Monte Carlo Simulation approach for economic risk analysis of an emergency energy generation system

Accepted Manuscript Monte Carlo Simulation approach for economic risk analysis of an emergency energy generation system

Hebert Zaroni, Letícia B. Maciel, Diego B. Carvalho, Edson de O. Pamplona PII:

S0360-5442(19)30161-6

DOI:

10.1016/j.energy.2019.01.145

Reference:

EGY 14618

To appear in:

Energy

Received Date:

28 May 2018

Accepted Date:

27 January 2019

Please cite this article as: Hebert Zaroni, Letícia B. Maciel, Diego B. Carvalho, Edson de O. Pamplona, Monte Carlo Simulation approach for economic risk analysis of an emergency energy generation system, Energy (2019), doi: 10.1016/j.energy.2019.01.145

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ACCEPTED MANUSCRIPT

Monte Carlo Simulation approach for economic risk analysis of an emergency energy generation system Hebert Zaroni1, Letícia B. Maciel2, Diego B. Carvalho*2, Edson de O. Pamplona1 1Institute 2Institute

of Production Engineering & Management, Federal University of Itajuba, Itajuba, Minas Gerais, Brazil of Electric and Energy Systems, Federal University of Itajuba, Itajuba, Minas Gerais, Brazil

A B S T R A C T

(SHORTER ABSTRACT IN THE LAST PAGE)

Electric generators are largely employed as emergency power sources by preventing some facilities from sudden interruptions of electric energy supply. They may also be used to reduce the energy demand from the power grid by providing electricity over the peak periods. This paper aims to evaluate the owners' economic risk of purchasing an electric generator in order to provide energy during the peak time. The study considers different rated powers of diesel and natural gas-based generators as well as cases with and without an extra expense due to the carbon credit (CCr), which is a cost generated by the emission of greenhouse gases (GHG). Net Present Value (NPV) is used as a method for the economic feasibility analysis while Monte Carlo Simulation (MCS), a stochastic approach, is performed to evaluate the economic risk. To verify the applied methodology and accomplish the goals of this work, a Brazilian university project is taken as a case study and the campus is assumed to be an investor of an electric generator. The analysis is performed considering that the facilities are fed energetically during short periods of the day. All rules from Brazilian energy market are taken into consideration. Diesel and natural gas-based generators are able to guarantee a low risk of return on investment to investors and such risk is truly dependent on the generator rated power. Diesel generators present a narrow range of rated powers with a high probability of positive NPV whereas natural gas-based engines show a wide range of them with a null risk of an unprofitable purchase. In cases where carbon credits are considered as extra costs, the probability of a failed business is always higher than the cases they are not taken into account, although the carbon credits have no high sensitivity in the risk analysis. Keywords: Diesel generator, Natural gas generator, Net Present Value, Monte Carlo Simulation, Economic risk analysis

Nomenclature (-)Taxyear (+)Taxyear a b CCr CCrprice cd cDG cNG cNGgenerator CO&M_DG_hour CO&M_DG_year cO&M_NG

Amount of costs per year related to taxes as expenses (US$) Amount of costs per year related to taxes as incomes (US$) Specific consumption at zero load (L/h) Specific consumption (L/kWh) Carbon Credit CCr price per tonne of CO2 (US$/tCO2). Price of diesel per unit of volume (US$/L) Capital cost per unit of DG rated power (US$/kW) Price of natural gas per unit of volume (US$/m³) Capital cost per unit of NG generator rated power (US$/kW) O&M cost per hour of DG (US$/h). Annual O&M cost of DG (US$) NG-based engine O&M cost per MWh (US$/MWh)

Correspond author e-mail address: [email protected] *

ACCEPTED MANUSCRIPT CO&M_NG_gen_year confins Cost_diesel(year) Cost_NG(year) Cost_non-p_e_year CostDG_CCr_year CostDG_CCr_year CostNGgenerator_CCr_year D DG E Eg emssDG_GHG emssNGgenerator_GHG Epp eprice FC FCpartial GHG IDG INGgenerator IR ir kd ke MCS NG NPV O&M P pdf pis PIS/CONFINS Pload PNPV Rb rev(m) REVyear Rf Rm t tR WACC Y&Rflags

βleveraged θ(m)

NG-based generators annual O&M cost (US$) CONFINS rate (%) Annual diesel costs (US$) Annual NG costs (US$) Generators non-provided energy cost (US$) DG CCr annual cost (US$) Annual DG CCr cost (US$) Annual NG generator CCr cost (US$) Weight of debt (%) Diesel Generator Weight of equity (%) Generator provided energy (kWh) Unitary diesel generator emission (kg CO2eq./L) Unitary natural gas generator emission (kg CO2eq./kWh) Peak period energy (kWh) Mean energy price (US$/kWh) Fuel consumption at full load (L/h) Fuel consumption at partial load (L/h) Greenhouse Gas DG initial investment (US$) NG generator initial investment (US$) Income tax IR rate (%) Cost of debt Cost of equity Monte Carlo Simulation Natural Gas Net Present Value Operational and Maintenance Rated power (kW) probability density function PIS rate (%) Governmental taxes Operating power (kW) Accumulated probability of positive NPVs Risk premium (%) Monthly revenue (US$) Annual revenue (US$) Risk-free rate (%) Market expected return (%) Machines operating time per month (hours) Tax rate (%) Weighted Average Capital Cost Annual amount of income from tariff flags (US$) leveraged beta Coefficient that indicates the occurrence of tariff flags

