OPTIMAL RESERVOIR OPERATION

POLICY

DETERMINATION FOR UNCERTAINT Y

CONDITIONS

S. A. Choudhari

Department of Mechanical Engineering, JSPM Narhe Technical Campus, Pune, (India).

E-mail: sumant.choudhari@gmail.com

M. A. Kumbhalkar

Department of Civil Engineering, JSPM Narhe Technical Campus, Pune, (India).

E-mail: manoj.kumbhalkar@rediffmail.com

D. V. Bhise

Department of Mechanical Engineering, JSPM Narhe Technical Campus, Pune, (India).

E-mail: dvbhise@gmail.com

M. M. Sardeshmukh

Department of Electronics and Telecommunication Engineering, JSPM Narhe Technical Campus,

Pune, (India).

E-mail: mmsardeshmukh2016@gmail.com

Reception: 30/11/2022 Acceptance: 15/12/2022 Publication: 29/12/2022

Suggested citation:

Choudhari, S. A., Kumbhalkar, M. A., Bhise, D., and Sardeshmukh, M. M. (2022). Optimal reservoir operation

policy determination for uncertainty conditions. 3C Empresa. Investigación y pensamiento crítico, 11(2),

277-295. https://doi.org/10.17993/3cemp.2022.110250.277-295

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ABSTRACT

In recent years, optimising reservoir operations has emerged as a hot topic in the field of water

resources management. Heuristic approaches to reservoir operation that incorporate rule curves and,

to some extent, operator discretion have been the norm in the past. With so many stakeholders

involved in water management, it can be difficult to strike a happy medium between everyone's needs

and wants. The dissertation proposes a method for transforming traditional reservoir operation into

optimal strategies, allowing users to take advantage of the rapid development of computational

techniques.

This research creates and applies a Multi Objective Fuzzy Linear Programming (MOFLP) model to

the monthly operating policies of the stage-I Jayakwadi reservoir located on the Godavari, the largest

river in the Indian state of Maharashtra. In order to formulate the problem, we use two objective

functions—maximizing irrigation releases and maximising power production releases. The constraints

of the study are considered, including turbine release, irrigation demand, reservoir storage capacity,

and continuity of reservoir storage. Utilizing linear membership functions, the objective functions are

fuzzily defined. All other model parameters except for the goals are assumed to be hard and fast rules.

Maximum Happiness Operating Policy (MOFLP) was used to determine the best course of action.

KEYWORDS

Jayakwadi Reservoir, Fuzzy Set Theory, Linear Programming, Irrigation.

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1. INTRODUCTION

The system engineering method for the water resources system employs a schematic analysis of the

numerous alternatives available to policy and decision makers. Each option presents a complex

problem with entangled effects, necessitating not only the consideration of a much larger number of

alternatives but also the analysis of each option in light of its impacts at a number of locations. The

system engineering method offers a flexible platform for constant assessment and re-planning in the

face of unforeseen circumstances. When applied with an understanding of its limitations, this strategy

has the potential to greatly enhance the management of water resource systems. The advent of digital

computers has allowed for the efficient examination of problems for mathematical solutions and the

management of vast amounts of data. Linear programming, dynamic programming, goal

programming, integer programming, simulation techniques, etc. are all examples of system

engineering approaches that find use in the water resources industry. However, there is no one solution

that works for every conceivable problem. The technique selected is determined by factors such as the

system's characteristics, the availability of data, the research's objectives, and the research's

constraints.

There are many potential goals and objectives for the water resources system, so the planner must pick

the best one. The nature of the system necessitates the use of deductive reasoning processes that can

eliminate irrelevant options and reduce thousands of metrics to a more manageable set. The same is

true for water resource development projects, in terms of both planning and management. Regulations

or principles are applied to reservoir management based on the quantity and timing of water that must

be stored and released. The following are some of the most widely accepted reservoir operation

principles for flood control and conservational uses in the context of single purpose, multipurpose, and

system reservoirs. These suggestions are meant to serve as broad, overarching guidelines. For the

proper operation of a reservoir or network of reservoirs, unique regulation schedules must be

developed after all relevant factors have been considered.

This research uses Multi Objective Fuzzy Linear Programming to create an optimal reservoir

operation model for the stage-I Jayakwadi reservoir on the Godavari River in Maharashtra (MOFLP).

