1
1
1
1 Department of Computer Science, University of Łódź
1,2,3
22/26, Matejki Str., Łódź, Poland
2 R&D Centre for Automation and Precise Instruments
11, Piramowicza Str., Łódź, Poland
3 Zamość Energy Corporation S.A.
1, Koźmiana Str., Zamość, Poland
(*) tel. +48 42 635 5221, fax +48 42 635 5017, e-mail: wbart@uni.lodz.pl
ABSTRACT: In the paper t he problem of the application of neural predictors for Short-Term Load Forecasting (STLF) for energy transactions planning in utility is presented.
Several aspects of this topic are discussed, including identification of different load patterns for holidays and customer profiles, estimation of prediction intervals and optimal size of the order, according to the financial conditions on the market .
Keywords: Short-term load forecasting, neural networks, energy market.
I. INTRODUCTION
Deregulation of the power sector in Poland and growth of the energy market implies necessity of the energy demand forecasting. Changes of the organizational conditions, especially development of local energy markets, and introduction of the power exchange and balancing market will increase the importance of the Short-term Load Forecasting
(STLF) in the distribution company.
In recent years a number of methods for energy demand forecasting in power systems was developed and described in the literature. The review of the various STLF techniques can be found among others in [1][13][16][17]. One of the standard tools for these purposes are currently the nonlinear statistical models. Among them good results have been achieved using artificial neural networks [2-3][5-7].
Neural network applications in STLF and other forecasting problems are in most cases concentrated on the single point predictions. Their performance is typically assessed on the basis of technical considerations (statistical tests of fitting error), without the discussion of the impact of the errors on the uncertainty of the decision processes associated with the obtained forecasts.
In this paper also topics associated with application of a neural network predictors for short-term energy transactions planning in power distribution company are discussed.
Because of the energy market regulations and prices resulted from the participation of the company in the exchange and balancing markets, the optimal size of the order can substantially differ from predicted expected value of the conditional target distribution of the energy demand. It means that the forecasting models based on statistical mean squared error evaluate inappropriate aspects of this problem. We investigate two approaches for relating neural STLF systems and decision analysis models.
II. DEMAND FORECASTING FOR ENERGY
TRANSACTION PLANNING
A. STLF with MLP-heuristic hybrid model
The short-term energy load forecasting in Polish utilities is associated with an energy transaction planning on Day Ahead
Market (DAM) on Polish Power Exchange, and participation in Balancing Market (BM) - nation wide market for handling imbalances between the supply and demand of the energy.
According to the market regulations the distribution company should prepare for a given day k the timetable of energy purchases for all 24 hours. The deadline for declaration of the orders to the market operator is 10 a.m. on a previous k1 day.
Taking into account, that the plan of transactions must be prepared earlier, based on information from at least a day k -2, this process requires two-day ahead hourly energy demand forecasts
After preliminary analysis as the basis for further examination following model of two-day ahead energy demand prediction was chosen [2][5]:
ED k
( t ) = f
ED ( t ) k − 2
,
( ED ( t ) k − 7
,
ED ( t
ED ( t − 2 ) k − 2
,
+ 1 ) k − 2
, TMIN k
,
ED
TMAX
( t k
,
− 1 ) k − 2
, d
1 k
,..., d
6 k
)
(1) where
ED k
( t )
- energy demand at hour t and day k , TMIN k
,
TMAX k
- temperatures for day k , d
1 t
d
6 t
- type of the week-day coding variables.
Forecasting model consisted of 24 equations, given by (1) (for each hour). The equations were modeled using MLP
(Multilayered Perceptron) neural networks, all with one hidden layer and structure {13-10-1} (13 units in input layer,
10 in hidden layer and 1 output unit).

Model (1) in the later stage was used in prediction of the load for typical days, excluding national and religious holidays, like Easter, May 3, November 1 and 11, Christmas, etc.
Holidays and days following immediately after holiday (in the paper called special days) show different behavior of the load pattern. For these special days the forecasting model was slightly modified. It is given by the equation (2):
ED k
( t ) =
ED ( t ) k − 2
, f ( ED ( t ) k − 7
,
ED ( t + 1 ) k − 2
,
ED ( t
ED
− 2 )
( mean k − 2
)
, k − 2
ED ( t −
, TMIN
1 ) k − 2
, k
, TMAX k
)
(2) where ED
mean
k
- mean energy demand in k -th day, other descriptions like for (1). All the equations, as in the previous case, has been modeled by separate perceptron networks
(MLP) with one hidden layer and structure {8-6-1} each.