1. Introduction Large facilities, such as hotels, supermarkets, hospitals, universities, etc.

demand for significant levels of energy use due to different services that have to be fulfilled and energetically fed over the entire year [1]. In order to avoid the lack of electricity supply,

ACCEPTED MANUSCRIPT those buildings may use means of producing their own electric energy through distributed power sources which concept is associated with a small-scale electricity generation technology located close to consumers [2]. Several of those facilities own on-site generation in the form of diesel generators (DG) [3]. Indeed, generators are versatile and reliable power sources, which provide vital energy and support to applications as varied as urban de-watering projects, manufacturing industries, and hospitals to name a few [4]. Although the main use of generators is to provide energy when the power grid is out of service, they may be utilized to reduce the facilities' energy demand from the power grid at times of peak electricity consumption [3]. There are many sorts of generators with different features that could be used as backup sources, but diesel and natural gas machines are preferred when large quantities of electric energy are required by consumers. Fossil fuels are widely used as energetic sources because of their high conversion efficiency into other types of energy such as electricity. However, due to the elevated rate of greenhouses gases emission during their combustion, fossil fuels have been replaced with some sorts of fuels which GHG emission into the atmosphere is lower. Another alternative is to connect fossil fuel-based electricity production to renewable sources in a hybrid energy system. Çetinkaya et al. [5] studied the effects of vegetable oil fuels on diesel engines performance and their exhaust emissions. They concluded that those fuels are promising options for diesel engines although they have problems such as flow, atomization and heavy particulate emissions. Valente and Almeida [6] studied the electric energy production in some Brazilian small villages through hybrid energy systems and have stated that a combination of a photovoltaic system and sets of diesel generators was, economically, the best energetic structure to bring about the electric energy production in those areas. As fossil fuel machines, NG-based engines are also used as distributed generation. Combined Heat and Power and Combined Cooling Heating and Power refer to electricity generation systems that recover and use waste heat and are classified as micro-scale (under 20 kW), small-scale (20kW - 1MW), medium-

scale (1 - 10MW), and large-scale (over 10MW) [2]. Residential consumers utilize micro-scale Combined Heat Power generation while commercial customers employ a smallscale one. As have been mentioned previously, researchers have studied the production of hybrid energy by renewable and fossil fuel generators systems. However, those nonfossil fuel sources which energy conversion occurs from natural resources such as sunlight, wind, and waterfall are highly susceptible to the external environmental variation that significantly affect the system performance [7]. Renewable energy sources are not suitable to generate power in emergency situations as they are rather dependent on weather and, therefore, an association with more reliable sources such as fossil fuel generators is necessary. In this paper, it was not considered renewable energy sources, but DG and NG-based generators. Although diesel burning is more efficient than NG fire, natural gas-based electricity generation has lower GHG emission and its costs are commonly lower than a diesel-based one. Economically, it is very hard to state which one is more profitable to the agent that pursue to acquire a backup source once several variables must be taken into account and a careful analysis should be performed in order to evaluate the purchase cost-effectiveness. NPV method is widely utilized by many works in literature, in particular when optimization is performed [8]. It allows business economic analysis and may aid investors in their decision-making. Specifically, in the energy field, that tool has been applied to several research projects [8–16]. NPV is an easy method to be understood and applied although one of its disadvantages is related to its treatment of information and uncertainty as a result of determinist cashflows that are usually assumed for simplicity [17]. MCS is a stochastic approach utilized mainly in cases with random variables. For this reason, it has been applied to many works which the main subject is economic risk analysis [18–22] as economical issues generally occur owing to parameters that behave randomly. Since NPV method is customarily accomplished by determinist criteria, it may be associated with

ACCEPTED MANUSCRIPT MCS in order to make the analysis closer to what occurs in a real-life situation [19]. This paper aims to evaluate the economic risk of the generators purchase to be operated over peak demand periods. The economic analysis considers two types of engines to generate electricity: DG and NG generators. Cashflows are performed through the project income statement which shows revenues from savings in not using the power grid as a supplier as well as expenses from O&M and fuel costs. CCr is taken as an extra expense in some cases. Carbon credit corresponds to a generic term that represents the right to emit one tonne of CO2 or the mass of another GHG with carbon dioxide equivalent. Carbon market was introduced in 1997 by the Kyoto Protocol and endorsed in the Rio+20 Conference for the purpose of civilization's multiple environmental crises [23]. In this work, four scenarios are proposed: a DG purchase without considering carbon credit costs; a DG acquisition taking account of an extra expense by CCr; an NG generator procurement ignoring CCr expenditure, and, finally, an NG generator purchase with carbon credit cost to be deducted from revenue. All Brazilian energy market rules are taken into consideration and a discount rate is employed. The generators rated power is switched among values in a range to verify the economic risk behavior according to the variation of that parameter. 2. Methodology The approach presented by this work analyzes the financial risk for investors by subjecting the NPV of energy projects to the MCS. The discount interest rate used in the NPV calculation is achieved by the WACC.

