the power indus-

try. Among various renewables, wind energy is considered as one of the most

3452 Resource Forecasting

promising alternatives [1]. However, the variable and uncertain nature of the

renewable resources, such as wind and solar, may affect the economic and reli- able operations of the power system [2], especially with increasing penetration

levels of wind and solar power [3]. Therefore, it is important and desired to

improve the accuracy of the wind and solar forecasting that is used in power system scheduling.

2.2 Wind Forecasting 2.2.1 Wind Forecasting Overview Different wind forecasting models have been developed in the literature, and

they can be generally classified into three groups [4]: (i) physical models that are usually based on numerical weather prediction (NWP) models;

(ii) statistical methods, most of which are intelligent algorithms based on

data-driven approaches; and (iii) hybrid physical and statistical models.

NWP models simulate the physics of the atmosphere utilizing physical laws

and boundary conditions. There exist a variety of challenges when directly adopting NWP models for wind forecasting, such as the accuracy, spatial

and temporal resolutions, domain, and hierarchical importance of the physical

processes. Based on the domain coverage, the NWP models could be divided into limited area models (LAMs) and global models (GMs) [5]. Several GMs

[6–8] have been developed to fulfill different forecasting needs, such as the Global Forecast System (GFS) and the Integrated Forecast Model. LAMs nor- mally produce higher-resolution forecasts than GMs. Different LAMs have been

developed for forecasting in different domains. Some of these are the High-

Resolution Limited Area Model [9], ALADIN [10], the Fifth-Generation Meso- scale Model [11], and High-Resolution Rapid Refresh (HRRR) [12].

Statistical models are trained using historical data and usually outperform

NWP models in very short-term forecasting (within 1-hour ahead) [13], par- tially due to the fact that NWP models normally take long time (e.g., hours)

to run. Both linear and nonlinear methods have been widely applied to wind

forecasting. Linear models, such as autoregressive moving average (ARMA) methods [14, 15], Box-Jenkins methods [16], Kalman filter [17], and Markov

Chain models [18, 19], are most widely used in the literature. Artificial neural

networks (ANN) and support vector machine (SVM) are the two most popular nonlinear methods for wind forecasting. Different ANN and SVM models have

been compared in many studies, and they performed inconsistently under dif- ferent conditions [20–22].

2.2.2 Big Data-Driven Wind Forecasting Much of the historical attention on wind and solar power forecasting has

focused on the day-ahead time frame due to the economic impacts of variable

renewables interacting with electricity markets and the unit commitment

346 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

process. Many of the new applications that require wind and solar power fore-

casting require more frequent updates and more granular forecasts. Big data- driven methods have been recently used to improve the accuracy of wind power

forecasting at different temporal and spatial scales [23–25].

Hours- to Day-Ahead NWP-Based Wind Forecasting The impact of atmospheric dynamics becomes more important for short-term

horizons from a few hours to day ahead, and NWP models often produce more accurate forecasts on these timescales. For example, the big data-driven Wind

Forecast Improvement Project (WFIP) was performed to improve short-term

wind power forecasts and determine the value of these improvements to grid operators [23]. WFIP encompassed two study regions: the northern study

region and the southern study region. The WFIP southern study region covers

most of the Electric Reliability Council of Texas (ERCOT) service area, as shown in Fig. 2. The data from additional sensors deployed for the WFIP project, as

well as tower data from a set of participating wind power plants within Texas,

were assimilated into most of the ensemble members; however, the data from the project sensors were withheld from some ensemble members to gauge their

impact on the forecasts [23]. The existing wind forecasting system at ERCOT

used Mesoscale Atmospheric Simulations System model forecasts with initial

FIG. 2

WFIP southern study region in ERCOT [24].

Large scale model

Ensemble of rapid-update short-term NWP forecasts

Statistical adjustment procedure

Ensemble composite algorithm

Wind plant output model

Observations

Final forecast

FIG. 3

Overall framework of the wind power forecasting system [24].

3472 Resource Forecasting

conditions and boundary conditions from the GFS and the North American

Mesoscale Model. Ensemble methods have been shown to produce more accu-

rate forecasts. The WFIP forecast system consists of an ensemble of high- resolution rapid-update NWP models. Each of these ensemble members incor-

porates a variety of model configurations, physics parameterizations, and data

assimilation techniques. The purpose of integrating all of these ensemble mem- bers into one system is to construct an optimized composite forecast able to

predict forecast uncertainty and assess the relative performance of different

modeling approaches. Fig. 3 shows the overall framework of the wind power forecasting system. The WFIP ensemble members include [23, 24]:

(1) The National Oceanic and Atmospheric Administration’s 3-km HRRR

model, updated hourly.

(2) Nine NWP models updated every 2 hours on a 5-km grid:

(b) Three configurations of the Weather Research and Forecasting

(WRF) model. (c) Three configurations of the Mesoscale Atmospheric Simulations

System.

(3) An Advanced Regional Prediction System model updated every 6 hours on a 2-km grid.

Minutes- to 2-Hour-Ahead Machine-Learning-Based Wind Forecasting Due to the nonlinear and nonstationary characteristics of wind speed, it is

challenging to develop a generic model based on a single machine learning

Wind speed

Wind direction

Neural network

Support vector machine

Random forest

Gradient boosting machine

First-layer forecasts

Ensemble algorithm

Final forecasts

Input vector Autocorrelation and partial

Autocorrelation analysis

Recursive feature elimination

Granger causality test

Principal component analysis

FIG. 4

The framework of the ensemble forecasting model [25].

348 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

algorithm that can produce the best forecasts at many different spatial and

temporal scales. Big data-driven methodologies could potentially improve

the accuracy of the wind forecasting. Fig. 4 illustrates a big data-driven multi- model wind forecasting methodology with deep feature selection methodol-

ogy [25]. First, features extracted from the data variables are determined by

a deep feature selection procedure and serve as inputs to the model. Four independent feature selection methods are included in the procedure and

implemented sequentially. The first-layer machine learning models are built

based on the selected feature combination. These models forecast wind speed or wind power as the output. A blending model is developed in the second

layer to combine the forecasts produced by different algorithms from the

first layer, and to generate both deterministic and probabilistic forecasts. Parameters of these models are optimally tuned by the grid search technique.

Machine learning algorithms have distinctive advantages. For instance, ANN

algorithms are adaptive by choosing different learning functions and loss

3492 Resource Forecasting

functions, but have overfitting issues when the training dataset is not long

enough. SVM is efficient to train and can provide relatively accurate results, but they are memory intensive and hard to tune. Tree ensemble algorithms

like random forests and gradient boosting machines can avoid overfitting

issues. The blending model is expected to integrate the advantages of differ- ent algorithms by canceling or smoothing the local forecasting errors.

2.2.3 Wind Forecasting Datasets The Wind Integration National Dataset (WIND) Toolkit was created through

the collaborative efforts of National Renewable Energy Laboratory and 3TIER and has been funded by the US Department of Energy, Office of Energy Effi-

ciency and Renewable Energy, Wind and Water Power Technologies Office

[26, 27]. The WIND Toolkit supports the next generation of wind integration studies. The WIND Toolkit includes meteorological conditions and turbine

power for over 126,000 sites in the continental United States for the years

2007–13 (Fig. 5), which was produced with the WRF model version 3.4.1. The meteorological dataset has 2 � 2-km horizontal resolution, nine vertical levels, a temporal resolution of 5 minutes, and covers a 7-year period

(2007–13). The simulations include a spin-up period of 48 hours. The model

FIG. 5

Map showing the site density of the 126,692 wind sites [27].

350 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

was restarted every month, and we used scale selective grid nudging. There are

three main datasets included in the WIND Toolkit [27]:

(1) The meteorological dataset includes basic information on the weather conditions in each 2 � 2-km grid cell, for example, wind profiles, atmospheric stability, and solar radiation data.

(2) A power dataset was created using the wind data and site-appropriate turbine power curves to estimate the power produced at each of the

turbine sites.

(3) A forecast dataset includes forecasts for 1-, 4-, 6-, and 24-hour forecast horizons.

2.3 Solar Forecasting

Solar power penetration in the United States is growing rapidly, and the Sun-

Shot Vision Study reported that solar power could provide as much as 14% of

US electricity demand by 2030 and 27% by 2050 [28]. At these high levels of solar energy penetration, solar power forecasting will become very important

for electricity system operations. Solar forecasting is a challenging task, and

solar power generation presents different challenges for transmission and dis- tribution networks [29]. On the transmission side, solar power takes the form

of centralized solar power plants, a nondispatchable component of the gener-

ation pool. On the distribution side, solar power is generated by a large number of distributed arrays installed on building rooftops and other sites. These arrays

can alter traditional load patterns by offsetting electricity use behind the meter.

Integrating large amounts of solar power into the grid can magnify the impact of steep ramps in solar power output, which poses challenges to system oper-

ators’ ability to account for solar variability. Forecast inaccuracies of solar

power generation can result in substantial economic losses and power system reliability issues because electric grid operators must continuously balance sup-

ply and demand.

