Linear Programming Application for Optimization Resource and Operational Cost of Microhydro Power - Politeknik Negeri Padang
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* Department of Business Administration, Politeknik Negeri Padang, Limau Manis, Padang 25000, Indonesia
E-mail: arni6965@gmail.com
Abstract
247
Linear Programming Application for Optimization Resource and
Operational Cost of Microhydro Power
Chairul Muharis# , Arni Utamaningsih
Department of Civil Engineering, Politeknik Negeri Padang, Limau Manis, Padang 25000, Indonesia
E-mail: ch_muharis@yahoo.com
— This paper examines the optimization of the procurement of microhydro power plants in Sangir Sub regency, South Solok regency, at West Sumatera. This area is a remote area with a difficult topography, a small population, and has not been reached by electricity from State Electricity Company. This microhydro power plant utilizes the Batang Sangir River as a source of turbine driving power. The limitations of non-governmental funding, technical limitations, and the distance of two rivers from residential areas require that field surveys and optimal calculations be carried out. This study uses linear programming to optimize operational costs and select the most suitable river resources, with Pom for Windows software. Based on the linear programming calculations, this study decided that the optimal project to be implemented are Batang Aro, Batang Sangir and Batang Liki, while the Batang Belangir cannot be funded in the same year.
Keywords — Linear Programming, Microhydro, Resource Optimization, Operational Cost.
NTRODUCTION
I. I
Indonesia is an archipelagic country that still has many remote areas and has not been reached by electric lighting by State Electricity Company. These areas generally have difficult topography to reach and have a small population. On the other hand, electricity lighting is a basic necessity of the community in meeting its needs, including the need to access information to increase productivity and promote the regional economy. Micro hydro Power Plant is one of the cheapest alternative energy sources that can be applied in remote areas. The use of fossil-based fuels that take place as current trends can lead to environmental damage at the local, regional and global levels. The provision of adequate energy and environmentally friendly is one of the requirements for sustainable socio-economic development. Microhydro Power Plant is a potential renewable energy resource as one solution when the world is experiencing an energy crisis.
This paper aims to study the Microhydro Power Plant in South Solok, West Sumatera by utilizing the Batang Sangir River, along with its tributaries, namely Blangir Batang, Batang Aro and Batang Liki as turbine power source. River trunks that have a large slope and water discharge in rural areas Sangir sub regency, South Solok regency save the potential of hydro power large enough and can be utilized for this project. Starting from the situation then it is necessary to study and development about the implementation of microhydro power plants by utilizing the skewed system. In this system some of the river water is directed to the carrier channel then flowed through a penstock to the turbine. After the turbine, the water is returned to the original flow, so as not to damage the environment or reduce water for agricultural purposes.
Water will flow into the turbine through the runner blades that will rotate the turbine shaft. This rotation will rotate the generator to generate electrical energy.
Dragicevic and Bojic [1] have shown that as energy and equipment costs increase, the selection of energy systems becomes increasingly important by considering the most economical placement process. Dragicevic and Bojic [1] use linear programming techniques as a method to minimize total cost for a condensation procurement project in Serbia. Linear Programming technique is used to determine the optimum value of all variable designs, as well as to achieve minimum cost. Energy procurement system is generally a system whose elements are complex, and each sub-system is mutually correlated and unpredictable component behaviour. Mathematical applications in the Linear Programming method help simplify the complexity so that optimal decision making can be achieved.
In some literatures, the Linear Programming method is often applied in the case of energy engineering optimization, for example in the chemical industry with the constraint function of minimal procurement costs [2], on gas turbine and pump systems with minimal operational costs [3]. Linear programming can also be applied to civil construction engineering, such as minimal cost analysis for the procurement of residential buildings [4], and non-industrial heat supply systems with minimal daily operational cost constraints [5].
