Ht = Average height in meters of the reservoir in the time period t i, j = Index of the characteristic inflow volume in the time period t and t+1 IDt = Irrigation demand in Mm3 in the time period t. Reservoir capacity at MDDL St = Storage in Mm3 at the beginning of time period t.
INTRODUCTION
PURPOSE OF THE STUDY
Generally, dynamic programming (DP), linear programming (LP), nonlinear programming (NLP), and simulation techniques are used to derive the optimal operating policy. Recent research has shown that these new techniques have the potential to develop improved reservoir operation policies.
METHOD OF INVESTIGATION
The deterministic PD is solved for different numbers of reservoir characteristic deposits. Finally, the effect of considering different reservoir characteristic storage numbers on the performance of SDP models is analyzed through reservoir simulation.
LITERATURE REVIEW
INTRODUCTION
PREVIOUS WORKS ON RESERVOIR OPERATION
- INTRODUCTION
- LINEAR PROGRAMMING (LP) MODELS .1 DETERMINISTIC LP MODELS
- STOCHASTIC LP MODELS
- NONLINEAR PROGRAMMING (NLP) MODEL
- DYNAMIC PROGRAMMING (DP) MODELS .1 DYNAMIC PROGRAMMING (DP)
- DETERMINISTIC DYNAMIC PROGRAMMING (DP) MODELS Young (1967) was the first to apply the deterministic dynamic programming
- STOCHASTIC DYNAMIC PROGRAMMING (SDP) MODELS
- MODEL USED AS COMBINATION OF TWO OR MORE METHODS
- ARTIFICIAL NEURAL NETWORK (ANN) MODEL
- GENETIC ALGORITHM (GA) MODEL
Fuzzy rule-based modeling, artificial neural network (ANN) approach, and genetic algorithms (GAs) are some of the recent techniques used in reservoir operation. This review was intended to present conclusions reached by previous state-of-the-art reviews and to provide ideas for closing the gap between theory and practice.
PREVIOUS WORKS ON SYNTHETIC STREAMFLOW GENERATION
- INTRODUCTION
- LITERATURE REVIEW
McLeod and Hipel (1978) based on careful comparisons of the fits of ARMA and fractional Gaussian noise models to long streamflow sequences using the Akaike information criterion (AIC) (Akaike 1978) showed that ARMA models should be preferred . They concluded that the results obtained using ANNs compared well with those obtained using statistical models. 2002) presented a hybrid model based on artificial neural networks for multivariate synthetic flow generation.
CONCLUSION
The ability of a GA to interface directly with a trusted simulation model is a major advantage. ANNs have also been attempted to generate synthetic flow and are reported to compare well with statistical models. The literature review also revealed that the effectiveness of different models varies from problem to problem and that the potential of newer techniques in deriving the optimal operational policy remains to be fully explored for different situations.
However, the effectiveness of the policies resulting from these recent techniques must be assessed through a critical comparison with the policies resulting from several long-standing traditional techniques.
THE RIVER SYSTEM AND THE RESERVOIR
- INTRODUCTION
- THE RIVER SYSTEM
- BASIN DESCRIPTION
- CLIMATE AND RAINFALL
- AVAILABILITY OF STREAMFLOW DATA
- PAGLADIA RESERVOIR
- LOCATION
- GEOLOGY OF THE DAM SITE
- PURPOSES OF THE RESERVOIR
- PRINCIPAL FEATURES OF THE PAGLADIA PROJECT The project is recommended for a full reservoir level (FRL) of EL 87.5 m
- EVAPORATION
- CONCLUSION
The main tributaries of the Pagladia River are (1) the Mutunga, (2) the Nona and (3) the Baralia. The Nona tributary joins the proposed Pagladia reservoir immediately downstream and the Baralia tributary joins further downstream of the reservoir. The area downstream of the proposed dam site is affected by flooding almost every year.
The project is planned to irrigate 54160 ha GCA, on the right bank of the Pagladia River downstream of the dam area, with a net irrigable area of 34630 ha.
PROBLEM FORMULATION
- INTRODUCTION
- PHYSICAL FEATURES OF THE RESERVOIR AND DISTRIBUTORY SYSTEM
- OBJECTIVE FUNCTION AND CONSTRAINTS
- OBJECTIVE FUNCTION
- CONSTRAINTS
- CONCLUSION
Therefore, the demand for each month of the year is the highest demand for irrigation water and water demand for hydropower. Again, the discharge from the reservoir must be such that it does not violate the upper bound (storage capacity at full tank level) and lower bound (dead storage) constraints at the end of each month. Ht = average height (in meters) of the accumulation during the time period t (turbine tail span is EL 74.5 m).
