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# LCOE and PV

### Photovoltaics energy: Improved modeling and analysis of the levelized cost of energy (LCOE) and grid parity – Egypt case study

This paper presents improved modeling and analysis of the levelized cost of energy (LCOE) associated with photovoltaic (PV) power plants.

#### Points covered

1)The presented model considers the effective lifetime of various PV technologies rather than the usual use of the financial lifetime. Parametric and sensitivity studies are also presented for overcoming the uncertainties in the input data and for searching of the significant options for LCOE reduction. 2)The salient outcome of this paper is that the effective lifetime has a significant impact on both the LCOE and the lifetime energy production.

#### Introduction

1)There are 3 main SOlar technologies:- Solar PV Thermal PV Concentrated Solar power 2)Paper mainly focuses on direct Solar conversion (Solar PV) There are 3 geenration of Solar PV:- i)Crystalline PV (80%of market) ii)Amorphous PV(10-12%market) iii)Concentrating PV cell(R&D) 3)Only 0.2% of the gloabal market utilize the solar PV for generation of electricity, the main reason is its cost.http://www.appropedia.org/Special:Preferences 4)The LCOE is sensitive to small changes in the input variables and assumptions. The main input variables are the discount rate, average system cost, financing method and incentives, average system lifetime, and degradation of energy generation over the lifetime. 5)The Grid parity and Break even cost of the Solar PV are basically the point at which the cost of Solar generated electricity is equal to the cost of the electricity purchased by the grid.

#### MOdel LCOE and grid parity

1)The LCOE captures capital costs, ongoing system-related costs and fuel costs – along with the amount of electricity produced– and converts them into a common metric: \$/kWh.2 2)the sum of the present value of the LCOE multiplied by the energy generated should be equal to the net present value of costs. 3)Consequently, the LCOE is usually determined as the average cost of energy over the lifetime of the project such that the net present value (NPV) becomes zero in the discounted cash flow (DCF) analysis. 4)In general, the efficiency of power plants is reduced with time; the time-dependent reduction in the efficiency is called output degradation. As any power plant, PV generators exhibit output degradation too. The energy generated in a given year (Et) is then equals to the rated energy output per year (Eo) multiplied by the degradation factor(1-d)^t. 5)The net annual cost of the project include all the cost paid at the beginning of the project- initial cost, maintenance and operation cost and even rate of interest of the year. In this paper no incentives have been considered. 6)For this paper SAM has been used to determine the energy production and the LCOE. It uses the NREL meteorological irradiance data for analysis. 7)In the SAM, two important factors should be taken into consideration. These two factors are Analysis Period and Loan Term. Analysis period is defined as the number of years covered by the analysis and determines the number of years in the project cash flow while the loan term defines as the number of years required to repay a loan. 8)There are two life times for a PV financial and effective. Financial life time is the duration the PV works. And effective life time evn consdiers the degradation of PV. 9)In the SAM, two important factors should be taken into consideration. These two factors are Analysis Period=effective life time and Loan Term=financial life time. 10)Thus depending on whether the effective life time is greater then the financial life time we get two equation for LCOE 11)Even the inverter replacement , operation and maintenance cost should be considered while calculating the LCOE. 12)Determining grid parity depends on various factors local price of electricity, solar PV price that depends on size and supplier, geographical region.

#### Case study results

1)The study shows that the region where the cost is maximum is base of system cost, maintenance and operation cost, installation cost respectively. 2)If effective life time is not considered the data regarding the LCOE and the energy generation estimated by the software greatly varies. In other words including effective time we get improved performance of PV system in terms of LCOE na d Energy generation. 3)Sensitivity analysis shows that the BOS and loan rate shows significant impact on LCOE.

### Assumptions and the Levelized Cost of Energy for Photovoltaics

Generally, LCOE is treated as a definite number and the assumptions lying beneath that result are rarely reported or even understood. In this paper MOnte-Carlo simulation is used to do LCOE calculation.

#### Introduction

For PV to attain deep market penetration, its costs must be comparable to those from fossil fuels, though it should be noted that there are substantial hidden costs associated with fossil fuels that are generally not accounted for such as pollution and climate change. The cost of conventional electricity is rising while the cost of solar electricity is dropping, so wide-scale grid parity is likely at some point in the future.