This problem is framed with two goals in mind—irrigation release and hydropower generation—along

with a number of constraints, and is then solved in an iterative fashion. Using linear membership

functions, the objective function is fuzzy-valued. With the exception of the goals, it is assumed that all

other model parameters are discrete. MOFLP is used to find a happy medium by maximising both the

fuzzified objectives and the level of satisfactions. Potential outcomes for varying degrees of decision-

maker satisfaction with objective measures are generated using the MOFLP model. Also, the optimal

policies were determined for various incoming conditions using MOFLP.

The study's overarching objective was to demonstrate how system analysis methods can be used to

optimise water resources management in service of measurable goals. Given the shift in policy and the

growth in the agricultural, industrial, and domestic sectors, any water resource system, whether

currently in place or soon to be implemented, should be able to meet the demand. Traditional methods

dominate the system for managing food resources. However, system analysis and mathematical

optimization techniques have been found to be helpful. Educating the public about the benefits of

innovative approaches to water resource problems is, therefore, crucial.

The following are some of the goals of this research.

•

Development of a MOFLP model featuring both loose and hard constraints and a fuzzy

objective function.

•

The optimization model is used to analyse the efficiency of the Jayakwadi reservoir at its

initial stage.

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•

Decision-makers are given a plethora of options thanks to lingo's (Language for Interactive

General Optimization) use in the development of optimal operating policies.

The functioning of dam reservoirs is an important factor in water management research and planning.

The research compared the effectiveness of three policies for improving reservoir performance: the

Standard Operation Policy (SOP), the Hedging Rule (HR), and the Multi-Objective Optimization

(MOO). The point of MOO was to boost dependability metrics while simultaneously reducing

exposure. Coordination of the equilibrium between the interests of stakeholders in conventional

ecological operations is difficult. It was proposed that multiple parties work together to manage a

reservoir. The results show that the value of coordinated operation decreased by 0.184, 0.469, and

0.886 in a normal year, a dry year, and an exceptionally dry year, respectively. Soil and Water

Assessment Tool (SWAT) and HEC-ResPRM were used to model and optimise the Nashe hydropower

reservoir operation in the Blue Nile River Basin. Stream flow into the reservoir was determined using

the SWAT model, which accounted for both short- and long-term effects of LULC changes [1-4].

A nested method is presented for the generation of reservoir scheduling models. Scheduled operations

at the Three Gorges-Gezhouba (TG-GZB) cascade reservoirs serve as the basis for this system. A five-

level framework for efficient scheduling has been developed using this method. It is unrealistic to

expect DRSs to be redesigned to account for every conceivable negative scenario. An 11-step process

is provided for dynamically modelling the available features of a DRS. The proposed framework was

found to be useful for locating major influences on system performance [5,6].

The reservoir system can be optimised with the help of LP. A LP model was implemented by Palmer

and Holmes [7] in the Seattle Water Department's expert system for managing drought. During a

drought, Randall et al. [8] analysed how a multi-state water resource system functioned. Although

most reservoir systems are non-linear, LP demands that they be made linear. This includes the

constraints and the objective function. For the short-term, annual operation of an irrigation reservoir,

Chaves and Kojiri[9] developed a deterministic LP model. Jangareddy and Nagesh Kumar [10]

developed a chance constrained LP model to account for unpredictable cash inflows. Approximating

solutions is possible via successive LP (SLP), just as approximating non-linear functions is possible

via linear functions. Examples of SLP's application to multi-reservoir optimization problems are

provided by Chang et al. [11]. In [12], Akter and Simonovic used LP to develop a system-wide

operational and strategic plan for Adelaide's head works. Using LP, Shi et al.[13] detail a process for

optimising power generation from the Highland Lakes on the Lower Colorado River in Texas over the

course of a day. Consequently, LP can only be used for solving problems involving linear functions. In

some cases, the optimization result may be worth less if simplified.

Short-term hydropower generation optimization research by Leta et al. [4] and Ghanbari et al. [14]

demonstrated that the problem could be solved by rewriting it with only linear constraints on outflow

release and storage content. An additional approach to the reservoir operation problem is the so-called

Dynamic Programming method. Biswas et al. [15] developed a model of irrigation for the

management of temporary reservoirs. The model consists of a crop water allocation model and an

operating policy model developed with deterministic dynamic programming. Arunkumaret al. [16]

also developed a DP model to solve the problem of water delivery from two reservoirs to an irrigation

district at once. Predicted information is updated in the model, including evapotranspiration from

crops, evaporation from reservoirs, and inflows. Nasseri et al. [17] were the first to introduce fuzzy

linear programming as a variant of traditional LP. After looking at LP problems with fuzzy objectives

and constraints and presenting an FLP-like LP problem, we see that the min operator is a useful

aggregator for these functions. Ren et al[18] .'s proposal to use parametric programming to solve FLP

has proven to be the most well-liked approach. Using their method, the optimal answer to the problem

can be determined for a wide range of parameter values. RossT. J. [19] provided an illustration of how

to use linear membership functions to solve fuzzy linear problems. In this research, we focused on the

specific scenario of a fuzzy member with a linear membership function. They investigated problems

where the right-side and technological coefficient are the only two uncertain variables. In their