2.3.1 Solar Forecasting Overview Solar power output is directly proportional to the magnitude of solar irradiance

incident on PV panels. To integrate high penetrations of solar energy genera- tion, accurate solar forecasting is required at multiple spatial and temporal

scales. Solar irradiance variations are caused primarily by cloud movement,

cloud formation, and cloud dissipation. In the literature, researchers have developed a variety of big data-driven methods for solar power forecasting,

such as statistical approaches using historical data [30–32], the use of NWP models [33, 34], tracking cloud movements from satellite images [35], and tracking cloud movements from direct ground observations using sky cameras

[35, 36]. NWP models are the most popular method for forecasting solar

Table 1 Solar Forecasting Methodologies [38]

Methods Description/Comment Forecast Horizons

Physical approaches

NWP models NWP models are the most popular method for forecasting solar irradiance more than 6 hours or days in advance

4 hours to days ahead

Total Sky imagers (TSI) TSIs are used to extract cloud features or to forecast short-term GHI

0–30 minutes ahead

Statistical approaches

Statistical methods Statistical methods were developed based on autoregressive or artificial intelligence techniques for short-term forecasts

0–6 hours ahead

Persistence forecasts Persistence of cloudiness performs well for very short-term forecasts

<4 hours ahead

3512 Resource Forecasting

irradiance several hours or days in advance. Mathiesen and Kleissl [34] ana-

lyzed the global horizontal irradiance (GHI) in the continental United States forecasted by three popular NWP models: the North American Model, the

GFS, and the European Centre for Medium-Range Weather Forecasts. Lorenz

et al. [37] showed that cloud movement-based forecasts likely provide better results than NWP forecasts for forecast timescales of 4 hours or less; beyond

that, NWP models tend to perform better. In summary, forecasting methods

can be broadly characterized as physical or statistical. The physical approach uses NWP and PV models to generate solar power forecasts, whereas the statis-

tical approach relies primarily on historical data to train models [38]. Recent

solar forecasting studies [39, 40] integrated these two approaches by using both physical and historical data as inputs to train statistical models. These solar

forecasting methods are summarized in Table 1.

2.3.2 Big Data-Driven Solar Forecasting

Hours- to Day-Ahead NWP-Based Solar Forecasting As part of the project work performed under the SunShot Initiative’s Improv-

ing the Accuracy of Solar Forecasting program, a system for improving solar

forecast, Watt-sun, has been developed. Watt-sun uses big-data information processing technologies and applies machine-learnt, situation-dependent

blending of multiple models to enhance system intelligence, adaptability,

and scalability. The algorithm which provides the best accuracy for the last 2 days is selected for future solar power forecasts. Numerical results show

30% improvement in solar irradiance/power forecast accuracy compared with

forecasts based on the best individual method, and 10% improvement com- pared with model forecasts processed by machine learning methods without

situation categorization. Detailed information about the Watt-sun forecast

method can be found in [40, 41].

352 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

Minutes- to 2-Hour-Ahead Sky Imaging-Based Solar Forecasting Fig. 6 shows a short-term 1-hour-ahead GHI classification forecasting frame-

work [42]. In addition to pattern recognition, the framework contains two other parts: the data preprocessing module and the GHI forecasting module.

In the data preprocessing module, a three-step technique is applied to improve

the pattern recognition and forecasting performance. The forecasting module is divided into three model sets: Model Set I (MSI), Model Set II (MSII), and

Model Set III (MSIII). The first two sets of models forecast GHI for the first 4 day-

light hours of each day. Then the GHI values in the remaining hours are fore- casted by an optimal machine learning model determined based on a weather

pattern classification model in the third model set. The weather pattern is deter- mined by an SVM classifier.

2.4 Renewable Forecasting Performance Evaluation Metrics

A suite of generally applicable, value-based, and custom-designed metrics for renewable forecasting considering different time horizons, geographic loca-

tions, and applications was developed by Zhang et al. [29]. The developed

renewable forecasting metrics can be broadly divided into four categories: (1) statistical metrics for different time and geographic scales, (2) uncertainty

quantification and propagation metrics, (3) ramp characterization metrics, and

(4) economic metrics. A brief description of the metrics is given in Table 2, and detailed information about each metric can be found in [29, 43]. A smaller

value indicates a better forecast for most of the metrics, except for Pearson’s cor-

relation coefficient, skewness, kurtosis, distribution of forecast errors, and ramp characterization metrics.

G1

G3

G21

G22

G23

D a ta

g ro

u p 2

D a ta

g ro

u p 1

D a

ta g

ro u

p 3

SVM classification

model

Pattern recognition

GHI forecasts

Location information

Sky images

Actual GHI

Normalization

Reconstruction

Elimination

M o d e l S

e t II

MS 21

MS 22

MS 23

M o d e l S

e t II I

MS 31

MS 32

MS 33

1-day-ahead persistence

model

M o d e l S

e t I

ForecastingFeature extraction and data preprocessing

FIG. 6

Overall framework of the short-term GHI forecasting based on sky imaging and pattern recognition [42].

Table 2 Metrics for Renewable Energy Forecasting [29]

Type Metric Description/Comment

Statistical metrics

Distribution of forecast errors Provides a visualization of the full range of forecast errors and variability of solar forecasts at multiple temporal and spatial scales

Pearson’s correlation coefficient Linear correlation between forecasted and actual wind/solar power

Root mean square error (RMSE) and normalized root mean square error (NRMSE)

Suitable for evaluating the overall accuracy of the forecasts while penalizing large forecast errors in a square order

Maximum absolute error (MaxAE) Suitable for evaluating the largest forecast error

Mean absolute error (MAE) and mean absolute percentage error (MAPE)

Suitable for evaluating uniform forecast errors

Mean bias error (MBE) Suitable for assessing forecast bias

Kolmogorov-Smirnov test integral (KSI) or KSIPer

Evaluates the statistical similarity between the forecasted and actual wind/solar power

OVER or OVERPer Characterizes the statistical similarity between the forecasted and actual wind/solar power on large forecast errors

Skewness Measures the asymmetry of the distribution of forecast errors; a positive (or negative) skewness leads to an over-forecasting (or under-forecasting) tail

Excess kurtosis Measures the magnitude of the peak of the distribution of forecast errors; a positive (or negative) kurtosis value indicates a peaked (or flat) distribution, greater than or less than that of the normal distribution

Uncertainty quantification metrics

R�enyi entropy Quantifies the uncertainty of a forecast; it can utilize all of the information present in the forecast error distributions

Standard deviation Quantifies the uncertainty of a forecast

Ramp characterization metrics

Swinging door algorithm Extracts ramps in wind/solar power output by identifying the start and end points of each ramp

Economic metrics 95th percentile of forecast errors Represents the amount of nonspinning reserves service held to compensate for wind/solar power forecast errors

3533 User Energy System State Estimation

3 USER ENERGY SYSTEM STATE ESTIMATION

3.1 Overview

Power system load forecasting has its use in planning as well as system opera- tions. Better load forecasting can result in reduced operational costs and

improved system reliability. Normally, system operators pay more attention

to the aggregated load at a distribution substation, which could contain many distribution feeders because the load and generation are physically separated in

354 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

the confidential hierarchy grid. With the increased DER penetration, the distri-

bution level load forecasting has gained more attraction. The distribution level load forecasting faces more challenge because it contains more stochastically

abrupt deviations. Further, the load itself can become resource when providing

DR, the needs to estimate the DR capability at future time are critical for both operators and DR providers to better schedule the service. This section will

introduce the data-driven load forecasting as well as DR forecasting using user

energy system state estimation.

3.2 Load Forecasting

The load forecasting time horizon can be divided into short term, medium term,

and long term. Short-term load forecasting (STLF) usually predicts the electricity demand from 1 hour to 1 week ahead and is used to facilitate the day-ahead and

real-time resource scheduling in power systems [44]. The term “very short-term

load forecasting” is also used, which focuses on demand forecasts less than 1 hour ahead [45, 46]. Medium-term load forecasting (MTLF) is usually from

1 week to 1 year ahead and is used for maintenance scheduling as well as con-

tract negotiation in energy markets [47]. Long-term load forecasting (LTLF), which covers a time period of more than 1 year, is mainly used for expansion

planning of power grids in order to accommodate future demand [47].

Many models and methods have been developed for load forecasting. The most commonly used methods for MTLF and LTLF are the end-user approach, which

takes into account the end-user behaviors [48]; and the econometric approach,

which studies the relationship between energy consumption and other factors, such as weather conditions and economic factors [47]. During the past decades,

research efforts have been focused on STLF, since it plays an essential role in

power system operation. Various approaches have been applied to STLF, including time-series methods [49, 50], regression-based methods [51, 52],

and artificial intelligence-based methods [53–55].

An overview of the most commonly used STLF models and approaches is pro-

vided in the following. More comprehensive reviews of load forecasting

methods, especially STLF methods, can be found in [47, 56, 57].

