Design aspects and probabilistic approach for generation reliability evaluation of MWW based micro-hydro power plant

Renewable and Sustainable Energy Reviews 28 (2013) 917–929

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

Design aspects and probabilistic approach for generation reliability evaluation of MWW based micro-hydro power plant$ R.K. Saket n,1 Indian Institute of Technology (Banaras Hindu University), Department of Electrical Engineering, Varanasi, Uttar Pradesh 221005, India

art ic l e i nf o

a b s t r a c t

Article history: Received 20 April 2013 Received in revised form 31 July 2013 Accepted 11 August 2013 Available online 21 September 2013

This paper presents the design aspects and probabilistic approach for the generation reliability evaluation of an alternative resource: municipal waste water (MWW) based micro-hydro power plant (MHPP). Annual and daily flow duration curves have been obtained for design, installation, development, scientific analysis and reliability evaluation of the MHPP. The hydro-potential of the waste water flowing through sewage system of Brocha sewage plant of the Banaras Hindu University campus is determined to produce annual flow duration and daily flow duration curves by ordering the recorded water flows from maximum to minimum values. Design pressure, roughness of the pipe's interior surface, method of joining, weight, ease of installation, accessibility to the sewage system, design life, maintenance, weather conditions, availability of material, related cost and likelihood of structural damage have been considered for the design of a particular penstock for reliable operation of the developed MHPP. MWW and selfexcited induction generator (SEIG) based MHPP is developed and practically implemented to provide reliable electric power to charge the battery bank. Generation reliability evaluation of the developed MHPP using the Gaussian distribution approach, safety factor concept, peak load consideration and Simpson 1/3rd rule has been presented in this paper. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Sewage system Municipal waste water Reliability evaluation Gaussian distribution Simpson 1/3rd rule Self-excited induction generator Annual and daily flow duration curves

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 918 Brief descriptions on basic components of developed MHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 2.1. Selection of penstock pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 2.2. Selection of turbine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 2.3. Selection of generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919 Flow – duration curves, power estimation and reliability indices evaluation of MHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920 3.1. DFDC and AFDC of developed MHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920 3.1.1. DFDC of monsoon season (July, August and September) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920 3.1.2. DFDC of post-monsoon and pre-winter season (October, November and December) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920 3.1.3. DFDC of winter and pre-summer season (January, February and March) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921 3.1.4. DFDC of summer season (April, May and June) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921

Abbreviations: BHU, Banaras Hindu university; MWW, Municipal waste water; SWW, Sewage waste water; BSP, Brocha sewage Plant; BSS, Brocha sewage station; MHPP, Micro-hydro power plant; MHPS, Micro-hydro power system; SHPP, Small hydro power plant; SHPG, Small hydro power generation; FDC, Flow duration curve; AFDC, Annual flow duration curve; AAFDC, Average annual flow duration curve; DFDC, Daily flow duration curve; ADFDC, Average daily flow duration curve; MFDC, Monthly flow duration curve; SHPGS, Small hydro power generation system; MHPGS, Micro-hydro power generation system; SEIG, Self-excited induction generator; PMG, Permanent magnet generator; HDPE, High density poly ethylene; uPVC, un-plasticized polyvinyl chloride; WWF, Waste water flow; MTTF, Mean time to failure; MTBF, Mean time between failures; MTTR, Mean time to repair; GDA, Gaussian distribution approach; PLC, Peak load considerations; SFC, Safety factor concept; LDC, Load duration curve; SLDC, Stepped load duration curve; LOLP, Loss of load probability; SF, Safety Factor; LPS, Litters per Second; MHT, Micro-hydro turbine; MHP, Micro-hydro power; MHPG, Micro-hydro power generation; SPS, Sewage power station; IST, Indian standard time; DPLVC, Daily peak load variation curve ☆ This work was supported in part by the Department of Electrical Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, Uttar Pradesh, India. n Tel.: þ 91 542 6702837, þ 91 9451067022, þ 91 9889848412. E-mail addresses: [email protected], [email protected] 1 R.K. Saket was with the Electrical and Electronics Engineering group, Birla Institute of Technology and Science, Pilani (Rajasthan), India and Rajiv Gandhi University of Technology, Bhopal, Madhya Pradesh, India. 1364-0321/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.rser.2013.08.033

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3.1.5. Interpretation of ADFDC and AAFDC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921 3.2. Power estimation of developed MHPP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922 3.3. Reliability indices evaluation using flow duration curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922 4. Probabilistic approaches for reliability evaluation of developed MHPGS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 4.1. Gaussian distribution approach (GDA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 4.2. Reliability evaluation based on peak load consideration (PLC) and safety factor concept (SFC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 4.3. LOLP evaluation using Simpson 1/3rd rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 923 5. Result and discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924 5.1. Discussion on reliability evaluation of MHPP using GDA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924 5.1.1. Case: I evaluation at constant load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924 5.1.2. Case: II evaluation at constant generation capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 924 5.2. Discussion on reliability evaluation using SFC and PLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 5.2.1. Case: I evaluation at constant load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 5.2.2. Case: II evaluation at variable load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 5.3. LOLP evaluation using Simpson 1/3rd rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926 5.3.1. Case: I LOLP evaluation for 5 steps of SLDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926 5.3.2. Case: II LOLP evaluation for 10 steps of SLDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926 5.3.3. Case: III LOLP evaluation for 20 steps of SLDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927 5.3.4. Case: IV LOLP evaluation for different steps of SLDC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927 6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928

1. Introduction Micro-hydro power generation system (MHPGS) is one of the popular renewable energy sources in the developing countries. MHPGS has obtained increasing interests in the 21st century due to their ecological irreproachability and acceptable prices for generating electrical power without producing harmful pollution and green house gases. MHPGS based on municipal waste water (MWW) is considered as an environment friendly renewable energy source since this can be sized and designed to limit the interference with river flow and canal flow. Most of the MHPGS's operate in isolated mode for rural electrification of remote villages where the population is very small and extension of the distributed grid system is not geographically and financially feasible due to the high cost investment in a power transmission system. Small hydroelectric power generation systems (SHPGS's) are relatively small power sources that are appropriate in many cases for individual users or groups of users who are independent of the electricity supply grid. Although this technology is not new, its wide application to small waterfalls and other potential sites like MWW based system are new [1]. SHPGS's are the application of hydroelectric power on a commercial scale serving a small community and are classified by power and size of waterfall. Small hydro-power plants (SHPP) can be divided into mini-hydro (less than 1000 kW capacity), and micro-hydro power system (MHPS) which has less than 100 kW capacity. Hydroelectric power is the technology of generating electric power from the movement of water through rivers, streams, and tides. Water is fed via a channel to a turbine where it strikes the turbine blades and causes the shaft to rotate. To generate electricity the rotating shaft is connected to a generator which converts the motion of the shaft into electrical energy [2]. Generally, in an autonomous MHPS, the small hydro-power generators (SHPG's) are the main constituents of the system and are designed to operate in parallel with the local power grids. The main reasons are to obtain economic benefit of no fuel consumption by micro-hydro turbines (MHT), enhancement of power capacity to meet the increasing demand, to maintain the continuity of supply in the system, etc. Small/micro-hydro is highly fluctuating in nature and will affect the quality of supply considerably and may even damage the system in the absence of proper control mechanism. Main parameters to be controlled are

