IEEE Senior Member Siddhartha Kumar Khaitan
email: skhaitan@iastate.edu

A Survey Of Techniques for using Neural Networks in Power Systems

Neural network (NN) is a machine learning approach modeled after biological nervous system, which estimates computation results that depend on a large number of inputs. In recent years, NN has been used for a wide range of management and optimization purposes in power system. This paper presents a survey of techniques for using NN in power systems. We highlight key attributes of these works to reveal their commonalities and differences. This survey is expected to help researchers in gaining insights into potential of NN in transforming next-generation power systems.

I. INTRODUCTION

An artificial neural network is computational method which is founded on human neural networks. Multiple nodes (neurons) connected together form a single or multiple layer(s). The line connecting the nodes shows their weight relationships and by adjusting them, an NN can model a desired function. By virtue of allowing non-linear modeling, NN serves as a powerful tool for modeling and controlling complex systems that depend on a large number of inputs. NN can handle stochastic variations in the scheduled operating points and can provide faster and more accurate modeling than several other methods. Also, it contains built-in capability for learning and data-filtration. When intelligently combined with other artificial intellignce techniques, NN can model a broad range of problems.

Due to its features, NN has been used for several power system optimization tasks in last two decades. In this paper, we present a survey of techniques of using NN in power systems. Since the applications of NN in power system are far too many to cover in a research paper of this length, we especially focus on use of NN in load-forecasting, fault detection and diagnosis, stability analysis, finding power quality disturbance, load-flow study, etc 1 .

II. A BRIEF BACKGROUND ON NN

We present a brief review of NN and refer the reader to prior work for more details [START_REF] Haykin | Neural Networks: A comprehensive foundation[END_REF]. NN works by learning the functional relationship between input and output based on training with past input-output pattern. An NN consists of an input layer, hidden layers and an output layer of neurons. The weight relationships between two neurons are represented using a line between them. The number of hidden layers and weights are chosen to minimize the estimation error. In BP NN, the output may be compared to a reference and the error value may be used to adjust the weights.

Optimization of NN involves a careful choice of its architecture and parameters to achieve high accuracy and low processing time. For example, in BPNN, using large number of iterations during training can provide higher accuracy, but it also increases training time. For this reason, different NN variants have been proposed, e.g., RBF establishes input to output map using local approximators which require few weights and hence, this network can be quickly trained with only few samples. [START_REF] Quan | Short-term load and wind power forecasting using neural network-based prediction intervals[END_REF][START_REF] Amjady | Short-term wind power forecasting using ridgelet neural network[END_REF][START_REF] Bhaskar | AWNN-assisted wind power forecasting using feed-forward neural network[END_REF][START_REF] Li | Bayesian adaptive combination of short-term wind speed forecasts from neural network models[END_REF][START_REF] Barbounis | Long-term wind speed and power forecasting using local recurrent neural network models[END_REF]] PV (photovoltaic) electricity generation forecasting [START_REF] Kardakos | Application of time series and artificial neural network models in short-term forecasting of PV power generation[END_REF][START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF] Locating and diagnosing faults [START_REF] Ekici | Energy and entropy-based feature extraction for locating fault on transmission lines by using neural network and wavelet packet decomposition[END_REF]25,[START_REF] Wu | An automotive generator fault diagnosis system using discrete wavelet transform and artificial neural network[END_REF][START_REF] Vasilic | Fuzzy ART neural network algorithm for classifying the power system faults[END_REF][START_REF] Cardoso | Application of neuralnetwork modules to electric power system fault section estimation[END_REF][START_REF] Bhowmik | A novel wavelet transform aided neural network based transmission line fault analysis method[END_REF][START_REF] Seyedtabaii | Improvement in the performance of neural networkbased power transmission line fault classifiers[END_REF][START_REF] Gupta | Neural network based early warning system for an emerging blackout in smart grid power networks[END_REF][START_REF] Meng | A self-adaptive RBF neural network classifier for transformer fault analysis[END_REF]] Monitoring (transient) voltage stability [START_REF] Bahmanyar | Power system voltage stability monitoring using artificial neural networks with a reduced set of inputs[END_REF][START_REF] Zhou | Online monitoring of voltage stability margin using an artificial neural network[END_REF][START_REF] Tiwari | Neural network predictive control of upfc for improving transient stability performance of power system[END_REF][START_REF] Mishra | Neural-network-based adaptive UPFC for improving transient stability performance of power system[END_REF][START_REF] Lin | Intelligent neural network-based fast power system harmonic detection[END_REF][START_REF] Zhengyou | Study of a new method for power system transients classification based on wavelet entropy and neural network[END_REF] power system stabilization [START_REF] Mehraeen | Power system stabi-lization using adaptive neural network-based dynamic surface control[END_REF][START_REF] Segal | A self-tuning power system stabilizer based on artificial neural network[END_REF] Load flow studies [START_REF] Gupta | Neural network based early warning system for an emerging blackout in smart grid power networks[END_REF][START_REF] Karami | Radial basis function neural network for power system load-flow[END_REF] Power quality disturbance [START_REF] Uyar | An expert system based on s-transform and neural network for automatic classification of power quality disturbances[END_REF][START_REF] Bhende | Detection and classification of power quality disturbances using S-transform and modular neural network[END_REF] State estimation [START_REF] Manitsas | Distribution system state estimation using an artificial neural network approach for pseudo measurement modeling[END_REF][START_REF] Pandey | Application of radial basis neural network for state estimation of power system networks[END_REF] We now summarize the key ideas of research works.