In model (2) for special days, some heuristic adjustments associated with interpretation of input variables and selection of training data were used [5-7][10]:
− Holidays were treated as Sundays, i.e. training and validation sets have included both, Sundays and holidays, and ED ( t ) k − 7 means the last Sunday before holiday, and
ED ( t ) k − 2 means the second working day before holiday.
− The days after holiday were treated as Mondays, i.e. training and validation sets have included both,
Mondays, and the days after holiday, and for this group
ED
t
k − 7 means the last Monday before holiday, and
ED ( t ) k − 2 means the last working day before holiday
− The days two-day after holiday were treated as Tuesdays, i.e. training and validation sets have included both,
Tuesdays, and the days two-day after holiday, and
ED ( t ) k − 7
means the last Tuesday before Special day, and
ED
t
k − 2 means the last working day before holiday.
Table I
Forecasting errors for two-day ahead hourly energy demand prediction with MLP-heuristic model [kWh]
MAE MAX
AE
MAPE MAX
APE
MAE MAX
AE
MAPE MAX
APE
1 5734 45024 2.95% 17.85% 13 9404 75128 3.99% 24.94%
2 5982 48629 3.29% 32.23% 14 9011 56653 3.90% 25.36%
3 5363 43410 3.03% 29.18% 15 8640 84081 3.66% 31.43%
4 4802 29749 2.69% 20.46% 16 10066 87559 4.04% 33.81%
5 4744 22744 2.68% 14.49% 17 11546 245102 4.52% 69.33%
6 5689 35994 3.15% 18.28% 18 9501 72582 3.80% 26.28%
7 9643 136834 4.79% 70.38% 19 9888 116248 4.05% 39.67%
8 9186 92392 4.24% 44.14% 20 9851 78784 4.02% 33.16%
9 7884 87711 3.38% 37.06% 21 9061 49750 3.52% 23.23%
10 7819 56593 3.33% 27.40% 22 7943 51960 3.19% 21.23%
11 7960 67791 3.41% 27.41% 23 7202 64635 3.10% 29.79%
12 8492 77793 3.64% 27.11% 24 6073 57685 2.85% 28.78%
Average over all 24 hours 7978 3.55%
Daily energy demand forecasts 118366 1053697 2.21% 15.92%
The forecasting system described above was tested using three and a half years long data set originated from Zamość
Energy Corporation S.A. (ZKE) in Poland, from beginning of
1998 to the end of first half 2001. The testing set contained all days from the above period, including weekends and holidays. Obtained results are presented in Table I. For performance assessment standard statistical error measures have been used: MAE - Mean Absolute Error, MAX AE -
Maximum of Absolute Error, MAPE - Mean Absolute
Percentage Error, MAX APE – Maximum of Absolute
Percentage Error.
Average error MAPE of the prediction equals around 3.5%.
Obtained results are typical for hourly load forecasts with longer time horizons. For comparison purposes the system was tested also against daily energy demand forecasts, calculated from hourly predictions. Results obtained for this case are significantly better. Average error dropped to the
2.2% level, maximal error did not exceed 16%.
B. Identification of the customers with irregular demand cycles
During analysis of the system performance for some periods of time unexpected large errors of the prediction were observed. Further investigations showed possibility of their reduction after elimination from the data loads of the cement plants supplied from the distribution network of the company.
It appeared that for current energy demand level of ZKE irregular production cycles of large, concentrated receives constitute serious error source of the forecasts. For verification of this hypothesis comparative studies were carried out, performed for ZKE load without cement plants.
Results for this case are presented in Table II.