3.2.1 Conventional Methods Conventional STLF approaches adopt statistical methods to model the relation-

ship between demand and external factors that may influence demand. A variety

of models have been used for load forecasting, including persistence method, time-series methods, regression analysis, and Kalman filtering-based methods.

Persistence model uses the previous day (or the corresponding day in the previous week) as a prediction. Such a method is sensitive to the rare events

(e.g., the day in the last week is the Thanksgiving Eve day).

3553 User Energy System State Estimation

Time-series approaches model electricity demand as a time-varying random

process and use historical data to predict future demand by exploiting the inter- nal pattern of the time-series data. The most often used time-series methods

include ARMA [58], autoregressive integrated moving average (ARIMA) [50],

ARMA with exogenous variables (ARMAX) [59, 60], and autoregressive inte- grated moving average with exogenous variables (ARIMAX) [47]. These

methods model future demand as a function of historical values of load

consumption and other factors, such as time and weather.

Regression analysis is employed to model the relationship between electricity

demand and external factors, such as weather, the hour of the day, and cus- tomer type. Multiple regression techniques have been applied to load forecast-

ing, including linear regression [51], nonparametric regression [61], and robust

regression [62].

State-space models have also been used to model the time-varying load, and

Kalman filtering-based algorithms are adopted to provide a recursive update of the load in the near future [63, 64].

Since the actual relationship between the load and influencing factors is non-

linear and complex, the major challenge of using the aforementioned methods for load forecasting is how to develop an accurate model to represent electricity

demand.

3.2.2 Artificial Intelligence-Based Methods In recent years, artificial intelligence-based methods, such as ANNs and support

vector regression (SVR), have been applied to better model the complex rela- tionship between electricity demand and other factors and thereby better fore-

cast future demand.

ANNs are composed of a number of neurons, each of which has an activation

function converting its input to output. The neurons are interconnected to form

a multilayer network, which is used to define the relationship between the input variables and output variables. In load forecasting, ANN models are

trained to find the mapping between the load and influencing factors using his-

torical data. The mapping function is then used to forecast the future load [53, 65]. An extensive review of neural network methods for STLF is given in [66].

The SVR method uses a nonlinear mapping function to transform the input

data into a high-dimensional feature space, and then a linear regression is per- formed in this high-dimensional space [67].

Both the ANN and SVR methods have the capability to use nonlinear models to map the input and output variables and better capture the complex relationship

between the load and other influencing factors. A detailed review of various

356 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

computational intelligence techniques for STLF is provided in [68], including

ANN, SVR, and other artificial intelligence-based methods.

Moreover, hybrid approaches are also common in load forecasting, which com-

bines two or more aforementioned methods in order to achieve better forecast- ing accuracy [69–71].

3.2.3 Gaussian Process-Based Method Most load forecasting methods predict the electricity demand at the aggregated

level. For forecasting the demand of individual customers, different models will

be needed for different customers since each may behave differently. Therefore, there is a need for accurate and personalized demand forecasting algorithms for

individual customers.

In the following, a Gaussian process-based load forecasting algorithm is intro- duced. The Gaussian process-based method is highly flexible, since it can easily

incorporate different existing regression-based methods. Therefore, it can pro-

vide a personalized demand forecasting algorithm for each individual customer by incorporating the suitable model for the customer’s behaviors.

To visualize the distribution of load data, the Pacific Gas and Electric Company (PG&E) and OhmConnect data are analyzed for a proper statistical model.

Fig. 7A and B show the distributions of two normalized loads at two different

time stamps. The dashed lines are the fitted Gaussian distributions to the data. Fig. 7C shows the joint distribution of the same load in two time indices of a

day. Together with these three figures, the data analysis shows that the loads at

different time slots can be modeled as a multivariate Gaussian distribution. In order to check the Gaussianity rigorously, the K-squared test [72] and the

Jarque-Bera test [73] can be conducted.

Here, the data before the demand forecasting period of a particular day are

defined as a vector x of C elements, which may include features such as load,

temperature [74], and day of the week. Without loss of generality, the case when the target demand forecasting is a scalar y is considered. An underlying

function y(x) is inferred from a training set T ¼ fðxi,yiÞji ¼ 1,…,ng, where i is the historical day index and n is the total number of days in the training data- set. For compact notation, all input data are combined in a C � n matrix X, and the target variables in a vector y. Therefore, the training set can be written as

T ¼ ðX,yÞ. Similarly, {(X*, y*)} denotes the testing data, where X* is known, and y* is unknown.

The joint distribution of the training and testing data is:

y

y ∗

! ¼

mðXÞ mðX∗Þ

" # ,

CðX,XÞ, CðX,X∗Þ CðX∗ ,XÞ, CðX∗,X∗Þ

" # !

(A) (B)

(C)

FIG. 7

Gaussianity of residential customers’ loads at different time indices. (A) Histogram of normalized load distribution at one time index.

(B) Histogram of normalized load distribution at another time index. (C) Joint load distribution of the two time indices.

3573 User Energy System State Estimation

Therefore, a Gaussian process is specified by a mean, m(�), and a covariance

y ∗ ¼ mðX∗Þ + CðX∗,XÞCðX,XÞ�1ðy �mðXÞÞ (1)

And the covariance estimate is:

Covðy∗Þ ¼ KðX∗,X∗ Þ�KðX∗,XÞ � ½CðX,XÞ + λI��1CðX,X∗Þ (2)

where λ is a hyperparameter.

After setting up the framework, data can be used to design the covariance

functions.

• Embedding distance-based correlation: A future load equals the

summation of a past load and the change between them. This leads to a stronger correlation of load values between two time slots closer to each

other. As shown in Fig. 8, the correlation decreases from a 1-hour interval

to an 11-hour interval for the PG&E dataset and OhmConnect dataset.

FIG. 8

Autocorrelation with different intervals. The x-coordinate represents load at time t. The y-coordinate

represents load at time t + t0, where t0 is the time interval between loads at two indices.

358 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

Therefore, a squared exponential covariance is employed based on Euclidean distance.

• Embedding periodic pattern: From Fig. 8, the correlation increases again

to a 24-hour interval, indicating a daily periodic pattern. As different residential customers may have different periodicities with different

weights, periodic patterns are automatically detected and embedded into

the covariance function. • Embedding piecewise linear pattern in temperature: As loads are usually

sensitive to temperature, the temperature is also used in the covariance

function.

Fig. 9 shows the simulations of the Gaussian process-based method with the

PG&E dataset with different training and testing lengths.

• Use 2 weeks of hourly load as a training set to forecast 1 week of hourly load.

• Use 4 weeks of hourly load as a training set to forecast 1 week of

hourly load. • Use 1 week of hourly load as a training set to forecast 4 weeks of

hourly load.

As shown in Fig. 9, the mean estimate learns features of periodicity and tem-

perature, and the 95% confidence zone covers true values for the week in

the forecast. This happens even when the training set length is very short. It gives both highly confident mean estimates and trends of the uncertainty.

In addition to the load domain analysis in Fig. 9, the results for the error domain analysis of three different methods are shown in Fig. 10 for all users

in the PG&E data. These methods include a moving average model, a regression

Time (h) Time (h)

Time (h)

0

H o u rl y

lo a d

100 200 300 400 500 900600 700 800

True value Gaussian proc. 95% CI for GP

(B)

0

H o u rl y

lo a d

100 200 300 400 500 900600 700 800

True value Gaussian proc. 95% CI for GP

(C)

0 0

5

10

15

20

25

0

5

10

15

20

25

0

5

H o u rl y

lo a d

10

15

20

True value Gaussian proc. 95% CI for GP

25

100 200 300 400 500 600

(A)

FIG. 9

Estimation comparisons with different training set lengths and different forecasting time horizons. (A) 2 weeks training, 1 week testing.

(B) 4 weeks training, 1 week testing. (C) 1 week training, 4 weeks testing.

3593 User Energy System State Estimation

model taking into account the time of week and the temperature, and the Gaussian process-based method.

As shown in Fig. 10, the Gaussian process-based approach has the smallest error, no matter how long the forecasting is. Especially for very long-time

horizons—up to 17 weeks—the Gaussian process-based method is much more

robust than the other two methods.

Comparing to other load forecasting methods, the Gaussian process-based

method has a mean estimate that is equivalent or better than the estimates gen-

erated by currently used baseline estimation methods. Also, Gaussian process- based method naturally provides the prediction of uncertainties inherent in the

customer loads while deterministic method does not provide such functional-

ity. Finally, the accuracy and the ability for providing confidence intervals are enhanced by Gaussian process-based method’s flexibility of an adaptive com-

ponent design according to customer behaviors.

2 0

M A

P E

10

20

30

40

50

60

Average Regression Gaussian proc.

70

80

90

3 5 9

Forecast range

17 weeks

FIG. 10

Error domain analysis.

