International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
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
* Department of Business Administration, Politeknik Negeri Padang, Limau Manis, Padang 25000, Indonesia E-mail: arni6965@gmail.com
Abstract— 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.
I. INTRODUCTION
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].
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
248 implemented, a science management approach is needed to determine which project options provide the most benefits in funding. The purpose of this study is to make decisions, which of the three existing tributaries provide the most optimal utility given the limited number of operational costs.
II. MATERIALANDMETHOD
The method used in this study is linear programming by presenting various data that needs to be considered as a function of objectives and function of constraints in mathematical formulas. In order to create an appropriate mathematical model, adequate surveys are conducted with respect to the technical and socioeconomic requirements to be met. The following are the technical and socio-economic requirements:
a. Technical Requirements:
1) The required river water discharge is available throughout the year and can be met by the average river flow during the dry season.
2) Adequate plunge height, which together with flow discharge produces a large hydro power potential. 3) The project uses appropriate technology for its
manufacture, operation and maintenance to be carried out using local labour.
b. Socioeconomic Aspects:
1) The existing microhydro power potential is a resource that can support rural development. The existence of the microhydro project can help the development of socio-economic potential that is basically quite large.
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 project provided by the community at Sangir sub regency, South Solok, regency, West Sumatra.
3) The electricity business of the microhydro project is economically accountable, in the sense that the potential of existing consumers can absorb the production of electricity generated with the selling price determined based on the principles of self-help local communities. 4) The potential of existing human resources can be
expected to manage the microhydro project properly and reliably.
This project must meet all technical requirements and socioeconomic aspects. A survey was conducted to ensure that the project met all criteria. The most important requirement was the readiness of human resources to be actively involved in this project. Without local community support, this project can not operate smoothly and sustainably. Once all the requirements were met, the microhydro installation system was applied. The microhydro installation system that we applied, we present in Figure 1, the following:
Fig 1. Sketch of Microhydro Power Plant Installation Source: processed ourself
Technical requirements and socioeconomic aspects are the first survey work and should be reasonably feasible, so that it can proceed at a later stage. In the following stages will be discussed the existing conditions of the procurement plan of these microhydro generators, which include: budgeted funds, project location, river flow data, budget data of each activity location, recapitulation of all data required in
linear programming calculations. All the required data will be presented in mathematical models accordingly and processed with the help of Pom for Windows software [6].
c. Source of Fund and Cost
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
249 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 Sangir Sub Regency, South Solok Regency
Micro hydro
Source: Survey results and calculations
d. Location of Microhydro Power Plant Project
This Microhydro Power Plant Project is located in Sangir 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.
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:
TABLE II
Capacity of Power Generated Based on River Discharge The Name of The River River Discharge (m3/s) Capacity (Kwh)
Batang Belangir 0.39 178.060
Batang Aro 0.17 77.616
Batang Sangir 0.47 214.585
Batang Liki 0.34 155.232
Source: Survey results and calculations
f. Recapitulation of All Microhydro Project Data
The following data is summarized from the various data
Recapitulation of All Microhydro Project Data
Micro hydro Users Power Capacity
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.
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:
(1)
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
250 maximize or minimize from a linear objective function in the following form:
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, theX1 = 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, X1+X2
1, reflectsthe 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. 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 packages provides useful “what if” analysis [18].
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
251 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:
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
Solution-> 0 1 1 1 Optimal Z-> 631
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:
TABLE V
POM iteration results for Windows
Iteration Level Added constraint Solution type Solution Value X1 X2 X3 X4 Optimal 631 0 1 1 1 1 0 NONinteger 689.54 0 1 1.78 0 2 1 X3<= 1 NONinteger 665.8 1 0 1 0.52 3 2 X4<= 0 INTEGER 575 1 0 1 0 4 2 X4>= 1 NONinteger 665.12 0.29 0.71 1 1 5 3 X1<= 0 NONinteger 664.84 0 1 1 1.19
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
252 investment cost of the cable and transmission lines, in which case each location has different cost variations.
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].
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.
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.
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 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.
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.
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.
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].
REFERENCES
[1] S. Dragicevic, and M. Bojic, “Application of Linear Programming in
Energy Management”, Serbian Journal of Management, vol. 4(2), pp. 227-238, 2009.
[2] I. Grossman, and J. Santibaniez, “Applications of Mixed-Integer
Linear Programmingin Process Synthesis”, Computer and Chemical Engineering, vol. 4(4), pp. 205-214, 1980.
