Neural Networks Based Forecasting of Electricity Markets

8/3/2019 Neural Networks Based Forecasting of Electricity Markets

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A PAPER PRESENTATION ON

NEURAL NETWORKS BASED FORECASTING

OF ELECTRICITY MARKETS

SUBMITTED BY,

G.Mahendranath & E.Kranthikumar,final B-TECH(E.E.E)

([email protected],

kranthi [email protected])

Narayana Engineering college,Nellore.

Contact address:

G.Mahendranath,

S/O:G.Parandhamulu,D/NO:18-1-308,

Acharistreet,Nellore.

Contact:No: 98669066169949369270

0861-2324639
mailto:[email protected]:[email protected]


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Abstract:

This paper deals with load forecasting of : the short and medium-term

load forecasting. This Load forecasting was usually performed using

statistical time series and regression methods.Among these methods,

the ARMA and ARIMA models (Autoregressive (Integrated Moving

Average) were very popular in the near past. The researches and

results in the last 2 or 3 years show a significant change of the

interest in load forecasting from traditional to artificial intelligence

based methods. Thus, scientists have proved that an Artificial Neural

Network (ANN) produces the same or best results compared to

an ARIMA model. This finding demonstrated that, in fact, statistical

models could be viewed as special cases of ANNs, and hence an

ANN is a more powerful and more flexible tool to forecast load

behavior.


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1. Introduction

It is a common place that load forecasting plays an important role in the planning

and operation of power systems. At present, as electricity markets appear all over the

world, problems like long and short term electricity contracts, market prices and energytrading in general involve more and more outputs from load forecasters. Typically, load

forecasting can be long term, medium term, short term or very short term. Long

term forecasting refers to intervals of years in advance and it is applied primarily to

system development planning. For shorter intervals (from several months to one year),the medium term load forecasting deals with problems like fuel supply scheduling or

maintenance planning. Load prediction for one day to one week ahead is the field of short

term load forecasting and refers to the balance between electricity consumption andgeneration as an efficient way to control the operation of the system and the electricity

market. Finally, the very short term load forecasting problem deals with the balance

between consumption and generation during shorter time intervals (e. g. 10 minutes) .

.

2. Artificial Neural Networks:

The main advantage of using ANNs to forecast system load lies in their ability tolearn the dependencies between the exogenous parameters and the forecasted load. The

exhaustive description of the ANNs matter is not the subject of this paper. However, for

completeness this section presents the basics of ANNs architectures and learningalgorithms.

2.1. The Multilayered Perceptron

An MLP is a collection of simple processing units highly interconnected, which

process the information fed to the input units (see Figure1.a). These units, called neurons,are organized by layers. Typically, the neurons in the input layer serve only for

transferring the input pattern to the rest of the network, without any processing. Theinformation is processed by the hidden and output neurons. Figure 1.b shows the internal

structure of a neuron. Each neuron has a certain number of inputs, but only one output.

For a certain neuron the inputs could originate from external stimuli or could representthe output of the other neurons. Signals travel from one neuron to others through special

links or connections. The importance of a connection between neurons i and j is

described by its weight wij.

The MLP is operated in two steps: the training stage and the generalization stage.

In both stagesthe first operation to be performed is theforward propagation. An inputpattern is fed to the inputlayer and transferred to the hidden units. Theoutput of eachneuronxj is multiplied by theweights of the outgoing connections wij and thenfed out to


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the input of the neurons in the nextlayer. The inputs of a neuron are summed up to form

the net input neti, and the activation function fiproduces the output of the neuron oi =fi

(neti). This operation is repeated for all neurons in thenetwork until the outputs of alloutput neurons have been computed. This is a forward propagation step.

The MLPs most popular learning rule is the error back propagation algorithm.At the beginning of the learning stage all weights in the network are initialized to small

random values. The algorithm uses a learning set, which consists of input desired

output pattern pairs. Each input output pair is obtained by the off line processing ofhistorical data. These pairs are used to adjust the weights in the network to minimize the

Summed Squared Error (SSE) which measures the difference between the real and the

desired values over all output neurons and all learning patterns. After computing SSE, the

error back propagation step computes the corrections to be applied to the weights.

