Deepak Singhal2011

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Electricity price forecasting using artificial neural networks

Deepak Singhal, K.S. Swarup

Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600 036, India

a r t i c l e i n f o

Article history:

Received 5 December 2006

Received in revised form 1 December 2010Accepted 9 December 2010

Available online 1 February 2011

Keywords:

Forecasting

Artificial neural networks

Open power market

Power trading

Market-clearing price (MCP)

Price forecasting

a b s t r a c t

Electricity price forecasting in deregulated open power markets using neural networks is presented. Fore-

casting electricity price is a challenging task for on-line trading and e-commerce. Bidding competition is

one of the main transaction approaches after deregulation. Forecasting the hourly market-clearing prices(MCP) in daily power markets is the most essential task and basis for any decision making in order to

maximize the benefits. Artificial neural networks are found to be most suitable tool as they can map

the complex interdependencies between electricity price, historical load and other factors. The neural

network approach is used to predict the market behaviors based on the historical prices, quantities

and other information to forecast the future prices and quantities. The basic idea is to use history and

other estimated factors in the future to fit and extrapolate the prices and quantities. A neural network

method to forecast the market-clearing prices (MCPs) for day-ahead energy markets is developed. The

structure of the neural network is a three-layer back propagation (BP) network. The price forecasting

results using the neural network model shows that the electricity price in the deregulated markets is

dependent strongly on the trend in load demand and clearing price.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

Market operations in electric power systems involve the deter-

mination of forecasted values of electricity prices in addition to the

load demand over a future horizon. Independent Power Producers

(IPPs) or market players depend on the forecasted values of electric

prices to decide strategies to broadcast sell and buy bids for sell-

ing and buying of power in the power trading market. Spot pricing

of electricity requires the determination of the electricity price in

real-time. Accurate forecasting of electricity prices are necessary

for the entities to participate in the biding process. Knowledge of

the electricity prices over a wider horizon are required for day

ahead market in deciding the units to be committed, termed as

price based unit commitment, to bidding available power genera-

tion over the operating scenario.

The electric power industry has over the years been dominatedby large utilities that had an authority over all activities in gener-

ation, transmission and distribution of power within its domain of

operation. Such utilities have often been referred to as vertically

integrated utilities. Such utilities served as the only electricity pro-

vider in the region and were obliged to provide electricity to every-

one in the region. The utilities being vertically integrated, it was

often difficult to segregate the costs incurred in generation, trans-

mission or distribution. Therefore, the utilities often charged their

customers an average tariff rate depending on their aggregated

cost during a period. The price setting was done by an external reg-

ulatory agency and often involved considerations other than eco-

nomics. The wholesale power markets have been growing

everywhere at a fast pace because of the ongoing deregulation of

the power industry. Power production industry is clearly demarked

from power transmission industry. Power trading as a result has

become a very important part of power industry.

An important input to the decision-making activities of a Genco

is a good forecast of the market prices. This is important because an

accurate forecast of the short-term market price helps the Genco to

bid for power sell or buy appropriately and strategically, thereby

providing higher returns. Bilateral contract prices also have a ten-

dency to be indirectly affected by spot-price trends. Thus good spot

market price forecasts can help set up profitable bilateral contracts.

In the short-term markets, continuous trading up to 2 h in advance

of real-time is possible. In these markets, the prices can be highlyvolatile to system conditions such as sudden outages, and external

factors such as temperature variations, and rainfall. It is usually of

great interest to Gencos and other market players to have a good

forecast toolbox for these prices. Price forecast in the general sense

also include forecast of futures and forward market prices [1].

These forecasts may be carried out months or even a year in ad-

vance. These forecasts may be useful if the Genco is contemplating

investments in generation capacity, market risk analysis, produc-

tion and maintenance planning, among others. Most often the Gen-

co has an in-house price forecast tool based on available

forecasting methods such as the conventional linear regression

analysis technique, to cater to the need of a price forecast.

0142-0615/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijepes.2010.12.009

Corresponding author. Tel.: +91 44 2257 4440; fax: +91 44 2257 4402.

E-mail address: [email protected] (K.S. Swarup).