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presentation of a fully fuzzy linear programming approach for multifunctional reservoir operating

rules, Regulwar, Gaurav, and Kamodkar[20–23] outlined a number of advantages. This study

investigates and applies the completely fuzzy linear system, which is a fuzzy linear system with fuzzy

coefficients and fuzzy variables, to the reservoir operating problem, in order to determine the optimal

release strategy for the Jayakwadi reservoir, which is located in the state of Maharashtra in India. And

then they presented a paper on how to derive multipurpose single reservoir release policies using fuzzy

constraints. Despite significant progress, reservoir operation research has been incredibly slow to

translate into actual practise, as pointed out by Chaudhari and Anand [24]. Simonovic discussed the

issues with reservoir operation models and the solutions to make them more appealing to operators.

Intuitionistic fuzzy set theory is a variant of fuzzy set theory that incorporates rejection and acceptance

probabilities in such a way that their sum is less than one [25]. Solution proposals for intuitionistic

fuzzy optimization [26] typically involve re-framing the optimization problem in light of the degree of

rejection of restrictions and values of the impractical objectives. To rank agricultural best management

practises, a case study of South Texas is used to illustrate the utility of a multi-criteria decision-making

model based on Attanassous Intuitionistic Fuzzy Sets (A-IFS) methodology [26]. The intuitionistic

fuzzy optimization method proposed in [20] is widely recognised as a powerful optimization tool by

researchers around the world. This strategy aims to maximise acceptance while minimising rejection;

the current strategy [28] additionally minimises hesitation when accepting new information. In most

cases, the optimal irrigation planning model cannot be found by solving the crisp multiobjective

problem because the objective functions, restrictions, and variables are highly uncertain, imprecise,

and ambiguous in nature and depend on a large number of uncontrolled parameters. Since non-

membership in the fuzzy set is a complement of membership in the set, the maximum of the

membership function will always minimise non-membership. Since the degree of acceptance and

rejection are defined simultaneously and are not additive, intuitionistic fuzzy sets tend to yield

superior results [29]. A computational method for solving a multiobjective linear programming

problem using an intuitive fuzzy optimization model is presented. To investigate how the model makes

use of belonging/not-belonging status, a comparison of the effects of linear and nonlinear membership

functions is provided [30]. A fuzzy multi-objective intuitionistic nonlinear programming model is

developed for irrigation planning in both dry and wet conditions. The model's ability to accommodate

uncertainty and resistance provides guidance to decision-makers in alleviating water scarcity [31].

Intuitive fuzzy multi-objective linear programming problem is provided using triangular fuzzy

numbers and mixed constraints. Several linear and nonlinear membership functions are used to

transform the original problem into a crisp linear/nonlinear programming problem, which can then be

solved using the appropriate crisp programming approach [32]. Intuitionistic fuzzy optimization, an

extended form of fuzzy optimization, considers user satisfaction, model rejection, and uncertainty as

performance metrics [33]. Expert system, belief system, and information fusion model applications

should consider both the truth membership supported by the evidence and the falsity membership

opposed to the evidence [34], even though this is outside the scope of the fuzzy set and interval valued

fuzzy set. However, intuitionistic fuzzy sets, a generalisation of fuzzy sets, account for both true and

false membership. However, intuitionistic fuzzy sets are the only ones capable of dealing with

incomplete information; contradictory or ambiguous data cannot be processed. Neutrosophic sets

explicitly quantify truth membership, indeterminacy membership, and falsity membership, and these

three types of membership are completely separate from one another [35-38]. Many single valued

neutrosophic set (SVNS) operations have been established, and investigations into their basic

properties continue [39–42]. A new multiobjective optimization framework is proposed for use in a

neutrosophic context. The proposed approach [43–45] can be used to simultaneously deal with

indeterminacy and falsehood.