#### LCOE

1)It is an assessment of the economic lifetime energy cost and lifetime energy production. 2)The financial cost not only includes system cost but also maintenance, operations, insurance, different type of depreciation schedules, tax, subsidies and other compelxity.

#### Assumptions associated with energy production

1)The key is to use the best available data, but more importantly to understand the source of the data and the uncertainty associated with it. 2)Assumptions to be made are- Subsidies by government Insurance cost Inflation rate federal tax rate state tax rate lifetime span

##### Solar insolation data

The time series method to forecast the annual solar insolation in the coming 30 years based on the historial montly solar insolation data.

##### Power conversion efficiency

Many analysis consider LCOE as a constant but this not the case. It is a varying factor which should be consider during LCOE analysis.When the sunlight is less not only will a PV panel produce less power in many cases it will also do so less efficiently. Moreover, the dependence of efficiency on insolation is not necessarily linear. Other factors affecting the efficiency are the partial shadowing from clouds, temperature and so on.

As with the previous parameters, system degradation rate is generally treated as a single value in LCOE calculations despite the fact that it is known that even within a single PV installation individual panels will degrade with substantially different rates.

#### Assumption associated with Cost

##### Real discount rate

In addition to risks assocaited with solar insolation levels and the preformance of PV technologies at a specific location, there is also financial uncertainty in terms of the time value of money. It Depends on future interest rate falls or rise with respect to the inflation rate.

##### Maintenance and operation cost

Upkeep of a utility-scale PV system will vary widely depending on the local conditions.

##### Carbon market or Tax

A carbon tax is an alternative maket-based approach that directly taxes emissions and thereby provides an incentive to reduce pollution.

##### Subsidies and tax rate

As with inputs such as solar insolation, taxes and incentives for promoting solar energy also vary widely by location. For the United States, there is a valuable online database that compiles the various state, local, utility, and federal incentives and policies.

#### Analyzing the influence of assumptions

1)Monte Carlo simulation performs uncertainty analysis by building models of possible results through the substitution of a range of values—a probability distribution—for any factor that has inherent uncertainty. By using probability distributions, variables can have different probabilities of different outcomes occurring. 2)Monte-carlo simulation provide number of advantages- Probabilistic result, sensitivity analysis, correlation of input. 3)The results of Monte-carlo simulation gives broad distributions, which emphasizes the shortcomings of calculations that use singular input parameters. 4)Using Monte-Carlo simulation at different location to calculate LCOE of Solar PV module. The LCOE comparison can be done for the different location. 5)This sort of information is of tremendous potential value to investors, utility companies, insurers, and other stakeholders who need to ascertain the risk associated with a new installation.

### Profitability of PV electricity in Sweden

The paper mainly focus on detailed study of profitability of PV electricity. Levelized cost of Energy(LCOE) and payback period are presented for a PV system that is installed to replace retail electricity with PV electricity.

#### Overview

Even after the subsidy was pass to for connecting PV system to grid still only 43.1 MW PV power was generated by 2013 in Sweden. Lack of sun-shine is not the reason for the limited PV power installed. The reason is The production cost of PV is today higher than the production cost of other electricity production technologies used in Sweden. However, the PV installation price has reduced considerable in 2012-2013. Therefore, there is a growing interest to install PV to replace retail electricity.

#### LCOE

The basis of profitability depends on LCOE. The parameters that were shown to have the most effect on the LCOE were investment cost, life, and yield, system degradation, discount rate and lifetime. A private residential system has to pay 25% VAT with investment price. A residential private system was recorded to pay 2.5 kUSD/kW including VAT, whereas, a non private was recorded to pay minimum 1.5 kUSD/kW. A fixed operation and maintenance real cost 15USD/kW each year was applied. yield of about 800–1100 kWh/kW per year can be expected during a year with typical solar irradiation for systems with reasonable good azimuth, tilt and without major shading effects. A degradation rate of 0.5% per year. The discount rate varies depending on the type of investor. Therefore, a span of 3-6% in discount rate can be found for other applications than private households. A common guarantee on PV module is 80% of the rated power after 20-25 years.

#### Profitability

To calculate the profitability it is needed to predict the PV electricity value over the life time of the system. One part is the PV electricity that will replace bought electricity, with a value equal to the retail electricity price. The other part is the value of excess electricity that is fed into the grid.