the system frequency and voltage, which determine the stability and quality of the supply. In a MHPGS, frequency deviations are mainly due to real power mismatch between generation and demand. Reactive power balance in the hybrid system can be obtained by making use of a variable reactive power device e.g. static VAR compensator [3]. Comparisons of various penstock materials have been presented considering friction, weight, cost, corrosion, joining and pressure for reliable operation of the MHPP. Hybrid power systems are the most attractive option for the electrification of the remote locations. These include high cost because of the system complexity, site specific design requirements and the lack of available control system flexibility. Many countries have targets and aspirations for growth in renewable energy. If a new alternative generation technology is introduced that makes a relatively low contribution to the reliability of meeting peak demand then additional capacity may be needed to provide system margin and cost is improved on the rest of the system. Quantification of the system costs of additional renewable in 2020 has been presented in [4]. MHPP using sewage waste water (SWW) neither requires a large dam nor is land flooded. Only waste water from different parts of the city is collected to generate power which has minimum environmental impact. After proper chemical treatment, water is provided to farmers for irrigation purpose. MHPGS using MWW of sewage plant can offer a stable, inflation proof, reliable, economical and renewable source of electricity. This alternative technology has been appropriately designed, developed and practically implemented at the Brocha sewage plant (BSP) of the Banaras Hindu University (BHU) campus. Reuse of the MWW can be a stable, inflation proof, economical, reliable and renewable energy source of electricity in the power scenario of the 21st century [5]. This paper is organized as follows: Section 1 presents an overview on MHPGS based on MWW. The selection criteria and brief descriptions on basic components of designed and developed MHPGS at BHU campus is described in Section 2. Selection criteria of penstock pipe materials, water turbines and various generators for different head are explained in this section. Annual, monthly and daily flow duration curves (AFDC, MFDC and DFDC) have been obtained for design and development of the MHPP based on MWW by recording water flow rates in Section 3. Generation reliability of constructed MHPP has been evaluated using the Gaussian distribution approach

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Nomenclature sc sd sL C C

Standard deviation of generation capacity Standard deviation of load demand Standard deviation of load generation capacity of MHPP Mean capacity of the plant

(GDA), peak load considerations (PLC), safety factor concept (SFC) and Simpson 1/3rd rule in Section 4. Results and analytical discussions are presented in Section 5. Section 6 concludes this project work as an energy scenario of the 21st century.

2. Brief descriptions on basic components of developed MHPP The principal components of the MWW based MHPGS are waste water tank, penstock pipe, water turbine and induction generator. MWW and self-excited induction generator (SEIG) based MHPGS has been designed developed and constructed at the Brocha sewage station (BSS) of the Banaras Hindu University, Varanasi (Uttar Pradesh) India during the session: 2008–2009 [1]. Prototype MHPGS has been designed; installed and tested using farmland irrigation water flowing in canals at Taiwan. The designed micro-hydro power (MHP) unit consists of a water wheel containing 16 blades, a mechanical shaft, two bearings, a gear box and a permanent magnet generator (PMG) and inverters. The low rotational speed of the water wheel can be speeded up to the required rotational speed of the PMG through the designed gear box [6]. The following principal components of the developed MWW based MHPGS have been designed for reliable operation of the system. 2.1. Selection of penstock pipe The penstock is the most expensive item in this project which may cost up to 40% of the total project cost. It is worthwhile to optimize its design to reduce cost. The choice of size and types of materials depends on several factors for a particular penstock i.e. design pressure, roughness of pipe's interior surface, method of joining, weight and ease of installation, accessibility to the site, design life and maintenance, weather conditions, availability, relative costs, likelihood of structural damage and so on [1]. The most commonly used materials for a penstock are mild steel, high density poly ethylene (HDPE) and un-plasticized polyvinyl chloride (uPVC), because of their suitability, availability and approvability. The uPVC exhibits excellent performance over mild steel and HDPE in terms of least friction losses, weight, corrosion, cost etc. Comparison of the penstock materials considering friction, weight, corrosion, cost, joining and pressure have been explained in [4]. uPVC material is selected and used for the design of the penstock pipe for development of this project. 2.2. Selection of turbine The hydraulic turbine receives mechanical hydraulic energy and converts it to mechanical rotational energy, made available at its axis which is connected to an electric generator. The efficiency of a turbine is a function of many variables, such as: nominal power of turbine, type of the turbine, percentage of turbinated fluid, physical position of the axis in relative to the vertical plan etc. The choice of water turbine depends mainly on the head and SWW flow rate for installation of the MWW and SEIG based MHPP.

Φ(β) f(Pd) f(C) Pd d

P PF PS

919

area under the normal distribution curve Normal distribution function for load Normal distribution function for capacity Demand at developed MHPP Average or mean load at the plant failure probability of power plant success probability of power plant

The selection also depends on the desired running speed of the generator. To adjust variations in stream flow, water flow to these turbines is easily controlled by changing nozzle sizes or by using adjustable nozzles. Turbines used in the hydro system can be classified as Impulse (Pelton, Turgo and Cross flow), Reaction (Francis, Propeller, and Kaplan) and water wheels (under-short, breast-shot and overshot). Groups of the water turbine for various heads available at BSP for SWW based MHPP is described in Ref. [5]. The reliability and performance of the developed MHPGS based on MWW and SEIG are dependent on the turbines/water wheels efficiency. Kaplan turbine is used for reliable performance, installation and establishment of this project.