Electrical Power and Energy Systems 33 (2011) 550555

Contents lists available at ScienceDirect

Electrical Power and Energy Systems

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i j e p e s
http://dx.doi.org/10.1016/j.ijepes.2010.12.009mailto:[email protected]://dx.doi.org/10.1016/j.ijepes.2010.12.009http://www.sciencedirect.com/science/journal/01420615http://www.elsevier.com/locate/ijepeshttp://www.elsevier.com/locate/ijepeshttp://www.sciencedirect.com/science/journal/01420615http://dx.doi.org/10.1016/j.ijepes.2010.12.009mailto:[email protected]://dx.doi.org/10.1016/j.ijepes.2010.12.009


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1.1. Electricity pricing

In a power market, the price of electricity is the most impor-

tant signal to all market participants and the most basic pricing

concept is market-clearing price (MCP). Generally, when there is

no transmission congestion, MCP is the only price for the entire

system. However, when there is congestion, the zonal market-

clearing price (ZMCP) or the Locational Marginal Price (LMP)could be employed. ZMCP may be different for various zones,

but it is the same within a zone. LMP can be different for different

buses. The bidding decision making process for optimal electricity

supply is formulated as a Markov decision process. The suppliers

are modeled with their bidding parameters with corresponding

transition probabilities. Fundamental conceptual framework for

market and bidding decision making is presented in [1]. Market

clearing tool for market operator of a pool based electricity mar-

ket is presented. The problem is formulated as a mixed-integer

linear programming problem. The results of the new market

clearing procedure are presented for 20 generating units for

24 h duration [2].

The most distinct property of electricity is its volatility. Vola-

tility is the measure of change in the price of electricity over a gi-

ven period of time. It is often expressed as a percentage and

computed as the annualized standard deviation of percentage

change in the daily price (other prices such as weekly or monthly

prices can also be used), Compared with load, the price of elec-

tricity in a restructured power market is much more volatile.

From the curves, we learn that the load curve is relatively homo-

geneous and its variations are cyclic and the price curve is non-

homogeneous and its variations show a little cyclic property.

Although electricity price is very volatile, it is not regarded as

random. Hence, it is possible to identify certain patterns and rules

pertaining to market volatility. For example, transmission conges-

tion usually incurs a price spike which is not sustained as elec-

tricity price would revert to a more reasonable level (this is

known as mean reversion in statistics). It is conceivable to use

historical prices to forecast electricity prices. Accordingly, weuse a training scheme to capture perceived patterns for forecast-

ing electricity prices.

The fundamental reason for electricity price spike is that the

supply and demand must be matched on a second-by-second basis.

Other reasons follow:

Volatility in fuel price

Load uncertainty

Fluctuations in hydroelectricity production Generation uncertainty (outages)

Transmission congestion

Behavior of market participant (based on anticipated price) Market manipulation (market power, counterparty risk)

Because of the special properties of electricity, the price of elec-

tricity is far more volatile than that of other relatively volatile com-

modities. The annualized volatility of oil future contracts is around

30%; it is around 50% for natural gas future contracts, while about

60% for electricity future contracts. In electricity spot markets,

annualized volatility is above 200%. Because of the significant vol-

atility, it is difficult to make an accurate forecast for the spot mar-

ket of electricity. This is evidenced by the fact that the existing

price forecasting accuracy is far lower than that of load forecasting.

However, price forecasting accuracy is not as stringent as that of

load forecasting.

The power awarded to each bidder is determined based on the

individual bid curves and the MCP. All the power awards will be

compensated at the MCP. After the auction closes, each bidderaggregates all its power awards as its system demand, and per-

forms a traditional unit commitment or hydrothermal scheduling

to meet its obligations at minimum cost over the bidding hori-

zon. Suppliers bidding decisions are coupled with generation

scheduling since generator characteristics and how they will be

used to meet the accepted bids in the future have to be consid-

ered before bids are submitted. Therefore bidding decision must

consider the anticipated MCP, generation award and costs, and

competitors decisions. The MCP and MCQ (Market ClearingQuantity) are the most important power market indicators. Fore-

casting the hourly MCP and MCQ in daily power markets is the

most essential task and basis for any decision making in the

power market.