the company, discounted back to its present value [14]. Eq. (1) illustrates NPV calculation: NPV   Initial disbursement  Present Value (1 )

NPV may also be found by the interest rate, the total cash flow, and the time according to Eq. 2 [18]: T

yNPV ,0 (T , i D )   CF tot , (1  i D )  with:

yNPV,0: net present value related to τ = 0 CFtot,τ: total cash flow (CF) in the period including investment, operational, financing cash flows and liquidation revenue for τ = T iD: discount interest rate T: number of balance periods (generally given in years). The project is accepted if NPV ≥ 0, and the higher is NPV the more attractive is the business [8]. The investor expectations with respect to proper interest on equity are represented by the discount interest rate iD which influences the NPV value significantly and serves as an indicator of opportunity cost [18]. Several risk factors affect the NPV result and they were considered as random variables. Once an economically attractive project in this study has an NPV > 0, at a certain discount rate (r), the probability of feasibility is given by Eq. (3) [21]: 

P NPV 0 ( x 1...x n ; r ) 

 pdf ( NPV ) dNPV (3) 0

2.1. Net Present Value One of the investors' concerns over applying capital to a new business is to create value. An enterprise only creates value when NPV is higher than the initial disbursement [24]. The Net Present Value is defined as the sum of the present value of the net cash flow [15]. It is an indicator of the value or magnitude of an investment and takes into account the initial cash outflow for enterprise's purchase and the annual revenues (the cash inflows) of

(2)

 1

where PNPV > 0 represents the accumulated probability of positive NPVs in the project; pdf (NPV) represents the probability density function of NPVs in the project, and xi denotes the project's random variables. 2.2. WACC The Weighted Average Capital Cost (WACC) is the utilized method to find the discount interest rate presented in Eq. (2) and

ACCEPTED MANUSCRIPT (3). WACC is acquired through the Eq.(4) [25]:

WACC  kd D (1  t R )  k e E

(4)

where kd represents the cost of debt; D represents the weight of debt, in percentage, that is applied to the investment; tR is denoted as the tax rate; ke portrays the cost of equity that is also applied to the investment, and, finally, E represents the weight of equity in the investment. Specifying the terms, the cost of debt is obtained assuming the interest rate percentage, after inflation. The cost of equity is obtained through the calculation of the Capital Asset Pricing Model (CAPM), applying the country risk premium. The Brazilian risk premium may be obtained from the Institute of Applied Economic Research (IPEA) website and its value, in 2017, was 2.89%. The Eq. (5) shows CAPM formula [25]: k e  R f   leveraged ( R M  R f )  R B

(5)

where R f is the risk-free rate and the  leveraged is the leveraged beta that measures the project risks related to the market and it was obtained from the unleveraged β of the power sector, which is given in the sector beta table in Ref. [26]. Its value was assumed to be equal to 0.54. R M denotes the market expected return and

R B is the Risk Premium. Those parameters are also obtained from Ref. [26] and their values are 2.45% and 5.69%, respectively. The Eq.(6) is needed to find the β which is calculated from the unleveraged β for the energy sector [27]. Using this data, the WACC was calculated as 8.44% per year. 

D

 leveraged   unleveraged 1   (1  t ) E 

(6)

2.3. Monte Carlo Simulation MCS is a state-of-the-art methodology in risk analysis and finance [18]. Stochastic optimization methods have been implemented in many studies and Monte Carlo Simulation approach is one of the most popular [28]. It is a

very useful tool in insurance, sports, capital budgeting, marketing research, strategic planning, etc. [19] and may also be employed within the context of risk management of distributed energy infrastructures [22]. Today risk management is an integral part in any project assessment and MCS is an experiment that repeats a process or situation a large number of times and generates a large number of random samples linked to specific variables [19]. In order to apply MCS approach correctly, input variables have to be considered as independent random quantities, i.e. they must not be correlated to each other [18]. As an industry benchmark, 10,000 iterations are sufficient to obtain reliable results [19]. According to Arnold and Yildiz [18], one of the most important steps of Monte Carlo approach is the determination of the required probability density functions for input variables. They still state that if a data based on a specific pdf may not be associated with it owing to the lack of suitable data, a knowledge based on empirical approximation ought to be used instead. Urbanucci and Testi [22] present the steps to perform MCS approach: I. To assign a probability density function (pdf) to each model input data xi II. To generate N possible values for each input data, by means of random samples of its pdf III. To combine the random samples to get N input vectors IV. To perform the simulation of the model N times, one for each input vector. At this point, a vector of results is provided, and an input-output mapping of the model is defined V. The set of the output data (y1...y2...yN) defines the probability density function of the result of the simulation Before performing the MSC technique, a sensitivity analysis of the deterministic model may be carried out to rank the model input variables in accordance with their importance for the sensitivity of the model [18]. Within the sensitivity analysis of the deterministic model, a single input parameter is varied systematically within a predefined range of