2.3. Selection of generator Induction and synchronous generators are used in power plants and both are available in three phase or single phase systems. Induction generators are generally appropriate for MHPGS [1]. Induction generator offers many advantages over a conventional synchronous generator as a source of isolated power supply. Reduced unit cost, ruggedness, brush less (in squirrel cage construction), reduced size, absence of separate DC source and ease of maintenance, self-protection against severe overloads and short circuits, are the main advantages [8]. Capacitors are used for excitation and are popular for smaller systems that generate less than 10–15 kW. Use of induction generator is increasingly becoming more popular in MHP application because of its simpler excitation system, lower fault level, lower capital cost and less maintenance requirement. However, one of its major drawbacks is that it cannot generate reactive power as demanded by the load. Most of the early stages MHPP are equipped with synchronous generators [9]. SEIG is used at installed MHPGS. In general, SEIG is applicable for the unregulated prime mover speed. Working principle of SEIG depends on the minimum shaft speed to start generation. Generation voltage of SEIG depends on the shaft speed, residual magnetism, reduced permeability at low magnetization and value of the capacitor connected to the machine. Reliability of the self excitation must be very high during generation period. It is achieved either by increasing the speed or increasing the capacitor value or both. Residual magnetism and permeability of the rotor iron core cannot be changed during operating condition of the SEIG. However, capacitor value and shaft speed can be changed [10]. The generation of the SEIG depends only on the shaft speed, if maximum values of the capacitors or fixed capacitors are used. Terminal voltage of the SEIG is directly proportional to the shaft speed. If shaft speed of the SEIG is decreased below the particular value of the speed, then generation will stop. This particular value of shaft speed is called the minimum value of speed or threshold speed [11]. This has a particular constant value, where generation starts and stops. SEIG generates voltage when shaft speed of the generator is equal or greater than this minimum value of the speed. Similarly, if shaft speed of generator is below than the minimum value of the threshold speed, SEIG cannot generate any voltage. Many times generation failure is noticed due to lower shaft speeds i.e. threshold speed of the SEIG. Reliability condition of the power generation only

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depends on the shaft speed. So evaluation of the success and failure probabilities of the MWW based MHPP is required [11]. 3. Flow – duration curves, power estimation and reliability indices evaluation of MHPP In this paper, annual, monthly and daily flow duration curves (FDC) have been obtained for the development and installation of the MHPP by recording water flows from maximum to minimum values. Annual flow duration curve (AFDC) and daily flow duration curve (DFDC) of the developed system have been obtained for the performance and reliability evaluation of the MHPGS. The AFDC and DFDC are used to assess the expected availability of water flow, flow variations and power capability to select the type of the turbine and generator [4]. According to FDC there is a difference in waste water flow (WWF) between summer (March–June) and winter (November–February) cycles and this can affect the power output produced by the installed MHPP. The generation of the developed MHPP depends directly on the SWW flow rate which fluctuates seasonally and regionally. The Indian subcontinent is largely subject to four seasons: monsoon or rainy season (July–September), post-monsoon period (October–early December), winter season (December–early March) and summer season (March–June). The SWW flow rates can have a very big variation throughout the year implying that the energy availability for generation can not be considered as the nominal value estimated into the MHPP project. These variations have been considered for the estimation of the total expected power generation [4]. Peak load demand has considered for evaluation of reliability of the MHPGS at different generation capacities, load demand and atmospheric variations. Output power has been estimated at different flow rates and heads available in sewage system of the Banaras Hindu University (BHU), Varanasi, India. Reuse of MWW of the city can be a stable, inflation proof, economical, reliable and renewable energy source in the power scenario of the 21st century [5]. 3.1. DFDC and AFDC of developed MHPP In this paragraph, daily flow duration curves (DFDC) and annual flow duration curves (AFDC) have been obtained by recording the MWW flows from maximum to minimum values. For development of the DFDC of any month of the assessment year, 24 h of the 15th day of each month is considered for the flow rate measurement. DFDC and AFDC of the developed plant have also been obtained from the average values of the 3 years duration (from July 2009 to June 2012) for power estimation and reliability evaluation of the MHPG system as shown in Figs. 5 and 6 respectively. The educational calendar or academic session of the BHU starts from July and ends in June every year. Plant data are collected for three academic sessions from July, 2009 to June, 2012 regularly for power estimation and reliability evaluation of the developed MHPP. Peak load demand at different working conditions of the generation capacity, load demand and atmospheres variations have been considered to evaluate the reliability of the MHPG system. 3.1.1. DFDC of monsoon season (July, August and September) The Indian subcontinent is subject to monsoon or rainy seasons from July to September. The rainy season is dominated by the humid south west summer monsoon, which slowly sweeps across the country starting in the June. The new academic session of the BHU starts in July, which is rainy season. Therefore, waste water flow (WWF) rate mostly reaches the maximum point from July to September as shown in Fig. 1. Maximum WWF rate of around 6 m3/s is recorded during the evaluation of the developed MWW based MHPP. During these 3 months the average MWW flow rate is above 5 m3/s. Hourly variations in the SWW are considered for

Fig. 1. DFDC for July, August and September months.

24 h as shown in Fig. 1. The number of failure of generation due to minimum speed and repair time is low as described in the Figs. 8 and 9. The operating time of the MHPGS during this period is high due to availability of the SWW at BSP of the BHU campus.

3.1.2. DFDC of post-monsoon and pre-winter season (October, November and December) The winter season period in Indian subcontinent is from last October to early February. The year's coldest months are December and January, when temperatures average around 5–15 1C in the north India. During October and November, MWW flow rate decreases due to starting of the winter season. Two long holiday periods on Dashahara and Deewali festivals in India during these months decrease the SWW flow rate of the sewage plant. December provides semester break period as well as coldest atmospheric conditions in north India. Therefore, MWW flow rate decreases and comes down into its deep point in December. After October and November the average MWW flow rate decreases from 5 m3/s to below than the 4 m3/s as shown in Fig. 2. During October and November, the number of generation failure and repair time both are higher than in the monsoon season (July, August and September) as shown in Figs. 8 and 9. The operating time of the MHPGS decreases during these months. SWW flow rate during December is near about 4 m3/s. Number of failures and repair time of the developed system are high and operating time is low during December as described in the Figs. 8 and 9.

Fig. 2. DFDC for October, November and December months.

R.K. Saket / Renewable and Sustainable Energy Reviews 28 (2013) 917–929

Fig. 3. DFDC for January, February and March months.

3.1.3. DFDC of winter and pre-summer season (January, February and March) For the SWW based MHPP where the flow can vary in a wide range from one season to another and the filling are of small capacity, there are intervals when the flow is too low and the power plant cannot operate. Similarly, intervals when the SWW flow is too high, thus a significant amount of power is wasted. These variations have been described graphically in Figs. 1–4. MWW flow rate increases in January due to starting of the even semester from the first week of this month. But it does not reach up to the maximum point due to winter days. Flow rate increases in last February and March during spring season but do not reach up to the maximum point due to holidays on Holi festival. During February and March SWW flow rate is 5.8 m3/s which is suitable for power generation. The average flow rate decreases from 5 m3/s to below than 4.5 m3/s in January as shown in Fig. 3. SWW flow rate at BSP is measured by plant workers. A record register for SWW flow rate and water level is maintained by the BSP employees. Various data are available at BSS of the BHU since 2006 for power estimation and reliability evaluation using ADFDC and AAFDC of the developed plant as explained in Figs. 5 and 6. Hourly variations in WWF and water head have been considered for performance evaluation of MHPP and described in Fig. 3. The number of failures of generation and repair time decreases as compared with the report of December. However, the operating time of the MHPGS is increased during these months. Power availability, generation reliability and operating time are decreased during January month.