III. CLASSIFICATION AND OVERVIEW

1. Researchers have used several variants of NNs and their training methods, e.g. MLP NN [START_REF] Siwek | Ensemble neural network approach for accurate load forecasting in a power system[END_REF][START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF][START_REF] Azadeh | Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors[END_REF][START_REF] Demiroren | Middle anatolian region short-term load forecasting using artificial neural networks[END_REF][START_REF] Kandananond | Forecasting electricity demand in Thailand with an artificial neural network approach[END_REF][START_REF] Uyar | An expert system based on s-transform and neural network for automatic classification of power quality disturbances[END_REF], radial basis function NN [START_REF] Singh | A self-selecting neural network for short-term load forecasting[END_REF][START_REF] Kandananond | Forecasting electricity demand in Thailand with an artificial neural network approach[END_REF][START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF][START_REF] Meng | A self-adaptive RBF neural network classifier for transformer fault analysis[END_REF][START_REF] Mishra | Neural-network-based adaptive UPFC for improving transient stability performance of power system[END_REF][START_REF] Karami | Radial basis function neural network for power system load-flow[END_REF][START_REF] Pandey | Application of radial basis neural network for state estimation of power system networks[END_REF], probabilistic NN (PNN) [START_REF] Tripathy | Power transformer differential protection based on optimal probabilistic neural network[END_REF], adaptive wavelet neural network [START_REF] Bhaskar | AWNN-assisted wind power forecasting using feed-forward neural network[END_REF], BP NN [START_REF] Bakirtzis | A neural network short term load forecasting model for the greek power system[END_REF][START_REF] Xiao | BP neural network with rough set for short term load forecasting[END_REF][START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF][START_REF] Azadeh | Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors[END_REF][START_REF] Lee | Short-term load forecasting using an artificial neural network[END_REF][START_REF] Wu | An automotive generator fault diagnosis system using discrete wavelet transform and artificial neural network[END_REF][START_REF] Tripathy | Power transformer differential protection based on optimal probabilistic neural network[END_REF], generalized regression NN [START_REF] Li | A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm[END_REF][START_REF] Wu | An automotive generator fault diagnosis system using discrete wavelet transform and artificial neural network[END_REF], fuzzy wavelet NN [25], etc.

2. Some researchers intelligently combine multiple NNs to bring their best together [START_REF] Siwek | Ensemble neural network approach for accurate load forecasting in a power system[END_REF][START_REF] Li | Bayesian adaptive combination of short-term wind speed forecasts from neural network models[END_REF][START_REF] Guo | Improving market clearing price prediction by using a committee machine of neural networks[END_REF].