2.2. Self Organizing Feature Maps:

Another type of ANN is the Kohonen network, also known as the Self

Organizing Feature Map(SOFM). SOFMs were inspired by the way human sensorialsegments are mapped into the cortex: spatial relationships among stimuli correspond to

spatial relationships among neurons. Unlike MLP, which uses unsupervised learning,

SOFMs were especially conceived for unsupervised learning, also called self

organization. A self organizing neural network learns by itself, without any information

about the right answer or the right value(s) it must produce at the output. The information

concerning these characteristic features is created during the learning process and isstored in the weights of synaptic connections. These weights form a set ofprototypes.

The Kohonen network uses a grid of neurons. Each neuron from this grid is associated to

a class or category, hence the name of class neuron. Each class neuron can bedescribed by its position in the grid and a prototype. The prototype is specified by the

weights of synaptic connections between the class neuron and the input neurons (seeFigure 2). The self organizing process occurs during the learning stage. First, theprototypes of all class neurons are initialized, for example to small, random values.

Then, all patterns from the learning set are applied one by one to the input layer. Each

pattern xp is compared to the prototypes wu, and the class neuron with the smallest

distance ||wuxp|| is chosen to be the wining neuron U*. Then the prototype of the winingneuron is modified to become closer to the current pattern, using a learning rate. The

force of the self organizing algorithm proposed by Kohonen consists in modifying the

prototype not only for the wining neuron U*, but for all neurons inside a certainneighborhood of the wining neuronNU*.


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During the generalization stage, the

Kohonen network is used to identify or

recognize patterns. The unknown pattern is

applied to the input, and compared to all prototypes in the network. The nearest

prototype is chosen and used thereafter in

accordance with any specific request of the

application.

3. General load characteristics

Any model for the short or medium term load forecasting is greatly influenced

by then characteristics of the load to be predicted. The time series that describe the daily

load profiles in a system are non stationary processes, affected by weather conditions

(especially temperature, but other parameters that could be considered are humidity orwind speed), special events (strikes, sport events) and the randomness of the industrial

consumption. As a rule, the most stable group of consumers, whose load changes

following a common pattern that can be assessed, is the group of residential loads. Asfor considering special events and / or the randomness of industrial loads in the

forecasting model, these are very difficult tasks and, as far as the author knows, there

are no references to mention them.

The shape of the load profiles describes usually a daily and weekly periodicity.

However, the load profile for tomorrow or the next week is not just a simple copy of the

load profile from today or this week. Instead, the load profile is slightly modified fromday to day and week to week, to reflect changes in consumers behavior or weather

conditions. Typically, daily load profiles are classified as week days (from Monday to

Friday)and weekend days (Saturday and Sunday). Some authors consider separateanalysis for each weekend day, while others deals with separate analysis for 3 types of

week days, i. e. (a) Monday,(b) Tuesday to Thursday and (c) Friday. In the last case the

shapes of the load profiles are similar for all week days except the morning of and theevening of Friday as shown in Figure 3.

A special type of day is the holiday. Some authers group the holidays with theweekend days, and assimilate them with Sundays . However, some holidays (e. g. the

Easter, or the Christmas) have completely different load profiles and must be considered

separately, as in reference. During weekend days and holidays the load lowers with 6 to

11 % as compared to the load in week days, and the shape of the load profiles changes


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dramatically. For usual length of the data history (2 to 3 years), the number of weekend

days and holidays is much smaller than the number of normal week days, hence the need

of a special approach to forecast special days load. The basic approach for special daysforecasting consist in preparing an initial forecast using the normal day model, followed

by a correction action, to take into account the presence of a weekend day or holiday.