3.1.4. DFDC of summer season (April, May and June) The summer season in the Indian subcontinent is from April to June. May and June are the hottest months in the North India. Temperature averages around 35–45 1C during these months in India. In April, MWW flow rate is standard for electricity generation. Summer vacation of the BHU starts from May to June, so MWW flow rate again decreases during these two months. The average flow rate decreases from approximately 5 m3/s to 4.5 m3/s during these months as shown in Fig. 4. The number of failures of generation and repair time are approximately low in April due to unavailability of water head. However, the operating time is approximately low in April. Number of generation failure and repair time increases during the May and June as shown in Figs. 8 and 9. However, the operating time of the MHPGS decreases due to unavailability of the MWW during the summer vacation.

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Fig. 4. DFDC for April, May and June months.

Power generation is impossible during June due to unavailability of the SWW flow rate and water head at BSP of the BHU campus.

3.1.5. Interpretation of ADFDC and AAFDC Average daily flow duration curve (ADFDC) and average annual flow duration curve (AAFDC) of the MWW based MHPP from July 2009 to June 2012 are analyzed for average power estimation of the developed MHPP as shown in the Figs. 5 and 6 respectively. Average values of the ADFDC described power generation period from 05.00 am to 08.00 pm IST as shown in Fig. 5. Similarly, average values of the AAFDC present suitable months for operation of the developed MHPP. January–April and July–December are

Fig. 5. ADFDC for 3 years (July 2009–June 2012).

Fig. 6. AAFDC for 3 years (July 2009–June 2012).

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R.K. Saket / Renewable and Sustainable Energy Reviews 28 (2013) 917–929

30

40000 Flow Rate(lps) 05 Flow Rate(lps) 10

Power Output (w)

30000 25000

Flow Rate(lps) 15

20000

Flow Rate(lps) 20

15000

25 20

Average Failure

35000

15 10

Flow Rate(lps) 40

10000

5

Flow Rate(lps) 60 5000

0 July Aug Sep

Flow Rate(lps) 80

0 2

4

8

10

15

20

40

60

80

Oct

Nov Dec

Realistic power output of the MWW based MHPP depends on the theoretical power available and efficiency factor of the plant. The theoretical amount of output power available from a MHPS is directly related to the WWF rate, waste water head and the force of the gravity [1]. To calculate the actual power output from MHPP, friction losses in the penstock pipes and the efficiency of the turbine and generator are considered. Typically overall efficiencies for electrical generating systems can vary from 50% to 70% with higher overall efficiencies occurring in high head systems [11]. Therefore, to determine a realistic power output as shown in Table 1, the theoretical power must be multiplied by an efficiency factor of 0.5–0.7 depending on the capacity and type of system [1,11]. The efficiency factor of 0.7 has been used for reliability evaluation of the developed MHPP based on SWW. Graphical representation of the typical power output with various MWW heads and water flow rates are illustrated in Fig. 7. Power estimation at different flow rates as presented in Table 1 is carried out from the data available in the developed MHPP of the BHU campus. 3.3. Reliability indices evaluation using flow duration curves In generation reliability studies, it is usual to consider the energy sources for generation as always available. This implies that the only cause of generation unavailability is the failure of the generation unit of the MHPP. However, in SWW based MHPP, where a reservoir does not exit, the energy availability cannot be considered 100% reliable [12]. The objective of this paper is to present an approach for evaluating MWW based MHPP generation availability that can be applied to generation system reliability. And to generation planning studies, which consider both the uncertainties of SWW flow rate and generation unit operation. SEIG shaft speed depends on the MWW flow rate. The threshold speed of the MWW and SEIG based MHPG system has been calculated from the experimental results. The value of threshold speed of MWW is 3.5 m3/s for this particular case. Thus, shaft speed of the SEIG due to MWW flow rate lower than the 3.5 m3/s,

Mar April May June july

Fig. 8. Average failure Chart of MHPGS (July 2009–June 2012).

Fig. 7. Output power estimation with different heads and water flow rates of MHPP.

3.2. Power estimation of developed MHPP

Feb

Duration(Months)

Head (m)

operating time

Repair time

45000 44500 44000 Times(min.)

suitable for generation of electricity due to availability of the SWW flow rate and water head at BSP of the BHU campus. Various interpretations for average power estimation of the MHPP have described graphically in Figs. 5 and 6. According to available average FDC's of the developed sewage power station, the average value of the WWF rate is 4.67 m3/s. Operating zone of the SPS for a particular day for generation of electricity is presented graphically in Fig. 5. Similarly, operating zone for a particular month of the year is described in Fig. 6.

Jan

43500 43000 42500 42000 41500 41000 40500 40000

Duration

Fig. 9. Average repair and operating time of the developed system.

Table 1 Output power estimation (w) with different SWW heads and water flow rates. Municipal waste water flow rate in litters per second (m3/s) 5 SWW head (m) Output 2 49 4 98 8 196 10 245 15 368 20 490 40 980 60 1470 80 1900

10

15

20

40

60

power (W) estimation of developed MHPP 98 147 196 392 588 196 294 392 784 1176 392 588 784 1568 2352 490 735 980 1960 2940 735 1103 1470 2940 4410 980 1470 1960 3920 5880 1960 2940 3920 7840 14,112 2940 4410 5880 14,112 21,168 3920 5880 7840 18,810 28,224

80

784 1568 3136 3920 5880 7840 18,816 28,224 37,632

generation will stop. So, reliability of the generation failure due to lower speed from the threshold speed is examined successfully. For reliability evaluation of the MHPP, ADFDC of each month have been drawn to get idea of the failure and success generation at particular time. Generation time, repair time and number of times when generation fails for each month have discussed successfully in Figs. 8 and 9 for reliability evaluation of the system. Reliability indices like: failure rate (λ), repair rate (m), mean time to failure (MTTF), mean time to repair (MTTR) and mean time between failure (MTBF) of the system have been evaluated and included in Table 2. Evaluation of the number of generation failure and its repair time of every month have presented in this section. These data are calculated from the sewage flow rate at BSP of the BHU campus. Total time for the average data collection is three years (July 2009–June

R.K. Saket / Renewable and Sustainable Energy Reviews 28 (2013) 917–929 Table 2 Evaluation of Failure rate, Repair rate, MTTF, MTTR and MTBF for case: I. Reliability indices

Session: I (2009–2010)

Session: II (2010–2011)

Session: III (2011–2012)

