E-21
Stochastic Operation for multi-purpose reservoir using neuro-fuzzy systems
〇Paulo Chaves・Toshiharu Kojiri・Tomoharu Hori
1. Introduction
A new approach for system optimization, named stochastic fuzzy neural network (SFNN), is proposed. It can be defined as a neuro-fuzzy system stochastically trained to yield a quasi optimal solution. The method intends to overcome some of the problems related to stochastic dynamic programming (SDP) models, such as the required backward calculation scheme. For validation of the proposed method, a real case of storage reservoir optimal operation is considered with inflow discharge as the stochastic variable.
2. Methodology
Figure 1 shows the flowchart of the overall calculation procedure for the SFNN optimization model where inflow values are considered as stochastic variables based on conditional probabilities. According to Figure 1, first the SFNN model is initiated with a set of parameters, which can be randomly created. Then the expected probabilities are calculated based on the given conditional probabilities tables. Having a set of parameters for the neuro-fuzzy system, it is possible to obtain the end-of-period storage level St+1, as St and It-1
values are known. For each stochastic inflow value It,k, we can obtain a release value Rt,k
based on the reservoir mass balance equation.
ANN Parameters t = t + 1
k = k + 1
ANN Model with Input: It-1 & St & Output: St+1 Ek= E(It,k, St, St+1, Rt,k) . Pexp[It,k/It-1]
k = K?
t = T? Eexp= Σ(Ek) : Ft= Ft-1+ Eexp
Final Fuzzy-NN Parameters
GA Operators FT= max?
Validation & Application
NO YES YES YES NO NO
Fuzzification of It-1 based on the same limits of the Cond. Prob. Calculation of Expected Cond. Prob. Pexp[It,k/It-1] based on Fuzzified It-1
Figure 1. Flowchart for calculation of SFNN
This operation is carried out for the whole training period T. If the parameters of the
neuro-fuzzy system are considered to be optimal, giving the maximum or quasi maximum value for the recursive function then the training process can stop.
To deal with the uncertainties related to discretization of inflows in finding the stochastic inflows, we propose the use of conditional probability of fuzzy events. Figure 2 shows how the intervals are divided in both cases, discrete and fuzzy representative interval. XL VL L M H VH XH 1 2 3 4 5 6 7 Inflow Gra d e Linguistic Variables Discrete Intervals Inflow
min 10 30 50 70 90 max Inflow Cumulative Probability (%)
5 20 40 60 80 95100
0 Inflow Cumulative Probability (%)
Figure 2. Discretization of discharge
The multiple purpose characteristic of the system is handled with fuzzy theory for easier comparison of different objectives.
3. Results
After comparing results with other dynamic programming (DP) approaches for the same optimization problem, the SFNN model showed improvements in the final optimization results, Figure 3. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 SDP
TraditionalSDP FuzzyInflow SFNN DDP Max.Expected FNN Max.Expected Optimization Scheme Mi ni mum & St. D eviati o n 0.84 0.85 0.86 0.87 0.88 0.89 0.90 0.91 Final Recurssi ve F un ct ion Val ue St. Deviation Minimum Average