Until now there is no consistent methodology to determine the relevant

parameters to be used as independent variables in short or medium term load

forecasting. In most cases these variables are chosen using a linear correlation analysiswith respect to the load values. However, considering that subsequently these variables

shall be used as input to an essentially nonlinear model (namely the ANN), the linear

correlation criterion raises some validity questions.

As a rule, the main parameters considered as independent forecast variables are:

(a)generalvariables: year, month, hour, day of the year, day of week, holiday;

(b) weather conditions: temperature, wind speed, humidity, etc;

(c) loadvariables: load values at different moments in the load history (e. g. loadvalues with 1, 2, 24 or 168 hours before the forecasting moment); (d)special,functionalvariables: different types of functions (exponential, logarithmic, trigonometric, etc)having as arguments any variable in (a), (b) or (c).

4. Short term load forecasting:

Short term load forecasting provides daily load profiles with hourly or half hourly load values for one day to one week in advance. At present, the most commonly

used forecast methods are those based on ANNs. Some of these methods will be

described briefly hereafter.

There is a reach literature providing references about short term load forecastingwith ANN. Among many structure of ANNs, two architectures are commonly used: theMLP and the Kohonen network. Among different types of MLP used as forecasting

models, three architecture could be considered as representative: (a) networks for 1 hour

forecast; (b) networks for 24 hours forecast and (c) modular networks for 24 hours

forecast.


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4.1. Networks for 1-hour forecast

The basic architecture of the MLP for this type of networks is shown in Figure 4.The output layer comprises only one neuron, which produces the forecast for one hour.

Using the network in Figure 4 sequentially, it can generate the forecast for the entire day

(24 or 48 values). The number of input neurons varies from one model to another. Forexample, Table 1 shows the input values used for three different models of MLP.

For this type of architecture, the forecasting procedure uses real data for the first hour

only (h = 1). For the rest of the hours (h = 2, 3, ) at least one of the input values is a

forecasted one. Hence an error propagation process appears, which could generateimportant errors for hours late in the day. The test shows however that, due to positive

and negative errors compensation, this propagation process is not so harmful as feared.

4.2. Networks for 24-hours forecast:

For this type of network the architecture is similar to that in Figure 4, except that

the output layer contains not only one, but 24 neurons, which forecast 24 hourly valuesfor a daily load profile. The structure of the input layer is similar to the one in the case of

1-hour forecast, as shown in Table 1, for two references. References report a maximum

absolute mean error of 4 %.

4.3. Modular networks for 24-hours forecast:

This approach uses two or more modular, interconnected MLPs, which generate a24 hours forecast. Each module is responsible for the load forecast for a certain moment

of the day, using certain input variables. An example of such a modular approach is the 3

generations forecaster model described in references. The input values for the first andlast generations are described in Tables 2. The last generation architecture consists of two

ANNs with 24 outputs each. The first ANN produces a basic forecast; the second ANNgenerates a set of 24 correction values, which added to the load profile values of the

previous day determine the load profile forecast for the next day. These values and thebasic forecast produced by the first ANN are processed by a RLS (Recursive Least

Squares) Combiner to produce the final forecasted load profile. The maximum mean

error reported in reference is 2.99 %.

Another modular forecasting model was described in which uses 4 modules, with

the following functionality. Module I, or the Basic ANN generates a 24 hours loadforecast using hourly values for the load and the temperature in the previous day , a

forecast for the temperature in the current day and a special code for the day of week. The

second module is used to predict the peak and valley load values used then in the thirdmodule as input data to produce a second 24 hours forecast for the current day. Thisforecast and the one produced by the first module are processed inside Module IV (the

Adaptive Combiner) to produce the final forecast. No error values are reported in this

reference.

4.4. Self-organizing architectures:


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A special case of load forecasting using ANN is the one described in reference ,

which uses a self-organizing Kohonen network to produce a basic forecast. The SOFM

comprises a grid of 20 * 20 = 400 class neurons with 48 hourly load values: 2 loadprofiles for the previous day and the forecasting day respectively. The basic forecast

produced by the SOFM is updated using a fuzzy model to take into consideration weather

conditions. The maximum absolute mean error reported is less then 1%.