Failure rate (λ) Repair rate (m) MTTF (r) MTTR (m) MTBF (T)

0.0115 f/h 0.765 r/h 86.952 h 1.306 h 88.26 h

0.276 f/day 18.3 r/day 3.623 days 0.0544 day 3.6774 days

100.74 f/yr 6701.4 r/yr 0.0099 yr 0.00015 yr 0.0101 yr

923

Above transformation corresponds to rotation of axis by θ angle. Following substitutions have made in Eq. (5). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Let sin θ ¼ ðsc = P 2d þ s2C Þ and cos θ ¼ ðsd = P 2d þ s2C Þ In view of the above substitution in Eq. (5), Success probability of the MHPP is given written as follows: Z 1Z β 1 0:5ðx′2 þ y′2 Þ e dy′dx′ ð6Þ Ps ¼ 1 1 2π P d where β ¼ pCffiffiffiffiffiffiffiffiffiffiffi 2 2 sd þ sC

2012). July, August, September, March and April have less number of generation failure and repair time. Thus, success probability of system is high during these months. December, January, May and June months are not the suitable periods for generation due to unavailability of the suitable MWW flow rates. Thus, success probability of the developed system is low during these months. Average failure and average repair chart verses operating time of the MHPP have been illustrated in Figs. 8 and 9 respectively.

4. Probabilistic approaches for reliability evaluation of developed MHPGS Reliability is the probability of system performing its function adequately for an intended period of time under the operating conditions intended. According to this statement success probability, adequate function, time period and operating condition are the basic attributes of the system reliability [13]. Reliability indices and success/failure probabilities have been evaluated using Gaussian distribution approach (GDA), peak load consideration (PLC) and safety factor concept (SFC) and Simpson 1/3rd rule successfully. 4.1. Gaussian distribution approach (GDA) The load model of the MWW based MHPP station is Gaussian distributed for a specified time interval [7,8]. f ðP d Þ ¼

2 1 pffiffiffiffiffiffie0:5ððP d P d Þ=sd Þ sd 2π

ð1Þ

The aggregate generation capacity model of the installed MHPG system is Gaussian distributed system [1–5]. 2 1 f ðCÞ ¼ pffiffiffiffiffiffie0:5½ðCC Þ=sc  sc 2π

ð2Þ

The failure probability (PF) for the above generation and load models of the developed system is described as follows: P F ¼ ð1P s Þ

ð3Þ

The success probability (Ps) of the developed power system using GDA can be expressed as follows [7,8]: Z 1Z C 2 2 1 e0:5½ðCC Þ=sc  e0:5ððP d P d Þ=sd Þ dc:dP d ð4Þ Ps ¼ 1 1 2πsc sd Putting, x ¼ ððCC Þ=sc Þ and y ¼ ððP d P d Þ=sd Þ Above Eq. (4) can be written as follows after simplification according to substitution conditions.  Z 1 Z z 2 2 Ps ¼ e0:5ðx þ y Þ dy dx ð5Þ 1

1

where Z ¼ ððsc x þ C P d Þ=sd Þ Further making substitution in (5) as follows, consider x΄ ¼x cos θ þy sin θ y΄ ¼ x sin θþy cos θ

The limit β comes out to be independent of x′. Further Eq. (6) is simplified as follows:  Z β Z 1 1 ′2 ′2 pffiffiffiffiffiffie0:5ðx Þ dx′ e0:5ðy Þ dy′ Ps ¼ 2π 1 1 Z þβ 1 2 pffiffiffiffiffiffie0:5ðy′ Þ dy′ ¼ φðβÞ ð7Þ Ps ¼ 2π 1 The numerical value of φ(β) is the area under the normal distribuRβ tion curve having mean¼0 and standard deviation 1 ½Nð0; 1Þ ¼ 1 and this value can be conveniently obtained from standard normal distribution table. Failure probability vs. generating capacity curves have been plotted for different value of the capacity and load models using Eq. (7) in Section 5. 4.2. Reliability evaluation based on peak load consideration (PLC) and safety factor concept (SFC) The probability distribution function of generation capacity is obtained as Gaussian. Peak loading of the system dominates over low-level loading, whereas, the probability of failure under low load level condition is negligible. If Pdmax is the peak load on the MHP system, the safety factor ‘S’ is defined as follows: S ¼ C=P d max

ð8Þ

The generating capacity ‘C’ of the installed MHPP is normally distributed and S is a random variable. At constant Pdmax the distribution of the safety factor ‘S’ will also be normally distributed [7]. The safety factor function is given as follows: P ffiffiffiffiffiffi e0:5ððPdmax SC Þ=sc Þ f s ¼ pdmax 2π sc

ð9Þ

Safety factor S has a Gaussian distribution with mean. S¼

C sc and ss ¼ P dmax P dmax

Probability of failure of the system is given as follows: " # Z 1 2 P ðð1ðC=P dmax ÞÞ=sc Þ pdmax ffiffiffiffiffiffi e0:5ððsc =P dmax Þ=ss Þ ds ¼ ϕ PF ¼ P dmax 2π ss 1

ð10Þ

ð11Þ

The failure probability of installed MHPP has obtained using Eq. (11) at different generation capacity and peak loads. PF vs. ðC=P dmax Þ curve has been plotted for reliability evaluation of the system using safety factor concept. These curves can be used as a standard curve for evaluating the failure probability of the generating capacity using Eq. (11). 4.3. LOLP evaluation using Simpson 1/3rd rule Failure probability of developed MHPP is evaluated with more realistic model as load duration curve. The individual daily peak loads can be arranged in descending order to form a cumulative load model which is known as the daily peak load variation curve (DPLVC). The resultant model is known as the load duration curve (LDC) when the individual hourly load variance used [14]. Generation model adopted in this system has Normal distribution function. The reliability

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evaluation is based on maximum average generation capacity available. The probability of load exceeding the generation capacity is called the loss of load probability (LOLP). A ‘loss of load’ will occur only when the capability of the generation capacity remaining in service is exceeded by the system load level. The LDC is divided into a number of steps to produce the multi step model. This is an approximation: the amount of approximation can be reduced by increasing the number of steps [14]. Maximum 100 steps of the SLDC are considered for evaluation of the LOLP of developed system. Various steps of the stepped load duration curve (SLDC) indicate variation in load during 24 h operation of the power system. Following approximation is based on the Simpson's 1/3rd rule for evaluation of the reliability index: LOLP. LOLP of the developed system using SLDC is written as follows: Z P d ðtÞ Z 100 2 t 1 pffiffiffiffiffiffi e0:5ððCC Þ=sc Þ dcdt LOLP ¼ ð12Þ 100 1 2π sc 0 Putting,