3. Several works also use co-management approaches, such as wavelet packet decomposition [START_REF] Ekici | Energy and entropy-based feature extraction for locating fault on transmission lines by using neural network and wavelet packet decomposition[END_REF], GramSchmidt orthogonalization [START_REF] Bahmanyar | Power system voltage stability monitoring using artificial neural networks with a reduced set of inputs[END_REF], wavelet entropy [START_REF] Zhengyou | Study of a new method for power system transients classification based on wavelet entropy and neural network[END_REF], Meyer wavelet [START_REF] Amjady | Short-term wind power forecasting using ridgelet neural network[END_REF], least square weighted fusion algorithm [25], S-transform [START_REF] Uyar | An expert system based on s-transform and neural network for automatic classification of power quality disturbances[END_REF][START_REF] Bhende | Detection and classification of power quality disturbances using S-transform and modular neural network[END_REF], DWT [START_REF] Wu | An automotive generator fault diagnosis system using discrete wavelet transform and artificial neural network[END_REF][START_REF] Bhowmik | A novel wavelet transform aided neural network based transmission line fault analysis method[END_REF][START_REF] Gaing | Wavelet-based neural network for power disturbance recognition and classification[END_REF], particle swarm optimization [START_REF] Quan | Short-term load and wind power forecasting using neural network-based prediction intervals[END_REF][START_REF] Meng | A self-adaptive RBF neural network classifier for transformer fault analysis[END_REF][START_REF] Tripathy | Power transformer differential protection based on optimal probabilistic neural network[END_REF], Gauss-Newton method [START_REF] Tiwari | Neural network predictive control of upfc for improving transient stability performance of power system[END_REF], Lyapunov stability analysis [START_REF] Mehraeen | Power system stabi-lization using adaptive neural network-based dynamic surface control[END_REF], principle component analysis [START_REF] Siwek | Ensemble neural network approach for accurate load forecasting in a power system[END_REF][START_REF] Adepoju | Application of neural network to load forecasting in Nigerian electrical power system[END_REF], fuzzy c-means [START_REF] Meng | A self-adaptive RBF neural network classifier for transformer fault analysis[END_REF], fruit fly optimization [START_REF] Li | A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm[END_REF] self-organized map [START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF], rough set [START_REF] Xiao | BP neural network with rough set for short term load forecasting[END_REF]25], etc.

4. Several researchers use real data from power systems in different countries, e.g., Australia [START_REF] Quan | Short-term load and wind power forecasting using neural network-based prediction intervals[END_REF], Brazil [START_REF] Carpinteiro | A hierarchical neural model in short-term load forecasting[END_REF], Canada [START_REF] Zhang | Artificial neural network for load forecasting in smart grid[END_REF], China [START_REF] Xiao | BP neural network with rough set for short term load forecasting[END_REF], Egypt [START_REF] Osman | Neural network based approach for short-term load forecasting[END_REF], Greece [START_REF] Bakirtzis | A neural network short term load forecasting model for the greek power system[END_REF], India [START_REF] Bhowmik | A novel wavelet transform aided neural network based transmission line fault analysis method[END_REF], Iran [START_REF] Azadeh | Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors[END_REF], Malaysia [START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF], Nigeria [START_REF] Adepoju | Application of neural network to load forecasting in Nigerian electrical power system[END_REF], Poland [START_REF] Siwek | Ensemble neural network approach for accurate load forecasting in a power system[END_REF], Singapore [START_REF] Quan | Short-term load and wind power forecasting using neural network-based prediction intervals[END_REF], Spain [START_REF] Amjady | Short-term wind power forecasting using ridgelet neural network[END_REF], South Korea [START_REF] Lee | Short-term load forecasting using an artificial neural network[END_REF], Thailand [START_REF] Kandananond | Forecasting electricity demand in Thailand with an artificial neural network approach[END_REF], Turkey [START_REF] Demiroren | Middle anatolian region short-term load forecasting using artificial neural networks[END_REF], UK [START_REF] Manitsas | Distribution system state estimation using an artificial neural network approach for pseudo measurement modeling[END_REF] and US (most others). Clearly, NN has been used for powersystem studies across the globe.