Maximum reservoir storage at the beginning or end of any month = 312.64 Mm3 (= 472.64 Mm3 (storage at MWL) – 160.0 Mm3 (flood control reserve storage)), which is the storage capacity of the reservoir at full reservoir level ( FRL).
SYNTHETIC STREAMFLOW GENERATION
INTRODUCTION
THOMAS-FIERING MODEL
AUTOREGRESSIVE MOVING AVERAGE (ARMA) MODELS
The stochastic component of the current series was obtained by removing the periodic component. The periodic component of the series has been removed by representing it as a Fourier series of the form. To check the suitability of the ARMA (2, 0) model, the residual set Vt generated by the model was then subjected to diagnostic checking using modified Ljung-Box_Pierce (Ljung and Box, 1978) statistic.
Using these values of Φ1 and Φ2, the stochastic part of the streamflow series has been generated using the following recursive equation starting from any month.
ARTIFICIAL NEURAL NETWORK (ANN) APPROACH
- FUNDAMENTALS OF ANN
- TRAINING OF ANN
- CHOOSING THE BEST NETWORK
- ANN BASED MODEL FOR SYNTHETIC STREAMFLOW GENERATION
- DVELOPING THE ANN COMPONENT
- GENERATING SYNTHETIC STREAMFLOW
The number of neurons in the hidden layer of the neural network has been finalized after a track-one error procedure using different combinations of learning rate and momentum factor. Fig.5.8 Reduction of MSE for networks with different numbers of neurons in the hidden layer. But the network with 5 neurons in the hidden layer gives the smallest value of MRE.
Therefore, a network with five neurons in the hidden layer was considered the best network in this study.
COMPARISON OF SYNTHETIC STREAMFLOW GENERATED BY DIFFERENT MODELS
The average of the synthetic series generated by the ANN-based model is 82.2 Mm3, compared to the observed average of 78.5 Mm3. On the other hand, the average of the synthetic series generated by the Thomas fiering model and the ARMA (2,0) model is 87.3 Mm3 and 86.3 Mm3, respectively. The standard deviation of the synthetic series generated by the ANN-based model, the Thomas-Fiering model and the ARMA (2,0) model are 99.03 Mm3, 61.1 Mm3 and 108.0 Mm3, respectively, compared to standard deviation of 96.2 Mm3 of the observed streamflow series.
Among all the synthetic streamflow series, the skewness coefficient of the synthetic series generated by the ANN-based model is found to be closest to that of the observed streamflow series.
CONCLUSION
Mean, standard deviation, and slope coefficient of 100-year synthetic monthly streamflow series with different models and 40-year observed monthly streamflow series.
RESERVOIR OPERATION MODEL USING DETERMINISTIC DYNAMIC PROGRAMMING
- INTRODUCTION
- MODEL FORMULATION USING DETERMINISTIC DYNAMIC PROGRAMMING
- MODEL FORMULATION
- DISCRETIZATION OF STORAGE
- INPUT DATA
- MODEL RESULTS
- MULTIPLE LINEAR REGRESSION MODEL
- PERFORMANCE EVALUTATION OF DPR MODELS
- ARTIFICIAL NEURAL NETWORK (ANN) MODEL
- TRAINING AND TESTING OF ANN .1 TRAINING OF ANN
- PERFORMANCE EVALUTATION OF DPN MODELS
- CONCLUSION
Three different discretizations of the conservative storage are used in the deterministic dynamic programming model. The number of neurons in the hidden layer of the neural network was finally determined after performing a trail-and-error procedure using different combinations of learning rate and momentum factor. The MSE and MRE values of the network with four neurons in the hidden layer are close to those of the network with ten neurons in the hidden layer.
However, the MSE and MRE values for the network with 4 neurons in the hidden layer are also small and close to those of the network with 10 neurons in the hidden layer.
RESERVOIR OPERATION MODEL USING STOCHASTIC DYNAMIC PROGRAMMING
INTRODUCTION
MODEL FORMULATION USING STOCHASTIC DYNAMIC PROGRAMMING (SDP)
- ASSUMPTIONS
- STATE VARIABLES
- DISCRETIZATION
- TRANSITION PROBABILITY MATRIX
- STATE TRANSFORMATION
- SDP RECURSIVE EQUATION
- TERMINATION CRITERIA
In the reservoir operating model in this study, the reservoir release is a function of initial storage of the reservoir and current month inflow to the reservoir. The first order Markov chain has the property that the value Xt of the process at time t depends only on its value. The reservoir storage state transformation is governed by the mass balance (continuity equation) as given in chapter 4.
The recursive equation 7.4 is solved subject to the following constraints as discussed in Chapter 4. Reservoir Continuity Constraint:.
