Neural Network Based Optimum Model for Cascaded

Hydro Power Generating System

C.G.S.GunasekaraCeylon Electricity Board

Kandy, Sri Lankacgsgunasekaragyahoo. com

Abstract The objective of this research is to model acascaded hydro power generating reservoir system in order to getthe maximum usage of the stored hydro potential to generateelectricity. In this study, two models have been developed. Firstmodel to schedule the generator loads and the second model to,predict the water levels of the ponds. Then, both models havebeen integrated to dynamically simulate the variation of pondlevels and to explore the feasibility of maximizing generationelectricity under the given circumstances.

In this research a range of historical data available, havebeen used to investigate and to evaluate the correlation betweeninputs and outputs. As this is a multi dimensional, non-linearmulti input/output (MIMO) system, application of ArtificialNeural Network (ANN) technology to model this system isexplored by discovering a working mechanism of the system fromthe examples of past behavior. Then, by coupling the above twoneural network models, developed for generator load schedulingand pond water level monitoring, system was dynamicallysimulated to explore the feasibility of maximum electrical powergeneration, while keeping the pond water levels stable, within thefeasible operating constraints.

Keywords-Cascaded hydro-power system, optimum model,non linear system modeling, Neural networks, predicting andscheduling

I. INTRODUCTION

Optimization of generation of electricity and flow controlin a cascaded multi-reservoir hydro power generating system isa complex task. Due to cascaded operation of the multi-reservoir system and due to complexity of the otherparameters which affects to the characteristics of the system, awell defined methodology is required to operate the systemeconomically. Rainfall is an uncertain and random factor onewhich influences to the characteristics of the system and henceto the operation of the system. The system is made up ofsubsystem with non-linear characteristics such as ponds,reservoirs, turbines generators and the system is multi-dimensional in nature. Input variables have cyclic patterns suchas variation of water levels, variation of daily load pattern andweekly load pattern. During the last decade various studieshave been carried out on non-linear system identification andcontrol, pattern clarification, function approximation,optimization, pattern matching and on associate memories.

Lanka Udawatta *, Sanjeewa Witharana'University of MoratuwaMoratuwa, Sri Lanka

lanka@ieee. org, +sanjeewa@ieee. org

ANN is a technology that is capable of discovering patterns ina set of data if such patterns exist [1] [2]. ANN is a learningsystem that tactically discovers the working mechanism;characteristics of a system from examples of the past behaviors,Thus for a complex multi-dimensional system, for whichexplanatory theories are lacking, but data regarding pastbehaviors is available, ANN is a powerful tool of investigation.The recent interest in the use of artificial neural networks inthis nature of problem has a rapid growth where otherconventional modeling techniques are not successful. Inaddition to function approximation and regression it has otheruseful capabilities [11]. However in this research the attentionis focused only of its non-linear function approximationcapability as a learning system. The purpose of this study istwo fold: Predicting reservoir water levels and schedulinggenerator loads are focused. Further more, scheduling ofgenerator loads are carried out by considering the water levelsof reservoirs and the machine availability. Modeling ofreservoir levels is analyzed by taking the variation of waterlevels due to the power generation and rainfall. Due to thenonlinear inherent properties of the total problem, both of thesystem modeling was done by using two feed forward neuralnetworks. This paper is devoted for developing a model tosimulate the behavior the system using ANN [14].

In this study real data is taken from the Laxapana cascadedhydro power generating system for simulating the proposedmethodology and as a case study. Laxapana Hydro powergenerating scheme is a cascaded system that, operates underthree (3) levels as shown in Fig 1. It consists of sub systemswith non linear characteristics as shown in Table VI. The maintwo branches of the cascade starts at the upper most reservoirswhich deliver water to the Wimalasurendra (PHI) and Canyon(PH2) power houses respectively; the first level ofthe cascadedsystem. The water discharge through PHI and PH2 machines isbeing collected at Norton (pond 1) and Canyon (pond 2) and isreleased for electricity generation to the second level of thecascaded system PH3 and PH4 power houses respectively. Theabove two main branches join at Laxapana forming pond 3,where the discharge of PH3 and PH4 are being collected andfed to the lower most power house and the third level of thecascaded system. The total installed capacity of powergenerating scheme is 325 MWs.

1-4244-0555-6/06/$20.00 (©2006 IEEE ICIA 2006Page 51

k k

a k '(bk+ Ewij P)hZE W kh(b, w, P ))i J. ~~~~~~~~~~(2)

i Jj,k denotes number of input ,hidden layer and output layerunits. Following equation gives general form of a multi layerneural network.

ai ibk+E l j kE Wjk Pj Pk +

j kE IJkl PkPk PI+***)

(3)

(1),(2),(3) denotes the layer numbers and others are usualnotations.