1.2. Electricity price forecasting methods

There are various methods adopted for the forecasting of future

market price. One approach to predict the market behaviors is

regression. The basic idea is to use the historical prices, quantity

and other information such as load forecast, and temperatures to

predict the MCPs. That is, use history and other estimated

factors in the future to fit and extrapolate the prices and

quantity.

Important methodological issues and techniques for electricity

load and price forecasting are presented in [3]. Computationally

intensive methods like variable segmentation, multiple modeling,

combinations and neural networks for forecasting demand side

and strategic simulation using artificial agents for the supply side

are used. Conceptual framework for designing price forecasting

approaches are presented [4]. Modeling competitive market

behavior in capturing uncertainty in inputs/outputs with adapt-

ability and transparency is presented. Model of Market-clearing

price (MCP) and Database for forecasting electricity prices is de-

scribed. Forecasting Energy prices using neural networks and fuz-

zy logic and their combination is discussed in [5]. Historical

behaviors of spot prices was evaluated for these methods.

Emphasis is placed on the identification of important parameters

which influence the forecasted quantity. Basic framework of arti-ficial neural network for load forecasting based on historical load

data and temperature is presented [6]. A multi layer perception

using three hidden layers is implemented for accurate load

forecasting.

A phase space is reconstructed from the scalar time series

representing the chaotic characteristics of electricity price. The

main features of thee attractors are extracted and the surrogate

data method is used. Global and Local price forecasting model

based recurrent neural network is proposed and applied for the

New England Market. [7]. An artificial intelligence method

using both fuzzy C- means (FCM) algorithm and recurrent neural

network (RNN) is used for forecasting the LMPs. The RNN

were trained using historical prices for two months from Penn-

sylvania, New Jersey and Maryland (PJM). The RNN was foundto forecast electricity prices with reasonable amount of accuracy

[8].

System marginal price short term forecasting (48 h) using a

three layer artificial neural network employing data from Victo-

rian power system is presented [9]. Model sensitivity test for in-

put variable selection validation is discussed to justify the

concept of influence of input variables on the output. Electricity

price forecasting based on chaos theory is presented which is

based on the fact that electricity price possesses chaotic charac-

teristics, where the Lyapunov and components and fractal dimen-

sions of the attractors are extracted. An accurate phase space is

reconstructed by multivariable time series constituted by electric-

ity price and its correlated factors. A recurrent neural network is

employed for Global and Local electricity price forecasting[10,11].

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2. Problem description and formulation of proposed

methodology

2.1. Factors considered in price forecasting

There are many factors that may influence the market auction

result, such as system load of the entire area covered by the mar-

ket, power import to and export from outside the market throughlong term contract, the available hydro energy, fuel price, etc. In or-

der to forecast MCP, these factors can be used as input variables if

available. Therefore input variable selection is extremely impor-

tant. Based on experience of the market analysts and correlation

analysis, the following factors can be considered as input variables.

2.1.1. Historical MCPs

The historical MCPs are natural selections since history and fu-

ture are correlated. The hourly MCPs demonstrate some cyclic

characteristics. The basic cycle is 24 h. In a week span, each days

pattern would be different especially between a weekday and

weekend. Therefore week is also a cycle. On the other hand, the

system load is different in a year for different seasonal climate. This

would be reflected in the MCPs. Clearly year is a cycle too. There-fore there are at least three cycles in MCPs: day, week and year.

The average on peak and off peak MCPs of last few weeks as inputs

can provide the trend information over the recent past.

2.1.2. System loads

Load fluctuations could impact price. On the other hand, price

fluctuations could impact load values. Thus, load forecasting and

price forecasting can be combined into a single forecasting model.

Therefore the historical load and forecasted load are used as input.

2.1.3. Fuel prices

The fuel costs are main part of total generation cost. The change

in fuel prices may affect the market prices.

A well-established nonlinear regression method is artificialneural network. Neural networks have been used for pool price

forecasting [12]. Several techniques based on neural networks, fuz-

zy systems and other intelligent methods have been widely em-

ployed for forecasting the electricity price [13,14].