This research applies linear programming, but in contrast to some literatures which have been submitted above which prioritize technical constraint factor only. This study also discusses the limitations of economic resources in relation to non-governmental funds. In this study we examine the microhydropower system by utilizing the flow of Batang Sangir river along with its three tributaries to develop the potential of hydropower into the potential of electricity, especially in the flow of rivers that have a large slope and discharge. In order for the project to be optimally implemented, a science management approach is needed to 1) The existing microhydro power potential is a resource determine which project options provide the most benefits in that can support rural development. The existence of the funding. The purpose of this study is to make decisions, microhydro project can help the development of socio- which of the three existing tributaries provide the most economic potential that is basically quite large. optimal utility given the limited number of operational costs. 2)
The cost of making the microhydro project can be overcome by a non-governmental organization, cooperative or other small and medium private business unit. In the project discussed the cost of making this
II. AND METHOD MATERIAL project provided by the community at Sangir sub
The method used in this study is linear programming by regency, South Solok, regency, West Sumatra. presenting various data that needs to be considered as a
3) The electricity business of the microhydro project is function of objectives and function of constraints in economically accountable, in the sense that the potential mathematical formulas. In order to create an appropriate of existing consumers can absorb the production of mathematical model, adequate surveys are conducted with electricity generated with the selling price determined respect to the technical and socioeconomic requirements to based on the principles of self-help local communities. be met. The following are the technical and socio-economic
4) The potential of existing human resources can be requirements: expected to manage the microhydro project properly and a.
Technical Requirements: reliably. 1)
The required river water discharge is available This project must meet all technical requirements and throughout the year and can be met by the average river socioeconomic aspects. A survey was conducted to ensure flow during the dry season. that the project met all criteria. The most important
2) Adequate plunge height, which together with flow requirement was the readiness of human resources to be discharge produces a large hydro power potential. actively involved in this project. Without local community
3) The project uses appropriate technology for its support, this project can not operate smoothly and manufacture, operation and maintenance to be carried out sustainably. Once all the requirements were met, the using local labour. microhydro installation system was applied. The microhydro installation system that we applied, we present in Figure 1, b. Socioeconomic Aspects: the following:
Fig 1. Sketch of Microhydro Power Plant Installation Source: processed ourself
Technical requirements and socioeconomic aspects are linear programming calculations. All the required data will the first survey work and should be reasonably feasible, so be presented in mathematical models accordingly and that it can proceed at a later stage. In the following stages processed with the help of Pom for Windows software [6]. will be discussed the existing conditions of the procurement plan of these microhydro generators, which include: c. Source of Fund and Cost budgeted funds, project location, river flow data, budget data Microhydro Power Plant Procurement is established of each activity location, recapitulation of all data required in through the collection of community self-help fund and community members contributions, individual donations, and community business units. The collected funds are around IDR700,000,000. The collected funds are used to be entirely mutual and non-profit oriented. Project work not only requires self-help funds, but is also assisted by self-help facilities owned by local people, for example the use of vehicles in the form of cars and motorcycles, carpentry tools, and labor donations during project surveys, project preparation and implementation non-technical projects. Based on microhydro cost budget data on all river projects, a project recapitulation budget was prepared as shown in Table 1 below:
TABLE I Recapitulation of Microhydro Cost Budget
Source: Survey results and calculations
The mathematical formulation of the linear programming procedure is as follows: specify a group of variables x1, x2, x3, ......, xn in a system of linear equations or linear inequalities like the following formula:
RESULT AND DISCUSSION Hillier and Liebermen [8] stated that linear programming is a mathematical model to describe problems in a linear function. Linear Programming is a mathematical technique applied to problem solving with respect to the function of minimization or maximization of a number of independent variables. Linear programming is a commonly used and highly suitable method applied to complex industrial systems. Linear programming is a very flexible technique by using a system of equations directed at a specific goal. Linear programming can be used in solving the problem of allocation of finite sources optimally. Computer technology, with software pom for windows can be easily operationalized to aid calculation iteration.