IV. NN FOR LOAD FORECASTING

By virtue of its ability to estimate functions depending on multiple possibly unknown inputs, NN has been successfully used for load forecasting in power system. Table II summarizes the lookahead period used in different studies on load forecasting. Also note that some researchers account for impact of factors such weekend/weekday [START_REF] Adepoju | Application of neural network to load forecasting in Nigerian electrical power system[END_REF][START_REF] Bakirtzis | A neural network short term load forecasting model for the greek power system[END_REF][START_REF] Osman | Neural network based approach for short-term load forecasting[END_REF][START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF][START_REF] Lee | Short-term load forecasting using an artificial neural network[END_REF], weather or season [START_REF] Osman | Neural network based approach for short-term load forecasting[END_REF][START_REF] Park | Electric load forecasting using an artificial neural network[END_REF][START_REF] Chen | Online 24-h solar power forecasting based on weather type classification using artificial neural network[END_REF] and university semester [START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF] on electricity consumption. Bakirtzis et al. [START_REF] Bakirtzis | A neural network short term load forecasting model for the greek power system[END_REF] present an NN-based short-term load forecasting model which can predict daily load profile with a lead time of 1 to 7 days. Their model accounts for both holidays/normal-days and daily temperatures. They use BP algorithm for training NN. They observe that updating the NN-parameters daily provides higher accuracy than updating them monthly, which in turn is more accurate than training them yearly. Khamis et al. [START_REF] Khamis | Electricity forecasting for small scale power system using artificial neural network[END_REF] present an MLP NN for weekahead load forecasting. They use BP algorithm for training NN. They evaluate their approach using a power plant which supplies power to a university. They show that their approach achieves good accuracy.

Azadeh et al. [START_REF] Azadeh | Annual electricity consumption forecasting by neural network in high energy consuming industrial sectors[END_REF] present an NN-based model for forecasting electricity consumption in high-energy consuming industries, e.g., chemical industry. Due to large fluctuation in energy consumption in these industries, regression methods do not provide high accuracy, whereas their supervised MLP-based NN model is accurate. They experiment with different number of hidden nodes and different architectures and training parameters and find the optimum configuration. They confirm the accuracy of their model by using analysis of variance approach and Duncan's test.

Amjady et al. [START_REF] Amjady | Short-term wind power forecasting using ridgelet neural network[END_REF] propose a ridgelet NN based model which uses ridge functions as activation functions of its hidden nodes. The wind power depends on the speed and direction of the wind. They use Meyer wavelet to construct the ridge functions of the ridgelet NN. The NN is trained using differential evolution method with crossover and selection mechanisms.

Their model can accurately predict the day-ahead wind power from wind farms.

Osman et al. [START_REF] Osman | Neural network based approach for short-term load forecasting[END_REF] note that rapid changes in temperature can lead to high error in NN-based day-ahead load forecasting models. They analyze weather data to find the factors which correlate strongly with load changes. Based on this, they use the most correlated weather data to train and test their NNbased load forecasting model. The input parameters of NN are determined by correlation analysis of weather data. They use a 3-layer feed forward NN and experiment with different number of hidden neurons to find the optimum configuration. They also account for factors such as seasons, weekday/weekend, etc.

Bhaskar et al. [START_REF] Bhaskar | AWNN-assisted wind power forecasting using feed-forward neural network[END_REF] present an NN-based approach for wind power forecasting which does not use numerical weather prediction. Their approach works in two steps. In first step, wavelet decomposition of wind series is performed and adaptive wavelet NN is employed for regressing upon each decomposed signal and estimating wind speed up to 30 hours ahead. In second step, nonlinear mapping is established between (observed) wind speed and (forecasted) wind power by using an FFNN. FFNN is more suitable for second step than adaptive wavelet NN since wind power series is discontinuous as the output power from wind turbine becomes zero when wind speed falls below a low-threshold and above a high-threshold. They show that their method can accurately forecast wind power.

Xiao et al. [START_REF] Xiao | BP neural network with rough set for short term load forecasting[END_REF] present a 'rough-set BP NN' for shortterm load forecasting. Use of rough set allows effectively dealing with uncertain and partial data and complex data with multiple factors. They consider condition attributes such as temperature, humidity and sunlight and goal attributes such as maximum and minimum load. By analyzing the significance of each condition attribute, they reduce condition attributes containing bad data. Then, they filter data that are noisy and have only weak connection with output. During training, momentum method is used for reducing sensitivity of local parts of error curve. This restrains converging of their model to local minimum. Also, adaptive learning rate is used and this along with above-mentioned steps reduce NN training time. They show that their method provides higher forecasting accuracy than BP NN.