2.2. Implementation of the forecasting model

The electricity price data was collected for eight months. The

Neural Network is trained with the data of six months. It is tested

for various days of a particular month. The days include the day

with normal trend, day with small spike and the day with large

spike. The collected data contains eight months data which gives

the values of total demand and price at every time slot. The time

steps are half hourly which mean that one day contains 48 timesteps. In our model we will take the historical prices, historical

and forecasted demands and time indices as inputs as these are

the information that is gathered from the data. The inputs to the

neural network consist of the time indices, electricity price and

load demand data. Historical information of electricity prices and

past load demand constitutes important inputs for predicting the

electricity price. The output of electricity price can take several

durations, namely hourly, daily and weekly forecasting. Forecast-

ing of load demand is mostly hourly, whereas electricity price is

for more frequently to facilitate spot pricing of electricity. Power

trading in electric power markets usually use price signals varying

over a wide range. Day ahead markets use requires forecasted

prices at least 2 days in advance. To simulate the market power

conditions, day ahead forecasting for electricity prices for 48 h iscarried out in this work.

The inputs to the Neural Network forecaster are:

1. Day of week

2. Time slot of Day

3. Forecasted Demand i.e. D(t)

4. Change in demand i.e. D(t) D(t-1)

5. Price (one day ago) 3 inputs i.e. P(t-47), P(t-48), P(t-49)

6. Price (one week ago) 3 inputs i.e. P(t-335), P(t-336), P(t-337)7. Price (two weeks ago) 1 input i.e. P(t-672)

8. Price (three weeks ago) 1 input i.e. P(t-1008)

9. Price (four weeks ago) 1 input i.e. P(t-1344)

Table 1 shows the inputs to the neural network for electricity

price forecasting.

The first two inputs are chosen as they are the time indices. A

third and fourth input represents the current status of the market

and as demand is inter related with price, they are one of the

Table 1

Neural network input for electricity price forecasting.

No. Parameter Inputs Relation1 Time information Day of week 1

2 Time slot of day 1 t

3 Load demand Forecasted demand 1 D(t)

4 Change in demand 1 D(t) D(t-1)

5 Historical price

information

Price (one day ago)

3 inputs

3 P(t-47),P(t-

48),P(t-49)

6 Price (one week ago)

3 inputs

3 P(t-335),P(t-

336),P(t-337)

7 Price (two weeks ago)

1 input

1 P(t-672)

8 Price (three weeks

ago) 1 input

1 P(t-1008

9 Price (four weeks

ago) 1 input

1 P(t-1344)

Fig. 1. Neural network model for price forecasting.

552 D. Singhal, K.S. Swarup/ Electrical Power and Energy Systems 33 (2011) 550555


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important inputs. The rest of the inputs are historical price values.

Fifth input represents the price one day ago at the same time step

and the steps near it. This input represents the latest market trend

as the day is a cycle. Sixth input represents the price one week ago

at the same time step and the steps near it. This also represents the

trend of the market for a longer period. The remaining inputs are

the prices of two, three and four weeks ago respectively. These

are considered since week is a cycle. Thus there are thirteen inputs

used to forecast the system price at any given instant.

Fig. 1 shows the Neural Network for price forecasting which

contains three layers of neurons (two hidden layers and one output

layer). The first layer has 10 neurons and tansig function, second

layer has five neurons and tansig function and the output layercontains one neuron with linear function.

2.3. Data pre-processing and post-processing

The training data before given to neural network is pre-pro-

cessed. The pre-processing scheme is as follows.

An upper limit of price is set up and following condition is

applied.

PP if PP UL

UL ULLogP

UL

if P> UL

(1

The upper limit is set to be 70 $/MWh as most of the points are

below this limit. To recover the price after limiting the spikes a

Post-processing scheme is applied which is as follows

Table 2

Predicted and actual values of prices for day with normal trend, small and large spike in prices.

Time Electricity price ($/MWh) for 48 h with normal trend, small and large spikes.