III. TRAINING THE NN

A. Training model IFollowing Fig 2 shows the inputs/outputs selected for

developing the model 1 for scheduling the generator loads.

Water level(at time t)

Reservoir 1-Castlereigh, Reservoir 2-Moussakele, Pondl, PH1-Norton,Pond2, PH2-Canyon, PH3-Old Laxapana, PH4-New Laxapana, Pond3 -

Laxapana, PH5- Polpitiya

Figure 1. Laxapana Cascaded Hydro power Generating system

II. DETERMINATION OF NN ARCHITECTURE

A. Overview ofmodelingIn this research this problem is considered as a system

identification problem, with non-linear multi-dimensionalinputs/outputs. To simplify the modeling process, system isdecomposed into two models; (1) for predicting the individualgenerator loads for existing pond water levels and other inputsas shown in Fig 2, (2) for predicting the variation ofpond waterlevels for a given set of generator loads and other existinginputs as shown in Fig 3.

B. General FrameworkforANN modelA multi-layer feed forward network consists of input layer,

out put layer and several hidden layers. The input layer passestheir output to the first hidden layer or (with skip layerconnection) to directly to output layer. Each of the hidden layerunits takes a weighted sum of its inputs, adds a constant (thebias) and calculates a fixed function (Dh of the result. This isthen passed to the hidden units in the next layer or to the output unit(s).The fixed function is given by

Total power W I(at time /) lInput laver

Figure 2. General architecture of model 1

Watei leve(at time I)

Geerat Loads -

(at time ) lnput layNwf(z)= exp (z)/(1+ exp (- z))

The output units apply a threshold function Oo to the weightedsum of their inputs plus their bias. If the input are Pi andoutputs are ak for one hidden layer,

Figure 3. Inputs / outputs for water level predicting model 2

Page 52

(1)

TABLE I. ARCHITECTURE VS PERFORMANCE

NNarchitecture

27-25-15-1327-24-16-1327-25-16-1330=25-20-1330-26-20-1330-27-20-13

Training2.763.162.419.74.35..6

Error (SSE)

Testing

8.798.879.042.52.44.3

8

Validation7.677.136.162.02.64.0

Number of hidden layers and the number of neuron in eachlayer was determined by trial and error. Initially, on training thenetworks the learning rate (q) was set to 0.01. Early stoppingmethod [2] was used to stop the training and 'trainbr' algorithmwas used as the training algorithm [13]. A data set consisting of1000 records were selected for training the NN. The best NNarchitecture was determined from results tabulated in Table 1.The lowest training, validation and testing errors obtained are(i.e. Training error= 4.3, Testing error=2.4 , Validation error=2.6 SSE ) According to the results '30-26-20-13' gives the bestperformance for il=0.01 which is the default Learning rate ofMatlab NN tool box [3] [9].

B. Effect oflearning rateLearning rate plays a vital role in back propagation training,

the weight updating characteristics is given by the 'delta rule'as given below by the equation (4),

A w 7 (a t i() P 4)

6Fzz_-/

) Exo 4F

2F

0 0.2 0.4Learning rate (eta)

Figure 4. Performance for different learning rates

IV. SIMULATION RESULTS

A. Model iPerformanceThere are 13 generator units in the system. In order to

reduce the number of outputs and to improve the accuracy,

loads of the Old Laxapana (PH3) generator out puts 5 to 9,consisting of total capacity of 50 MW have been summed upand taken as one output for evaluating the performance. Theresults presented in Table II shows the correlation betweenactual and simulated outputs obtained by feeding the test data.

where q is the learning rate, a, and t, are the actual and targetvalues correspond to the kth component of the ith trainingvector. Awij is the change in the weight to the correspondssimulated output a,.

Fig 4 shows the results obtained by training the '30-26-20-13'model for different learning rates. When the = 0.18, SSEreaches a minimum giving the best performance.

C. Training model 2

Then, the same procedure was adopted as earlier fortraining the model 2. In this case pond water level variation is a

continued non-linear variation where as in the previous modelthe generator load variations are discrete and non-linear.Hence, early stopping method with the 'trainbr' algorithm was

used to train the network with the default learning rate, of q =

0.01. The training, validation testing errors were reasonablylow. (Training SSE = 0.610544, Test SSE = 1.49636,Validation SSE = 0.0814324) for Canyon pond model.Therefore, need of changing did not arise in this case.