[3] M.R. Spakovsky, V. Curti, and M. Batato, “The Performance Optimization of A Gas Turbine Cogeneration/Heat Pump Facility
with Thermal Storage”, Journal of Engineering for Gas Turbines and Power, ASME transactions, vol. 117(3), pp. 2-9, 1995.
[4] S.I. Gustafsson, and M. Bojic, “Optimal Heating-System Retrofits in
Residential Buildings”, Energy-The International Journal, vol. 22(9), pp. 867-874, 1997.
[5] R. Yokohama, and K. Ito, “A Novel Decomposition Method for MILP and Its Aplication to Optimal Operation of A Thermal Storage
System”, Energy Converzation and Management, vol. 41(16), pp. 1781-1795, 2000.
[6] I. Parinduri, and S. Havid, Teknik Riset Operasi Menggunakan POM QM for Windows 3, Yogyakarta: Penerbit Deepublish, 2016. [7] B. Triatmodjo, Hidrologi Terapan, Cetakan kedua. Yogyakarta:
Penerbit Beta Offset, 2015.
International Conference of Applied Science on Engineering, Business, Linguistics ISSN : 2598-2532 and Information Technology (ICo-ASCNITech)
Politeknik Negeri Padang and Politeknik Ibrahim Sultan, 13-15 October 2017
253 [9] B. T. Denton, “AusWest Timbers Uses an Optimization Model to
Improve Its Manufacturing Process”, Interfaces, vol. 38(4), pp. 341-344, 2008.
[10] G. Duran, M. Guajardo, J. Miranda, D. Saure, S. Souyris, A.
Weintraub, and R. Wolf, “Scheduling the Chilean Soccer League by Interger Programming”, Interfaces, vol. 37(6), pp. 539-555, 2007. [11] C.H. Martin, “Ohio University’s College of Business Uses Interger
Programming to Schedule Classes”, Interfaces, vol. 34(6), pp. 460-465, 2004.
[12] C.H. Matthews, “Using Linear Programming to Minimize the Cost of
Nurse Personnel”, Journal of Health Care Finance, vol. 32(1), pp. 37-49, 2005.
[13] K. Pasupathy, and A.M. Borja, “Integrating Excel, Acces, and Visual Basic to Deploy Performance Measurement and Evaluation at the
American Red Cross”, Interfaces, vol. 38(4), pp. 324-340, 2008. [14] S. Harrod, “A Spreadsheet-Based, Matrix Formulation Linear
Programming Lesson”, Decision Sciences Journal of Innovative Education, vol. 7(1), pp.249-257, 2009.
[15] T. Dilisusendi, “Optimasi Pendanaan Program Listrik Pedesaan Seluruh Indonesia Menggunakan Program Linear”, in Tesis, Program Magister Perencanaan dan Kebijakan Publik, Universitas Indonesia, 2009.
[16] Kementerian Energi dan Sumber Daya Mineral, “Manajemen Rantai Penyediaan dan Pemanfaatan Energi Nasional”, Jakarta: Pusat Data
dan Teknologi Informasi Kementerian ESDM, p.73, 2016.
[17] J. Heizer, and B, Render, Operation Management: Sustainability and Supply Chain Management, Eleventh Edition, London: Pearson Education, Inc, 2014.
[18] J.A. Lawrence Jr., and B.A. Pasternack, Applied Management Science: Modeling, Spreadsheet Analysis, and Comunication for Decision Making, Second Edition, California: John Wiley & Sons, Inc, 2001.
[19] Kementerian Energi dan Sumber Daya Mineral Republik Indonesia,
“Peraturan Menteri Nomer 19 Tahun 2015 tentang Pembelian Tenaga Listrik dari Pembangkit Listrik Tenaga Air dengan Kapasitas sampai dengan 10 MW (Sepuluh Megawatt) oleh PT Perusahaan Listrik Negara (Persero)”, Jakarta: Kementerian ESDM Republik
Indonesia, p.1., 2015.
[20] A.B. Martin, E Richards, and E. Gunn, “Comparing the efficacy of linear programming models I and II for spatial strategic forest
management”, Canadian Journal of Forest Research, vol. 47 (1), pp.16-27, 2016.
[21] J.H. Yoo, “Maximization of hydropower generation through the
application of a linear programming model”, Journal of Hydrology, vol. 376(1-2), pp. 182-187. 2009.
[22] C. Beltran-Royo, “Two stage stochastic mixed-integer linear
Linear Programming Application
for Optimization Resource and
Operational Cost of Microhydro
Power
by
Chairul Muharis, Arni Utamaningsih
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Linear Programming Application for Optimization Resource
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