Adepoju et al. [START_REF] Adepoju | Application of neural network to load forecasting in Nigerian electrical power system[END_REF] present an NN for hour-ahead load forecasting. Their model considers five inputs, viz. load of previous hour, day and week, the hour of the day and the day of the week. They first filter noisy data and then apply PCA which helps in orthogonalizing the components of input data and eliminating components which have least contribution in data variation. Afterwards, data values are normalized so that they range between 0 and 1 and this avoids NN saturation.

Karami et al. [START_REF] Karami | Radial basis function neural network for power system load-flow[END_REF] use RBF NN with a fast hybrid training scheme to solve load-flow problem in power system. They note that since operating conditions are required for solving the nonlinear algebraic equations of load-flow, the output of load-flow can be seen as the function of operating condition (input). This allows using NN for solving this as a function approximation problem. For training data, they only consider those load-flow problems which are solvable and once trained, the NN model can produce outputs for both solvable and unsolvable problems. RBF NN model requires smaller time for converging than MLP NN model.

Kandananond et al. [START_REF] Kandananond | Forecasting electricity demand in Thailand with an artificial neural network approach[END_REF] use an NN model to predict annual electricity demand. They account for many factors which impact electricity consumption, e.g., population, export revenue, stock index and gross domestic product. They utilize two NN architectures, viz. MLP and RBF. They observe that when the number of hidden layers ranges between 5 and 10, MLP network provides lower error than RBF. The benefit of RBF is that it finds input to output map using local approximators, which requires fewer weights. They also compare NN model to multiple linear regression and autoregressive integrated moving average. NN model provides lower error than these methods, although these methods have the benefit of using simpler structure and requiring smaller computation time.

V. NN FOR FAULT DIAGNOSIS

NNs are highly useful for locating and diagnosing faults due to their prediction and classification capabilities. Dong et al. [25] present a fault diagnosis approach for power transformers, which uses rough set and fuzzy wavelet NN (FWNN) integrated with least square weighted fusion algorithm (LSWFA). They utilize knowledge reduction capability of rough set for simplifying the input of FWNN, e.g., rough set method reduces training samples and input dimension which simplifies network structure and reduces learning time. Rough set is also used to find rules whose 'support' and 'confidence' fulfill a given criteria. Fault diagnosis is performed using these rules. FWNN along with LSWFA is used for cases which cannot be analyzed by above mentioned rules. For this, seven trained FWNNs with varied correlative training parameters, number of hidden layers and learning rates are used to individually diagnose the fault. Finally, result of sevenchild FWNN are fused with LSWFA to find out the fault type and the fused result. Their technique has good diagnostic ability and can discover thermal faults, e.g. low, middle and high temperature overheating, high/low-energy discharge, etc.

Wu et al. [START_REF] Wu | An automotive generator fault diagnosis system using discrete wavelet transform and artificial neural network[END_REF] use DWT and NN for diagnosing and classifying faults in automotive generators. Their approach extracts features using DWT for reducing complexity of feature vectors. Both generalized regression NN and back-propagation NN are used for classifying and comparing five types of generator output signal, viz., single phase stator coil fault, voltage regulator disconnected, one diode fault, two diode fault and normal condition. For this, energy distributions for different faults are detected. BPNN is a wide learning rule for MLPs and it works in two steps: a feed forward phase where external input at input nodes is propagated forward for computing output signal at output unit and a backward phase where connection strengths are modified based on the difference between computed and observed signals at output unit. However, BPNN also has large learning time and needs many iterations to converge to a desired value. By comparison, GRNN has faster learning rate and does not require large amounts of weight computations. GRNN can approximate any arbitrary function between input and output vectors based on training data. Only probability density function is required for the functioning of GRNN. Thus, their technique uses both BPNN and GRNN to bring their best together. Their approach can effectively diagnose faults and works for automotive generators with varied engine operating conditions.

Zhengyou et al. [START_REF] Zhengyou | Study of a new method for power system transients classification based on wavelet entropy and neural network[END_REF] present an approach for classifying several power system transients, e.g., primary arc, short circuit fault, breaker switching, capacitor switching, lightning disturbance and lightning strike fault. Based on WT, they define wavelet energy entropy and wavelet entropy weight and study their distribution. Wavelet facilitates transient signal analysis and entropy provides a measure of uncertainty and hence, using these concepts together provides good characterization of the signal. Also, entropy weight shows the importance of every entropy in the signal and it helps in reducing the dimension of signal features used for classification. Use of wavelet energy entropy and wavelet entropy weight allow discovering important local features, but by themselves, they cannot classify all types of signals and hence, they use the features extracted by them as input of a BPNN which performs classification of transients. The weights in the neural network are adjusted to minimize the error. Their classification approach has high accuracy.