ACCEPTED MANUSCRIPT values. All the other input variables are maintained constant with base-case value [18]. 3. Brazilian distribution energy market In Brazilian distribution energy market, consumers are classified into two distinct groups: A and B. That classification occurs according to the consumer’s voltage level requirement. Clients who demand a voltage level over 2,3 kV such as industrial facilities, shopping malls, and some commercial buildings belong to the A group whereas B group comprises clients who demand a voltage level equal or lower than that value such as residential customers. With respect to A group, it is mentioned four subdivisions: A1, A2, A3, and A4 in Ref. [29]. Each one of them comprises a range of voltage level values. Consumers are classified into those subgroups in accordance with their voltage level requirement and universities are commonly placed in the A4 subgroup. Some energy market rules may or may not be applied to clients as the application of those depends on which group the consumers belong to. There is a set of tariffs that are related to the consumers' power and energy demand and it is named as tariff category. That set of tariffs is applied to users according to the group that they are included in and it is divided into three categories for those who belong to A group: blue, green, and conventional. For those who comprise B group, the categories are: white and conventional. Each category is described in accordance with Ref. [30] as follows: in the blue category, the energy and the power demand tariff prices are different according to the period of the day that the energy is being required; in the green one, only energy tariff prices are distinct during the period of the day while the power demand tariff price is the same over the whole day; in the conventional category, tariffs prices are independent of the period of the day that the energy is being demanded.

The period of the day is very important for some tariff categories since the energy tariff price vary in line with it. Ref. [30] describes distinct tariffs in relation to the daily period and name them as: peak, intermediate, and off-peak tariffs. The peak tariff is charged if the electric energy is required over the period that comprises three consecutive hours per day and only during workdays. That period is defined by the energy company, which takes account its electric system load curve. The intermediate tariff is only applied to those consumers that belong to B group and it is charged over a period that comprises two hours: an hour immediately previous and an hour immediately further to the peak hours. The last one: off-peak tariff is charged over the period that covers a set of consecutive daily hours that are complementary to those that are defined in peak and intermediate tariffs. Fig. 1 shows the tariff categories by groups as well as the period of the day in which tariffs are related to. A common term employed in the Brazilian distribution energy market is tariff flags which are extra costs charged at the monthly energy bill due to the lack of energy production from renewable sources. Currently, the electric energy in Brazil derives mainly from hydroelectric plants which are dependent on water to generate power. In some specific situations such as over dry periods, those renewable sources decrease their electric energy supply and thermal power plants are activated as backup power sources in order to maintain a sufficient energy generation and attend the country energy demand [31]. However, as thermal power plants provide power to the whole electric system at a higher cost, the energy production becomes more expensive. Since electricity distribution companies are not able to raise their energy price monthly, the cost of providing a more expensive energy is charged at electric energy bill in the form of tariff flags. There are three types of tariff flags: red, yellow, and green [31].

ACCEPTED MANUSCRIPT

Fig. 1 - Tariff categories classified by groups and the period of the day they are related to

The appearance of the flags is signaled monthly by ANEEL, a Brazilian energy agency, according to the situation of the energy generation national system [30]. The green flag represents no additional cost to the energy bill whereas yellow and red flags add a certain amount of expense to the energy bill on overall debt. Further, there are some governmental taxes that are included in the electric energy bill such as: PIS, CONFINS, and the income tax (IR). PIS and CONFINS are social taxes and their rates are 0.65% and 3.00% of the total energy cost, respectively while IR rate is 1.27% of the total cost. 4. Mathematical modeling It is relevant to carry out some mathematical calculations in order to accomplish the aims of this work. The computation process involves technical and economic issues and it is described as follows. 4.1. Diesel consumption

and

NG

generators

fuel

A DG is characterized by its fuel consumption as well as its efficiency [32]. Several works in the literature [32–35] show that the DG fuel consumption may be modeled mathematically by a two variables linear function. Noguera et al. [36] utilize a set of

regressions elaborated from the information provided by some manufacturers to estimate the parameters of the DG fuel consumption function and inform that this parameter is in line with the engine rated power. Furthermore, the fuel consumption of generators which work under full load conditions differs from those that operate at partial load conditions. In this paper, the regression method was applied to both sorts of engines: diesel and natural gasbased generators and some data was considered from two power generation specialist companies [37,38]. Eq.(7) is used to calculate the fuel consumption of the diesel and NG generators at full load in (L/h) and (m³/h), respectively: FC  b  P  a

(7)

where FC is the hourly fuel consumption at full load (L/h or m³/h), b and a are the specific consumption (L/kWh or m³/kWh) and the fuel consumption at zero load of the generator (L/h or m³/h), respectively [35], and P is the generator rated power (kW). The parameters of Eq.(7) is obtained through the diesel and NG consumption regression curves. Fig.2 presents those curves and the equations that simulate the generators fuel consumption. Both with R² = 1.

ACCEPTED MANUSCRIPT that the revenue is generated only when the electric energy comes from generators rather than the power grid. Eq.(9) shows the modeling of the monthly revenue attainment as well as some constraints considered in this work.

