Electricity price forecasting using Enhanced Probability Neural Network

doi:10.1016/j.enconman.2010.06.006

Energy Conversion and Management

Volume 51, Issue 12, December 2010, Pages 2707-2714

https://doi.org/10.1016/j.enconman.2010.06.006 Get rights and content

Abstract

This paper proposes a price forecasting system for electric market participants to reduce the risk of price volatility. Combining the Probability Neural Network (PNN) and Orthogonal Experimental Design (OED), an Enhanced Probability Neural Network (EPNN) is proposed in the solving process. In this paper, the Locational Marginal Price (LMP), system load and temperature of PJM system were collected and the data clusters were embedded in the Excel Database according to the year, season, workday, and weekend. With the OED to smooth parameters in the EPNN, the forecasting error can be improved during the training process to promote the accuracy and reliability where even the “spikes” can be tracked closely. Simulation results show the effectiveness of the proposed EPNN to provide quality information in a price volatile environment.

Introduction

Deregulating the power market creates competition and a trading mechanism for market players. It moves from the cost-based operation to a bid-based operation [1], [2]. “Electricity” has become a commodity that the price could be volatile in the energy market where the sudden “spikes” could even appear. To forecast price accurately is an important task for producers, consumers, and retailers. According to price forecast, participants can develop their bidding strategies to maximize the profit with lower risks. Price forecasting also helps investors to better planning the Grids.

In the US, Pennsylvania–New Jersey–Maryland (PJM) power market [3] is commonly known as one of the successful market models. PJM market that operates the competitive market is coordinated by an Independent System Operator (ISO) to determine the Locational Marginal Price (LMP) according to the status of system nodes. The LMP at each node will then reflect not only the price of voluntary bids but also the overhead of delivering energy to locations. Generally, LMP includes three components: an energy cost component, a transmission congestion component, and the marginal loss component. LMP in a pool is different for different locations while the energy cost can be identical for all the nodes. A feasible and practical method for LMP forecasting will funnel a better risk management for all market participants.

Many factors including load, historical prices and temperature could impact the LMP. The loads and prices in the wholesale market are mutually intertwined activities. Loads are heavily affected by the weather parameter, so the prices are strongly volatile with the changing weather. Another factor is the time of use at various levels of day, week, month, season, and year. Price could rise hundred of times the normal value to reflect the volatility. In PJM, LMP is introduced at nodes. Congestion occurs when a transmission flow exceeds its limits. Line flow information becomes an important factor in price forecasting. It is complicated to perform LMP forecasting, especially finding the best strategy in a world of uncertainties. Reported techniques to forecast day-ahead prices include time series models [4], weighted nearest neighbors techniques [5], auto regressive integrated moving average models (ARIMA) [6], Mixed ARIMA models [7], [8], and Markov models [9]. These approaches can be very accurate with sufficient information and computation time, however, there is no approach with satisfactory performance in dealing with the spikes. Recently, Artificial Neural Network (ANN) has been applied to forecast prices in various markets [10], [11], [12], [13], [14], [15], [16]. ANN is a simple, powerful, and flexible tool for forecasting, providing better solutions to model complex non-linear relationships than the traditional linear models. ANNs have weaknesses in the determination of network architecture and network parameters. Running in a dynamic environment, especially for online applications, traditional ANN network can become the bottleneck in adaptive applications [17]. Among ANNs, the Probability Neural Network (PNN) can function as a classifier, and it has the advantages of a fast learning process, requiring only a single-pass network training stage without any iteration for adjusting weights, and it can adapt itself to architectural changes. However, PNN can only classify the data for categorical input data type. Since, there is no mechanism for adjusting parameters in the course of recalling. To deal with the continuity problem, a large amount of information needs to be obtained during the learning stage. In order to solve this problem, this paper uses Orthogonal Experimental Design (OED) to improve the traditional PNN.

OED is an effective tool for robust design and an engineering methodology for optimizing process conditions which are minimally sensitive to various causes of variations. The characteristics of OED are: (1) results obtained through few experiments; (2) good recurrence of result in the same experimental environment; (3) simple construction of mathematical model with the application of orthogonal array; (4) simple analytical procedure. Combining PNN [18] and OED [19], an Enhanced PNN (EPNN) is proposed in this paper. OED is used to adjust the smoothing parameters in EPNN learning stage to improve the training ability, and a good performance with a close spike tracking capability can be seen. This paper developed day-ahead forecasts for electricity price using EPNN, based on similar-day PJM market model. Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) obtained from the forecasting results demonstrate that EPNN can efficiently forecast the price for any day of a week.

Section snippets

Orthogonal Experimental Design

EPNN contains the learning stage and the recalling stage. Although the structure of traditional PNN is simple, it may cause errors in non-classification problems because it has no mechanism for adjusting the concatenated key parameters. To improve this process, this paper uses OED to find the optimal smoothing parameter σ_k to increase the accuracy of prediction.

Orthogonal experiment uses a small amount of experimental data to construct a mathematical model, which is derived from orthogonal

Enhanced Probability Neural Network

EPNN consists of the input, hidden, summation, and output layers. The unknown input vector X = [x₁, x₂, … , x_i, … , x_n], i = 1, 2, … , n, is connected to the input layer. The number of hidden nodes H_k, k = 1, 2, … , K, is equal to the number of learning data sets, while the number of summation nodes S_j and output nodes O_j, j = 1, 2, … , m, are equal to the forecasting points. The weights $w_{ki}^{IH}$ connecting the kth hidden node with the ith input node, and $w_{jk}^{HS}$ connecting the jth summation node with the kth hidden node, are

The implementation of EPNN

Daily LMP profiles are similar on weekdays but different on Saturdays and Sundays. The fluctuation of LMP may come from the loads, transfer flow, and temperature changes. EPNN is capable of coping with complicated interactions between those factors and LMPs. Hence, those factors can be taken into account as inputs to the EPNN. In this paper, three-layer network based on EPNN are shown in Fig. 3.

The input layer contains three input variables – loads, temperature, and transfer flow. The hidden

Results

The data of PJM website [3] were used to train and test the proposed method. For comparison purpose, PNN and Back-progation Neural Network (BPN) were also built for tests. The data set was divided into two parts, the training data and testing data as in Table 5. The training data were used for training and updating the biases and weight. The test data were used to test the proposed methods after training. The simulation was implemented with Matlab on a PIV-2.6 GHz computer with 512 MB RAM

Fig. 5

Conclusions

EPNN integrated the PNN and OED to forecast LMPs based on similar days. PNN has the capability of dealing with varied and complicated relations between input and output data, and OED helps with the appropriated regulation of smoothing parameters to improve the forecasting results. The actual data of PJM were used to demonstrate the performance of EPNN. For selected days and weeks under study, the daily and weekly RMSE values are calculated, and it shows that EPNN can even track the spikes

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View full text

Electricity price forecasting using Enhanced Probability Neural Network

Abstract

Introduction

Section snippets

Orthogonal Experimental Design

Enhanced Probability Neural Network

The implementation of EPNN

Results

Conclusions

IEEE Trans Power Syst

Electr Power Syst Res

Energy Convers Manage

Energy Convers Manage

Eng Appl Artif Intell

Evolution toward standardized market design

IEEE Trans Power Syst

Market operations in electric power systems

Forecasting next-day electricity prices by time series models

IEEE Trans Power Syst