Ekici et al. [START_REF] Ekici | Energy and entropy-based feature extraction for locating fault on transmission lines by using neural network and wavelet packet decomposition[END_REF] present an approach for accurately and efficiently estimating location of a transmission line fault. They obtain faulty voltage and current signals using simulation and decompose them using wavelet packet transform (WPT). WPT is different from wavelet transform (WT) in that WPT splits not only approximations but details also. WPT can divide the entire time-frequency plane, whereas WT can analyze low-band frequency only. The features extracted are used to train and test NN for estimating fault location. Since with increasing data size, the overhead of analysis increases, they apply entropy and energy criteria to wavelet packet coefficients to reduce the size of feature vectors. They show that enforcing energy criterion on current signals after WPT is effective in reducing dataset size and it also allows accurate estimation of fault locations. Manitsas et al. [START_REF] Manitsas | Distribution system state estimation using an artificial neural network approach for pseudo measurement modeling[END_REF] present a technique for pseudo measurement modeling for distribution system state estimation (DSSE). Their technique uses load profiles and a few power flow measurements obtained from load flow simulations to train NN. Gaussian mixture model is used to model the error between NN output and target power injection. During DSSE execution, real measurements are employed as input to NN for generating pseudo measurements. Variance of pseudo measurements is generated using the error model. They employ NN-based pseudo measurement modeling for state estimation and show that it achieves high accuracy. Also, the accuracy increases with increasing number of inputs to NNs and number of voltage measurements.

VI. NN FOR STABILITY ANALYSIS

We now review works which use NN for studying and improving stability of power system [START_REF] Khaitan | A survey of high-performance computing approaches in power systems[END_REF].

Bahmanyar et al. [START_REF] Bahmanyar | Power system voltage stability monitoring using artificial neural networks with a reduced set of inputs[END_REF] present an NN model for online monitoring of voltage stability margin (VSM) of power system. VSM is computed as the estimated distance between current operation state to the maximum voltage stability limit. They use NN-based sensitivity method and GramSchmidt orthogonalization to find the least number of input variables required for approximating VSM with high accuracy and speed. They use a single NN model for estimating VSM for multiple system topologies which avoids the need of training a new NN for a change in system topology. For this, every single line failure is evaluated and ranked in decreasing order of VSM value. Then, a single MLP NN is used for estimating the VSM for base operating conditions and for a few worst-case conditions. Their approach can predict VSM for various system topologies and operating conditions.

Zhou et al. [START_REF] Zhou | Online monitoring of voltage stability margin using an artificial neural network[END_REF] present an NN-based approach for efficiently estimating the long-term voltage stability margin. They use an MLP network structure with one hidden layer having five neurons. To train the NN, they randomly generate many cases with different load/generation levels. These cases are verified using a power flow program to only select feasible cases. Further, a continuation power flow (CPF) program is employed for generating the P margin which works as a voltage stability index for each input data. Beginning with an initial operating point, CPF program traces curve along a given load direction till the voltage collapse point to compute the load P margin and this serves as the target output of NN. Finally, input features and output index are used in the NN training algorithm. Once trained, the NN can predict voltage stability margin for even previously unseen cases. They show that stability margin can be best estimated by phase angles and node voltage magnitudes. Also, their approach can estimate stability margin under both normal and N -1 contingency conditions and based on it, suitable control action can be taken.

Tiwari et al. [START_REF] Tiwari | Neural network predictive control of upfc for improving transient stability performance of power system[END_REF] present an NN predictive controller for unified power flow controller (UPFC) to achieve better transient stability. They use BP learning approach for training NN along with LevenbergMarquardt algorithm for accelerating the convergence. This NN is used during predictive control of UPFC. To predict future control inputs, damped Gauss-Newton method with 'backtracking' as the line search method for step selection is used. Compared to conventional schemes, NN can model non-linear plant with higher accuracy. For predicting the present value of the active output power, NN uses the quadrature component of the series injected voltage and the active output power at past two instants. They use a twolayer feedforward NN with 4 inputs, one hidden layer with 15 sigmoidal neurons and one output neuron. They evaluate their technique for several operating conditions and transients and show that their NN-based predictive controller achieves better damping performance compared to conventional PI (proportionalintegral) controller.