Source: Survey results and calculations III.
4 Batang Liki 175 212.000.000 155 Cost (IDR) No.
3 Batang Sangir 300 325.000.000 215
78
2 Batang Aro 156 122.000.000
1 Batang Belangir 275 265.000.000 178
Micro hydro Users Power Capacity Plant (Household) (Kwh)
TABLE III Recapitulation of All Microhydro Project Data
f. Recapitulation of All Microhydro Project Data The following data is summarized from the various data required in the calculation through the formation of linear programming functions. The data is also supplemented by the number of heads of households that are user communities in each of the locations that are fed by the creeks. Here is a table that contains data that is ready to be processed in linear programming:
Batang Belangir 0.39 178.060 Batang Aro 0.17 77.616 Batang Sangir 0.47 214.585 Batang Liki 0.34 155.232
Sangir Sub Regency, South Solok Regency Micro hydro
3 /s) Capacity (Kwh)
The Name of The River River Discharge (m
TABLE II Capacity of Power Generated Based on River Discharge
e. Plan and Discharge Capacity The design stage consists of calculating the discharge using the Log Pearson Type III method [7], which is an empirical method to estimate an event based on a previous time series record of data retrieved from field observation data. Based on the probability statistics of occurrences with a certain re-occurrence expected to occur in the future can be met or exceeded. For the planning of this project re- established 10 years, which is equal to the estimated age of this microhydro productive. After the discharge plan obtained results, followed by calculate the capacity of power to be generated. The results of the calculation of plan discharge and power capacity for the four rivers are as follows:
Sub regency, South Solok Regency, West Sumatera. After a field survey, 4 (four) villages are defined as the location of the self-supporting microhydro project development. The four locations are: Belangir, Aro, Sangir, and Liki villages. Because of limited funding and microhydro capacity requirements should be below 500 KW, local community leaders must decide to select 3 (three) most likely locations. In relation to the distance between the Belangir and Batang Aro project sites and the settlements far enough, they decided to choose one of the two tributaries.
d. Location of Microhydro Power Plant Project This Microhydro Power Plant Project is located in Sangir
Source: Survey results and calculations
4 Batang Liki 212.049.500 212.000.000 Rounding (IDR) No. Total cost (IDR)
3 Batang Sangir 324.280.000 325.000.000
2 Batang Aro 121.947.500 122.000.000
1 Batang Belangir 264.469.800 265.000.000
Plant
(1) Notation aik is a constant coefficient, xk is an unknown problem variable, and m is a number of existing constraints. Linear programming procedures can be classified into
- 156X
- 300X
- 175X
- 122X
- 325X
- 212X
, X
1 (6)
X
1
, X
2
, X
3
4
1 + X
0 and interger (7) Notation:
X1 = Batang Belangir Microhydro Project X2 = Batang Aro Microhydro Project X3 = Batang Sangir Microhydro Project X4 = Batang Liki Microhydro Project
In this model, the decision variable solution can be zero or one. If a project is not selected to work, then the value of the decision variable representing the project is zero. Conversely, if a project is selected to do, then the decision variable is worth one. The last restriction, X
1 +X
2
1, reflects the contingency of microhydro mine project (X1) or Batang Aro (X2) but not both. For the sum of X1 and X2 to be smaller or equal to one, then one of these variables has one or both values of zero. This model is also called mutually exclusive limitation.
b.
2
X
maximize or minimize from a linear objective function in the following form: (2) ck notation is constant coefficients and all linear programming solution codes of all variables should not be negative .