#### Retail Electricity Price

The PV electricity used for self-consumption will have the same value as retail electricity price, excluding the fixed subscription costs. There are two prices one transfer of electricity from distribution operator ans second is buying electricity from the company. For the present case it is considered to be 14-15 US¢/kWh, excluding VAT. A significant difficulty is to predict the retail price during such a long period as the life time of the PV system i.e. 30 years. It was considered to be 18 US¢/kWh for a duration of 30 years.

#### Self consumption

The consumption of PV power varies a-lot especially in residential area depending on the amount of power required for the house. The size of the panel also matter. A typical 50% consumption for a house is considered.

#### Credits from distributor

When excessive electricity is fed into grid the Distributor is suppose to pay you for that. This compensations payed by DSO are not much and also varies from DSO to DSO and area you live in. Typically for this case it is 0.6-1.1 US¢/kWh.

#### Other factors

1)Tax deduction 2)Electricity trading price 3)Electricity certificates 4)Certificate of origin 5)Electricity mean present value

#### Results

1)Electricity yield varies depending on investment and discount rate. 2)A payback period can be calculated by a formula presented in the paper. 3)The payback period as function of the mean present value of PV electricity and investment cost. 4)For other investors then private investors the payback years increases as the discount increases. 5)As electricity mean value increases the pay back period decreases.

### The cost of storage - how to calculate the levelized cost of stored energy (LCOE) and applications to renewable energy generation

The paper mainly provides a new framework for the calculation of levelized cost of stored energy. The framework is based on the relations for photovoltaics amended by new parameters.The framework allows for comparisons between different storage technologies. The newly developed framework model is applied to derive the LCOE for a PV and storage combined power plant. In general, the combined levelized cost of energy lies between the LCOE of PV and LCOE of storage.

#### Overview

As the investment cost for renewable energy as deceasing steady it is not far that the subsidies will shutdown. This paper outlines the methodology to calculate the levelized cost of energy for combined PV and storage power plants. However, the methodology is applicable to other scenarios as well.

#### LCOE

The Levelized Cost of Energy (LCOE) is defined as the total lifetime cost of an investment divided by the cumulated generated energy by this investment. The LCOE is the (average) internal price at which the energy is to be sold in order to achieve a zero NPV(net present value).

#### LCOE of PV

This can be calculated using a given formula in the paper where it is considered only some amount of energy is being utilized of what is total being produced.

#### LCOE of Storage system

The levelized cost of energy for storage systems is calculated in a similar manner as for PV generation. The total cost of ownership over the investment period is divided by the delivered energy.The cost consists of a term similar to PV, in which total cost during lifetime is divided by the cumulated energy delivered by the system. Due to the fact, that no energy is generated a second term exists that models the energy purchase from generation plants or from the grid. The energy input into the storage system will be a certain amount of the total generated energy output. The energy output of the storage system is the energy input reduced by the average energy roundtrip efficiency ηSt of the storage system over the lifetime. Sometimes it is more convenient to consider the output energy of the storage system.

#### LCOE of PV+Storage system

1)The total lifetime cost is the sum of the cost of PV energy generation and the cost of storage. The energy output of the PP is the sum of directly used energy from PV and the amount that is taken from PV to the storage system and then released to the output of the PP. 3)The energy that can be used directly should be used directly, minimizing the energy storage. So design energy storage as small as possible else it will be uneconomical. 2)The usable PV output energy is energy generated at the output of PV excluding the one fed into the grid system. Of this usable energy only some part is stored into the energy storage system. 3)The total cost of power plant is sum of cost of PV generation + the cost of storage.

### Break-Even Cost for Residential Photovoltaics in the United States: Key Drivers and Sensitivities

The Technical report mainly focuses on break even cost of solar PV with electricity being purchased from the grid. Break even cost is the point at which the cost of the electricity generated by solar PV is equals to electricity being purchased from the grid. It is even called as 'grid parity'. The break even function depends on many variables solar resources, local electricity prices, and other incentives, this factors vary regionally and so the break even cost will also vary. The break even cost is the cost at which the net present cost of the PV is equal to the net present benefit from the system. This can be used to determine the installed system cost required for electricity price(\$/W) or the price of electricity (\$/kWh) required for a given installed system cost.