 E pp ( m )  e price rev ( m )    E g  e price

if E pp ( m )  E g

(9)

if E pp ( m )  E g

where rev(m) is the revenue generated in a specific month (US$), Epp(m) is the peak period energy demanded by the university in a certain month (kWh), Eg is the electric energy provided by the generator (kWh), and eprice is the price of the electric energy per kWh (US$/kWh). The electric energy derived from the generators is assumed to be provided steadily and it is modeled according to Eq.(10): E g  P  t  Fig. 2 - Diesel and NG consumption curves

As shown in the Fig.2, the parameters b and a for diesel-based generators are equal to 0.250 and 0.000, respectively. For NG-based generators, those values are 0.278 and 1.438, respectively. Although Eq.(7) is used to estimate the fuel consumption of generators which work under full load conditions, it is not suitable to measure the fuel consumption of machines that work at partial load. In order to predict accurately the generators fuel consumption at partial load conditions, Eq.(8) is performed: FC partial  FC 

P load P

(8)

where FCpartial is fuel consumption at partial load (L/h or m³/h) and Pload is the generator operating power (kW). The presented equation do not simulate precisely the partial load fuel consumption, though it is a good approximation. 4.2. Revenue attainment and some extra incomes The project's revenue is obtained through the power production from the engines. It means

(10)

where t is the monthly time in hours that the machines are maintained in operation and η is the efficiency of the generator which is considered due to the energy losses that occur in the engines. An expense is assumed in the case of Epp > Eg as the generators are not able to supply the consumer demand sufficiently and, therefore, part of the energy ought to derive from the electricity grid. In order to develop the project's cash flow, annual revenues are required and they may be found by the Eq.(11): 12

REV year   rev ( m )

(11)

m 1

Besides the revenue, other incomes are taken into account in this paper. The taxes which were previously discussed were calculated on the generated revenue, which, in turn, were taken as cash inflows. However, in cases where the peak period energy was greater than the energy provided by the generators, the amount calculated from those taxes were considered as inflows and outflows. The outflows come from the energy that could not be supplied by the generators and must be derived from the power grid. The taxes are levied on the cost of the energy that proceeds

ACCEPTED MANUSCRIPT from that grid. Eq.(12) presents the amount of cash related to annual taxes and used as inflow. The amount of expenses related to those taxes is shown further. 12

() Tax year  ( pis  confins  ir )   rev ( m ) (12) m 1

where (+)Taxyear is the total amount of income calculated on taxes (US$), pis, confins, and ir are the taxes rates of PIS, CONFINS, and IR (%), respectively. Likewise, tariff flags that eventually might arise at the energy bill are only considered as costs if the demanded energy has been derived from the grid. If the generators have provided the electric energy otherwise, the overall amount of money related to the tariff flags expense will be taken as inflow. It was considered a value equal to 10% of the revenue as yellow and red flags. The Eq.(13) presents the calculation of income from tariff flags. 12

Y & R flags  0.1   rev ( m )   ( m )

(13)

m 1

where Y&Rflag corresponds to the annual amount of income generated by yellow and red flags (US$), 0.1 refers to 10%, and θ is a coefficient that assumes either the null value or the unit and indicates the occurrence of a tariff flag (dimensionless). It is noticeable that θ equal to zero takes the Eq.(13) to a null value while a unit of θ corresponds to a flag which value is 10% of the monthly revenue. The occurrence of each flag: yellow or red, as well as their appearance jointly, is presumed to have the same value: 10% of the revenue, whereas the green flag does not present any additional cash inflow. Tariff flags are considered as outflows if the electric energy is provided by the power grid rather than generators. 4.3. Initial investment and costs calculations There are several sorts of costs that were considered in the analysis such as initial disbursement, maintenance (O&M) costs, fuel costs, and costs due to taxes, tariff flags and electric energy that has not been derived from the power generators.

4.3.1. Initial investment The initial investment is the first expense that corresponds to the total amount of cash spent in the acquisition of the set of generators. Commonly, this initial cost is in line with the generator rated power as mentioned in Ref. [39]. The total disbursement is obtained in accordance with the Eq.(14) and Eq.(15):

I DG  P  c DG I NGgenerator  P  c NGgenerator

(14) (15)

where IDG and INGgenerator are the DG and NG generators set total initial investments (US$), respectively, and cDG and cNGgenerator are the capital costs per unit of DG and NG generator rated power (US$/kW), respectively. 4.3.2. O&M and fuel costs In order to maintain the generators proper functioning, it is necessary to refuel them very often as well as keep a regular maintenance. The costs of refueling are dependent on if the generators work in full or partial load conditions. The Eq.(16) and Eq.(17) show the calculation of diesel and NG costs, respectively, to supply the machines. 12  c  if E pp  E g  d  FC ( m )  t ( m ) m 1  Cost diesel   (16) 12 ( year ) c  FC t if E pp  E g  d m 1 partial ( m ) ( m ) 12  c  if E pp  E g  NG  FC ( m )  t ( m ) m 1  Cost NG   (17) 12 ( year ) c  FC t if E pp  E g  NG m 1 partial ( m ) ( m )

where Cost_diesel(year) and Cost_NG(year) are the annual diesel and NG costs (US$), respectively; cd and cNG are the prices of diesel and NG respectively per unit of volume (US$/L and US$/m³, respectively). Besides the costs of fuel, there are some other expenses related to the maintenance of the generators. The costs of O&M of diesel-based machines may be calculated in accordance with Ref.[40]. That reference shows that diesel

ACCEPTED MANUSCRIPT generators O&M costs may be found through some formulas that consider the engines' rotational speed. One of those formulas comes from 1500 rpm-rotational-speed generators and it was taken into account in this work. Eq.(18) presents it.