1
Application of linear programming in the field of industry to assist managers in making decisions has been done, as well as research reports have been widely published abroad. Denton [9] describes the attractiveness of various topics and the updated application of operational research methodology in industry (novelity). Duran [10] uses interger programming to solve the problem of scheduling the Chilean soccer league. Martin [11] also uses interger programming to solve class scheduling problems at Ohio University. Matthews [12] uses linear programming to minimize the cost of nurses' personnel at a busy American hospital. The cost of nurse personnel occupies the largest portion of the hospital budget, so linear programming is used to evaluate and optimize the utility of nurse personnel in the internal environment of the hospital. Pasupathy and Borja [13] utilize Integrating Excel, Access, and Visual Basic software to develop measurements and evaluate the performance of American Red Cross organizations. Furthermore, Harrod [14] made a teaching innovation in the field of decision making by developing Spreadsheet-based software and formulating linear programming into the matrix.
Research using linear programming application has not been done in Indonesia. Dilisusendi [15] conducted an evaluation of rural electricity finance optimization throughout Indonesia using linear programming. Dilisusendi's evaluation results [15] show that rural electricity funding throughout Indonesia is still not optimal in 2008 and can still be cost savings and increased access to electricity by 10% nationwide in 2009. Data and Information Technology Center Ministry of Energy and Mineral Resources [16] using a linear programming approach in managing the national supply and utilization chains. Linear programming is used to formulate Java power production optimization problems. The developed linear model has the objective function of minimizing the cost per unit of power, ie the total cost incurred from the point of generation to the point of load per unit of power. Minimized costs consist of fixed cost of generator, variable cost of production, transmission cost with five function constraints related to total effective capacity, total power generated and transmitted.
a.
Problem Model Formulation Mathematical models in linear programming have a certain structure that is standard, so that reality can be explained well by the model. Heizer and Render [17] stated that in linear programming, reality can be read directly through the mathematical functions that represent the model. The linear programming application in this case is to make a choice decision according to the priority scale by focusing on the objectives and the various obstacles that exist in the field. The purpose of the microhydro power plant procurement project is to provide electricity to residents living near the watershed. The distance from the Belangir and Batang Aro project sites with the settlement is far enough, so they decided to choose one between the two tributaries. This condition is formulated in the mathematical model as a function of constraint X1 + X2
1, reflecting the contingency of microhydro mine project (X1) or Batang Aro (X2) but not both. Conditions in the field stated that the Batang Belangir microhydro (X1) project can serve 275 houses with a power capacity of 178 Kwh, but must be financed with a value of IDR265,000,000 which makes the project not feasible. The development of Batang Aro microhydro gives optimal results to serve 156 houses with capacity of 78 Kwh and operational cost of IDR122,000,000. In this case, the construction of Batang Aro microhydro is more feasible compared to Batang Belangir for the total funding worth IDR700,000,000 available. Based on the various data that has been recapitulated in Table 3, the following model formulation is made in Linear Programming:
Maximize Z = 275X
2
1 + 78X 2 + 215X 3 + 155X 4 <= 500
3
4
(3) Limitation: 265X
1
2
3
4
<= 700 178X
POM for Windows Calculation Results A Linear Programming model seeks to maximize or minimize a linear function, subject to a set of linear constraints [18]. The linear model in this project consists of the following components: 1) a set of decision variables; 2) an objective function; and 3) a set of constraints. There are efficient solution techniques that solve linear programming models. The output generated from linear programming package s provides useful “what if” analysis [18]. Linear programming helps simplify the initially complex problem. Calculation of electric power capacity generated by river flow discharge varies on each tributary. The Log Pearson Type III is used to calculate the discharge design based on the measured river flow data at the time of the field survey. The Log Pearson Type III is a developed distribution of a series of probability functions that can be used for almost all empirical probability distributions. Three important parameters in Log Pearson Type III distribution are: average price, standard deviation and skew coefficient. After that the data is converted into logarithmic form so that it gets the discharge design with certain repetition period. Based on the discharge design of a certain repeat period can be calculated the amount of power generated (in units of Kwh). Based on the calculation of Linear Programming Microhydro Batang Belangir (X1) project capable of producing power capacity of 178 Kwh, but keep in mind that the total capacity generated by microhydro project should not be more than 500 Kwh. Referring to Regulation of the Minister of Energy and Mineral Resources No. 19 of 2015 [19], the procurement of electrical energy in this study is classified under 10 Megawatts. Microhydro is commonly used for power plants that produce the output of hydropower potentials below 500 Kwh, while mini hydro for output 500 Kwh up to 1000 Kwh, for a larger output than that referred to as hydro power.