360 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

3.3 User Energy System State Estimation: Demand Response

Electricity consumers are becoming active resources in terms of providing DR. The Federal Energy Regulatory Commission defines DR as electric usage adjust-

ments by the consumers from their normal consumption patterns [75, 76]. Such adjustments are in response to (1) changes in the price of electricity over

time, or (2) incentive payments designed to induce lower electricity consump-

tion at usage peaks or when system reliability is jeopardized [77]. Different than load forecasting, DR capability of certain user energy systems can be estimated

through the baseline evaluation.

TraditionalDRprogramsareusuallydesignedforlargecommercialcustomers,as their usage is predictable. Therefore, the deterministic baseline evaluation can be

used for the electricity consumption estimation based on the no-DR period [78,

79]. The difference between an estimated normal consumption and the actual usage is subsequently used to calculate the savings as shown in Fig. 11 [80–82].

Deterministic methods such as simple load average and temperature-based linear regression are used for commercial customers with satisfactory results

[74, 83, 84]. For example, DR programs had great success with large power

consumption users [85]. GreenTech Media reported in 2013 that 8.7 million in revenue had been generated within 7 months in the PJM Interconnection

by conducting DR in system operation with mostly large customers, reducing

the use of 80 traditional coal power plants in peak power supply [85].

0 Time

Actually did

If no signal

E n

e rg

y co

n su

m p

tio n

FIG. 11

Deterministic baseline estimation and its rewarding mechanism.

3614 Power System State Estimation

Although large customers currently create a significant portion of the revenue in the DR programs, the smaller residential consumers hold the key to potential

growth in the DR customer number and the DR revenue. For example, 9.3

million customers had participated in DR programs by March 2016 in the United States, but more than 90% of them are in the residential sector [86].

In addition to making profits, DR at the residential level is becoming an attrac-

tive solution for the radically increased renewable generation to balance local power flow [87].

The drawback to traditional baseline estimation methods lies in their failure to utilize the historical data to capture the dynamics of complex user behaviors

[84, 88], which is of particular importance for small to medium consumers

with more variability [89]. One can also use the idea of control groups [90–92]; however, it may be hard to uniquely define the best control group that properly captures the uncertainty in user behavior of the treatment group

(enrolled customers). As large utility companies have started to make historical data available to approved third parties (e.g., the Green Button initiative in Cal-

ifornia [93]) machine learning-based techniques can be used to capture the

uncertainty at the consumer level. Similar to the content in load forecasting, Gaussian process regression can be used for DR as well. After which, automatic

feature extractions can be employed to dynamically embed consumer behav-

iors into the mean and variance estimates.

4 POWER SYSTEM STATE ESTIMATION

4.1 Overview

Power system state estimation was developed decades ago and now forms the backbone of all control center applications. Operators collect thousands of

measurements from meters and relays through supervisory control and data

362 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

acquisition (SCADA) systems to solve for the system states, namely voltage

magnitude and angle at all buses. With the fully solved system state variables, the power flow of the system can be calculated. The SCADA system can be seen

as an early “big data” resource in power system. With the addition of PMUs,

system state variables at many locations can be directly monitored. Advanced state estimation techniques have been developed and implemented for a better

awareness of grid state conditions.

4.2 Conventional Nonlinear State Estimation

Power system state estimation aims to find the system state at a point in time

(i.e., voltage magnitudes and phase angles) based on a set of measurements. Conventional static estimation uses the measurements, which are taken at

one snapshot in time to estimate the corresponding system states of this time

instance.

Let x ¼ ½θ2,θ3,…,θn,jV1j,jV2j,…,jVnj�T denote the vector of system states includ- ing the voltage magnitude and the phase angle at every bus except the phase angle at the reference bus 1 is set to be θ1 ¼ 0. Let z ¼ [z1, z2, …, zm]T represent the vector of collected measurements including the active and reactive power

injections at buses, power flows in the network, and voltage magnitudes. The relationship between the collected measurements and the system states

can be written as:

z ¼ hðxÞ + ω (3)

where h ¼ [h1(x), h2(x), …, hm(x)]T is the vector of nonlinear functions map- ping the states to measurements and ω ¼ [ω1, ω2, …, ωm]T is the measurement noise vector. Usually, the measurement noises are assumed to be independent Gaussian random variables with zero mean and variance σ2i (i.e., ω � N ð0,ΣÞ), where the covariance matrix Σ is a diagonal matrix with the ith diagonal ele- ment as σ2i . In practice, the measurement set is redundant, resulting in an over- determined nonlinear equation system (3).

The goal of state estimation is to find an estimate x̂ of the true state x given the measurement set z. The most widely used approach for static state estimation is

the weighted least squares (WLS) method. The best estimate of system states is

found by:

x̂ ¼ arg min x

JðxÞ ¼ arg min x

z�hðxÞð ÞTΣ�1 z�hðxÞð Þ (4)

Since the optimization problem is a nonlinear least squares problem, the

Gauss-Newton method is used to find the best estimate in an iterative manner. At iteration k, the estimated state vector xk is updated using [94]:

3634 Power System State Estimation

xk + 1 ¼ xk + Δxk (5)

GðxkÞΔxk ¼ HTðxkÞΣ�1 z�hðxkÞ � �

(6)

GðxkÞ ¼ HTðxkÞΣ�1HðxkÞ (7)

where Δxk is the update on the estimated system state at iteration k, and H(xk) is the Jacobian matrix of the vector function h(x) evaluated at xk as:

HðxkÞ ¼ ∂hðxÞ ∂x

����x¼xk (8) The matrix G(x) is the gain matrix, and Eq. (6) is referred to as the normal equa-

tion of the WLS algorithm.

The iterative procedure is terminated when the mismatch between the calcu-

lated measurement values using the system states and the actual measurement

values is below a predetermined threshold.

4.3 PMU Data-Based Linear State Estimation and Dynamic State Estimation

With the broad development of PMUs in power systems to directly measure the

system states, state estimation problems have naturally expanded to include

PMU measurements. Several new techniques of state estimation have been developed to better understand grid conditions under all circumstances.

Among them, linear state estimation [95] and dynamic state estimation [96] have seen broader development.

Because of the simultaneous collection of measurements across the system

through PMUs, the linear model of the system can be constructed and solved [95]. The synchrophasor-based linear state estimation problem considers no

correlation between adjacent states.

z ¼ V

Iflow

� � ¼

II

yA + ys

� � x + e (9)

where z is the measurement vector vertically concatenated voltage and current measurements and x is the complex state vector. The II matrix is an incidence

matrix which identically relates the state vector to voltage measurements. The

admittance matrix relates the state vector to current measurements.

Assume PMU measurement is available at two adjacent nodes, the linear equa-

tion can be solved as

364 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

Vi

Vj

Iij Iji

2 6664

3 7775¼

1 0

0 1

yij + yi0 �yij �yij yij + yi0

2 6664

3 7775 �

Vi

Vj

� � (10)

Another important feature of the PMU measurements is that they can capture the

electromechanical dynamics of the power system [96]. Therefore, dynamic state

estimation was developed to use PMU measurements to derive the dynamic states of the power system, such as the generator speed. The system dynamic model can

be generally represented by a set of differential and algebraic questions:

dxðtÞ dt

¼ f xðtÞ,yðtÞ,tð Þ (11)

0 ¼ g xðtÞ,yðtÞ,tð Þ (12)

where x and y are the dynamic and algebraic states of the system. A set of PMU

measurements z can be directly related to the system states and measurement

error by:

z ¼ h xðtÞ,yðtÞ,tð Þ + η (13)

A standard least square estimation is then performed to minimize the measure- ment error compared with the system dynamic model outputs, deriving a

dynamic state estimation.

It is also worth mentioning that a linear state estimator can be used for system dynamic state estimation. The system dynamic models are constructed the

same way, but instead of least square solutions, robust linear models (least absolute value)-based solutions can be derived [97].

4.4 Predictive State Estimation 4.4.1 Forecasting-Aided State Estimation Unlike conventional power system state estimation which estimates the system states at a certain time sample based on measurements taken at this snapshot,

forecasting-aided state estimation provides a recursive update of the state esti-

mate by taking into account the state transition over time. Mathematical models [98] describing the state trajectory have been employed to forecast

the system states in the near future, resulting in a priori state estimate. With

the newly received measurement data, the forecast system states are once again refined, rendering a more accurate state estimate. By incorporating short-term

state forecasting, the performance of the state estimation can be improved,

especially in dealing with missing measurements.

Most existing forecasting-aided state estimation approaches are based on the

Kalman filter [98, 99]. Machine learning algorithms, such as ANNs, have also

3654 Power System State Estimation

been used to provide state forecasting and thereby aid the state estimation

[100–102]. A more comprehensive review of forecasting-aided state estimation is given in [103].

4.4.2 Predictive State Estimation With the increasing penetration of renewable energy resources, the system

states become more variable and unpredictable. Besides individual forecasting

for variable resources and loads, state forecasting can greatly help operators proactively operate the systems and reduce the operation cost [104]. This sec-

tion introduces a fast and high-accurate system state forecasting approach

based on historical data and a machine learning algorithm.