C

O&M DG _ hour



 0.242  0.3505 P   15.2  120.8 600

(18)

where CO&M_DG_hour is the O&M cost per hour of a diesel-based engine (US$/h). There are other formulas applied in the literature to estimate O&M costs of other types of engines. Ref. [40] still presents those formulas used to estimate the costs of gasolinebased engines and 3000 rmp-rotational-speed diesel engines. They are shown through eq.(19) and (20), respectively. However, they are not applied to this work as eq.(18) is used as standard formula. (19) 

CO & M

gasoline based

(20)

CO & M

3000 rpm  engine

(0.4005  0.1532 P ) 15.2  120.8 400

(0.747  0.1184 P) 15.2  120.8  400

To find the annual cost (US$), the Eq.(21) is performed.

C

O&M DG _ year

C

12

O&M DG _ hour

  t( m )

(21)

m 1

The annual O&M costs of NG-based generators are computed according to the Eq.(22) 12 E  pp ( m ) c  if E pp ( m )  Eg  O&M   NG m  1 1000 (22) C O&M   12 E ( NG gen _ year ) g (m) c if E pp ( m )  Eg &M    ONG m  1 1000 

where CO&M_NG_gen_year is the NG-based generators annual O&M cost (US$) and cO&M_NG is the NG-based engine O&M cost per

MWh that is provided by the machines (US$/MWh). 4.3.3. Generators non-provided energy cost In some cases, generators are not able to provide sufficient power to supply the energy demand to consumers. That generally occurs when the generators rated power is low compared to the clients' power demand. Although the machines may provide some energy, they are not capable of generating the total power that is demanded by the customers and thus part of that energy must be derived from the power grid and a charge for that is levied. The annual cost corresponds to the generators non-provided energy and is obtained from the Eq.(23)  12   ( E pp ( m )  Eg )  e price if E pp ( m )  Eg (23) Cost_ non p _ e  m  1 ( year ) 0 if E pp ( m )  Eg 

where Cost_non-p_e_year is the cost related to the energy that is not derived from the generators but from the electricity grid (US$). 4.3.4. Taxes and CCr costs Taxes are taken as incomes if the consumed energy comes from the owners' own generation. They are expenses, however, if it derives from the grid. As incomes, they may be calculated annually by Eq.(12) while Eq.(24) shows the computation of those taxes considered as costs. 12  ( pis  confins  ir )  e  E pp ( m )  Eg  price  m 1  ()Tax year   if E pp ( m )  Eg (24)  if E pp ( m )  Eg 0 

where (-)Taxyear is the total amount of tax charged annually as expense owing to generators non-provided energy (US$). A carbon credit is a term employed to design the amount of decrease of greenhouse gas emissions from an emission source [41]. A cap-and-trade program creates a market for GHG emissions and operates by setting a limit

ACCEPTED MANUSCRIPT (cap) to the amount of GHGs that firms are allowed to discharge [23]. Organizations and entities may buy and sell emissions permits on an open market if they make investments in technology or projects that reduce their emissions [42]. Although the CCr is commonly employed in large industries, it may be used for small-scale energy production plants in order to analyze the economic impact of GHG emission. Gamberi et al. [43] study a design of an off-grid photovoltaic-battery-diesel generator hybrid system economically and environmentally taking the GHGs emission into consideration. Once DGs and NG generators are fossil fuel sources that emit a large quantity of GHGs as they are in operation, the CCr is taken as an expense in this work. Eq.(25) presents the calculation of CCr cost for the DG analysis.

 CCrprice  emssDG _ GHG  Cost DG _ CCr    1000 year    12   FC ( m )  t m  1  12  FC partial ( m )  t  m 1

if E pp ( m )  Eg

(25)

if E pp ( m )  Eg

where CostDG_CCr_year is the DG CCr annual cost (US$), emssDG_GHG is the unitary diesel generator emission (kg CO2eq./L), and CCrprice is the CCr price per tonne of CO2 in the carbon market (US$/tCO2). The NG generator CCr cost is obtained from the Eq.(26)  CCrprice  emssNGgenerator _ GHG Cost NGgenerator _ CCr   1000 year   12 if E pp ( m )  Eg   E pp ( m ) m  1  12  E if E pp ( m )  Eg g (m)  m 1 (26)