2. FUZZY SET THEORY

First introduced by Regulwar and Kamodkar, fuzzy sets permit a looser membership criterion. For

data that does not neatly fit into predetermined categories, fuzzy set theory provides a solution (i.e.,

fuzzy). Any method or theory that relies on "crisp" definitions, such as classical set theory,

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mathematics, and programming, can be "fuzzified" by replacing them with those of a fuzzy set with

more nebulous boundaries. The extension of crisp theory and analysis to fuzzy techniques is powerful

in solving real-world problems, which invariably involve some degree of imprecision and noise in the

variables and parameters measured and processed for the application. Fuzzy logic uses language

variables such as "high," "middle," and "low" to represent a range of numbers. Since fuzzy logic

allows for overlap, these categories can be mixed. For instance, a flow of 10 units could be partially or

fully classified as either "baseflow" or "interflow." Fuzzy set theory encompasses a wide range of

related disciplines, including but not limited to fuzzy logic, fuzzy arithmetic, fuzzy mathematical

programming, fuzzy topology, fuzzy graph theory, and fuzzy data analysis. There are two names for

collections of clearly defined pieces: classical and crisp. In any given situation, there exists a set called

the universal set that always and forever includes all of the elements of all other sets under

consideration. The characteristic function of the set A is a formal way to say whether or not an element

of A is in the set.

Similar to this, a fuzzy set A of a set X can be described as a set of ordered pairs, each containing a

first element from X and a second element from the interval [0, 1], with exactly one ordered pair

present for each of X.

µA(x): X → [0, 1]

2.1 FUZZY RESERVOIR OPERATION MODEL

The specific stages that are taken for modelling reservoir operation with fuzzy logic are as follows:

Sharp inputs like inflow, reservoir storage, and release are converted into fuzzy variables during step

a) Input Fuzzification; step b) Fuzzy Operator Creation Based on Expert Knowledge Base; step c)

Fuzzy Operator Application to Create Single Number Representing Each Rule's Premise; step d) Rule

Implications Definition; and step e) Defuzzication.

The first step in creating a fuzzy reservoir operation model is determining the degree of membership

functions. Fuzzification yields a fuzzy degree of membership, wherein the inputs are members of all

relevant fuzzy sets via the member, and the output is typically between 0 and 1. Regardless of the

variable being used, the input is always a precise numerical value. The fuzzy rule set is formulated

using the accumulated wisdom of professionals. If the storage is low and the inflow is moderate in

period t, then the release is moderate. The rule basis should always be developed using the existing

expert knowledge on the specific reservoir. Once the inputs have been fuzzified, it is possible to

determine the extent to which each premise for each rule has been met. if the rationale behind a

particular rule is recognised. When a premise of a given rule consists of more than one part, a fuzzy

operator can be used to reduce the number of possible outcomes down to a single one. However many

membership functions are fed into the fuzzy operator, the output is always a single trust value.

Operators in fuzzy logic, like AND and OR, abide by the rules of traditional two-valued logic.

Depending on the context, the AND operator can be interpreted as either the conjunction (min) of

classical logic or the product (prod) of its two parameters. The probabilistic OR (prob or) approach is

an alternate form of the OR method that is analogous to the disjunction operation in classical logic.

The outcome of implication takes the shape of a fuzzy set. This is defuzzified for application. A fuzzy

set is used as the input for the defuzzification process, and the output is one distinct integer. The

"centroid" evaluation, which yields the centre of the area under the curve, is a typical defuzzification

technique. The "bisection" defuzzification method is another option; it provides the bisection of the

output fuzzy set's base.

Algorithm for MOFLP

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The following algorithm (for maximisation problem) can be used to solve the MOFLP model.

Step 1:

Find the best (Z1+ and Z2+) values and worst (Z1- and Z2-

) values corresponding to the set (decision

variables) of solutions (X*) for each objective (Z1 and Z2

) when you solve the model as a Linear

Programming (LP) problem.

Step 2:

Define a linear membership function µk(x) for each objective as

Step 3:

An equivalent LP problem (crisp model) is then defined as

Maximize

Subject to

And

And all the original constraint sets and non negativity constraints for X and .

Step 4:

Solve the LP problem formulated in step 3. The solution is

(i.e., maximum degree of overall

satisfaction) which is achieved for the solution X*. The corresponding values of the objective

functions are Z1* and Z2* obtained and this is the best compromise solution.

