Table 2: Diesel System Econometrics for Nigeria (Rural Community Utilization)
(Ajayi Et Al., 2014)
Load Calculation
Load profiles for rural and remote communities should not be merely assumed, but must be well analyzed. Notwithstanding, they have been discovered to be a far below those of urban communities. A number of researchers discovered that characteristically on the average, 1 kWh/day per home is required in rural community homes (Clean Energy Project, 2005; Lambert et al, 2006). Nonetheless, for the intention of this study, the energy demand requirement of the rural communities were developed based on individual power rating of each appliance generally utilized in each home as presented in Table 3 and 4 (General Wattage Chart, 2013; How much electricity, 2013; RETScreen 4 Software, 2013; Ohijeagbon and Ajayi, 2014; Ajayi et al., 2014)). Consequently, each home is estimated to consume as 1.4kWh/day, based on the analysis of Tables 3 and 4, with a calculated primary peak load value of 46 kW. Fig. 1 presents the 24 hours hourly load profile for the communities.
Table 3: General Wattage Chart for Some Household Appliances
(Ohijeagbon and Ajayi, 2014; Ajayi Et Al., 2014)
Table 4: Electricity Consumption Analysis for a Rural Community of 200 Homes
(Ohijeagbon and Ajayi, 2014; Ajayi Et Al., 2014)
Fig 1: Average Daily Load Profile Used for Design of Hybrid Energy Systems in Rural Areas of Nigeria
(Ohijeagbon and Ajayi, 2014; Ajayi Et Al., 2014)
Modeling the Photovoltaic (PV) Project
Description of the Solar Radiation Algorithm
The solar radiation algorithm utilized is described as a progression of three basic
steps presented in the figure below (see Figure 2) (Ohijeagbon and Ajayi, 2014; Ajayi et al., 2014):
Figure 2: Flowchart for Tilted Irradiance Calculation
Calculation of Hourly Global and Diffuse Irradiance
Solar radiation can be considered to be of two parts: beam radiation, and diffuse radiation. Therefore, the tilting algorithm utilized, uses the knowledge of beam and diffuse radiation for every hour of an average day.
PV Array Model
The model created by Evans served as the PV array model (Evans, 1981).
Modeling the Wind Speed Distribution
Wind Energy Model
Since weibull probability density function (WPDF) has been found to significantly fit with experimental long-term distribution for various sites (Ajayi et al, 2011), the wind speed profile characterization and analysis for each site was carried out using the WPDF.
Cost Benefit Analysis
Economics plays a critical role in selecting potential energy sources. Renewable and non-renewable energy sources have proven to be very diverse in cost characteristics. Renewable sources are usually higher in initial capital costs and low in operating costs, while conventional non-renewable sources usually tend to be vice-versa. The life-cycle cost (or NPC) analysis consists of, costs of initial construction, component replacements, maintenance, fuel, cost of buying power from the grid, and miscellaneous costs. On the other hand, revenues include, income retrieved from sales to the grid, in addition to any salvage value occurring at the end of the project lifetime. When evaluating the NPC, costs are taken as positive and revenues are seen as negative. Therefore, a negative NPC value signifies a net present value (NPV).
The annualized cost for each component is made up of, the capital, replacement, maintenance, and fuel costs, as well as salvage value and other costs or revenues. Further to this, the annualized costs are summed for each component, plus any miscellaneous costs, thus resulting in the total annualized cost of the system.
The total net present cost is:
1
where Cann,tot= total annualized cost, the project lifetime, and CRF( â‹…) is the capital recovery factor, given by the equation:
2
where, i, is the annual real interest rate (the discount rate) and N is the number of years.
The annualized capital cost of each component is evaluated as follows:
3
where: Ccap = initial capital cost of the component
To determine the annualized replacement cost of a system component, the salvage value at the end of the project lifetime is subtracted from the annualized value of all replacement costs that occurred throughout the lifetime. It is noteworthy that the annualized replacement cost may be negative since it includes the annualized salvage value.
Each component’s annualized replacement cost is evaluated as follows:
4
is a factor that takes into account the fact that the component lifetime can be different from the project lifetime:
5
the duration of replacement cost, is given by:
6
Where, INT ( ) is the integer function, that returns the integer part of a real value.
The salvage value S of each component is given by:
7
is the remaining life of the component at the end of the project lifetime:
8
= replacement cost of the component.
SFF ( ) = sinking fund factor
= lifetime of the component
The sinking fund factor is a ratio used to calculate the future value of a series of equal annual cash flows and it is given as;
9
The total O&M cost is a sum that comprises of: the system fixed O&M cost, any penalty for capacity shortage and penalty for emissions (if any).
The total annual O&M cost is given as:
10
where:
= system fixed O&M cost ($/yr)
= the penalty for capacity shortage ($/yr)
= the penalty for emissions ($/yr)
The capacity shortage is calculated using the following equation:
11
where:
= capacity shortage penalty ($/kWh)
= total capacity shortage (kWh/yr)
Therefore, the total annualized cost is:
12
Where =annual project revenue ($/yr)
The levelised cost of energy (LCOE) is therefore:
13
Where,is the total annualized cost, and are the total amounts of primary and deferrable load, respectively, that the system serves per year, and is the amount of energy sold to the grid per year.