Tripathy et al. [START_REF] Tripathy | Power transformer differential protection based on optimal probabilistic neural network[END_REF] present a PNN for discriminating between the internal fault of a power transformer and the magnetizing inrush. To determine operating condition of the transformer, they use the ratio of voltage-to-frequency and amplitude of differential current. They compare the performance of their heteroscedastic-type PNN with that of conventional homoscedastic-type PNN, feedforward back propagation (FFBP) NN and harmonic restraint method. Since the variance of homoscedastic PNN cannot be ascertained analytically, it needs a training and a validation phase before the testing phase. Heteroscedastic PNN does not require a validation data set, however, it requires determination of optimal smoothing parameter which generally depends on the dataset. To obtain this optimal smoothing factor, they use particle swarm optimization which is a heuristic approach. They show that heteroscedastic PNN achieves higher accuracy than homoscedastic PNN and harmonic restraint method. Compared to FFBP NN, their heteroscedastic PNN requires much less training time and has better generalization properties. Further, their method does not require selecting threshold value and is unaffected from the different harmonics contained in operating signals. Also, selection of suitable smoothing factor improves the performance and classification accuracy of PNN.

Bhende et al. [START_REF] Bhende | Detection and classification of power quality disturbances using S-transform and modular neural network[END_REF] present an approach for detecting power quality (PQ) disturbance. They use S-transform, which due to its very good time/frequency resolution characteristics, can correctly analyze PQ disturbance under noisy conditions and provides better performance than wavelet transform. The features extracted by S-transform are applied to a modular NN for classifying PQ disturbances. Modular NN solves a bigger problem by dividing it into smaller tasks and thus, reduces complexity, improves classification accuracy and learning capacity. For each class of PQ disturbance, one NN module is used and all the modules are mutually-independent. For final decision, all the modules are combined together. Their approach is effective in detecting and classifying PQ disturbances.

VII. USING MULTIPLE NNS

Since no single NN model may be optimal for all cases, multiple NNs can be combined to make accurate decision.

Siwek et al. [START_REF] Siwek | Ensemble neural network approach for accurate load forecasting in a power system[END_REF] note that most studies train multiple NNs, choose the best one and discard the remaining networks. Instead, they account for all networks by combining them into one ensemble system and using the aggregate output as the final forecast. They experiment with three networks, one based on MLP and two based on self-organizing networks: crisp self-organization and fuzzy self-organization. To combine their results, they evaluate different integration approaches, e.g., simple average, weighted average, PCA and blind source separation (BSS). They use this approach for day-ahead load forecasting. They show that their ensemble method provides higher accuracy than using individual prediction results. Also, in terms of decreasing accuracy, the integration methods can be ordered as BSS > PCA ≈ weighted averaging > simple averaging.

Li et al. [START_REF] Li | Bayesian adaptive combination of short-term wind speed forecasts from neural network models[END_REF] use Bayesian combination algorithm to integrate 1-hour-ahead wind speed forecasts of three NNbased models, viz. BP, adaptive linear element network and RBF. Their approach first obtains best time series forecasts for each NN model for different performance metrics (e.g., MAE, MAPE, RMSE) and then integrates them in one time series using Bayesian method. Bayesian method generates an averaged model by assigning weights to different models based on their estimated posterior probabilities. While individual NNs do not consistently provide high accuracy, the Bayesian combination approach provides accurate forecasts.

Guo et al. [START_REF] Guo | Improving market clearing price prediction by using a committee machine of neural networks[END_REF] propose a technique for combining predictions from multiple networks to bring their best together. They find the prediction variance of each NN which depends on current input and the historical data. They use a Bayesian inference-based approach to compute weighting coefficients while accounting for the prediction qualities of networks. The probability that the true input/output (I/O) relationship at the next instant will follow a specific network mapping, is used to evaluate the weighting coefficient. Also, based on prediction covariance matrices (i.e. prediction quality), the transition possibility that the true I/O relationship switches from one mapping to another between the current and the next instant, is computed. Their approach of combining multiple networks provides higher accuracy than using individual networks and an ensemble-averaging based approach of combining multiple networks.