2.2 CASE STUDY

The Godavari River runs the length of the Deccan Plateau, from the Western Ghats to the Eastern

Ghats. It all starts 80.46 km from the Arabian Sea, in the Nasik district of Maharashtra. Godavari,

which rises to a height of 1066.81 m and flows south and east across Maharashtra and Andhra

Pradesh, finally empties into the Bay of Bengal 96.56 km below Rajamuhendry. The Jayakwadi dam is

located on the Godavari River in the Aurangabad district of the Indian state of Maharashtra. The

catchment area of the reservoir is 21,750 km2 in size. There are currently 2171 Mm3 of usable storage

and a total of 2909 Mm3 available. There is a total installed capacity of 12 MW for generating

electricity (pumped storage plant). An area of 1,41,640 acres under command is irrigated. Kharif

receives 22% of the total, Rabi 45%, two seasons 28%, hot weather 3%, and perennial crops 4.5% of

the total. The entire power generation system has a capacity of 12 MW (pumped storage plant). The

total irrigable area within the command zone is 1,41,640 acres. Kharif receives 22% of the total

irrigation, Rabi 45%, two seasons 28%, hot weather 3%, and perennial crops 4.5%. Stage-1 of the

Jayakwadi Project Report proposes the construction of a dam over the Godavari River in the Paithan

1 1

( )

Z Z

−

+−

−

≤−

2 2

( )

Z Z

−

+−

−

≤−

λ

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Tehsil of the Aurangabad district of Maharashtra, with a live storage capacity of 2170 cumec. The

longest dimension of the dam is 9997 metres, and its greatest height is 37.73 metres (without the

overflow). The dam has a discharge capacity of 18150 cumec, 27 radial gates measuring 12.50 by 7.9

metres, and an overflow section measuring 417 metres in length. A lined, left-bank canal, 208 km in

length, receives water from the Paithan Dam and irrigates a 1,41,640 hectare (ICA) area in the districts

of Aurangabad, Jalana, Parbhani, and Ahmednagar.. The index map is shown in figure 1.

Table 1 shows the maximum irrigation demand and 75% dependable inflow. 75% dependable monthly

inflows are estimated using the Weibull plotting position formula.

Table 1: Maximum irrigation demands and 75% dependable inflow.

Figure 1. Index Map of Jayakwadi Project.

Formation of MOFLP model:

Application of MOFLP is demonstrate through the case study, Jayakwadi reservoir stage-1 in

Maharashtra state, India. Problem is formulated with two objective function viz. Maximization of

release for irrigation and maximization of release for hydropower production, with the following

constraints and is solved in an iterative manner. All other model parameters other than the objectives

are thought to be crisp in nature..

The study's two goals that were taken into account are:

Sr no. Months

Maximum irrigation

demand

Mm3

75% dependable

InflowMm3

1 June 3.50 112.762

2 July 3.90 320.25

3 August 0.60 610.66

4 September 33.60 600.00

5 October 93.70 147.75

6 November 109.00 116.46

7 December 66.90 85.53

8 January 45.00 37.65

9 February 46.10 21.462

10 March 75.10 19.562

11 April 95.30 25.50

12 May 57.50 46.587

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(1) Maximization of release for irrigation (i.e., RI) and

(2) Maximization of release for hydro power production (i.e., RP)

Max Z1 = Max (TOTRI)

Max Z2 = Max (TOTRP)

where TOTRP is the total release for hydropower generation over all time periods, and TOTRI is the

total release for irrigation over all time periods (i.e., months). These objective functions can written as

Constraint

Turbine release constraint

Each month's release for the amount of hydropower the turbine will produce (RP) must be greater than

or equal to both the firm power (FP) committed for that month as well as the turbine's capacity (TC).

RPt≤ TC t = 1, 2........., 12

RPt≥ FPt t = 1, 2........., 12

Irrigation demand constraint

Release into the canal for irrigation (RI) need to be lower than or equal to the demand for irrigation

(ID). Release must also be more than the minimum amount of irrigation necessary for all time periods

in order to prevent crop wilting (30% of the irrigation demand in this instance is regarded as the

minimum irrigation requirement).

RIt≤ IDt t = 1, 2........., 12

RIt≥ 0.3IDt t = 1, 2........., 12

Reservoir storage capacity constraint

For all time periods, the reservoir's live storage should be below or equal to its maximum capacity

(SCAP).

St ≤ SC t = 1, 2........., 12

St ≥ Smin t = 1, 2........., 12

Reservoir storage continuity constraint

These restrictions apply to all time periods' turbine release (RP), irrigation release (RI), reservoir

storage (S), inflow (I) into the reservoir, overflows (O), and evaporation losses (L).

St + It – RIt + 0.9RPt – Ot – Lt – FCR – RWS = St+1

By considering the evaporation losses as a function of storage (Loucks et al., 1981) and by assuming a

linear relationship between reservoir water surface area and storage, continuity constraint can be

written as follows.