### A review of solar photovoltaic levelized cost of electricity

The paper mainly focus on the methodology of properly calculating the LCOE for solar PVe. Then a template is provided for better reporting of LCOE results for PV needed to influence policy mandates or make invest decisions. A numerical example is provided with variable ranges to test sensitivity, allowing for conclusions to be drawn on the most important variables.

#### Overview

A tipping point for solar adoption will be when the grid parity is achieved. In simple words the PV installation or the investment in PV world will increase when PV generated electricity cost becomes equal to the cost of the conventional electriicty purchased from the grid. Here the accuracy depends on the lifetime generation cost of the solar PV electricity. Levelized cost of energy is mainly considered for emerging technologies such as PV. Different levels of cost inclusion and sweeping assumptions across different technologies result in different costs estimated for even the same location.Reporting the wrong LCOE values for technologies can result in not only sub-optimal decisions for a specific project, but can also misguide policy initiatives at the local and global scale.

#### Review of Cost of electricity and LCOE

1)The final electricity price payed by the consumer is different from the cost of its production. 2)The method considers the lifetime generated energy and costs to estimate a price per unit energy generated. 3)The method usually does not include risks and different actual financing methods available for the different technologies. 4)Economic and financial systems have a large impact on the price of electricity, although the quality of electricity rarely changes, which is often not reflected by the LCOE. 5)Improvements to the LCOE for solar PV can be made once realistic assumptions and justifications are given, real financing variability is considered, and consideration is made for technological and geographical variability. 6)Understanding the true costs, energy production and system specifications would improve the capabilities of LCOE software like the Solar Advisor Model.

#### Methodology to calculate LCOE

1)Calculating the LCOE requires considering the cost of the energy generating system and the energy generated over its lifetime to provide a cost in \$/kWh (or \$/MWh or cents/kWh). 2)The net cost of the system must include cash outflow like the initial investment, interest payment,operation and maintenance cost, cash inflow such as govt. incentives. also with this it should even include all cost required transmission and connection fees and be dynamic for future project. 3)The LCOE is very dependent on the financing methods available and manufacturing cost reductions.

#### Results

1) The LCOE decreases with increasing interest rate, increasing discount rate and and increasing loan duration. 2)Discount rate has very small affect on LCOE 3)LCOE decreases as the energy generation price decreases and system duration increases. 4)LCOE decreases with decreased installation cost and increased energy output. 5)LCOE is less with less degradation rate.

### Economics of Solar Photovoltaic system

Notes:- 1)Solar photovoaltaic vary greatly in size and cost. Calculating the economics of the solar system gives us the idea about whether the solar Pv system is right for us. 2) Prices of solar Panels are declining which in turn is improving the economics of the Solar PV. 3)Find total cost of solar panel, inverter, mounting panel and installation. 4)Determining the payback period of the solar PV which in other words is the duration required to recover your investment. 5)Other factors that will pay important role in determining pay back period are the price of electricity per kWh and its inflation rate. 6)Net metering and incentives also pays an important role and it adds for benefit to the renewable system.

### Economic optimization and sensitivity analysis of photovoltaic system in residential buildings

The objective is to minimize the annual energy cost of a given customer, including PV investment cost, maintenance cost, utility electricity cost, subtracting the revenue from selling the excess electricity.

#### Overview

The power output of a PV system depends on the irradiance on the PV cells, the efficiency of PV cells used and the effective area of the PV cells. Therefore, it is necessary to choose the optimal size of PV cell in accordance with the application. An economic optimization design tool for optimal PV size based on technology information and current tariffs and policy has been developed.

#### Model overview

This model required input:- 1)Hourly irradiamce data 2)Hourly electricity load profile 3)Efficiency of PV 4) Capital cost, interest rate, electricity tariff, subsidies.

Result at output:- 1)Economical optimal PV installation 2)System performance characteristics.

The objective function is to reduce annual energy cost of given customer. This depends on system investment cost (excluding subsidies), cost for maintenance of the system, cost for buying electricity power from the spot market, income from selling electricity back into the grid.

#### Results

1)The cost of electricity purchase from the grid decreases as the PV capacity is increased. 2)Increasing PV capacity does not always led to cost saving, this is because the investment cost increases. 3)The CO2 emission can be reduced considerable by increasing the capacity of PV.

#### Sensitivity analysis of LCOE

1)The increase of both capital cost and interest rate leads to a linear increase of levelized cost; contrarily, a higher efficiency brings on a lower levelized cost. 2)the simple payback period is greatly effected by capital cost, efficiency and electricity sale price.