The historical system states from measurements such as PMUs are the training

data for the state forecaster. An extreme learning machine (ELM)-based algo-

rithm is used to forecast the future system states for the distribution system [105]. In the ELM algorithm, the input weights and biases are randomly gen-

erated, and the output weights are computed. This means the computational burden of calculating input weights and biases can be eliminated.

As shown in Fig. 12, the ELM-based system state estimator is designed as fol-

lows. In the training part, M observations are collected, and the observation set {α, γ} can be built as follows:

Input layer Hidden layer Output layer

FIG. 12

Concept of the ELM method.

366 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

α ¼

sð1Þ sð2Þ ⋯ sðmÞ sð2Þ sð3Þ ⋯ sðm + 1Þ ⋯ ⋯ ⋯ ⋯

sðM�mÞ sðM�m + 1Þ ⋯ sðM�1Þ

0 BBBB@

1 CCCCA (14)

and

γ ¼

sðm + 1Þ sðm + 2Þ

⋯ sðMÞ

0 BBBB@

1 CCCCA (15)

where s( j) is the jth observation, α is the input matrix, and γ is the output vector. Consider an ELM algorithm with K neurons in the hidden layer. The activation function ψ used to model the data observation set {α, γ} can be written as:

XK k¼1

ψkðξk,bk,αiÞβk ¼ Ψi (16)

where i ¼ 1, 2, …, M � m, k ¼ 1, 2, 3, …, K. ξk is the input weight vector con- necting the input α and the kth hidden neuron, βk is the output weight connect- ing the kth hidden neuron and output Ψ, and bk is the bias of the kth hidden neuron. The objective is to minimize the errors between the output of the acti-

vation function Ψ and γ. The objective function is as follows:

min β

J ¼ XM�m i¼1

Ψi �γi½ � 2

(17)

where the optimization variable set is β ¼ {β1, …, βK}. ξ ¼ {ξ1, …, ξK} and b ¼ {b1, …, bK} are randomly generated at the first iteration. Subsequently, the ELM can be used to forecast future system states with the optimized parameters.

The IEEE 123-bus distribution system is shown as a test example to illustrate the

behavior. A set of load data from a real utility SCADA system is used for evalu- ating the ELM-based state forecasting approach. As shown in Fig. 13, the sample

rate is 1 Hz, and the time period is 12 days, with a total data length of 1,036,800 points. There are a lot of abrupt stochastic deviations in the load profile of the

distribution system, as shown in Fig. 13, which can differ greatly from the trans-

mission system. In the numerical results, bus 47, 49, 68, 76, and 83 are chosen with the load profile in Fig. 13. Then the system states are computed to evaluate.

The training data are five times the testing data. To evaluate the ELM-based fore-

casting method comprehensively, the sliding window test is used to traverse the whole system state data. For example, the sliding window test employed with

1-hour-ahead forecasting can be illustrated as follows.

0 3 6 9 12

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5 × 102

Time (day)

L o a d (

kW )

FIG. 13

Load profile of IEEE 123-bus distribution system.

3674 Power System State Estimation

1. First, the system state data section from the first to the fifth hours is taken

as training data to determine the best parameters and build the

forecasting model. 2. In the second step, the system state data section from the fifth to the sixth

hours is taken as the test data to evaluate the performance of the

forecasting model. 3. In the third step, for the next round forecasting, the training data section

moves forward from the second to the sixth hours, and the test data

section moves from the sixth to the seventh hours. 4. When the test data section moves to the end of the load data, the sliding

window test with 1-hour forecasting is completed.

Short-term system state forecasting is studied at an hourly level in the literature

[106, 107]. The performance of the ELM-based state forecasting method at dif-

ferent time scales is shown in Table 3. Using the ELM-based state forecasting method, the 1 hour-ahead has the best performance and the 16 hour-ahead

forecasting has the largest forecasting errors. However, the MAPEs of voltage

forecasting are below 2.00%, with an average of 1.370%. The MAPEs of angle forecasting are below 2.50%, with an average of 1.872%.

Table 3 Performance of the ELM approach

Forecasting Type Voltage (%) Angle (%)

1 hour ahead 1.131 1.578

2 hours ahead 1.182 1.628

4 hours ahead 1.289 1.752

8 hours ahead 1.474 1.975

16 hours ahead 1.775 2.431

−10 −5 −1.5 0 1.5 5 10 15 0

5

10

15

20

25

30

35

40

−15 Prediction error (%)

75.17%

D e

n si

ty (

% )

FIG. 14

Percent error of 8-hour-ahead forecasting using ELM: voltage magnitude.

368 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

As shown in Fig. 14, in the histogram of voltage forecasting error, it is noticed

that more than 75% of the errors are accumulated between (�1.5%, 1.5%). Similarly, as shown in Fig. 15, in the histogram of voltage forecasting error, it is noticed that more than 75% of the errors are accumulated between

(�2.3%, 2.3%). Hence, in most of the time, the ELM-based approach can fore- cast the system states with very high accuracy. In some rare cases, the forecasting errors for voltage magnitudes and angles are larger than �10%. However, the cases with forecasting errors larger than �10% are below 1% for both the volt- age magnitudes and angles. The center of the voltage and angle forecasting error is 0, which indicates that the ELM-based approach performs accurately and is

unbiased.

−20 −15 −10 −5 −2.3 0 2.3 5 10 15 20 0

5

10

15

20

25

30

35

75.15%

Prediction error (%)

D e n si

ty (

% )

FIG. 15

Percent error of 8-hour-ahead forecasting using ELM: voltage angle.

Table 4 Comparison With Different Forecasting Approaches

ANN ARIMA GA-SVR Proposed Approach

MAPE (%) 1.702 9.972 3.146 1.725

Time (seconds) 897.2 25.7 767.3 17.1

3694 Power System State Estimation

To compare the performance of the ELM forecasters with the most common

ones in [108–111], the 8-hour-ahead forecasting is chosen as an example. The MAPE and time consumption are the average of voltage and angle forecast-

ing. As shown in Table 4, the ANN has the best accuracy performance in MAPE

comparison; however, it takes more than 40 times longer than the ELM approach. Furthermore, the accuracy of ANN is very close to the ELM approach.

Compared to the other approaches, the ELM approach has the best balance

between forecasting accuracy and time consumption. Overall, machine learn- ing methods demonstrate potential of accurately forecasting the power system

states.

4.5 Distribution System State Estimation

The distribution grid has been undergoing a dramatic transformation in recent years. The penetration level of DERs such as PV systems keeps increasing and

the electricity consumers have become active players because of their capabil-

ities of performing demand side management. The distribution system becomes more complex while more resources are available to provide control-

lability and flexibility at the same time. These changes impose great challenges

as well as opportunities on distribution system operations. Distribution system operators are in need of advanced energy monitoring and management systems

in order to properly monitor the system states and determine the appropriate control actions of available resources. Therefore, distribution system state esti-

mation plays an important role in the distribution system management as it

provides full visibility into a distribution system by estimating the voltage mag- nitude and phase angle at each system bus, as well as the power flow on each

distribution circuit branch, and thereby initial input to various control

functions.

Even though most of the existing distribution state estimation algorithms

inherit the paradigm of transmission-level state estimation [112, 113], distribu-

tion system state estimation has its unique features and challenges [114–116].

First, unlike the transmission system having redundant measurements, there

exist a limited number of measurement devices in the distribution system, resulting in the distribution system not being fully observable. Pseudo-

measurements, usually the load power consumption obtained from historical

370 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

data, can be used for the distribution system state estimation. However, the

accuracy of these pseudo-measurements may be limited.

Second, different models and algorithms are needed for the distribution system

state estimation. Distribution systems are naturally unbalanced due to the dif- ferent system configurations as well as unbalanced parameters and loads. Con-

sequently, three-phase modeling of the distribution system state estimation

problem is needed in order to accurately estimate the system states. Further- more, the low reactance/resistance (X/R) ratios render the commonly used

decoupled WLS algorithm for the transmission system state estimation not suit-

able for the distribution system.

Finally, as the distribution system is more often a radial or weakly meshed grid,

branch currents can be used as possible primary state variables instead of nodal

voltages, which may simplify the formulation of the distribution system state estimation problem.

With the deployment of more and more measurement devices in the distribu- tion system, such as smart meters, synchrophasors, and distribution sensors,

models and methods will be needed to facilitate the accurate estimation of dis-

tribution system states by utilizing the available measurement data, which is crucial for the implementation of distribution system state estimation.

5 CONCLUSIONS

Large volumes of heterogeneous data have been made available for power sys- tem coupled energy systems, from the variable generation resource measure-

ments, smart homes and buildings measurements, to high-resolution and

dynamic grid measurements. Data analytics are becoming more important and effective for power system operators, end users, generation operators,

and aggregators, to manage the grid and its assets in real time and even in a

look-ahead mode. This chapter presented data-driven applications for energy resource forecasting, energy consumption forecasting, as well as power system

state estimation and forecasting. Together, they will provide system operators with advanced awareness of system future conditions. Operators can then pro-

actively dispatch generators, schedule power flows and reactive power support,

preconfigure system topology, or preprocure ancillary services. Eventually, the capability of data analytics can enable a predictive operation paradigm of the

power systems in the future.