Table II
Forecasting errors for two-day ahead hourly energy demand prediction after excluding loads of the cement plants [kWh]
MAE MAX
AE
MAPE MAX
APE
MAE MAX
AE
MAPE MAX
APE
1 3628 27227 2.25% 18.59% 13 5778 60134 2.78% 35.88%
2 3373 24225 2.23% 19.51% 14 6279 59623 3.00% 34.13%
3 3245 23173 2.22% 19.47% 15 6322 63760 2.96% 34.54%
4 3146 20242 2.18% 17.28% 16 6849 60981 3.16% 35.71%
5 3646 21281 2.56% 19.00% 17 7337 63329 3.26% 23.49%
6 3997 23731 2.68% 21.77% 18 7306 56423 3.27% 23.58%
7 5316 42882 3.05% 29.10% 19 7969 54471 3.54% 31.57%
8 5704 70575 2.93% 41.58% 20 6850 40945 3.01% 28.27%
9 5326 72431 2.62% 40.99% 21 5531 43842 2.37% 20.86%
10 5437 68985 2.61% 37.73% 22 4514 35699 1.96% 15.60%
11 5545 60684 2.68% 35.69% 23 4176 27751 2.03% 13.79%
12 5995 63015 2.85% 37.00% 24 3861 23623 2.15% 15.08%
Average over all 24 hours 5297 2.68%
Daily energy demand forecasts 91569 896664 1.94 % 21.28%

Average error of the hourly energy demand prediction was very significantly reduced to the 2.68% level. Accuracy of the daily energy demand also was improved, but this effect was not so significant. The average error for this case dropped to
1.94%. It is visible that for daily demand forecasts impact of the irregular demand of large customers is weaker. The biggest improvement of the accuracy was achieved for morning peak zone.
C. Exploitation of the proposed system in Zamość Energy
Corporation S.A.
After completing of the laboratory works and final testing of the system ZKE implemented them in a real world on-line environment. After several months of operation the average error of the prediction (including cement plants) was equal around 3.2%. The significant improvement of the result have been achieved through the combination of the forecast form the system with corrections of the experienced operator. This approach allowed reducing the forecasting error to the 2.9% level [10].
III. PREDICTION INTERVALS FOR NEURAL STLF
MODELS
Taking into account decisions, based on the demand forecasts, it is very important to establish confidence bounds for the predicted loads. Prediction intervals (error bars) allow to assess the stability and to reduce uncertainty of the decisions.
Estimation of the prediction intervals requires assumption of the normality of conditional distribution of predicted (target) variable - in our case energy demand, conditioned on the input pattern of the model. Under this condition the
100(1α )% prediction interval is given by: f ( x , w ) ± t 1
N
− α
− k
/ 2 σ y
( x ) (3) where f ( x , w ) denotes output of the model for a given input vector x , and set of the weights w (forecasted expected value of the energy demand), σ 2 y
( x ) means the variance of the output variable around the expected value, and t 1 −
N
α
− k
/ 2 percentile of the t-Student distribution, N – number of training samples and k – number of weights.
The variance of the output distribution σ y
2 ( x ) can be decomposed into two following components:
σ 2 y
= σ 2 w
+ σ 2
ε
(4) where σ 2 w
( x ) denotes the variance of the model, associated with weights uncertainty (due to sampling effects of the training set from general population), and σ
ε
2 the variance of the random error.
Table III
Percentages of load observations inside prediction intervals for selected hours.
Confidence 7 a.m. 12 a.m. 5 p.m. 6 p.m. 8 p.m.
85%
90%
95%
87.20% 89.90% 89.90% 88.36% 83.70%
92.00% 92.90% 93.50% 92.24% 88.70%
95.80% 96.40% 96.10% 95.82% 94,40%
The random error variance σ
ε
2 commonly is estimated as variance of residual factor. There are several methods of assessment of the σ 2 w
( x ) variance, giving good results in
STLF context, e.g. delta method [4][6][8]. In our case the best results have been obtained using bootstrap approach, introduced by Efron and Tibshirani [11] and Heskes [12]:
Generate from the training set n samp
bootstrap samples, and train the neural network for each sample. The model variance, for given input pattern x is estimated using variance of the network output over the different samples
σ 2 w
( x ) = n samp
1
− 1 n i samp
= 1
( f ( x , w ( i ) ) − f ( x , w ) ) 2
(5) where f ( x , w ( i ) ) means output of the model obtained for i-th bootstrap sample, and f ( x , w )
is the mean over each samples: f ( x , w ) =
1 n samp n samp i
= 1 f ( x , w ( i ) )
(6)
The prediction intervals obtained with (3), (4) and (5) were validated using independent set of data. Results for several selected hours are presented in Table III. It contains percentages of load observations inside prediction intervals.
As we can see the obtained results are very close to the theoretical levels of confidence.
IV. THE OPTIMAL SIZE OF THE ORDER
The estimates of the energy demand given by the output of the regression-type models are uncertain. Errors in the forecasts and resulting inappropriate setting by the distribution company of the contracted amount of energy cause the imbalance between the demand and the supply. It is settled by the purchasing or selling of the additional energy on the balancing market. According to the rules of energy market in Poland, the energy transaction planning requires consideration of three following price elements:
− Market price - the price of the energy on the market (r
M
),
− Incremental price - the price of the receiving of the additional energy required for balancing the order with the actual demand. It is paid by the distribution company to the market operator
I
M
,
− Reductive price – the price of the resignation of the receiving energy required for balancing the order, paid by the market operator to distributor r
R
< r
M
.