CC sC

Table 3 Mean Capacity and Standard Deviation data. Capacity (W)

490

495

500

505

510

515

520

rc ¼ 5% rc ¼ 15%

24.5 73.5

24.75 74.25

25 75

25.25 75.75

25.5 76.5

25.75 77.25

26 78

¼Z

The LOLP expression for 100 steps of the SLDC using Eq. (12) is expressed as follows [1,5]: Z P d ðtÞ  Z 100 2 t 1 pffiffiffiffiffiffi e0:5ðZÞ dz dt LOLP ¼ 100 1 2π sc 0 Z LOLP ¼

100 0

! t P d ðtÞC φ dt 100 sc

ð13Þ

The LOLP based on SLDC of the developed system is evaluated by Simpson's 1/3rd rule for reliability approximation. LOLP of the system is evaluated considering LDC as SLDC with maximum 100 steps. This may be possible if daily load duration curve can be approximated as multilevel representation as in the case with Markov modeling of load in frequency and duration calculations. This paper presents LOLP evaluation for 5, 10 and 20 steps only. Generally load varies every moment during the 24 h operation of the system. Load varies many times in steps daily. SLDC of the power system is an important keyword for power system planning and reliability evaluation of system.

5. Result and discussions Failure probability as explained in Section 4 is evaluated using various set of data available at developed MHPP at BSS of the BHU campus using prababilistic approachs. Discussions on obtained results have been described as follows. 5.1. Discussion on reliability evaluation of MHPP using GDA 5.1.1. Case: I evaluation at constant load The failure probability of installed MHPP has evaluated keeping mean load constant at 480 W using Eq. (7). Standard deviation data have been evaluated and included in Table 3. The standard deviations for both generating capacity and mean load have assumed 10% of the generating capacity and mean load, respectively. The probability of failure has been evaluated for generation capacity C ¼490 W as Pf ¼0.3853. Generating capacity increased in step of 5 W at the fixed value of the mean load at 480W and the probability of failure has been evaluated using Eq. (7). Various plots of failure probability versus generating capacity are shown in the Fig. 10 selecting the following values of the standard deviations. (i) (ii) (iii) (iv)

Curve Curve Curve Curve

A: (sc ¼5% of capacity and sd ¼5% of load). B: (sc ¼5% of capacity and sd ¼15% of load). C: (sc ¼15% of capacity and sd ¼5% of load). D: (sc ¼ 15% of capacity and sd ¼15% of load).

Fig. 10. PF vs. C of the developed system at constant load.

5.1.1.1. Discussion on case: I. The various curves are labeled for various combinations of sc and sd. It is observed from A and B that for the same generating capacity of the MHPP system, the probability of failure with B is more than A. This is due to fact that large uncertainty involved in generating capacity distribution function. Similarly by observing the curve A and C for the same generating capacity the probability of failure for B is more than C and so on. From the curve D, the failure probability for any generating capacity is more than from other curves. In summary, the probability of failure increases with either increase of sc or increase of sd or both sc and sd. 5.1.2. Case: II evaluation at constant generation capacity The failure probability of installed MHPP at constant generation capacity (500 W) has evaluated using GDA in this section. The standard deviations for both generating capacity and mean load have been assumed 5% of the generating capacity and mean load respectively. The probability of failure has been evaluated for generation capacity C ¼500 W as Pf ¼0.4432. Now the load increased in step of 5 W at the fixed value of the mean capacity at 500 W and the probability of failure has been calculated. The mean load and standard deviation data for demand have presented in Table 4. Various plots of failure probability versus generating capacity are shown in Fig. 11 selecting the following values of the standard deviations. (i) (ii) (iii) (iv)

Curve Curve Curve Curve

A: (sc ¼ 10% of capacity and sd ¼10% of load). B: (sc ¼ 10% of capacity and sd ¼20% of load). C: (sc ¼ 20% of capacity and sd ¼10% of load). D: (sc ¼20% of capacity and sd ¼20% of load).

Table 4 Mean load and standard deviation data. Load (W)

490

495

500

505

510

515

520

rd ¼ 10% rd ¼ 20%

49 98

49.5 99

50 100

50.5 101

51 102

51.5 103

52 104

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925

Fig. 11. PF vs. generating capacity at constant capacity. Fig. 12. Failure Prob vs. Safety factor at variable load.

5.1.2.1. Discussion on case: II. If the mean load and generating capacity are equal then the probability of failure and the probability of success are exactly equal to 50%. It is same in the all cases independent of standard deviations as shown in Fig. 11. Below the intersection point the probability of failure increases as the variations sc and sd increases and above the intersection point it varies oppositely. The PF has been evaluated for sd ¼ 10% of 



L and sC ¼ 10% of C using Eq. (7) and the overall failure probability evaluated as 0.0594. If the values of standard deviations sC and s1 are increased from 10% to 20%, the overall failure probability increased by same values of generating capacity and load levels 

at fixed frequency of occurrence. At the value of sC ¼20% of C and 

sd ¼20% of L , the failure probability has been evaluated as 0.0986. 5.2. Discussion on reliability evaluation using SFC and PLC 5.2.1. Case: I evaluation at constant load This section discusses generating capacity adequacy evaluation based on safety factor and worst case loading condition, assuming maximum loading Pdmax ¼480 W on the system. The probability of failure has been evaluated in Table 5 for different values of generating capacity available at MHPP using Eq. (11). The curve has been plotted between probability of failure and safety factor (C/Pdmax) for different value of standard deviations as shown in Fig. 12 considering the following approximations: (i) (ii) (iii) (iv)

Curve Curve Curve Curve

A for sc ¼ 10% of C. B for sc ¼12% of C. C for sc ¼15% of C. D for sc ¼18% of C.

5.2.1.1. Discussion on case: I. It is observed from the curves A and B, the probability of failure with sc ¼12% of C is more than sc ¼ 10% of C for same generating capacity or safety factor of the system, Now if sc increased for same values of generation capacity and safety factor of the system, the Pf is increased. Failure probability of system decreased with increasing the safety factor for all values of the generation capacity. For any value of the safety factor of generation capacity, failure probability increases with increase in its standard deviation. All interpretations are described in Fig. 12. Probability evaluation is based on Eq. (11). Fig. 12 presents failure probability vs. safety factor approximation at constant load and variable generation capacity. Safety factor and failure probability have evaluated for different

Table 5 Generating Capacity and Standard Deviation. Capacity (W)

490

495

500

505

510

515

520

sc ¼ 10% sc ¼ 12% sc ¼ 15% sc ¼ 18%

49 58.8 73.5 88.2

49.5 59.4 74.25 89.1

50 60 75 90

50.5 60.6 75.75 90.9

51 61.2 76.5 91.8

51.5 61.8 77.25 92.7

52 62.4 78 93.6

generation capacity available at developed MHPP. For 10.5% safety factor, failure probability increases with increasing values of the standard deviation of the generation capacity. 5.2.2. Case: II evaluation at variable load If the maximum loading increased from Pdmax ¼ 480–510 W, 

for same value of safety factor (C /Pdmax) the various curves are shown in Fig. 13. (i) (ii) (iii) (iv)

Curve Curve Curve Curve

A for sc ¼10% of C. B for sc ¼12% of C. C for sc ¼15% of C. D for sc ¼18% of C.