### Economical and environmental analysis of grid connected photovoltaic systems in Spain

In this paper an economical study on PV installed is performed depending on different scenario depending on interest rates and energy tariff are considered. The following parameters are used to determine the profitability of a PV installation: the Net Present Value and the Pay-Back Period.

#### Economic valuation of Investment

Notes:- 1) The initial cost of the grid connected PV system This includes the cost of the generator Cgen, the cost of the inverter Cinv, the costs of the installation Cinst (including supporting structures, wiring, protective elements, engineering,etc.). The sum of these costs is the system cost Csystem. Likewise, Csub is the possible quantity of financial subsidy on the initial cost. 2)Net flow cash is the difference between the cash input generated by the investment and the payment or cash output the investment requires. 3)The income and expenditure vary from year to year due to inflation. 4)The Pay-Back Time (P), is the number of years needed to make the NPV of the cash flow, up to the present moment, to be equal to the initial outlay of the investment.

#### Case study

Notes:- 1)For the present case the data being considered is the annual irradiation at the place, the panel inclination and orientation, irradiation Losses. All this data can be used to determine the kWh for the PV system. 2)Assumptions are no shadow is there, and total energy generated by PV is sold. 3)For analysis various values for the subsidies are considered. 4)The economical analysis has shown that with the current prices, investment in a grid connected PV systems is generally profitable. 5)An increase in the sale price of the energy, with this remaining constant throughout the service life of the installations, would make shorter return times possible, thus attracting investors and so producing a mass investment in PV installation.

### Re-considering the economics of photovoltaic power

This paper mainly focus on This paper briefly considers the recent dramatic reductions in the underlying costs and market prices of solar photovoltaic (PV) systems, and their implications for decision-makers. In many cases, current PV costs and the associated market and technological shifts witnessed in the industry have not been fully noted by decision-makers. The perception persists that PV is prohibitively expensive, and still has not reached ‘competitiveness’.

PV power generation has long been acknowledged as a clean energy technology with vast potential, assuming its economics can be significantly improved. Inspite of having highly attractive benefits and proven technical feasibility, the high costs of PV in comparison with other electricity generation options have until now prevented widespread commercial deployment. The economics of PV depends on 3 metrices:-1)Price per watt( Capital cost of PV),2)LCOE,3)Grid parity LCOE and ‘grid parity’ are of special relevance to government stakeholders but require a wider set of assumptions. There is a clear requirement for greater transparency in presenting metrics so that they can be usefully compared or used in further analysis.

#### Price per watt

Notes:- 1)The most fundamental metric for considering the costs of PV is the price-per-watt of the modules. PV module factory prices have historically decreased at a rate (price experience factor) of 15-24%. 2)modules had a share of around 60% of the total PV system cost [20], but due to the extraordinary decline in module prices since 2008, its share in the total installed system cost has since decreased and now the BOS is the majority share in capital cost of PV installation. 3)Reducing the price/watt of the inverter being used will reduces the BOS of the system and hence the capital cost for PV installation.

#### LCOE

Notes:- 1)LCOE is most commonly used by policy makers as a long term guide to the competitiveness of technologies. 2)LCOE analysis considers costs distributed over the project lifetime. 3)The LCOE mainly depends on locations nd financing assumptions. 4)Variation in LCOE presented in various papers is due to certain assumptions, moreover, the lifetime of PV module is considered to 25 years in many papers but it is 40 years as the researcher suggests. 5)The variation in M&O of the PV module may be due to difference in scope of service provided. 6)Other variation are due to the type of project owner, the nature and stability of regulatory regimes, and regional differences in cost of capital. 7)The LCOE levelized costs of power generated by PV exhibit a particularly high sensitivity to load factor variations, followed by variations in construction costs and discount rate. 8)Uncertainty in LCOE is due to financial uncertainties (e.g., variation of discount rate) are a major determining factor of LCOE, followed by system performance (including geographical insolation variation), which equally represents a major contributor to the uncertainty in LCOE.

#### Grid parity

Notes:- 1)As noted with LCOE, however, behind the relatively simple concept of grid parity lies considerable complexity and ambiguity. 2)Many papers present that in few countries grid parity is already been achieved and in few they say it will be achieved in coming future. 3)This shows that how difficult is the concept to communicate.