ED ≥ y
1 − F
ED
( y )
R r
I
r
M
D = y y
D
ED < y
F
ED
( y )
R r
R
r
M
D = y-1
R 0
Fig. 1. Decision tree for marginal analysis of the order
The decision tree for determination of the optimal order size using marginal analysis is shown on Fig. 1. The profit margin resulted from the purchase of additional unit of the energy is equal:
− r
I
− r
M
if the order (forecast) y is equal or lower than the actual energy demand ED . We loose the price of purchase
− of additional unit energy on the market
M
, but we gain the price of purchase of this energy unit on balancing market r
I
, what is required in case of order amount y -1. r
R
− r
M
if the order (forecast) y is higher than the actual energy demand ED . We loose the price of purchase of additional unit energy on the market r
M
, but we gain the reductive price r
R of this unit.
The optimum of the expected profit is given by the order size, for which the expected profit margin ∆ E is approaching 0:
∆ E = ( r
R
− r
M
) F
ED
( y ) + ( r
I
− r
M
)( 1 − F
ED
( y )) = 0 (7) where F
ED
( ⋅ ) denotes the cumulative probability function of the predictive energy demand distribution ED . After simple calculation we determine from (7) an optimal amount of the energy order using following equation
F
ED
y *
r
I r
I
r
M r
R
(8)
The optimum value according to the financial criterion, given by (8) can substantially differ from expected value of the demand provided by the output of the neural network model, trained with sum-of-squares error function. Only if the price ratio on the right side of (8) is equal to 0.5 (it means that the financial risk of the prediction error is the same in plus and in minus) and distribution of the demand is symmetric both results are the same. For relating neural STLF systems and financial decision analysis models two approaches are investigated.
A. Neural-genetic (GANN) model trained with financial cost function
The financial environment can be included into the forecasting process by the replacement of the statistical square error function used during the neural network training stage, by the goal function resulted from underlying decision situation. According to the energy market prices discussed in previous chapter the cost associated with the single transaction for a given order size y can be expressed by: c ( y ) = yr
M
+ max( ED − y , 0 ) r
I
− max( y − ED , 0 ) r
R
(9)
The goal function for training the model can be developed by summing over the training set the cost terms (9) for the neural network outputs f ( x , w ) (1), and training values of the energy demand ED [9][14][15]:
E =
c ( f ( x , w )) (10) where x denotes inputs, and w weights of the network.
Taking into account the possibility of future extension of the model we have decided to train the neural network with genetic optimization scheme, because it is almost independent on complexity of the underlying decision problem. Cost function (10) is inconvenient for gradient neural network learning scheme, because it is nondifferentiable, but it is relatively simple, and it is possible to write appropriate weights changing equations. Further extension of the cost analysis model (e.g. including hedging strategy, hour-ahead energy market, etc.) will require application of the more complex goal functions, for which the gradient approach will not be applicable.
The basic parameters of the genetic algorithm were set as follows:
− population of chromosomes with real coding (set of 100 randomly generated chromosomes in the first step),
− tournament selection,
− one point crossover with a probability of crossing equal
0,8
− irregular mutation with a probability of mutation equal
0,007
− limit of generations from 500 up to 30000 epochs.
B. Correction of the forecasts based on assessment of the model variance
According to (8) estimation of the optimal size of the energy order according to the financial conditions requires determination of the cumulative probability distribution function of the predicted energy demand F
ED
( ⋅ ) . Assuming like for confidence intervals estimation, that distribution of the predicted distribution is also normal with probability density, i.e. ED ~ N ( f ( x , w ), σ y
( x )) from (8) we can obtain: y * = F
N
− 1
( f ( x , w ), σ y
( x ))

 r
I r
I
−
− r
M r
R


(11) or alternatively y * = f ( x , w ) +
y
( x ) F −
N (
1
0 , 1 )

 r
I r
I
−
− r
M r
R


(12) where F − 1 is inverse of the cumulative probability function of the normal distribution. As it is visible from (12) it is possible to obtain the optimal size of the order from the

forecast of energy demand given by neural network model, trained with square error function, by addition of the simple correction resulted from uncertainty of the model (given by its variance), and financial risk of the prediction.
The variance σ 2 y
( x ) can be calculated from (4) and (5), like in case of prediction intervals.