(1-at) St + It – RIt - RPt + 0.9RPt – FCR – RWS –Ot – Aoet= St+1

Where,

1 t

t=1

2 t

t=1

MAX Z RI

MAX Z RP

∑

∀

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at= AAet / 2

AA = Surface area of the reservoir per unit active storage volume.

Ao= Surface area of the reservoir corresponding to the dead storage volume.

et= Evaporation rate for month t in depth units.

RWS = Release for water supply.

FCR = Feeder canal releases.

3. PERFORMANCE ANALYSIS

For the purpose of reservoir management, a Multi Objective Fuzzy Linear Programming (MOFLP)

model has been created. By focusing on one goal at a time, the optimal and worst-case values (Z+ and

Z-) for both objectives (Z1 for release for irrigation and Z2 for release for power production) can be

calculated. LINGO is used to maximise irrigation water release and power generation water release

(Language for Interactive general optimization). When Z1 is maximised, Z2 is assumed to have its

worst possible value, and vice versa. These values are specified in table 2.

Table 2: Objective function values (Best and Worst).

When Z1 (release for irrigation) is maximised, hydropower generation (Z2) receives less power.

Maximizing hydropower generation, denoted by Z2, gives higher priority to releasing water for power

generation than releasing water for irrigation, denoted by Z1. The Jayakwadi scheme uses a reversible

turbine for its pumped storage. The weirs that store the excess water from the hydropower generation

and release it to the turbines downstream are only used during peak demand. The water is pumped

upstream from the downstream weir and into the reservoir during off-peak hours (midnight, for

example) using the same turbine.

After the objective function's upper and lower LINGO bounds are established, the second step is to

fuzzify the objective functions by considering a suitable membership function. In this analysis, we

focus on membership functions that are linear in nature.

The membership function for both the objectives Z1 and Z2

are shown in figures 2 and figure 3

respectively and can be stated as follows.

Objective function

(Maximization )

Best value

(Z+)

Worst value

(Z-)

Release for irrigation

(Z1) Mm3630.20 392.0843

Release for Hydro-power

Production (Z2) Mm3408.00 336.00

1 1

0 392.0843

392.0843

( ) 392.0843 630.20

630.20 392.0843

1 630.20

X Z

≤

⎧

⎪⎛ ⎞

−

⎪

=≤ ≤

⎨⎜ ⎟

−

⎝ ⎠

⎪

⎪≥

⎩

2 2

0 336.00

336.00

( ) 336.00 408.00

408.00 336.00

1 408.00

X Z

≤

⎧

⎪−

⎪⎛ ⎞

=≤ ≤

⎨⎜ ⎟

−

⎝ ⎠

⎪

⎪≥

⎩

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Fig.2 Membership function for Z1.

Fig.3 Membership function for Z2.

The following updated LP problem is created as the third phase of the algorithm by combining the

information mentioned before. Coefficients for constraints given below are obtained from the above

two equations.

Maximize

Subject to

And all the original constraints given in the model and ≥ 0

The amount of satisfaction obtained by simultaneously optimising the fuzzified objectives Z1 and Z2

is represented by the symbol

in this formulation. In the following stage, the LP model's solution is

discovered.

The result obtained as follows.

Z1* (Release of irrigation at the maximum level of satisfaction) = 630.20

Z2* (Release for Hydro power production corresponding to maximum level of satisfaction) = 408.00

The operating policy for maximization of release for irrigation is given in table 3 and maximization

for power production is given in table 4. The operating policy corresponding to maximum level of

satisfaction is given in table 5 and the results are shown in graph.

392.0843

630.20 392.0843

λ−

≤−

2336.00

408.0 336.00

λ−

≤−

λ

(Maximumlevelofsatisfaction = 1.00)

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Figure 4. Release for irrigation (for maximization of Z1).

Figure 5. Release for power production (for maximization of Z1).

Table 3: Operation policy for maximization of release for irrigation.

Table 4: Operation policy for maximization of release for Hydro power production.