B. Model 2 performanceA set of test data was fed into each of the pond models and

performance was evaluated. The regression analysis results inTable III shows the correlation between actual water levelvariation and the simulated variation

TABLE II. PERFORMANCE OF MODEL 1

Generatorno

23456789

Pondmodel

CanyonNorton

Laxapana

Corelation Coefficient R

0.9880.99 10..9900.9940.8060.9100.8150.8360.879

TABLE III. PERFORMANCE OF MODEL 2

Corelation Coefficient

0.9870.9970.973

Page 53

Training ...........

ValidationTesting ----

.4.

-

C. Maximizing Power GenerationTo examine the feasibility of increasing electrical power

generation we integrated the NN model 1 and 2 as shown inFig 5 Initial water levels of the ponds with other input fed intothe model 1. Then, outputs of model 1 (generator loads) werefed into model 2. This process was carried out iteratively for aspecified time period of 120 hours (240 number of records)with a sampling period of 30 minutes. The dynamic simulationresults obtained is shown in Fig 6. After that, Pt where Li is theindividual loads

13 (5)pt EL(L5k

k =

was increased by several steps while keeping all other inputssame and the system behavior was dynamically simulatedusing the integrated model. Corresponding water levelvariations of the ponds were recorded. Fig 7, and 8 shows thewater level variations corresponding to 16% increase and 2000 increase respectively. 16% increase is the maximumpossible increase for the considered duration while keepingpond water levels stable. (within minimum operating levelMOL and spill level)

Figure 5 Intergrated model for dynamic simulation

V DISCUSSIONIt can be seen from Fig 7, that when the value of Pt (i.e.

total load is increased by 20 00 Canyon pond level reaches tothe spill level and becomes unstable. So that water level ofCanyon pond has become the limiting factor for powergeneration during this period. Hence, the maximum feasiblegeneration increase is by 16 00 while keeping the ponds stable.It is shown in Fig 8.

When the total Load Pt is increased by a fraction, allindividual generator loads contributes to that increase. Hence,for a known load pattern we can find out the best possibleloading schedule for individual generator units which wouldhelp operate the system economically.

The percentage excess energy AE, generated due to 16%increase is given by the area between lowest and middlecurves in Fig 9 , which is equal to,

A E~.= ((Z pm (t)T - , p°(t)TT )I p (t)T)x100 (6)

where, pmax - power generated with maximum increase,

Po - power generated according to past performances

ZEMa - excess energy generated due to increased generationT - Sampling period (30 minutes)

Obtaining the normal and power corresponding to increasedgeneration from the excel sheet, 890 x 0.5 x 50 and 767 xO.5 x50 respectively.

Percentage energy increase,

SE = [(890 - 767) / 767] x 100 = 16.0 %

From the above result it can be noted that, when the value of Ptis increased, the actual generated energy also increases by thesame percentage. In this case the maximum possible increase is16 %. Amount of excess energy generated is given by,

AEma = E max (t).T - p 0 (t) (7)

Substituting the values from the excel data sheet for the 120hour period considered,

AEMax 890 - 767 = 123 x 0.5 x 50 MWhrs= 3075 MWhrs

Now, if we consider the average value of a thermal unit cost,using the typical values given in the Table IV obtained fromsystem control center (SCC) of Ceylon Electricity Board(CEB), which depends on various thermal and hydro unitcommitment constraints. Similarly unit cost of a hydro unitalso varies in a wide range depending on the water valuevariation over the time under different conditions as shown inTable 5. (arrow mark denotes whether the storage capacity ison the increase or decrease )

Hence, depending on the relative values of thermal andhydro unit costs the economic benefit varies. Consider thesituation given in the second raw of Table V, where the

TABLE IV. TYPICAL THERMAL UNIT COSTS

Plant typeCost

U$cts/KWh

Small GT GT7 Combine cycle Barge/Asea Diesel

22 17 9.75 6.35 6.50

Page 54

TABLE V. TYPICAL WATER VALUES

Castlereigh

Storage

22 t94 t95 1

Moussakele

ValueUScts/ StoraKWh

10.01 23.87.15 9611.58 92

AvgWatervalue

Lge U$cts/KWh

J1tI~

10.607.4411.59

water levels are in the rise and the storage capacities ofCastlereigh and Moussakele are 9400 and 96 respectively.Then, assuming a average thermal unit cost of U$cts 12.00considering the typical values given in Table V the energy

saving would be,

=(3075xlO00)KWHrs x (12.00-7.44) U$cts/ KWHr= 140,220 U$ / 120 hrs

Saving,28,044 U$ / day (for the period considered)

VI CONCLUSION

[3] Using Matlab ,version 6 ,The Mathwork Inc. [2000][4] Stuart Russell , Peter Norvig , Artificial Intelligence A Modern

Approach, pearson Inc [1995][5] Daniel E Rivera, System Identification for Process Application, Arizona

State University [1997]M. Young, The Techincal Writers Handbook.Mill Valley, CA: University Science, 1989.