C. Simulations and discussion of the obtained results
At this time the segment of long- and medium- term contracts between the producers and the energy distributors dominates the energy market in Poland, implying rather low volume of transactions on the power exchange. Also the balancing market in Poland is at relatively early stages of its development. The transactions with physical delivery and settlements run since September, last year. The real prices of the energy both in the DAM and balancing market cannot be at this time regarded as representative.
From this reasons presented in this paper methods have been tested using simulated market prices coefficients. As it was mentioned in chapter 2 the optimal size of the order depends on the price ratio on the right side of equation (8). The simulations contained performance analysis for three values of this ratio: C
I
=0,82; C
II
=0,24; C
III
=0,5. The first case represents situation when costs of overestimation of the order volume are much higher then underestimation. The second one concerns the opposite situation. The last coefficient represents situation when costs of both errors are more or less the same.
Results (for several selected hours) of the performance analysis in terms of the financial costs associated with forecasting errors of each discussed method are presented in
Table IV. The used abbreviations: ANN denotes “pure” neural network model, GANN - hybrid neural-genetic model described in part A, ANN_ADJ – neural predictor with financial adjustment described in part B. The data about energy demands and prediction errors came from one of the polish distribution companies. The costs in Table IV were calculated for one year long set of data.
Both discussed methods gave significant savings of the costs of the transactions in first two cases. Simulations showed that the costs associated with the neural prediction adjustment given by (12) are almost for all cases lower that for GANN model. It is not surprising that in case III where costs of the underestimation and overestimation of the energy demand are the same, the best results were achieved by the standard neural network predictor. In this case square error function correctly evaluates the financial aspects of the problem.
Deterioration of the results for ANN_ADJ model is insignificant, but for GANN is very clear.
In conclusion generally ANN_ADJ model is more reliable in our problem then GANN. It is also more flexible regarding to the changes of the prices of the energy on the market. It does not require retraining of the whole model, like in case of
GANN. But for more complex decision problems the simple and elegant solution like the given by (12) may not be applicable.
Table IV
Financial costs of the forecasting errors for selected hours (PLN)
Hour 6 12 17 18 24
ANN 12224 21461 24341 19827 11409
C
I
=0,82 GANN 9998 16996 21774 18309 10991
ANN_ADJ 9029 14007 15080 15252 11213
ANN
C
II
=0,24 GANN
17302
14909
26359
23476
28262
28615
30230
28476
20791
14584
ANN_ADJ 14034 21736 24900 23409 13183
ANN 21167 34340 37799 35856 23020
C
III
=0,5 GANN 22363 37959 48121 44495 24623
ANN_ADJ 21170 34328 37775 35869 23062
V. FINAL REMARKS
In the paper the problem of STLF in local utility is presented.
The presence of different load patterns for various types of days requires usage of several prediction models with special heuristic procedures for selecting the input data. Application of the collection of neural networks allows reducing the average error of the forecasts to the reasonable level.
The problem of uncertainty involved in STLF for relatively medium size utility is discussed. We present the study of confidence intervals calculation for the energy demand predictions.
The conditional expected value of the energy demand approximated by the neural network forecast does not necessarily indicate the optimal size of the order, according to the financial regulations associated with energy markets. Two approaches to the solution of this problem are presented. The first one is based on GANN - hybrid neural-genetic STLF system, trained with the financial cost function. The second approach relies on determining of the sources of uncertainty for classical neural predictor.
VI. REFERENCES
[1] Alfares H.K., Nazeeruddin M., “Electric load forecasting: literature survey and classification of methods”, International Journal of
Systems Science, 2002, vol.33, No.1, pp. 23-34.
[2] Bardzki W., Bartkiewicz W., Gontar Z., Zieliński J.S., “Short-Term
Electrical Load Forecasting in Transformation Period”,
[3]
[4]
[5]
[5]
International ISCC/IFAC Symposium on Neural Computation,
Vienna, Austria, September 1998, pp. 324-328.
Bardzki W., Bartkiewicz W., Gontar Z., Zieliński J.S., “A survey of short-term load forecasting algorithms for transient period”, IX-th
International Conference on Present-Day Problems of Power
Engineering, Gdańsk - Jurata, Poland, June, 1999, vol. 5, pp. 11-18.
Bartkiewicz W., “Confidence intervals prediction for the short-term electrical load neural forecasting models”, Elektrotechnik und
Informationstechnik. 1(117), 2000, pp. 8-12.