5. Medium-term load forecasting:

Almost all short-term forecasting techniques use as independent variables certainweather condition information such as temperature, humidity or wind speed. As for the

medium-term load forecasts, it is almost impossible to take into consideration such

influence factors, as the forecasting period is much wider, and detailed and accurateweather predictions might not be available. As a consequence, in reference the author has

analyzed the possibility to take into consideration some macroeconomic indicators (MEc)

such as the Consumer Price Index (CPI) or the Inflation Rate, the Average Salary Earning

(ASE) and the Currency Exchange Rate (CER), available from official organisms.

One major component of an electricity market is the bulk market, which is a

medium term market, where trading arrangements between generators and suppliers arebased on bilateral contracts. Typically, a bilateral contract is concluded between the two

parts for a period of one year. The New Electricity Trading Arrangements (NETA),

already in place in UK, offer forward and futures contracts which can shorten this periodto few months, weeks, days, or even hours. If we consider the long-term alternative,

contracts set fixed energy quantities, which generators sell to suppliers at fixed prices.

Even for the NETA whose prices vary on the market the offer of a new contract is thesame thing as concluding a usual bilateral contract. Thus, electricity quantities are

expressed as mean hourly (or half hourly) values for a number of days. For example, onecan use a classification with 4 types of day for each month, or 48 characteristic days inone year. These 4 types of day are: [Mo + Fr], [Tu + We + Th], [Sa] and [Su]. The

medium-term forecasting model uses the selforganization process in Kohonen networks

or SOFMs. Twelve SOFMs have been used, one for each month of the year. Each SOFM

has four class-neurons, corresponding to the four characteristic days in a month, and 50input neurons for load and MEc data. The input layer has the following structure (see

Figure 5): neurons 1-24 (the load profile with 24 hourly values for day D, year Y-1);

neuron 25 (the value of the MEc indicator for day D, year Y-1); neurons 26-49 (the loadprofile with 24 hourly values for day D, year Y); and neuron 50 (the value of the MEc

indicator for day D, year Y). The weights of the connections between each class-unit and

the input units describe the prototype associated to that class. The learning algorithm usedwith the SOFM is the winner-take-all strategy combined with a fuzzy procedure. This

approach avoids the sensitivity of the traditional algorithm with respect to the order the

learning patterns are presented to the network. In fact, it is a sort of batch learning

strategy.


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6. Experience with short and medium-term load forecasting in the Romanian

system:

The Romanian National Energy Regulating Authority (ANRE) has developed a

portfolio of decisions and recommendations and put into place the energy market in

Romania. Today, the Romanian electricity market offers regulated access to about 45eligible consumers. In order to become eligible for electricity supply, and thereafter to

choose the supplier, the electricity consumption of a company must be greater than 40

GWh. Though several new suppliers have recently obtained the official agreement fromANRE, the main electricity supplier in the Romanian system is Electrica S.A. and its

subsidiaries.

6.1. Experience with short-term load forecasting:

The ANN forecasting model was developed using data from several electricity

subsidiaries in Romania. The basic model is a MLP whose architecture is depicted in Fig.

6. Based on a correlation analysis we have chosen to use the following input variables:

load data: (a) hourly load values: P(h k) k= 1, , 5;(b) daily load values: P(h 24 k) k = 0, 1, 2;

(c) weekly load values:P(h 168 k) k = 0,

1, 2

weather data: (a) maximum daily temperature: Tmax(d);

(b) minimum daily temperature: Tmin(d);

(c) mean daily temperature: Tmean(d)

day of week code: (a) D = 0.5 weekend days;(b) D = 1.0 week days.


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hour code: H=00001; H=00010; H=00011; H=11000;

Compared to the MLP architectures described in section 4, the architecture from

Figure 6 is a 1-hour forecast type network.

Some results obtained using this model will be described using load data provided

by one Electrical subsidiary.Table 3 shows the correlation coefficients for this subsidiary.