Specifications of Wind Turbines and Solar Panel Used in this Study
PGE turbines (HOMER Software, 2013) were cumulatively utilized for this research to study the wind standalone system (WSS), each having the specification indicated in Table 6, while the Enercon turbine is employed for edistributed generation.
It is noteworthy that when revenues from the project far surpasses other incurred costs, i.e. (the annual operating cost of the project), and the summation of . It results in a negative total annualized cost, that reflects in a negative LCOE which is termed levelised value of energy (LVOE) (Ohijeagbon & Ajayi, 2015); which reveals the profitability of the project from an investors’ stance. Hence,
Table 6: Turbine Specification (Ajayi et al., 2014)
where: Vc = cut-in wind speed, VFi = low wind cut-out speed, VFo = high wind cut-out speed, VR = rated wind speed, PeR = rated power at rated wind speed.
Table 7 presents the solar panel specification used in this research with a collector area of 5.1 m2 rated at 1 kW by Sunpower. Consequently, in order to match the load demand, the solar collector area increases while other parameters in Table 7 remained constant (RETScreen 4 Software, 2013). Table 8 presents each components’ cost with their installation costs embedded used in designing the Hybrid Energy Systems (HES).
Table 7: PV System Specification (Ajayi Et Al., 2014)
Table 8: Cost of Components Used in the Design of HES (Installation Cost Embedded in Component Cost)
(Ajayi et al., 2014)
Fig. 3 shows the average monthly solar radiation profiles for a period spanning between 1987 and 2010. The figure reveals that the 24 years monthly average solar radiation varied between 2.93 (kWh/m²/d) in August for Iseyin (SW) and 6.468(kWh/m²/d) in April for Maiduguri (NE). More so, the period between July and August experienced the lowest solar radiation across the sites/states. Looking through the analyzed data, Maiduguri and Kano were found to be the sites/states with the superior solar profiles.
Fig 3: 24- Year Monthly Average Radiation (Kwh/M²-Day) for Sites in Nigeria
Fig. 4 reveals the average yearly solar radiation profiles for the period covering 1987 and 2010. Maiduguri (NE) is observed to have the highest yearly average radiation in 1997, while Enugu (SE) had the lowest in 2004. It was also discovered that the monthly solar data varied much more than the yearly solar radiation data. Further to this, Fig. 4 shows that the solar radiation profiles for all sites in Nigeria can be grouped broadly in two, namely; Northern Nigeria and Southern Nigeria, with very related characteristics within each group. The similarity in characteristics is a result of similar weather and climatic conditions within the same geographical region.
Taking into consideration the hours equaled or exceeded for a series of mean measured solar radiation (Fig. 5) across the studied period, the study revealed that the corresponding power generated for each site from the designed PV array is between about 49.2% – 51.1% of the hourly duration in a whole year. This however is due to solar radiation occurring only at daytime, unlike wind speed. Hence, Iseyin has a twenty four year average sunshine daily duration of about 5.46 hours, while Jos has 7.33 hours.
Fig 4: 24- Year Yearly Average Radiation (kWh/m²-day) for Sites in Nigeria
Fig. 5: Plot of 24 Years’ Annual Average Hours Equaled or Exceeded for Nigeria
Fig. 6 correlates the annual average solar radiation and PV module size for the 6 sites studied. Upon analysis, it was found that a good correlation subsists between incident irradiation and PV size. This relationship was observed to be inverse in proportionality between the two quantities, with the PV requirement growing with decline in solar radiation intensity. This can be attributed to the prevailing weight of daily global solar radiation on the sizing of photovoltaic systems. Fig. 6 also reveals an average 24 years annual solar radiation that ranged between Iseyin (SW) – 4.45 (kWh/m².day) and Maiduguri (NE) – 6.07 (kWh/m².day) with a matching PV rating of 190 kW and 115 kW respectively.