I. Normal trend price II. Price with small spike III. Price with large spike

Hour Predicted value Actual value Error Predicted value Actual value Error Predicted value Actual value Error

1 18.25 17.33 0.92 24.93 25.84 0.90 38.31 33.51 4.80

2 18.25 17.55 0.69 26.70 20.36 6.34 31.61 27.65 3.96

3 18.56 17.04 1.52 18.65 19.05 0.39 26.19 27.33 1.134 17.54 17.83 0.28 19.94 22.55 2.60 27.74 27.88 0.13

5 20.24 17.49 2.75 24.26 22.77 1.49 28.58 26.84 1.74

6 20.44 18.93 1.51 23.04 24.15 1.10 27.08 26.3 0.78

7 21.59 25.75 4.16 25.33 24.43 0.90 26.74 24.83 1.90

8 28.21 27.24 0.97 29.52 24.9 4.62 25.09 25.02 0.07

9 29.47 31.34 1.86 23.93 23.8 0.13 25.80 25.09 0.71

10 33.09 41.01 7.92 23.02 23.59 0.56 25.84 25.48 0.36

11 42.19 40.08 2.12 31.39 34.01 2.61 26.29 25.65 0.64

12 38.09 39.62 1.528 39.27 37.4 1.87 26.38 24.94 1.44

13 37.03 39.72 2.68 35.57 41.29 5.71 25.44 22.61 2.83

14 38.87 39.37 0.49 49.99 45.09 4.90 22.79 23.03 0.23

15 37.03 34.34 2.68 42.58 40.79 1.79 23.06 20.42 2.64

16 31.34 29.87 1.47 40.20 39.51 0.69 26.75 27.19 0.43

17 27.98 29.55 1.56 39.26 31.22 8.04 29.95 30.98 1.02

18 28.79 27.05 1.73 28.79 28.59 0.20 37.09 38.48 1.38

19 26.34 26.75 0.40 27.30 27.45 0.14 45.08 41.03 4.04

20 25.48 27.25

1.77 27.74 26.1 1.64 45.80 41.75 4.0521 26.09 29.8 3.70 23.82 26.88 3.05 41.262 42.18 0.91

22 30.80 31.71 0.90 27.45 26.88 0.57 41.56 39.89 1.67

23 34.30 28.27 6.03 27.32 26.58 0.72 38.63 33.13 5.50

24 28.49 28.92 0.43 26.67 24.64 2.03 30.95 28.43 2.52

25 29.67 26.12 3.54 23.93 24.64 0.70 27.28 27.93 0.64

26 28.32 31.14 2.82 24.41 24.42 0.00 28.25 25.69 2.56

27 32.19 33.63 1.43 24.41 25.83 1.41 25.64 25.53 0.11

28 36.32 41.19 4.85 26.53 27.73 1.19 26.15 25.77 0.38

29 51.94 61.94 10.00 28.04 32.28 4.24 26.52 20.65 5.87

30 75.73 80.33 4.59 53.04 58.13 5.09 20.14 21.53 1.38

31 79.85 71.85 7.99 92.91 138.48 45.57 22.82 20.34 2.48

32 58.70 62.22 3.52 85.95 106.08 20.12 21.15 20.88 0.27

33 52.98 40.99 11.99 75.34 81.66 6.31 22.15 23.98 1.82

34 41.06 40.2 0.85 59.65 62.68 3.02 25.82 31.37 5.54

35 38.23 37.5 0.73 51.79 46.28 5.51 44.05 56.34 12.28

36 33.50 34.56 1.05 40.58 43.59 3.00 162.28 268.11 105.82

37 30.25 31.95 1.70 40.21 41.85 1.63 151.14 294.77 143.62

38 27.48 26.43 1.05 39.25 41.35 2.09 121.41 201.66 80.2439 35.43 36.98 1.55 38.49 38.81 0.32 82.25 82.16 0.09

40 33.64 31.29 2.35 36.84 41.39 4.54 47.93 52.3 4.36

41 37.23 38.7 1.47 45.96 49.13 3.16 44.13 50.85 6.71

42 37.03 33.69 3.33 40.81 41.24 0.42 54.49 58.58 4.08

43 33.59 36.94 3.34 35.91 39.46 3.55 47.29 44.65 2.64

44 30.21 27.3 2.91 38.48 33.51 4.97 39.21 37.88 1.33

45 25.48 29.09 3.61 31.86 27.65 4.21 35.19 39.79 4.59

46 27.75 27.15 0.59 25.90 27.33 1.42 34.92 32.84 2.08

47 26.86 25.09 1.77 27.48 27.88 0.39 30.68 34.54 3.85

48 22.10 22.25 0.14 26.17 26.84 0.66 35.01 27.3 7.70

MAE 2.655 0.682 9.282

RMSE 0.525 1.129 4.105

MAE: mean absolute error.