References [1] B.K. Sahu, M. Hiloidhari, D.C. Baruah, Global trend in wind power with special focus on the

top five wind power producing countries, Renew. Sust. Energ. Rev. 19 (2013) 348–359.

371References

[2] J. Wang, A. Botterud, R. Bessa, H. Keko, L. Carvalho, D. Issicaba, J. Sumaili, V. Miranda, Wind

power forecasting uncertainty and unit commitment, Appl. Energy 88 (11) (2011) 4014–4023.

[3] M. Cui, J. Zhang, A.R. Florita, B.-M. Hodge, D. Ke, Y. Sun, An optimized swinging door algo-

rithm for identifying wind ramping events, IEEE Trans. Sust. Energy 7 (1) (2016) 150–162.

[4] J. Mendes, J. Sumaili, R. Bessa, H. Keko, V. Miranda, A. Botterud, Z. Zhou, Very short-term

wind power forecasting: state-of-the-art, Tech. Rep., Argonne National Laboratory (ANL), 2014.

[5] S. Al-Yahyai, Y. Charabi, A. Gastli, Review of the use of Numerical Weather Prediction (NWP)

models for wind energy assessment, Renew. Sust. Energ. Rev. 14 (9) (2010) 3192–3198.

[6] N.P. Wedi, P.K. Smolarkiewicz, A framework for testing global non-hydrostatic models, Q. J. R.

Meteorol. Soc. 135 (639) (2009) 469–484.

[7] J.J. Traiteur, D.J. Callicutt, M. Smith, S.B. Roy, A short-term ensemble wind speed forecasting

system for wind power applications, J. Appl. Meteorol. Climatol. 51 (10) (2012) 1763–1774.

[8] J. Côt�e, S. Gravel, A. M�ethot, A. Patoine, M. Roch, A. Staniforth, The operational CMC-MRB

global environmental multiscale (GEM) model. Part I: design considerations and formulation,

Mon. Weather. Rev. 126 (6) (1998) 1373–1395.

[9] D.G. Jensen, C. Petersen, M.R. Rasmussen, Assimilation of radar-based nowcast into a HIR-

LAM NWP model, Meteorol. Appl. 22 (3) (2015) 485–494.

[10] C. Fischer, T. Montmerle, L. Berre, L. Auger, S.E. Ştefănescu, An overview of the variational assimilation in the ALADIN/France numerical weather-prediction system, Q. J. R. Meteorol.

Soc. 131 (613) (2005) 3477–3492.

[11] E. Pichelli, R. Ferretti, D. Cimini, G. Panegrossi, D. Perissin, N. Pierdicca, F. Rocca,

B. Rommen, InSAR water vapor data assimilation into mesoscale model MM5: technique

and pilot study, IEEE J. Select. Top. Appl. Earth Observ. Remote Sens. 8 (8) (2015) 3859–3875.

[12] N.S. Wagenbrenner, J.M. Forthofer, B.K. Lamb, K.S. Shannon, B.W. Butler, Downscaling sur-

face wind predictions from numerical weather prediction models in complex terrain with

WindNinja, Atmos. Chem. Phys. 16 (8) (2016) 5229–5241.

[13] Q. Hu, P. Su, D. Yu, J. Liu, Pattern-based wind speed prediction based on generalized principal

component analysis, IEEE Trans. Sust. Energy 5 (3) (2014) 866–874.

[14] E. Erdem, J. Shi, ARMA based approaches for forecasting the tuple of wind speed and direction,

Appl. Energy 88 (4) (2011) 1405–1414.

[15] H. Liu, E. Erdem, J. Shi, Comprehensive evaluation of ARMA-GARCH (-M) approaches for modeling the mean and volatility of wind speed, Appl. Energy 88 (3) (2011) 724–732.

[16] H. Silaghi, C. Costea, Wind speed prediction using Box-Jenkins method, J. Comput. Sci. Con-

trol Syst. (1) (2008) 208.

[17] M. Poncela, P. Poncela, J.R. Perán, Automatic tuning of Kalman filters by maximum likelihood

methods for wind energy forecasting, Appl. Energy 108 (2013) 349–362.

[18] A. Carpinone, R. Langella, A. Testa, M. Giorgio, Very short-term probabilistic wind power fore-

casting based on Markov chain models, in: IEEE 11th International Conference on Probabi-

listic Methods Applied to Power Systems (PMAPS), 2010, pp. 107–112.

[19] Z. Song, Y. Jiang, Z. Zhang, Short-term wind speed forecasting with Markov-switching model,

Appl. Energy 130 (2014) 103–112.

[20] M.A. Ghorbani, R. Khatibi, M.H. FazeliFard, L. Naghipour, O. Makarynskyy, Short-term wind

speed predictions with machine learning techniques, Meteorol. Atmos. Phys. 128 (1) (2016)

57–72.

[21] H. Chitsaz, N. Amjady, H. Zareipour, Wind power forecast using wavelet neural network

trained by improved Clonal selection algorithm, Energy Convers. Manag. 89 (2015) 588–598.

372 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

[22] G. Li, J. Shi, On comparing three artificial neural networks for wind speed forecasting, Appl.

Energy 87 (7) (2010) 2313–2320.

[23] J.M. Freedman, J. Manobianco, J. Schroeder, B. Ancell, K. Brewster, S. Basu, V. Banunarayanan,

B.-M. Hodge, I. Flores, The Wind Forecast Improvement Project (WFIP): a public/private part-

nership for improving short term wind energy forecasts and quantifying the benefits of utility operations. The Southern Study Area, Final Report, Tech. Rep., AWS Truepower, LLC, Albany,

NY, 2014.

[24] J. Zhang, M. Cui, B.-M. Hodge, A. Florita, J. Freedman, Ramp forecasting performance from

improved short-term wind power forecasting over multiple spatial and temporal scales,

Energy, 122 (2017) 528–541.

[25] C. Feng, M. Cui, B.-M. Hodge, J. Zhang, A data-driven multi-model methodology with deep

feature selection for short-term wind forecasting, Appl. Energy 190 (2017) 1245–1257.

[26] National Renewable Energy Laboratory, Wind Integration National Dataset (WIND) Toolkit, Available from: https://www.nrel.gov/grid/wind-toolkit.html (accessed 10.10.17).

[27] C. Draxl, B. Hodge, A. Clifton, J. McCaa, Overview and meteorological validation of the Wind Integration National Dataset (WIND) toolkit, National Renewable Energy Laboratory, Tech.

Rep., Golden, CO. NREL/TP-5000-61740, 2015.

[28] R. Margolis, C. Coggeshall, J. Zuboy, SunShot Vision Study, vol. 2, US Dept. of Energy, 2012. Available from: https://energy.gov/sites/prod/files/2014/01/f7/47927.pdf (accessed 10.10.17).

[29] J. Zhang, A. Florita, B.-M. Hodge, S. Lu, H.F. Hamann, V. Banunarayanan, A.

M. Brockway, A suite of metrics for assessing the performance of solar power forecasting, Sol. Energy 111 (2015) 157–175.

[30] A. Hammer, D. Heinemann, E. Lorenz, B. L€uckehe, Short-term forecasting of solar radiation: a statistical approach using satellite data, Sol. Energy 67 (1) (1999) 139–150.

[31] A. Sfetsos, A.H. Coonick, Univariate and multivariate forecasting of hourly solar radiation

with artificial intelligence techniques, Sol. Energy 68 (2) (2000) 169–178.

[32] C. Paoli, C. Voyant, M. Muselli, M.-L. Nivet, Forecasting of preprocessed daily solar radiation

time series using neural networks, Sol. Energy 84 (12) (2010) 2146–2160.

[33] R. Marquez, C.F.M. Coimbra, Forecasting of global and direct solar irradiance using stochastic

learning methods, ground experiments and the NWS database, Sol. Energy 85 (5) (2011)

746–756.

[34] P. Mathiesen, J. Kleissl, Evaluation of numerical weather prediction for intra-day solar forecast-

ing in the continental United States, Sol. Energy 85 (5) (2011) 967–977.

[35] R. Perez, K. Moore, S. Wilcox, D. Renn�e, A. Zelenka, Forecasting solar radiation—preliminary

evaluation of an approach based upon the national forecast database, Sol. Energy 81 (6)

(2007) 809–812.

[36] C.W. Chow, B. Urquhart, M. Lave, A. Dominguez, J. Kleissl, J. Shields, B. Washom, Intra-hour

forecasting with a total sky imager at the UC San Diego solar energy testbed, Sol. Energy

85 (11) (2011) 2881–2893.