The values are common values for the rest of subsidiaries. These values show a relativelyweak cross correlation of the load and a even weaker correlation of the load and the

maximum temperature. As to the load cross correlation, we expected a greater value of

the correlation coefficient for the daily and weekly historical data, as compared to therecorded values (0.764 and 0.778).

These values are in accordance with the behavior of the load illustrated by the

load profiles in Figure 7. Figures 7 (a) and 7 (b) show several load profiles for week days

and weekend days respectively. As one can see load profiles differ significantly for the

two day types (week or weekend days). Also, for the same type of day there are stilldifferences between load profiles, which is not a desirable behavior. On the other hand,

Figure 7 (c) shows the load profiles for 5 consecutive Wednesdays. As one can see, withfew exceptions, the load has an almost periodical behavior.

Due to the activation function used in the output layer, which takes values between 0and1, the load values had to be pre scaled to the same interval. On the other hand, the

learning data set was prepared using a scaling interval between 0.15 and 0.85. The second

scaling procedure was applied for two reasons: (a) to avoid saturation of sigmoidfunctions in the neighborhood of 0 and 1, and (b) to allow forecasted load to take values

greater than the maximum historical values (which form the learning data set). The tests

were carried out for a week in the mid December 1999. The results are depicted in Figure


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8 and Table 4. This forecasting model, together with a special interface was implemented

as a software tool, which is applied today in 9 electricity subsidiaries in Romania

Figure 7 Load profiles for: (a) 3 week days (Wednesday, Thursday andFriday);(b) 2 weekend days (Saturday and Sunday); (c) 5 consecutive Wednesdays.


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Figure 8 Real and forecasted load profiles for one week in the mid December1999

6.2. Experience with Medium-term load forecasting model:

The fuzzy SOFMs model described in section 5 has been used to performmedium-term load forecasts for the load profiles of the 48 characteristic days used in

bilateral contracts between generators and suppliers. The database consists of hourly load

profiles for the contour of an Electrica SA subsidiary and values for the MEc indicatorsfrom 1st April 1998 to 13th April 2000.

The learning data set was built using the input structure described in the previous section

and load and Mec data between 1st April 1998 and December 1999.The data for year

2000 will be used to test the SOFMs performances after training.


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For the learning stage of the SOFMs the patterns were arranged using the

following model: for each month M the learning data set contains data from the whole

month Mand other two weeks, one week from month M-1, and one week from monthM+1. This model aims to take into consideration the influence of the load and MEc data

in a month on the load level in the next month. The load profiles for each day of the week

have been chosen from this period, and regrouped according to the four characteristicdays. They resulted in six load profiles for each day of the week, that is 42 learning

patterns for each month.

These patterns were then used to train 12 SOFMs for each month of the year.

After the learning stage the forecasting data set was built as follows. Each day of the

forecasting month generates an input pattern, whose structure is: neurons 1-24 (the load

profile with 24 hourly values for day D, year 1999); neuron 25 (the value of the MEcindicator for day D, year 1999); and neuron 50 (the forecasted value of the MEc indicator

for day D, year 2000). This pattern is presented to the SOFM network and the winning

class-neuron is established. The winning class-neuron is determined on the basis of the

distances between the input pattern and the prototypes of each class neuron, using onlyinputs 1-25 and 50. The prototype associated to the input neurons 26-49 of the winning

class-neuron will be considered as the forecasted load profile for that day.

7. Conclusion:

Short and medium term load forecasting are important present day problems forboth power system and electricity market operation. For the short term load forecasting

the results in the literature and the authors experience recommend ANNs as feasible

solutions. As to the medium term load forecasting, our experience found that self organization and Kohonen networks could be a valuable and reliable approach. This

neural network based forecasting of electric markets or say, electric stations can fetch usmany advantages like, saving the time, man power, sudden break downs, there byincreasing the efficiency of the stations to provide efficient power supply, and power

supply with added advantages.

Documents

Neural Networks Based Forecasting of Electricity Markets