RMSE: root mean square error.



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PP if PP UL

UL 10PUL

UL if P> UL

(2

3. Numerical results

The Neural Network is trained with the data of 6 months.

It is tested for various days of a particular month. The days

include

The day with normal trend

The day with small spike

The day with large spike

The resulting price forecasts are described by two different

measures, the MAE and RMS error. The mean absolute error

(MAE) is a standard measure of accuracy used in forecasting.

MAE

Pni1

jPfi Paij

n3

The root mean square (RMS) error is also a standard measure

RMS1

n

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX

n

i1

Pfi Pai2

vuut 4

where n is the No. of time slots, Pfi is the time slot i predicted value,

Pai is the time slot i target value

Electricity Price forecasting has been carried out for the three

cases corresponding to Price spike with (i) normal trend (ii) small

spike and (iii) large spike. Table 2 shows the results with the three

case studies.

The MAE for electricity price with small spike (0.682) much less

than that of the normal trend (2.655) and large spike (9.282), how-

ever the RMSE for the price trend with small spike (1.129) is more

Fig. 2. Price forecasting with normal trend.

Fig. 3. Price forecasting with small spike.

Fig. 4. Price forecasting with large spike.

554 D. Singhal, K.S. Swarup/ Electrical Power and Energy Systems 33 (2011) 550555


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than normal trend (0.525) and much less than large spike (4.105).

An important inference from the results is that the MAE index

alone may provide erroneous results in evaluating the performance

of the ANN in forecasting. Both the RMSE and MAE indices should

be used together for performance evaluation of the forecasting

method used. This suggests the need to identify and use additional

performance indices for trend curves with high spike in electricity

price.Fig. 2 a shows the forecasted and actual value for normal trend

in electricity price. It can be observed that predicted value is very

close to the actual value. The neural network is able to track the

spike in electricity price and predict the price spike to a good

accuracy.

Neural Network Forecasting for a short and small spike in elec-

tricity prices is shown in Fig. 3. It can be observed that the pre-

dicted value is able to track the actual value for small variations

at 13th h and 42nd h, but is unable to accurately forecast for the

spike at 32nd h. The neural network is able to generalize the fore-

casting task at major intervals but degrades for local time period.

This may be attributed to the deficiency in input patterns contain-

ing more information about spikes. Feature selection and extrac-

tion of spike data during input processing and presentation as a

set of input patterns during training may further reduce the error

in forecasting to a substantial level.

Fig. 4 shows the forecasted and actual value with large spike in

electricity prices. Similar to small spike, the neural network is un-

able to track the large and sudden spike in electricity price. The

neural network is able to perform well at all time period, except

at the peak duration. Forecasting error during spikes is a major

concern for players to broadcast their sell and buy bids for the

sale and purchase of bulk amounts of power during spot pricing

of electricity. Further reduction in the forecasting error during

price spikes would help the power trading market and indepen-

dent players with better bidding strategies for efficient operation

and increase in savings and social benefit.

4. Conclusions

Forecasting electricity price using neural networks in open

power markets is presented. Accurate price forecasting is very

important for electric utilities in a competitive environment cre-

ated by the electric industry deregulation. The strong interdepen-

dence between load demand and electricity price is considered.

Historical information of load and electricity price in forecasting

the day-ahead price is presented. A simple price forecasting tool

using multi-layer neural network employing back propagation

algorithm has been developed as an aid to the power trading sim-

ulator. The neural network model was employed to forecast the

market-clearing prices (MCP) of the daily energy market. The fore-

casting results show that the model is efficient for days with nor-

mal trend, however shows a gradual degradation on performance

for days with price spikes. The results of the simulation have been

tabulated with a less than 16% error on a weekday and a less than20% error on a weekend. Price forecasting results show that elec-

tricity price in the deregulated markets can be forecasted with rea-

sonable accuracy. Electricity price forecasting can be made more

accurate by combining several techniques such as fuzzy logic, neu-

ral networks and dynamic clustering together. The price for the

days with price spikes can be forecasted better by considering

the inputs which can explain the reason for spikes so this can be

taken into account.

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