[37] E. Lorenz, D. Heinemann, H. Wickramarathne, H.G. Beyer, S. Bofinger, Forecast of ensemble

power production by grid-connected PV systems, in: 20th European PV Conference, Milano,

2007, pp. 3–9.

[38] S. Pelland, J. Remund, J. Kleissl, T. Oozeki, K. De Brabandere, Photovoltaic and solar forecast-

ing: state of the art, 2013, IEA PVPS, Task 14, Available from: http://www.iea-pvps.org/

fileadmin/dam/public/report/technical/Photovoltaic_and_Solar_Forecasting_State_of_the_ Art_REPORT_PVPS__T14_01_2013.pdf (accessed 10.10.17).

[39] Y. Chu, H.T.C. Pedro, L. Nonnenmacher, R.H. Inman, Z. Liao, C.F.M. Coimbra, A smart image-based cloud detection system for intrahour solar irradiance forecasts, J. Atmos. Ocean.

Technol. 31 (9) (2014) 1995–2007.

373References

[40] S. Lu, Y. Hwang, I. Khabibrakhmanov, F.J. Marianno, X. Shao, J. Zhang, B.-M. Hodge, H.

F. Hamann, Machine learning based multi-physical-model blending for enhancing renewable energy forecast-improvement via situation dependent error correction, in: IEEE European

Control Conference (ECC), 2015, pp. 283–290.

[41] IBM, Watt-Sun: a multi-scale, multi-model, machine-learning solar forecasting technology, Available from: https://energy.gov/eere/sunshot/watt-sun-multi-scale-multi-model-

machine-learning-solar-forecasting-technology (accessed 10.10.17).

[42] C. Feng, M. Cui, M. Lee, J. Zhang, B.M. Hodge, S. Lu, H.F. Hamann, Short-term global hori-

zontal irradiance forecasting based on sky imaging and pattern recognition, in: IEEE Power &

Energy Society General Meeting, Chicago, IL, 2017.

[43] J. Zhang, B.-M. Hodge, S. Lu, H.F. Hamann, B. Lehman, J. Simmons, E. Campos,

V. Banunarayanan, J. Black, J. Tedesco, Baseline and target values for regional and point PV

power forecasts: toward improved solar forecasting, Sol. Energy 122 (2015) 804–819.

[44] G. Gross, F.D. Galiana, Short-term load forecasting, Proc. IEEE 75 (12) (1987) 1558–1573.

[45] K. Liu, S. Subbarayan, R.R. Shoults, M.T. Manry, C. Kwan, F.I. Lewis, J. Naccarino, Comparison of very short-term load forecasting techniques, IEEE Trans. Power Syst. 11 (2) (1996)

877–882.

[46] W. Charytoniuk, M.S. Chen, Very short-term load forecasting using artificial neural networks, IEEE Trans. Power Syst. 15 (1) (2000) 263–268.

[47] E.A. Feinberg, D. Genethliou, Load forecasting, in: J.H. Chow, F.F. Wu, J. Momoh (Eds.),

Applied Mathematics for Restructured Electric Power Systems: Optimization, Control, and Computational Intelligence, chap. 12, Springer US, Boston, MA, ISBN 978-0-387-23471-7,

2005, pp. 269–285, https://doi.org/10.1007/0-387-23471-3_12.

[48] C.W. Gellings, Demand Forecasting for Electric Utilities, Fairmont Press, Inc., Lilburn, GA,

1992.

[49] M.T. Hagan, S.M. Behr, The time series approach to short term load forecasting, IEEE Trans. Power Syst. 2 (3) (1987) 785–791.

[50] N. Amjady, Short-term hourly load forecasting using time-series modeling with peak load esti-

mation capability, IEEE Trans. Power Syst. 16 (4) (2001) 798–805.

[51] A.D. Papalexopoulos, T.C. Hesterberg, A regression-based approach to short-term system load

forecasting, IEEE Trans. Power Syst. 5 (4) (1990) 1535–1547.

[52] T. Haida, S. Muto, Regression based peak load forecasting using a transformation technique,

IEEE Trans. Power Syst. 9 (4) (1994) 1788–1794.

[53] K.Y. Lee, Y.T. Cha, J.H. Park, Short-term load forecasting using an artificial neural network,

IEEE Trans. Power Syst. 7 (1) (1992) 124–132.

[54] A.G. Bakirtzis, J.B. Theocharis, S.J. Kiartzis, K.J. Satsios, Short term load forecasting using fuzzy neural networks, IEEE Trans. Power Syst. 10 (3) (1995) 1518–1524.

[55] B.-J. Chen, M.-W. Chang, et al., Load forecasting using support vector machines: a study on EUNITE competition 2001, IEEE Trans. Power Syst. 19 (4) (2004) 1821–1830.

[56] E. Kyriakides, M. Polycarpou, Short term electric load forecasting: a tutorial. in: K. Chen,

L. Wang (Eds.), Trends in Neural Computation, chap. 16, Springer, Berlin, ISBN 978-3- 540-36122-0, 2007, pp. 391–418, https://doi.org/10.1007/978-3-540-36122-0_16.

[57] H. Hahn, S. Meyer-Nieberg, S. Pickl, Electric load forecasting methods: tools for decision mak-

ing, Eur. J. Oper. Res. 199 (3) (2009) 902–907.

[58] S.-J. Huang, K.-R. Shih, Short-term load forecasting via ARMA model identification including

non-Gaussian process considerations, IEEE Trans. Power Syst. 18 (2) (2003) 673–679.

[59] H.-T. Yang, C.-M. Huang, C.-L. Huang, Identification of ARMAX model for short term load

forecasting: an evolutionary programming approach, IEEE Trans. Power Syst. 11 (1) (1996)

403–408.

374 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

[60] C.-M. Huang, C.-J. Huang, M.-L. Wang, A particle swarm optimization to identifying the

ARMAX model for short-term load forecasting, IEEE Trans. Power Syst. 20 (2) (2005) 1126–1133.

[61] W. Charytoniuk, M.S. Chen, P. Van Olinda, Nonparametric regression based short-term load

forecasting, IEEE Trans. Power Syst. 13 (3) (1998) 725–730.

[62] L. Jin, Y.J. Lai, T.X. Long, Peak load forecasting based on robust regression model,

in: International Conference on Probabilistic Methods Applied to Power Systems, IEEE, 2004, pp. 123–128.

[63] T. Zheng, A.A. Girgis, E.B. Makram, A hybrid wavelet-Kalman filter method for load forecast-

ing, Electr. Power Syst. Res. 54 (1) (2000) 11–17.

[64] H.M. Al-Hamadi, S.A. Soliman, Short-term electric load forecasting based on Kalman filtering

algorithm with moving window weather and load model, Electr. Power Syst. Res. 68 (1)

(2004) 47–59.

[65] D.C. Park, M.A. El-Sharkawi, R.J. Marks, L.E. Atlas, M.J. Damborg, Electric load forecasting

using an artificial neural network, IEEE Trans. Power Syst. 6 (2) (1991) 442–449.

[66] H.S. Hippert, C.E. Pedreira, R.C. Souza, Neural networks for short-term load forecasting: a

review and evaluation, IEEE Trans. Power Syst. 16 (1) (2001) 44–55.

[67] E.E. Elattar, J. Goulermas, Q.H. Wu, Electric load forecasting based on locally weighted

support vector regression, IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 40 (4) (2010)

438–447.

[68] S. Tzafestas, E. Tzafestas, Computational intelligence techniques for short-term electric load

forecasting, J. Intell. Robot. Syst. 31 (1–3) (2001) 7–68.

[69] M. Hanmandlu, B.K. Chauhan, Load forecasting using hybrid models, IEEE Trans. Power Syst.

26 (1) (2011) 20–29.

[70] R.-A. Hooshmand, H. Amooshahi, M. Parastegari, A hybrid intelligent algorithm based short- term load forecasting approach, Int. J. Electr. Power Energy Syst. 45 (1) (2013) 313–324.

[71] A. Kavousi-Fard, H. Samet, F. Marzbani, A new hybrid modified firefly algorithm and support

vector regression model for accurate short term load forecasting, Expert Syst. Appl. 41 (13) (2014) 6047–6056.

[72] R.B. D’agostino, A. Belanger, R.B. D’Agostino Jr., A suggestion for using powerful and infor- mative tests of normality, Am. Stat. 44 (1990) 316–321.

[73] C.M. Jarque, A.K. Bera, A test for normality of observations and regression residuals, Int. Stat.

Rev. 55 (1987) 163–172.

[74] K. Coughlin, M.A. Piette, C.A. Goldman, S. Kiliccote, Statistical analysis of baseline load

models for non-residential buildings, Energy Build. 41 (2009) 374–381.

[75] FERC, Reports on Demand Response & Advanced Metering, Available from: http://www.

ferc.gov/industries/electric/indus-act/demand-response/dem-res-adv-metering.asp (accessed

10.10.17).

[76] US Department of Energy, Benefits of demand response in electricity markets and recommen-

dations for achieving them Tech. Rep. 2006.