  

where CostNGgenerator_CCr_year is the cost of the GHG emission by the NG generator and emssNGgenerator_GHG is the unitary NG generator emission (kg CO2/kWh). The CCr market's trading has presented considerable volatility [42]. Dhavale and Sarkis

[42] have assumed a value of $10 per unit of CCr which, in turn, is presumed to increase by 10% each year. Therefore the cash flow considers a CCrprice equal to US$10 in the first year, US$11 in the second, US$12.1 in the third, and so on. 5. Case study The Federal University of Itajuba is a collegiate and public university with two campuses located in different cities. The city of Itajuba campus is sited in Southeast of Brazil and presents 37.25 km² of territorial area. The campus offers several undergraduate and graduate programs mainly in engineering fields and owns 5,000 enrolled students as well as 700 staff approximately. It has been seeking to purchase a set of generators, which main aim is to feed the university campus energetically in the case of a fault in power grid. However, since the energy is more expensive during the peak periods than the regular ones, generators could be utilized to provide cheaper energy during the peak time. The university demands an average amount of peak energy equal to 270 MWh/year approximately, which only corresponds to a part of the whole campus required energy. In

Table 1 - Monthly peak energy demanded by the university and mean energy price

Year: 2016

Month JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC

Energy price (US$) 0.43 0.44 0.42 0.41 0.42 0.42 0.43 0.42 0.43 0.44 0.43 0.85

Epp (kWh) 16,100 12,600 16,100 28,000 25,200 24,500 26,600 18,900 25,200 26,600 23,800 21,700

fact, the term peak energy represents the energy

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Fig. 3 - Sequence of steps of the employed methodology

that is consumed over the period of the day when the demand for energy is very high around the country rather than the campus. With that level of annual consumption, the university is put into the A4 subgroup and the tariff category selected by the campus is the green one. In this work, the economic risk analysis does not take the power demand into consideration. Table 1 shows the peak energy per month required by the university during the year of 2016 as well as the energy monthly price per kWh. From this table, it may also be obtained a mean energy price of US$0.46. It was also known that yellow and red flags occurred

within five months of the year of 2016 and their values were 10% of the overall cost approximately. It must be pointed out that it was considered a steady energy demand by the customer, i.e. it was assumed that the campus average energy requirement remains the same without having any sort of sudden change over the years. Furthermore, the generators are presumed to work during three hours a day over 22 workdays/month, which corresponds to 66 hours monthly. Thus, the machines monthly operating time is taken as 66.

6. Results and discussion

6.1. Input variables and previous sensitivity analysis

In order to apply NPV and MCS approaches in this work, some steps have been followed. First of all, a data collection is performed so that the project's cash flow is carried out as well as the NPV calculation. After that, the MCS input and output parameters are selected and a previous sensitivity analysis is carried out. The following step is to associate the input variables with a probability distribution function. Finally, at this stage, it is possible to find the project's NPV probability distribution and from the positive NPV likelihood be aware of investors chances to have a profitable business. Fig. 3 presents the sequence of steps that were described and performed while Table 2 that is showed in the appendix of this paper displays all the coefficients utilized to perform the methodology employed in this work.

The first step to perform the Monte Carlo approach is to select input variables that cause some sort of change in the output parameters. Among all the chosen input variables, there are some of them that provoke a slight variation in the output parameters while others vary the output in an abrupt manner when they alter themselves. To be aware of which parameters affect the output variables slightly and which of those alter the MCS response sharply is reasonable to perform a sensitivity analysis previously. In this paper, this type of analysis is conducted in order to identify the variables that vary the NPV significantly. There are 9 input variables that were selected in the DG case as follows: Mean energy price (US$/kWh), Diesel price (US$/L), b (L/kWh), Investment per rated power (US$/kW), a (L/h), GHG emission (kg CO2/kWh), Carbon Credit price (US$/tCO2), θ, and Peak energy (kWh). For the NG generator

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Fig. 4 - Previous sensitivity analysis of input variables

case, the same variables are considered, but NG price (US$/m³) is used rather than Diesel price (US$/L). It was not performed a previous sensitivity analysis in the cases where CCr was not included in since the same input variables were considered in the cases without CCr. Fig. 4 presents the previous sensitivity analysis for DG and NG generator cases and shows the variables that affect the output parameters at the most. The graphs in Fig. 4 are interpreted by the slope of the lines i.e., the steeper the slope, the more influential is an input variable for the output. From that, the variables that present a great slope and, thus, show the most impact to the output parameters in all cases are the Mean peak energy price, the generators b parameter, and the fuel price.

6.2. Association with pdf's After knowing how much each input data affects the project's NPV, each one of them should be associated with a probability distribution function. All the input data, except θ, was related to a triangular distribution function which demands three sorts of coefficients: the minimum, the maximum, and the likeliest value. As the name indicates, the triangular function is a triangle-shaped function which the likeliest value is in the top vertex of the triangle and, therefore, has the greatest chances to come about compared to the other values. The minimum and maximum values have the lowest probability to occur and they represent the two vertices at the base of the triangle. We could say that the closer a certain value is to the likeliest value, the higher is the probability of its occurrence.