The PF increases with increase of sC for same values of generation capacity. This is due to fact that large uncertainty involved in the generating capacity distribution factor. 5.2.2.1. Discussion on case: II. The failure probability of generation system is constant and equal to 50% for all curves at variable load if the safety factor is one. If safety factor is below one then the failure probability for sc ¼10% of C is more than sc ¼12% of C and if it is greater than one the failure probability is simply varies oppositely. Fig. 13 provides opposite approximations before and after the 100% values of the safety factor. Safety factor is the ratio of the generation capacity and peak load demand. Safety factor is one at equal values of the generation capacity and peak load. At this instant, failure or success probability both are 50% as shown in Fig. 13.Approximation of the Fig. 13 is based on the variable load and constant generation capacity. If generation capacity is higher than the load, failure probability of curve A is higher than the curve B, C and D. Similarly, if load is higher than the generation capacity, failure probability of the curve A is less than the B and vice versa.

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Fig. 14. LOLP vs. generation capacity for 5 steps.

Fig. 13. Failure probability vs. Safety factor at variable load.

Table 6 Generation capacity for evaluation of LOLP with stepped load duration curve.

Table 7 LOLP for 5 steps of the SLDC.

Capacity (W)

sc ¼ 10% of C

sC ¼ 10% of C

sc ¼ 20% of C

sc ¼25% of C

Loss of Load Probability for 5 steps of SLDC

500 550 600 650 700 800 850 900 950 1000 1050 1100 1150 1200 1250 1300 1350 1400

50 55 60 65 70 80 85 90 95 100 105 110 115 120 125 130 135 140

75 82.5 90 97.5 105 120.0 127.5 135.0 142.5 150.0 157.5 165.0 172.5 180.0 187.5 195.0 202.5 210

100 110 120 130 140 160 170 180 190 200 210 220 230 240 250 260 270 280

125.0 137.5 150.0 162.5 175.5 200.0 212.5 225.0 237.5 250.0 262.5 275.0 287.5 300.0 312.5 325.0 337.5 350.0

Capacity C

Curve D for sc ¼ 25% of C

Curve C for sc ¼20% of C

Curve B for sc ¼ 15% of C

Curve A for sc ¼ 10% of C

500 550 600 650 700 750 800 850 900 930 950 1000 1050 1110 1130 1190 1400 1550

0.0940 0.0930 0.0920 0.0910 0.0905 0.0900 0.0840 0.0805 0.0800 0.0700 0.0600 0.0500 0.0400 0.0300 0.0250 0.0170 0.0045 0.0035

0.0730 0.0720 0.0710 0.0700 0.0620 0.0600 0.0550 0.0500 0.0400 0.0450 0.0400 0.0300 0.0200 0.0150 0.0130 0.0080 0.0020 0.0010

0.0660 0.0650 0.0640 0.0630 0.0600 0.0550 0.0500 0.0400 0.0330 0.0300 0.0250 0.0150 0.0080 0.0055 0.0045 0.0035 0.0021 0.0005

0.0600 0.0550 0.0500 0.0400 0.0350 0.0250 0.0200 0.0150 0.0100 0.0080 0.0030 0.0025 0.0015 0.0010 0.0000 0.0000 0.0000 0.0000

5.3. LOLP evaluation using Simpson 1/3rd rule The generation capacity data for evaluation of LOLP has been obtained from installed MHPP as included in Table 6. LDC is designed and obtained a straight line with Pdmax ¼ 1000 W and Pdmin ¼ 300 W for reliability evaluation of the system using Simpson 1/3rd rule. Various plots for different steps of the LDC have been drawn for performance analysis and reliability evaluation of system considering different conditions using Eq. (13). Simpson 1/3rd rule approximation is used for maximum 100 steps of the SLDC in this paper. As discussed earlier, systems load varies in many steps during 24 h operation of the power system [14].

5.3.1. Case: I LOLP evaluation for 5 steps of SLDC Simpson 1/3rd rule is applied for reliability approximation of the developed system for various steps of the LDC. LOLP of the MHPP decreased with higher values of the generation capacity as approximated in Fig. 14. Assumed 5 steps of SLDC presents total 5 variations in load during evaluation of reliability. LOLP for 5 steps of the SLDC has been evaluated in Table 7 for different generating capacity of the installed MHPP. The curves A, B, C and D in Fig. 14 show the relations of LOLP and generating capacity at sC ¼10%, 15% 20%, and 25% of generating capacity respectively for 5 steps of the SLDC. The LOLP of the generation capacity of developed system increases with increasing values of sC. For same generating capacity available, if sC increases, the LOLP also increases according to Fig. 14.

5.3.2. Case: II LOLP evaluation for 10 steps of SLDC Fig. 15 represents the relation between LOLP and various generating capacity available in MHPGS with effects of various sC. The LOLP has been evaluated for 10 steps of load duration curve and

Fig. 15. LOLP vs. generation capacity for 10 steps.

R.K. Saket / Renewable and Sustainable Energy Reviews 28 (2013) 917–929

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Table 8 LOLP for 10 steps of the SLDC. Loss of Load Probability for 10 steps of SLDC Capacity C

Curve D for sc ¼25% of C

Curve C for sc ¼ 20% of C

Curve B for sc ¼15% of C

Curve A for sc ¼10% of C

500 550 600 650 700 750 800 850 900 930 950 1000 1050 1110 1130 1190 1400 1550

0.0950 0.0945 0.0824 0.0811 0.0802 0.0800 0.0760 0.0730 0.0720 0.0710 0.0600 0.0530 0.0400 0.0340 0.0250 0.0170 0.0045 0.0035

0.0730 0.0720 0.0710 0.0700 0.0620 0.0600 0.0550 0.0520 0.0400 0.0450 0.0400 0.0300 0.0200 0.0150 0.0130 0.008 0.0020 0.0010

0.0660 0.0610 0.0640 0.0650 0.0600 0.0550 0.0500 0.0400 0.0330 0.0300 0.0250 0.0150 0.0082 0.0055 0.0045 0.0035 0.0021 0.0005