Fig 6: Correlation between the Monthly Average Solar Radiation and Solar Panel Size for Nigeria
From Table 9, considering the most cost effective PV standalone system design having a Loss of Load Probability (LOLP) of 0.01 (Hontoria et al, 2005; Shen, 2009; Khatib et al, 2013), produced an average excess electricity corresponding to 26.3% of annual generation. The reason for this excess however, is due to a reduction in daily hours of sunshine during the rainy season period, when average sunshine duration ranges between 3 and 4 hours in the north and 1 to 2 hours in the south. Consequently, a design that will cater for a load profile of 200 rural homes must necessarily include a realistic battery charging requirement to account for the days of limited solar radiation. Hence, the battery days of autonomy ranged between 48.7 hours for NW and 68.9 hours for SS at a 50% initial state of charge, which was chosen in order to extend battery life (Hund et al, 2010; Hund, 2009; Hunt, 2009; Overview of the NERC regulations, 2012; Multi-Year Tariff Order, 2011; Branker et al, 2011; Lorenz et al, 2008). However, this unequivocally gives rise to an excess in energy generated annually when the period of higher sunshine duration is balanced with those of lower duration over an entire year. This excess can easily be harnessed in the form of generation known as embedded generation, which is defined as a form of generation where excess renewable energy generated by a consumer above 1 MW may be sold to a nearby distribution network (Overview of the NERC regulations, 2012; Multi-Year Tariff Order, 2011). This sales to the grid have the advantage of reducing the LCOE, as revealed by equation 13. It is also noteworthy that the excess may not be sold to the grid at all times, as it will be wasted when lower than 1 MW, if the optimum battery capacity by design could not take care of this excess. The battery specification employed in the study is presented in table 9. It reveals the optimized rated capacity (or nominal capacity) of the battery, which is the amount of energy that could be pulled out from it at a particular constant current, starting from a fully charged state.
Table 9: Technical Requirements Employed for the PV Standalone System Design
Fig 7: Comparison between Net Present Cost (NPC) and Initial Capital for PV Standalone System
An econometric ranking for all studied sites is presented in Table 10. The PV economics reveals that the LCOE is directly proportional to total NPC for all sites. More so, Fig. 8 shows the most excellent location in Nigeria by LCOE. It reveals that Iseyin is the poorest in terms of LCOE at $0.579/kWh and Kano is the finest with $0.398/kWh. Hence, the use of PV standalone systems equates to savings of 7.1% and 56% respectively on an equivalent DSS that will cover the same load for this communities, with the added advantage of savings in 279 tons of CO2 green house gas emissions (GHG).
Fig 8: LCOE for PV Standalone System
Table 10: Total NPC and LCOE Values for the PV Standalone System Design
Prospect of Standalone Wind-To-Electricity Project in the Sites
The results of wind profile analysis at the site are as shown in Figs. 9 and 10. A few of the sites have missing wind speed values for 2 to 3 years (2008-2010). Fig. 9 shows the average monthly wind speed profiles for a period spanning between 1987 and 2010. The figure reveals that the 24 years monthly wind speed varied between 3.476 (m/s) in November for Benin City (SS) and 10.062 (m/s) in December for Jos (NC). Fig. 10 reveals the average yearly wind speed profiles for the period covering 1987 and 2010. Jos (NC) is observed to have the highest yearly average wind speed – 11.783 m/s in 1993, while Iseyin (SW) had the lowest – 1.842 m/s in 1999. Moreover, the hours equaled or exceeded for a range of mean measured wind speeds across the period (Fig. 11) revealed that 67.2% of the data spread are values above 3.0 m/s for the poorest site in terms of wind profile, and 91.9% for the best wind profile in Jos. This discovery proves that majority of the sites are well-suited to contemporary wind turbines, since recent wind turbines for power generation have a cut-in speed of 3 m/s. Therefore, this reveals that wind power can be harnessed throughout the year with corresponding higher returns on investment.
Fig. 9: Plot of 24 Years’ Monthly Average Wind Speeds
Fig. 10: Plot of 24 Years’ Annual Average Wind Speeds
Fig. 11: Plot of 24 Years’ Annual Average Hours Equaled or Exceeded for Different Wind Speeds
Fig. 12: Plot of 24 Years’ Annual Average PGE 2025 Power Output Duration Curve (kW)
The hours equaled for power generated for each site from their respective turbine sizing based on particular wind speed profiles is presented in Fig. 12. The SS requires the highest turbine size of 100 kW, thereby generating more excess power than any other site, howbeit, for a very short period as it only generates power for equal or less than about 68% of the time. On the other hand, a site like Kano in the NW is sized at 50 kW because of a very favorable wind profile that makes this site consistently generate for 90% of the hourly duration in a year. As a result, Table 11 reveals that Benin city has the peak battery capacity requirement, which is to balance for approximately a third of the yearly hourly duration without turbine production.
Table 11: Technical Requirements and Correlation of Electricity Consumed as a Percentage of Wind Standalone Production
Table 11 reveals an average excess electricity equivalent to 54% of annual generation across all sites because wind power is generated on average, for about 80% of the time within the studied sites in Nigeria (see Fig. 11 & Table 11). This gives rise to wind energy generation over two-thirds of every hour of the day, thus, an average optimal battery size of 30.8 hours of autonomy suitably matches the load requirement. Also, it is revealed that for an average of about 24% of the annual hourly duration, the turbines can produce at the rated capacity since the rated speed for the PGE 20/25 turbines used in the design is 9 m/s (Fig. 11). This will certainly encourage good returns on investment and an opportunity for embedded generation (Overview of the NERC regulations, 2012; Multi-Year Tariff Order, 2011). Fromtable 12, it is observed that Wind Standalone System (WSS) is in general, more cost efficient due to an average savings of 80% on battery requirement in comparison to PV Standalone System (PSS).
Table 12: Econometrics Analysis for Wind Standalone System