Bartkiewicz W, Gontar Z., Zieliński J.S., “Neural-Heuristic approach to short-term load forecasting problems”, II International
ICSC Symposium on Neural Computation, Berlin, Germany, May
2000, pp. 740-744.
Bartkiewicz W., Gontar Z., Zieliński J.S., Bardzki W., “Uncertainty of the short-term load forecasting in utilities”, International Joint
Conference on Neural Networks, Como, Italy, July 2000, vol. VI, pp. 235-240.

[7]
[8]
Bartkiewicz W., Gontar Z., Matusiak B., Zieliński J.S., “Neural network based short-term load forecasting for energy market”,
Seminar “ENERGY MARKET’, Łódź, Poland, November 2001, pp. 3-6.
Bartkiewicz W., “Error bars for short-term load forecasting neural networks models”, X-th International Conference on Present-Day
Problems of Power Engineering, Gdańsk - Jurata, Poland, June
2001, vol. III, pp. 75-82.
Bartkiewicz W., Matusiak B., “Short-term load forecasting for [9] energy markets”, International Conference Neural Networks and
Soft Computing, Zakopane, Poland, June 2002, (in press).
[10] Bartkiewicz W., Gontar Z., Matusiak B., Zieliński J.S.,
Chmielewski M., Szady S., Experiences From Initial Exploitation of the Short Term Energy Demand Forecasting System in Zamość
Energy Corporation S.A, International Conference Modern Electric
Power Systems, Wrocław, Poland, September 2002, (to appear).
[11] Efron B., Tibshirani R., “An introduction to the bootstrap”,
Chapman & Hall/CRC, Boca Raton London New York Washington
D.C, 1993.
[12] Heskes T., “Practical confidence and prediction intervals”,
Advances in Neural Information Processing Systems 9, Mozer M.,
Jordan M., Petsche T. (eds.), MIT Press, 1997, pp. 176-182.
[13] Hippert H.S., Pedreira C.E., Souza R.C., “Neural networks for short-term load forecasting: a review and evaluation”, IEEE
Transactions on Power Systems, vol.16, No.1, 2001, pp. 44-55.
[14] Matusiak B., “Hybrid neural-genetic system for energy transaction planning”, III Conference Colloquia in Artificial Intelligence, Łódź,
Poland, October 2000, pp. 41-49.
[15] Matusiak B., Bartkiewicz W., “Linking neural predictor with decision models. The short-term load forecasting case study”, X-th
International Conference On Present-Day Problems of Power
Engineering, Gdańsk-Jurata, Poland, June 2001, vol. III, pp. 109-
116.
[16] Zieliński J.S., “Artificial Intelligence in load forecasting”, VII-th
International Conference On Present-Day Problems of Power
Engineering, Gdańsk-Jurata, Poland, June 1995, vol. II, pp. 109-
115
[17] Zieliński J.S., Hatziargyriou N.D., Pecas Lopes J.A., “AI in power systems-selected applications”, I Conference Colloquia in Artificial
Intelligence, Łódź, Poland, December 1996, pp. 16-24 and Acta
Universitatis Lodzensis, Folia Informatica , 1/1999, pp. 75-89.
VII BIOGRAPHIES
Witold Bartkiewicz received his M.Sc. in mathematics and Ph.D. in management from the University of Łódź. He is a lecturer in Computer
Science Department at the University of Łódź. Dr Bartkiewicz is the
Member of IEEE.
Zbigniew Gontar received his M.Sc. in computer science and cybernetics and Ph.D. in computer science in economy from the University of Łódź. He is a lecturer in Computer Science Department at the University of Łódź.
Dr Gontar is the Member of IEEE.
Bożena Matusiak received his M.Sc. in computer science and cybernetics and Ph.D. in management from the University of Łódź. She is a lecturer in
Computer Science Department at the University of Łódź.
Jerzy S. Zieliński , M.Sc. 1956; Ph.D. 1964; D.Sc. 1969; all degrees from the Technical University of Łódź. Full Professor, Head of the Department of
Computer Science, University of Łódź, R&D Deputy Manager in the
Research & Development Center for Automation and Precise Instruments,
Consultant in the Zamość Energy Corporation.
Author and co-author: two text-books, four monographs, more then 200
Journal Articles, Discussion Papers, conference Papers. Supervisor of 24 doctoral theses, more than 40 research projects. Current Research Activity:
Artificial Intelligence and Management Information Systems in Power.
Prof. Zieliński is the Senior Member of IEEE.