0.0600 0.0550 0.0560 0.0400 0.0350 0.0250 0.0210 0.0150 0.0130 0.0080 0.0030 0.0025 0.0015 0.0014 0.0000 0.0000 0.0000 0.0000

included in the Table 8. The curves A, B, C and D in Fig. 14 show the relations of LOLP and generating capacity at sC ¼10%, 15% 20%, and 25% of generating capacity respectively for 10 steps of the SLDC. The curves have been plotted for 10 steps as shown in the Fig. 15. The LOLP of system increases with increments in sC due to large uncertainty involved in the generating capacity distribution function. Nature of plots is identical as obtained earlier for 5 steps of the SLDC. For particular value of the generation capacity, LOLP of the system increases with standard deviation. Considered 10 steps of the SLDC indicate total 10 variations in load during 24 h operation of the developed system. 5.3.3. Case: III LOLP evaluation for 20 steps of SLDC The plots of LOLP vs. generating capacity for SLDC for 20 steps are drown from Table 9 and shown in Fig. 16. The curves A, B, C and D show the relation between LOLP and generating capacity for

Table 9 LOLP for 20 steps of the SLDC. Loss of Load Probability for 20 steps of SLDC Capacity C

Curve D for sc ¼25% of C

Curve C for sc ¼ 20% of C

Curve B for sc ¼15% of C

Curve A for sc ¼10% of C

500 550 600 650 700 750 800 850 900 930 950 1000 1050 1110 1130 1190 1400 1550

0.0900 0.0905 0.0901 0.0824 0.0813 0.0813 0.0810 0.0812 0.0800 0.0710 0.0600 0.0530 0.0400 0.0340 0.0250 0.0170 0.0045 0.0035

0.0730 0.0720 0.0710 0.0700 0.0620 0.0600 0.0500 0.0520 0.0400 0.0450 0.0400 0.0300 0.0200 0.0150 0.0130 0.0080 0.0020 0.0010

0.0660 0.0610 0.0640 0.0650 0.0610 0.0550 0.0500 0.0420 0.0330 0.0300 0.0250 0.0150 0.0082 0.0055 0.0045 0.0035 0.0021 0.0005

0.0600 0.0550 0.0560 0.0400 0.0350 0.0250 0.0210 0.0150 0.0130 0.0080 0.0030 0.0025 0.0015 0.0014 0.0000 0.0000 0.0000 0.0000

Fig. 16. LOLP vs. generation capacity for 20 steps.

the sC ¼10%, 15%, 20% and 25%, respectively. It is observed from curves C and D that for the same generating capacity of the power system, the LOLP with sC ¼15% of C is higher than sC ¼ 10% of C . Similarly from curves A and B it is observed that the LOLP of curve B is greater than curve A at same generating capacity. This is due to the fact that large uncertainty involved in generating capacity function. In summary, if standard deviation of generating capacity increases, the LOLP of developed system increases at same generating capacity.

5.3.4. Case: IV LOLP evaluation for different steps of SLDC The plots of LOLP vs. generating capacity considering different steps (curve A for 5 steps, curve B for 10 steps and curve C for 20 steps) for the SLDC have been illustrated in Figs. 17–20 for sc ¼10%, 15%, 20% and 25% respectively. For different values of the sc, MHPS has different LOLP for different steps of the SLDC as approximated in Figs. 17–20. These graphs are drawn from data of the Tables 7–9 for different steps of the SLDC. Fig. 17 is approximated for sc ¼10% of the generation capacity for 5, 10 and 20 steps. This figure is drown from the data available in Tables 7–9, for sc ¼ 10%, only. LOLP decreases with increasing generation capacity for all steps of the SLDC. Nature of the curves A, B and C of Fig. 17 indicates that generation system has near about same LOLP for different steps and all capacities of the SLDC. Small variation in graphical interpretation is due to different loadability of the system for different steps of the SLDC. Figs. 18 and 19 and 20 describe same approximation as discussed earlier on interpretation of Fig. 17. Small variation

Fig. 17. LOLP vs. generation capacity for sc ¼ 10%.

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6. Conclusions

Fig. 18. LOLP vs. generation capacity for sc ¼ 15%.

Fig. 19. LOLP vs. generation capacity for sc ¼ 20%.

Design aspects and probabilistic approach for reliability evaluation of the installed MHPGS have been described successfully in this paper. On the basis of the proposed concept and developed experimental MHPP at Banaras Hindu University campus, a number of experimental tests were performed for designing of AFDC, DFDC and SLDC. Generating capacity of installed MHPGS based on SWW for different water head available at BSS of the BHU has been evaluated successfully. Turbine – generator sets are recommended for different heads of MWW for reliable operation of the MHPP. SWW flow rate and available head have been measured considering summer/winter and day/night cycles. Typical power output has been estimated and measured at different flow rate and head of the BSP for calculation of reliability indices and reliability evaluation of generation capacity. Probabilistic approach based methodologies have been introduced in this paper for generation system reliability evaluation using different loads and generation capacity models. GDA, PLC and SFC approximations have been demonstrated successfully for evaluation of generation system reliability in this paper. Case studies with several conditions of the configuration of the developed MHPP at BHU campus revealed the good performance of the proposed methodology not only in terms of failure probability evaluation but also in related to the accuracy of the reliability indices. Case study introduced in this paper has been given to demonstrate the applications of the methodologies. The major portion of these evaluations comes from adequacy analysis based on power flow and optimization related with actions take to correct the system operation conditions. Further, in all cases it is confirm that LOLP increases with an increase in variance of load and generating capacity and hence, reliability of overall system decreases. Simpson 1/3rd rule is used for reliability evaluation of the stepped load duration curve of the developed power plant. LOLP vs. generation capacity curves for different steps of the SLDC have also justified the reliability conditions of the generation system. Future research work in this area is proposed for miniand micro-hydro power generation from irrigation canals and hilly fountains. Power engineers can also plan for pico and nano hydro power generation from overhead water tanks of the buildings to charge small chargeable batteries. Simpson's 3/8th rule and trapezoidal rule are proposed for better approximation and future research work on power system reliability evaluation.

Acknowledgment Author is grateful to Indian Institute of Technology (Banaras Hindu University), Varanasi, Uttar Pradesh (India) for partial financial support for carrying out this project work. He would like thank to Aanchal, Aakanksha, Siddharth and Siddhant for providing emotional supports during design work of this project. This work is heartily dedicated to sweet memories of the author's great father Parinibutta Ram Das Saket Vardhan who has passed away on August 17, 2008.

Fig. 20. LOLP vs. generation capacity for sc ¼ 25%.

in LOLP for any capacity of the MHPP is observed from Figs. 17–19 and 20. This variation is due to large uncertainties involved in the generation capacity distribution function of the developed MHPP. From above discussions, it is clear that Simpson 1/3rd rule gives considerable approximations for any step of the SLDC.

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