After devising a linear programming formula, all the data was added to the POM for Windows. The solution of this project selection process was done using POM for Windows software calculations. The input into the POM for Windows software is as follows:
Variable Type Value
Source: POM for Windows Output From the calculation result, it can be concluded that the microhydro project that gives the maximum solution to be done is the microhydro Batang Aro (X2), Sangir (X3) and Batang Liki (X4), while the Belangir (X1) can not be done with the available fund.
1 Solution value 631
1 X4 Integer
1 X3 Integer
X2 Integer
X1 Integer
TABLE VI POM iteration results for Windows
TABLE IV Input Calculation of POM for Windows X1 X2 X3 X4 RHS Equation form Maximize 275 156 300 175 Max 275X1 + 156X2 + 300X3 + 175X4 Constraint 1 265 122 325 212 <= 700 265X1 + 122X2 + 325X3 + 212X4 <= 700 Constraint 2 178 78 215 155 <= 500 178X1 + 78X2 + 215X3 + 155X4 <= 500 Constraint 3 1 1 = Constraint 4 1 X1 + X2 = 1 1 >= X1 >= 0
Source: POM for Windows Output The results of POM for Windows iteration are as follows:
11 5 X3>= 1 Infeasible 12 3 X1>= 1 NONinteger 655.85 1 0.69 1 13 4 X3<= 0 NONinteger 634.08 1 2.05 14 5 X4<= 2 Suboptimal 625 1 2 15 5 X4>= 3 Infeasible 16 4 X3>= 1 Infeasible 17 1 X3>= 2 Infeasible
4 2 X4>= 1 NONinteger 665.12 0.29 0.71 1 1 5 3 X1<= 0 NONinteger 664.84 1 1 1.19 6 4 X4<= 1 INTEGER 631 1 1 1 7 4 X4>= 2 NONinteger 648.15 1 0.47 2 8 5 X3<= 0 NONinteger 632.45 1 2.72 9 6 X4<= 2 Suboptimal 506 1 2 10 6 X4>= 3 Infeasible
TABLE V POM iteration results for Windows Iteration Level Added constraint Solution type Solution Value X1 X2 X3 X4 Optimal 631 1 1 1 1 NONinteger 689.54 1 1.78 2 1 X3<= 1 NONinteger 665.8 1 1 0.52 3 2 X4<= 0 INTEGER 575 1 1
Source: POM for Windows Input This program will process the data that has been entered into the program, and the program will process it in a series of iterations. The results of POM for Windows iteration are as follows:
Constraint 5 1 >= X2 >= 0 Constraint 6 1 >= X3 >= 0 Constraint 7 1 >= X4 >= 0 Variable type Integer Integer Integer Integer Solution-> 1 1 1 Optimal Z-> 631
The cost of each microhydro project contains three job descriptions of the project, which consists of preliminary work, civil construction work, and mechanical and electrical work. In civil works, the project is subdivided into three sub- jobs, namely: building work intake, penstock and panel house. In mechanical and electrical work, the project is divided into three jobs, namely: turbine, generator, panel and transmission work. Mechanical and electrical work absorbs the greatest cost of all microhydro project procurement, especially the cost of procuring turbines. However, more than that would be better, if the project also considers the fixed costs of the plant, which is the total fixed cost incurred on each plant if the plant is decided to conduct electricity production. Production variable costs also need to be considered in terms of the total cost per unit of power generated from each plant to meet demand at a load point. Transmission costs also need to be considered in connection with the costs incurred due to the transmission from the point of generation to the point of load. This cost is a variable cost per unit of power calculated from the
investment cost of the cable and transmission lines, in which case each location has different cost variations.