Month Irrigation

releases (RI) Mm3

Turbine releases

(RP)Mm3

Head over

turbine M

Storage

Mm3

Overflow

Mm3

Water

supply

releases

Mm3

FCR Mm3

June 3.50 28.00 25.59 948.41 0.00 30.00 0.00

July 3.90 28.00 25.99 959.15 0.00 30.00 0.00

August 0.60 28.00 27.26 1187.225 0.00 30.00 0.00

Septembe

33.60 28.00 28.94 1706.20 0.00 30.00 0.00

October 93.70 28.00 29.57 2170.599 0.00 30.00 50.00

November 109.00 28.00 29.15 2080.928 0.00 30.00 80.00

December 66.90 28.00 28.68 1924.644 0.00 30.00 70.00

January 45.00 28.00 28.17 1802.826 0.00 30.00 90.00

February 46.10 28.00 27.60 1626.343 0.00 30.00 60.00

March 75.10 28.00 27.03 1465.273 0.00 30.00 0.00

April 95.30 28.00 26.37 1288.857 0.00 30.00 0.00

May 57.50 28.00 25.80 1081.303 0.00 30.00 0.00

Total 630.20 336.00 330.15 18241.758 0.00 360.00 350.00

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Figure 6. Release for irrigation (for maximization of Z2).

Figure 7. Release for power production (for maximization of Z2).

Table 5: Operation policy for maximization of level of satisfaction i.e.λ = 1.00.

Month Irrigation

releases (RI)

Mm3

Turbine

releases

(RP) Mm3

Head

over

turbine M

Storage Mm3Overflow

Mm3

Water supply

releases

Mm3

FCR Mm3

June 3.50 34.00 28.32 1766.84 0.00 30.00 0.00

July 3.90 34.00 28.66 1752.17 0.00 30.00 0.00

August 0.60 34.00 29.86 1960.379 0.00 30.00 0.00

September 33.60 34.00 31.48 2461.784 0.00 30.00 0.00

October 93.70 34.00 32.06 2909.00 0.00 30.00 50.00

November 109.00 34.00 31.60 2805.272 0.00 30.00 80.00

December 38.7843 34.00 31.13 2636.895 0.00 30.00 70.00

January 15.00 34.00 30.69 2533.645 0.00 30.00 90.00

February 16.00 34.00 30.17 2374.729 0.00 30.00 60.00

March 26.00 34.00 29.67 2231.045 0.00 30.00 0.00

April 32.00 34.00 29.10 2076.413 0.00 30.00 0.00

May 20.00 34.00 28.57 1895.989 0.00 30.00 0.00

Total 392.0843 408.00 361.31 27404.161 0.00 360.00 350.00

Month Irrigation

releases (RI)

Mm3

Turbine

releases

(RP) Mm3

Head over

turbine M

Storage Mm3Overflow

Mm3

Water

supply

releases

Mm3

FCR Mm3

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Figure 7. Optimal release for irrigation (for maximum satisfaction level).

Figure 8. Optimal release for power production (for maximum satisfaction level).

Table 6: Maximized value of the objective function.

June 3.50 34.00 25.51 924.60 0.00 30.00 0.00

July 3.90 34.00 25.91 935.47 0.00 30.00 0.00

August 0.60 34.00 27.18 1163.530 0.00 30.00 0.00

September 33.60 34.00 28.85 1682.43 0.00 30.00 0.00

October 93.70 34.00 29.49 2146.759 0.00 30.00 50.00

November 109.00 34.00 29.07 2056.928 0.00 30.00 80.00

December 66.90 34.00 28.60 1900.43 0.00 30.00 70.00

January 45.00 34.00 28.10 1778.303 0.00 30.00 90.00

February 46.10 34.00 27.52 1601.624 0.00 30.00 60.00

March 75.10 34.00 26.94 1440.351 0.00 30.00 0.00

April 95.30 34.00 26.29 1264.189 0.00 30.00 0.00

May 57.50 34.00 25.71 1057.119 0.00 30.00 0.00

Total 630.20 408.00 329.17 17951.733 0.00 360.00 350.00

1.00

Z1* (Irrigation release corresponding to the

maximum level of satisfaction) 630.20 Mm3

Z2* (Release for Hydro power production

corresponding to maximum level of

satisfaction)

408.00 Mm3

(Maximum level of Satisfaction)

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4. RESULT AND DISCUSSION

The fuzzy logic tool box available with the MATLAB package is used for developing the

model(MATLAB).The inputs to the fuzzy system are inflows, storage, and time-of-year. The demand is

assumed to be uniquely defined for a period, and hence the variable time-of-year(the period number) is

taken as the equivalent input. The output is the release during the period. For the inputs and output

operations the logical and implication operators are taken as (with conventional Fuzzy notation),

Where the ‘And’ and ‘Or’ method corresponds to the conjuction(min) and disjunc- tion(max) operation

of classical logic.