VIII. FUTURE CHALLENGES AND CONCLUSION

As the size and complexity of power systems increase, the probability and impact of critical failures also increase. Such failures can lead to outages and have more severe economic and social impacts than ever before. However, many NN-based methods have been proposed and evaluated for smaller-size power systems. Going forward, researchers will need to design NN-based stability analysis techniques for large-scale power systems and also ensure that their computational time remains manageable.

The usefulness of NN depends crucially on the accuracy of its prediction. With increasing lookahead period, the forecasting error rises rapidly. Also, finding the input variables which actually impact the output may require insights into nature of problems. Further, in case of insufficient or unrepresentative training data, the NN model may be under or over-fitted. Due to the fast changing dynamics of power systems, they may present more challenges in accurate modeling compared to other systems. Moving forward, these challenges need to be effectively addressed.

Neural network computation presents high overhead and thus, necessitates high-performance computing (HPC) approaches [START_REF] Khaitan | A survey of high-performance computing approaches in power systems[END_REF][START_REF] Khaitan | Dynamic load balancing and scheduling for parallel power system dynamic contingency analysis[END_REF][START_REF] Khaitan | EmPower: An Efficient Load Balancing Approach for Massive Dynamic Contingency Analysis in Power Systems[END_REF][START_REF] Khaitan | Parallelizing Power System Contingency Analysis Using D Programming Language[END_REF][START_REF] Khaitan | Fast parallelized algorithms for on-line extended-term dynamic cascading analysis[END_REF][START_REF] Khaitan | High Performance Computing in Power and Energy Systems[END_REF][START_REF] Khaitan | High performance computing for power system dynamic simulation[END_REF][START_REF] Raju | High performance computing using out-of-core sparse direct solvers[END_REF][START_REF] Raju | High performance computing using out-of-core sparse direct solvers[END_REF]. In near future, acceleration of NN algorithms on HPC platforms will be crucial to realize the full gains of NNs. Similarly, use of NNs for solving other problems in power-system area [START_REF] Khaitan | Multifrontal solver for online power system time-domain simulation[END_REF][START_REF] Raju | Domain decomposition based high performance parallel computing[END_REF][START_REF] Khaitan | Design techniques and applications of cyberphysical systems: A survey[END_REF][START_REF] Khaitan | Cyber physical system approach for design of power grids: A survey[END_REF][START_REF] Venkatraman | A survey of techniques for designing and managing microgrids[END_REF][START_REF] Khaitan | VANTAGE: A Lyapunov exponents based technique for identification of coherent groups of generators in power systems[END_REF] is also highly essential.

In this paper, we presented a survey of techniques for using NN in power systems. We reviewed several control and management tasks which benefit from NN, such as loadforecasting, stability analysis, etc.

  Bhowmik et al. [29] present a technique to locate and classify faults on transmission systems. They use DWT for parameterizing and characterizing fault signals. Also, NN is used for classifying faults based on DWT signals. They evaluate different types of faults, e.g., single-line-to-earth fault, double line fault and three phase fault, which occur at different locations on transmission line. They extract fault signals to several scales on the wavelet transforms and use selected features of the wavelet transformed signals as input for a training process on NNs. They show that their technique is effective in locating and classifying the faults.

Table I

 I presents an overview and classification of techniques that use NN in power systems. Clearly, NN has been used for both traditional and renewable energy sources, and a variety of management tasks.

TABLE I .

 I NN based techniques for power system

	Classification	References
	Load forecasting	[2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
		12, 13, 14, 15, 16, 17]
	Wind power/speed forecasting

TABLE II .

 II Lookahead window in load forecasting methods

	Classification	References
	up to one hour	[3, 11, 16]
	up to 24 hours	[2, 7, 13, 16, 18, 20, 22, 23]
	up to 30 hours	[19]
	up to one-week	[6, 8, 9]
	up to year	[10, 15, 17]

We use the following acronyms in the paper: backpropagation (BP), discrete wavelet transform (DWT), feed-forward (FF), generalized regression (GR), mean absolute error (MAE), mean absolute percentage error (MAPE), multi-layer perceptron (MLP), principal component analysis (PCA), radial basis function (RBF), root mean squared error (RMSE).