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Linear programming has advantages, but also has limitations. Linear programming is an approach in making decisions with the assumption that reality is linearly formulated and additive. In this case, if a constraint involves two decision variables, the dimension diagram will be a straight line. Likewise, a constraint involving three variables will result in a plane and constraint involving n variables will produce hyperplane in a n-dimensional space. In this linear model the relationship between variables is proportional, which means that the degree of change or the slope of the functional relationship is constant, so the change in the value of the variable will result in the relative change of the value of the objective function in the same amount. Linear programming assumed additive can be interpreted as the absence of adjustment on the calculation of the criterion variable due to the interaction between variables [17].
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Future research can also apply linear programming to a wide range of problems, for example in managing forest resources [20], managing more complex hydro power. Yoo analyzes the effect and sensitivity of the model’s release and reservoir storage the maximization of hydro power energy generation based on calculations of optimal values [21]. Linear programming can also be combined to manage more complex and dynamic problems in conditional scenario or conditional expectation [22].
In future research the function of constraints in linear programming can be enhanced by adding various technical studies, eg constraints contained in turbines, generators, penstock. This study involves several experts who can make a more detailed study in accordance with the conditions in the field. In relation to economic feasibility, the future studies may also consider the project's financial viability or capital budgeting, ie a process of consistent long-term evaluation and selection of long-term investments to maximize project objectives. Capital budgeting can use Payback Period, Net Present Value, Internal Rate of Return (IRR), Return On Investment and Profitability Index.
Linear programming helps simplify initially complex problems and makes it easy to make decisions for its users. Linear programming has advantages, but also has limitations. Linear programming is an approach in making decisions with the assumption that reality is linearly formulated and additive. In linear programming all model parameters are assumed to be constant. In this case a decision problem is in a static framework, all parameters are known with certainty. In reality, model parameters are rarely deterministic, because they reflect both present and future conditions, so policy values are needed for the user.
Batang Belangir project can not be funded with the same budget year fund, in other words the Batang Belangir project is postponed for the coming year.
This paper examines the optimum procurement of microhydro power plants in Sangir Sub regency, South Solok Regency, West Sumatera. This area is a remote area with a difficult topography, a small population, and not yet accessible electricity from the State Electricity Company. River that is used as a source of turbine driving power is Batang Sangir River, along with its tributaries, namely Batang Belangir, Batang Aro and Batang Liki. This study uses the Linear Programming application to maximize the use of existing resources. The limited funding and technical constraints associated with the proximity of the project site with the settlement impacted the high cost of project work. The project decided to choose one of the rivers from two rivers that are far from residential areas to control costs. The projects undertaken are Batang Aro river project, Batang Sangir, Batang Liki, and Batang Belangir. The result of linear programming with Pom for Windows states that the
IV. CONCLUSSION Indonesia has many natural resources that have not been utilized optimally. Mountains that certainly have an abundant waterfall can be utilized as a renewable energy source. Potential waterfall resources can be used as microhydro power plants, so that remote areas can enjoy electric lighting with relatively easy and cheap maintenance costs.
In global conditions, things are often interacting and changing rapidly, so looking at things in a linear way becomes a new challenge. In this case, the accuracy and identification of critical factors in linear programming approach is needed, so that this program provides optimal benefits. In linear programming all model parameters are assumed to be constant. In this case a decision problem is in a static framework, all parameters are known with certainty. In reality, model parameters are rarely deterministic, because they reflect both present and future conditions. The circumstances of the future are very likely not known with certainty. Linear programming users should be fully aware of the realities that exist, especially for cases related to social values. Linear programming is simply a tool that is used as a decision-making approach, and it entirely takes the wise values of its users.
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