Step 1) fuzzy inference system tool:

The membership functions are used to determine the degree to which the inputs belong to each of the

relevant fuzzy sets as the initial stage in creating a fuzzy inference system. Fuzzy Controller has five

Inputs and one output. A fuzzy degree of Membership is the final outcome of the fuzzification process,

and the input is always a crisp numerical value constrained to the universe of discourse of the input

variable. The storage, inflow, RWS, ID, Evaporation and release were assigned the triangular

membership functions. The salient membership function for the input inflow and output power are

shown in figure 9.

Input For Data

Membership function values are traced to ‘very low’, ‘low’, ‘med’, ‘high’, ’very high’ of

storage, inflow, RWS, ID, Evaporation and release membership functions, respectively.

Figure 9. FIS editor.

Step 2) Membership function for input and output

The following describes the broad context in which the creation of a membership function takes place.

The scenario includes a knowledge engineer, one or more subject-matter experts, and a particular

knowledge domain of interest. The responsibility of a knowledge engineer is to draw out relevant

knowledge from specialists and convey it in a necessary sort of operational form. The knowledge

And Method

‘Min’;

Or Method

‘Max’;

Imp Method

‘Min’;

Defuzz

Method

‘Centroi

d’.

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engineer tries to extract information in the first step using propositions that are presented in plain

language. The knowledge engineer makes an effort to ascertain the definition of each language term

used in these statements in the second stage. The techniques used to build a membership function, as

determined by experts.

Types of triangular membership functions should be used as input. To display the various input fuzzy

variable ranges, the five membership functions "Very Low", "Low", "Medium", "High," and "Very

High," are employed.

Output: (RI)

The appropriate fuzzy rule for the period is activated once the reservoir storage and inflow levels

(high, medium, etc.) have been determined. A fuzzy set for the release is produced via the fuzzy

operator, implication, and aggregation. The Centroid of the fuzzy set is then utilized to produce a

crisp release.

Figure 10. Membership Functions For Variables.

Step 3) Rule Viewer (adding and editing of rules):

The Rule Viewer is a show how the shape of certain membership functions influences the overall

result. Rules shown in Rule Editor provide inference mechanism strategy and producing the control

signal as output. Different numbers of rules that used in the system will give the different result, so the

analysis for results will be conducted.

The operational rules were applied to generate a result for each rule before a combined operational

rule were applied which then combines the results of the rules. These rules in figure 11 were applied to

the inputs and the output of the Mamdani-type fuzzy inference system based controller. A new

approach is therefore investigated through the use of fuzzy logic to serve as a base or platform to build

an intelligent controller using a set of well-defined rules to guide its operational performance. By

contrast, a fuzzy inference system employing “if-then

” rules can model the qualitative aspects of

human knowledge and reasoning processes without employing precise quantitative analyses. It is

necessary to defuzzify the output fuzzy set in order to receive the output of the whole set of rules as a

single integer.

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Figure 11. Generated Fuzzy Rules.

5. CONCLUSIONS

Application of system techniques to water management has gained momentum over the years. Many

mathematical models have been developed and successfully applied for reservoir planning and

operation studies. The use of these models has greatly aided in providing a good sight into the

intricacies of the various aspects of problem in water management. The conclusions obtained from the

present study of various are summarized. The Multi-Objective Fuzzy Linear Programming (MOFLP)

model is created and employed to the reservoir operation problem to decide the optimal release policy

for the Jayakwadi Reservoir stage-1, Maharashtra state, India. Optimal policies are determined for

75% dependable inflows using MOFLP. Depending on the decision-choice maker's of priorities for

each target, these ideal policies may be put into practice for greater usage of the water resources. The

two objectives i.e., release for irrigation and release for hydropower production are thought about in

the study are maximization of irrigation release, and maximization of release for power production.

First the model is solved for maximization of irrigation release. The maximized irrigation release

obtained is 630.20 Mm3 and corresponding release for power production 336.00 Mm3. Then the model

is run for maximization of release for hydropower production. The maximized release for hydropower

production obtained is 408.00 Mm3 and corresponding irrigation release is 392.0843 Mm3.

The best and worst values of the two objective functions are decided. The objective functions are

fuzzified over the best and worst values of each objective functions. The maximum satisfaction level

for the fuzzified problem is obtained as 1.00. For this satisfaction level, maximized sum of release for

irrigation is 630.20 Mm3 and maximized sum of release for hydropower production is 408.00 Mm3.

Fuzzy rule based model considering singe objective is developed viz. release for irrigation. The model

is based on the "if-then principle," where "if" represents a vector of ambiguous premises and "then"

represents a vector of fuzzy consequences. Using mamdani method of FIS, the release for irrigation is

588 Mm3.

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