Since the recursive equations are solved for each period in successive years, the policy in each individual period t will be repeated in each subsequent year after several years. When this condition is met and when the expected annual performance is ftn+T. k,i)- is constant for all states k, i and for all periods t (the total period in a year is T) in one year it is considered that the policy reaches a stable state.
SDP MODEL APPLICATION
- DISCRETIZATION OF STATE VARIABLES .1 DISCRETIZATION OF STORAGE
- DISCRETIZATION OF INFLOW
- TRANSITION PROBABILITY MATRIX (TPM)
However, in this study, 20, 30 and 40 characteristic stocks have been considered for the conservative stocks of the reservoir in an attempt to find a good operating policy for Pagladia's multifunctional reservoir. The SDP models with 20, 30, and 40 numbers of characteristic bearings are called SDP1, SDP2, and SDP3, respectively, in this study. The transition probability of inflow of a certain class interval (Table 7.2) in a certain time period is estimated by counting how many times the next period inflow interval (j) followed the current period inflow interval (i).
This count is performed for all the next period lead-in intervals (all j's) for a particular current period lead-in interval (i) and all the frequencies are summed to have the total number of occurrences.
PERFORMANCE EVALUTATION OF SDP OPERATING POLICIES
- CRITERIA FOR RESERVOIR OPERATION PERFORMANCE
- SIMULATION AND RESULTS
While the total irrigation deficit is found minimum in the SDP3 model, the number of irrigation deficit months is found minimum in the SDP2 model. It is important to mention that when there is a deficit for irrigation, there is also a deficit for electricity production, which is not shown explicitly in table 7.5. The SDP1 model keeps the reservoir filled maximum number of times than the other two models.
CONCLUSION
GENETIC ALGORITHM MODEL FOR RESERVOIR OPERATION
INTRODUCTION
GENETIC ALGORITHMS (GAs)
- INTRODUCTION
- WORKING PRINCIPLE
- FORMULATION OF GAs
- REPRESENTATION SCHEMES
- FITNESS FUNCTION
- GA OPERATORS
- SELECTION APPROACHES
- CROSSOVER APPROACHES
- MUTATION APPROACHES
Each gene can be represented by a binary string defined in the allowed value range of the variable or by the actual value of the variable. The suitability of a chromosome as a candidate solution to a problem is an expression of the value of the objective function represented by it. The regular roulette wheel selection is then implemented using the decimal part of the expected count as the probability selection.
The parameter fmax is the objective function value of the worst feasible solution in the population; J is the number of constraints.
FORMULATION OF GA FOR RESERVOIR OPERATING POLICY
- FITNESS EVALUATION OF STRINGS
- SENSITIVITY ANALYSIS
- SENSITIVITY TO CROSSOVER AND MUTATION PROBABILITY
- SENSITIVITY TO POPULATION SIZE
However, in this formulation, coordinate values of the extreme endpoints of the release rule function are known. In the GA formulation in this study, for each of the unknown points, we need to set the upper and lower bounds of water availability and release. Usually, the population size is taken as 2 to 4 times the length of the queue (Rao 1996).
In some cases, fitness function was found to deteriorate when population size was increased to more than 3 times the string length.
FINDING OPTIMAL OPERATING POLICY
In this way, optimal operating policies were found using GA1, GA2, GA3 and GA4 models.
PERFORMANCE EVALUTATION OF OPERATING POLICIES DEVELOP BY GA MODELS
- SIMULATION AND RESULTS
From table 8.2 it is observed that the minimum squared deficit for the simulation period was obtained with the operating policy derived from the GA3 model. In terms of power output, the GA3 model is found to be slightly better than the other three GA models. Next to the GA1 model, the GA3 model keeps the tank full for the maximum number of times (72).
However, the GA3 model is found to be better than other GA models with respect to several important performance criteria.
CONCLUSION
Next to GA4 model, it is the GA3 model that wastes less water. The above comparisons revealed that operating policy obtained by all the GA models is competitive. Considering better performance of GA3 model in terms of total squared deficit, total irrigation deficit, number of irrigation deficit month and total power generation, the operation policy derived by GA3 model can be considered as the most effective one among all the operation policies derived by different WILL be diverted. models in this study.
COMPARISION OF RESERVOIR OPERATION MODELS
INTRODUCTION
COMPARISON OF RESERVOIR OPERATION MODELS
All GA models are found to be efficient in terms of the number of deficit months for irrigation. Among all the GA models, the GA3 model gives the minimum number of months of irrigation deficit. In all SDP models the number of irrigation deficit months is almost double that of the GA3 model.
In all DPR and DPN models, the number of months with irrigation shortages is almost four times that of the GA3 model.