[6] Ljung, L., Sjoberg, J., Hjalmarson ,H.,: "On neural networkmodel Structures in system identification " in Brittani, S.,Picci,G.,(Eds) Identification ,Adaptation, Learning ,NATO ASI SeriesSpringer, 1996.

[7] Hamdy A Taha , Operations Reserch an Introduction ,Parentice Hall[2003] J. Jones. (1991, May 10). Networks (2nd ed.)

[8] Horn R.A. and R Johnson, Matrix Analysis, Cambridge University[1985].

[9] Howard Demuth ,Mark Beale Neural Network Toolbox for use withMatlab .[1994-2004] Mathwork Inc.

[10] James A Anderson ,An Introduction to Neural Network,Massauchest Institute ofTechnology [1985]

[11] Hornik K Stinchcombe .M. White.H.'Multilayer feedforward networksare universal approximators'.Neural Networks, 2(1989),358-366

[12] CEB System Control Center ,Sri Lanka (2003) Operational Data ofLaxapana complex.

[13] Hagan M.T.Menhaj.M.'Training feedforward networks with theMarquardt algorithm' IEEE Trans On neural networks 5(1994),989-993

[14] Qin.S.Z.Su.H.T.McAvoy.T.J.:'Comparison of four neural net learningmethods for dynamic system identification '.IEEE Trans on neuralnetwork s 2(1992),52-262.

From the simulation results given from the integratedmodel it can be seen that 16 increase in power generationcould be achieved while keeping the ponds stable under thesame input conditions for the period considered. Whenevaluating the economical benefit, the relative unit costs ofthermal and hydro have to be considered which depend on unitcommitment constraints and water value respectively. Thismodel optimizes the usage of water by generating themaximum possible electrical power, while keeping the waterlevels of the three ponds stable. During a period where theupper main two reservoirs are spilling or about to spill,extracting the maximum possible usage of water by generatingthe highest possible electrical power would be an obviouseconomical benefit irrespective of the thermal unit cost or theprevailing water value. In other situations the economicalbenefit depends on the relative prevailing water value and thethermal unit cost which involves with the unit commitmentconstraints. Typical values have been used in the abovecalculation. According to that in a situation where the reservoirlevels are at 95 the saving is U$ 28,044 /day. When thewater levels increase further and as the water value goes downthe economical benefit due to increased generation would behigher.

REFERENCES

Norton Pond

QLcn

0

a)-o

au)

-a

a)

U-

°6 Canyon Pond

4L \or?.. _, ., .,,,

0 100 20020 Laxapana Pond

%: .w.0 ---. actual output (past performance)

dynamic simulation-100 100 200

Time ( no of records)

Figure 6. Dynamic simulation results of intergrated model

[1] Simpson Hakin, Neural Network, A comprehensive Foundation,Pearson Education Inc [1999] W.-K. Chen, Linear Networksand Systems (Book style). Belmont, CA: Wadsworth, 1993, pp. 123-135.

[2] James A Freeman / David M. Skapura, Neural Network AlgorithmsApplications and programming Techniques, Pearson Education Inc(1991

Page 55

Duration in Value2005 U$cts/

KWh

Jun 11.20Nov 7.72Dec 11.80

TABLE VI. LAXAPANA CASCADED SYSTEM CHARACTERISTICS

Norton Pond

IC)

U')0

0:

L-r

a)

3:

Time ( no of records )Figure 9. Energy curves due to increased generation

actual output (past performance).-- 15 increase------ 20 increase

100Time ( no of records)

Figure 7. Water level variation due to 20 % generation increase

Norton Pond

I--

'R

Laxapana Pond

100Time ( no of records )

Figure 8. Water level variation due to 16% generationincrease

Page 56

Power Capacity No of Turbine Flow RequirementHouse Gen Type m3/MW

unitsPHi 50 2 Francies 20PH2 60 2 Francies 23PH3 50 5 Pelton 10PH4 100 2 Pelton 8PH5 75 2 Francies [ 16

U-

C,)

0enau)

-Jau)au

a)