[77] V.M. Balijepalli, V. Pradhan, S.A. Khaparde, R.M. Shereef, Review of demand response under

smart grid paradigm, in: IEEE PES Innovative Smart Grid Technologies, India, 2011,

pp. 236–243.

[78] H.P. Chao, Demand response in wholesale electricity markets: the choice of customer base-

line, J. Regul. Econ. 39 (1) (2011) 68–88.

[79] R. Yin, P. Xu, M.A. Piette, S. Kiliccote, Study on Auto-DR and pre-cooling of commercial build-

ings with thermal mass in California, Energy Build. 42 (7) (2010) 967–975.

375References

[80] A. Buege, M. Rufo, M. Ozog, D. Violette, S. McNicoll, Prepare for impact: measuring large C/I

customer response to DR programs, in: ACEEE Summer Study on Energy Efficiency in Build- ings, 2006.

[81] J. MacDonald, P. Cappers, D. Callaway, S. Kiliccote, Demand Response Providing Ancillary

Services: A Comparison of Opportunities and Challenges in the US Wholesale Markets, Grid-Interop, 2012.

[82] H. Zhong, L. Xie, Q. Xia, Coupon incentive-based demand response: theory and case study, IEEE Trans. Power Syst. 28 (2) (2013) 1266–1276.

[83] N. Addy, S. Kiliccote, J. Mathieu, D.S. Callaway, Understanding the effect of baseline modeling

implementation choices on analysis of demand response performance, in: ASME Interna- tional Mechanical Engineering Congress and Exposition, 2012.

[84] K. Coughlin, M.A. Piette, C.A. Goldman, S. Kiliccote, Estimating demand response load

impacts: evaluation of baseline load models for non-residential buildings in California, Law- rence Berkeley National Laboratory, 2008.

[85] K. Tweed, Demand Response Payments Increase Significantly in PJM, 2013, Available from: http://www.greentechmedia.com/articles/read/demand-response-payments-up-significantly-

in-pjm (accessed 10.10.17).

[86] Federal Energy Regulatory Commission, State of the Markets Report, 2016, Available from: https://www.ferc.gov/market-oversight/reports-analyses/st-mkt-ovr/2015-som.pdf (accessed

10.10.17).

[87] R. Walton, EIA: FERC Order 745 to spark swift growth in demand response markets, 2016Available from: http://www.utilitydive.com/news/eia-ferc-order-745-to-spark-swift-

growth-in-demand-response-markets/414997/ (accessed 10.10.17).

[88] Y. Wi, J. Kim, S. Joo, J. Park, J. Oh, Customer baseline load (CBL) calculation using exponential

smoothing model with weather adjustment, in: Transmission and Distribution Conference

and Exposition: Asia and Pacific, 2009, pp. 1–4.

[89] J.L. Mathieu, D.S. Callaway, S. Kiliccote, Examining uncertainty in demand response baseline

models and variability in automated response to dynamic pricing, in: IEEE Conference on

Decision and Control and European Control, 2011.

[90] G.R. Newsham, B.J. Birt, I.H. Rowlands, A comparison of four methods to evaluate the effect of

a utility residential air-conditioner load control program on peak electricity use, Energy Policy

39 (2011) 6376–6389.

[91] J.L. Bode, M.J. Sullivan, D. Berghman, J.H. Eto, Incorporating residential AC load control into

ancillary service markets: measurement and settlement, Energy Policy 56 (2013) 175–185.

[92] L. Hatton, P. Charpentier, E. Matzner-Lober, Statistical estimation of the residential baseline,

IEEE Trans. Power Syst. 31 (2016) 1752–1759.

[93] D.S. Sayogo, A.P. Theresa, Understanding smart data disclosure policy success: the case of Green Button, in: ACM Proceedings of the 14th Annual International Conference on Digital

Government Research, 2013.

[94] A. Abur, A.G. Exposito, Power System State Estimation: Theory and Implementation, CRC

Press, Boca Raton, FL, 2004.

[95] K.D. Jones, J.S. Thorp, R.M. Gardner, Three-phase linear state estimation using phasor mea- surements, in: IEEE Power & Energy Society General Meeting, Vancouver, BC, 2013.

[96] E. Farantatos, G.K. Stefopoulos, G.J. Cokkinides, A.P. Meliopoulos, PMU-based dynamic state

estimation for electric power systems, in: IEEE Power & Energy Society General Meeting, Cal- gary, AB, 2009.

[97] A. Abur, A. Rouhani, Linear phasor estimator assisted dynamic state estimation, IEEE Trans. Smart Grid, 2016.

376 CHAPTER 16: Predictive Analytics for Comprehensive Energy Systems State Estimation

[98] A.M.L. Da Silva, M.B. Do Coutto Filho, J.F. De Queiroz, State forecasting in electric power sys-

tems., in: IEE Proceedings C (Generation, Transmission and Distribution), vol. 130, 1983, pp. 237–244.

[99] G. Valverde, V. Terzija, Unscented Kalman filter for power system dynamic state estimation,

IET Gener. Transm. Distrib. 5 (1) (2011) 29–37.

[100] A.P.A. da Silva, A.M.L. da Silva, J.C.S. de Souza, M.B. Do Coutto Filho, State forecasting based

on artificial neural networks., in: Proc. 11th PSCC, 1993, pp. 461–467.

[101] J.C.S. Souza, A.M.L. Da Silva, A.P.A. Da Silva, Data visualisation and identification of anom-

alies in power system state estimation using artificial neural networks, IEE Proc. Gener.

Transm. Distrib. 144 (5) (1997) 445–455.

[102] J.C.S. Souza, A.M.L. Da Silva, A.P.A. de Silva, Online topology determination and bad data

suppression in power system operation using artificial neural networks, IEEE Trans. Power

Syst. 13 (3) (1998) 796–803.

[103] M.B. Do Coutto Filho, J.C.S. de Souza, Forecasting-aided state estimation—Part I: panorama,

IEEE Trans. Power Syst. 24 (4) (2009) 1667–1677.

[104] E. Sortomme, M.M. Hindi, S.D.J. MacPherson, S.S. Venkata, Coordinated charging of plug-in

hybrid electric vehicles to minimize distribution system losses, IEEE Trans. Smart Grid 2 (1)

(2011) 198–205.

[105] G.-B. Huang, Q.-Y. Zhu, C.-K. Siew, Extreme learning machine: theory and applications,

Neurocomputing 70 (1) (2006) 489–501.

[106] J.M. Carrasco, L.G. Franquelo, J.T. Bialasiewicz, E. Galván, R.C.P. Guisado, M.A.M. Prats, J.

I. León, N. Moreno-Alfonso, Power-electronic systems for the grid integration of renewable

energy sources: a survey, IEEE Trans. Ind. Electron. 53 (4) (2006) 1002–1016.

[107] H. Jiang, Y. Zhang, J.J. Zhang, D.W. Gao, E. Muljadi, Synchrophasor-based auxiliary control-

ler to enhance the voltage stability of a distribution system with high renewable energy pen-

etration, IEEE Trans. Smart Grid 6 (2015) 2107–2115.

[108] D.M. Vinod Kumar, S.C. Srivastava, Power system state forecasting using artificial neural net-

works, Electr. Mach. Power Syst. 27 (6) (1999) 653–664.

[109] G. Zhang, B.E. Patuwo, M.Y. Hu, Forecasting with artificial neural networks: the state of the

art, Int. J. Forecast. 14 (1) (1998) 35–62.

[110] P.-F. Pai, W.-C. Hong, Forecasting regional electricity load based on recurrent support vector

machines with genetic algorithms, Electr. Pow. Syst. Res. 74 (3) (2005) 417–425.

[111] W.-C. Hong, Chaotic particle swarm optimization algorithm in a support vector regression electric load forecasting model, Energy Convers. Manag. 50 (1) (2009) 105–117.

[112] W.R. Cassel, Distribution management systems: functions and payback, IEEE Trans. Power

Syst. 8 (3) (1993) 796–801.

[113] M.E. Baran, A.W. Kelley, State estimation for real-time monitoring of distribution systems,

IEEE Trans. Power Syst. 9 (3) (1994) 1601–1609.

[114] Y.-F. Huang, S. Werner, J. Huang, N. Kashyap, V. Gupta, State estimation in electric power

grids: meeting new challenges presented by the requirements of the future grid, IEEE Signal

Process. Mag. 29 (5) (2012) 33–43.

[115] D. Della Giustina, M. Pau, P.A. Pegoraro, F. Ponci, S. Sulis, Electrical distribution system state

estimation: measurement issues and challenges, IEEE Instrum. Meas. Mag. 17 (6) (2014)

36–42.

[116] A. Primadianto, C.-N. Lu, A review on distribution system state estimation, IEEE Trans. Power

Syst. 32 (5) (2017) 3875–3883.

Book Chapters for Ideas/Chapter-17---Data-Analytics-for-Energy-Disaggreg_2018_Big-Data-Application-i.pdf