ACCEPTED MANUSCRIPT Likewise, if the value is closer to the minimum or maximum value, the chances of it is coming about are low. All the parameters, as well as their respective values that were discussed thus far and are presented in Table 2, were used as the likeliest value in the triangular function. The minimum value was considered to assume 90% of the likeliest value whereas the maximum value was taken as 110% of this value. Tariff flags values were multiplied by θ, a coefficient that was associated with a yes-no probability distribution function, which, in turn, is used to represent the occurrence or not of a tariff flag: a yes-status portrays its occurrence whereas no-status means it does not appear at the electricity bill. As tariff flags arise in five out of twelve university's monthly energy bills, the probability of occurrence of a yes-status is 40% whereas no-status must come about 60% of the times. Table 3 presents the minimum, the maximum and the likeliest value of each parameter considered in Monte Carlo Simulation. The peak energy variable is omitted in order to avoid large tables and repetitive information once the likeliest value of the monthly peak energy is shown in Table 1. The economic risk analysis is performed considering diesel and NG-based generators with different rated powers and also some scenarios that take account or disregard carbon credit costs. Several values of rated power have been taken in the analysis to know the economic risk behavior for different rated power values. The CCr is employed in some organizations that are involved in projects that reduce their GHG emissions. The carbon market allows those companies to sell the carbon permits to firms which GHG emission rate is rather high. The fossil fuels-based generators considered in this paper provide low power compared to large-scale energy production companies. Although the carbon permits exchange is used in this work, it is not appropriate to short-scale power generation cases. In the energy field, however, the CCr term is commonly applied to large undertakings related to renewable energy sources rather than fossil fuel-based sources. In cases where diesel and NG are used as fuels, for instance, the CCr becomes a cost instead of a credit as its name

suggest due to the high GHG emission rate they present. Although CCr is usually utilized by big companies that are able to trade relevant amount of GHG permits, it was used to verify how sensitive it is in the economic risk analysis. The carbon credit economic evaluation allows us to check how the GHG emission by fossil fuels affects the project economically in spite of its hypothetical feature. Fig. 5 presents the results obtained by four cases that were considered in the analysis: diesel-based electric generators disregarding CCr as an extra cost and the case where the CCr is taken as an expense, NG-based generators without considering the carbon credit and the case where it is taken into consideration. The graph portrayed in Fig. 5 shows the results of positive NPV probability for each generator rated power and for each created scenario in this work. The purchase of a generator is feasible for many rated power values whatever is the scenario analyzed. However, it is notable some differences among the scenarios. Those cases where CCr has not been considered show a little wider set of rated power values with a maximum of probability of positive NPV than the cases in which CCr is taken into account. It occurs because CCr is an extra cost that makes the probability of positive NPV declines. Further, generators based on NG in comparison with diesel-based generators own a broad range of rated power values in which a probability of 100% of positive NPV is reached. Indeed, for a scenario considering NG generators without CCr, the set of rated power values, which maximizes the probability of positive NPV, goes from 290 kW to 850 kW whereas for a similar scenario that takes DG instead, this range is from 330 kW to 450 kW. Out of these ranges, for DG cases the probability of positive NPV increases and decays softly near the lowest and the highest limits of the range, respectively, while it goes up and declines sharply, respectively, for NG generator scenarios.

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Fig. 5 - Results of the NPV analysis per generators' rated power

7. Conclusion An economic risk analysis of diesel and natural gas-based electric generators has been performed considering some scenarios that take account of carbon credit as an expense and some that disregard it. It is known that the generators rated power influences the economic risk analysis significantly and because of this reason several rated power values were employed in the analysis. It could be verified that diesel-based generators have a narrow range of rated power values which take the project close to a 100% profitable business whereas natural gas-based generators present a range that is truly wider than diesel-based ones as it is possible to be seen in Fig. 5. With respect to cases where carbon credit is considered as an extra cost, it was noticeable that the probability of positive NPV is always lesser than the cases where it is not employed. The carbon credit is a hypothetical consideration that permits an economic evaluation of how the GHG emission by fossil fuel-based machines could make a project unprofitable. By the observation of the previous sensitivity analysis, the input variable that the most affect the economic risk in all the cases is the Mean peak energy price followed by the generators b parameter and the fuel price. Those are the variables that considerably

influence the output response, thereby they are the most sensitive coefficients among all the selected data. Although the carbon credit cost causes a drop in the probability of positive NPV, it is not relevant to the business economic risk analysis. Acknowledgments The authors would like to acknowledge CAPES for the financial support. References [1]

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8. Appendix Table 2 - Values of coefficients

Unit

Value

Sources

Diesel generator Lifetime η cd cDG emssDG_GHG

years % (US$/L) (US$/kW) (kg CO2eq./L)

30 90 1.05 1,000 3.15

[44] [39] [34,45]

Natural gas generator Lifetime η cO&M_NG cNGgenerator cNG emssNGgenerator_GHG

years % (US$/MWh) (US$/kW) (US$/m³) (kg CO2eq./kWh)

30 90 4.48 680 0.80 0.42

Taxes confins ir pis

% % %

3.00 1.27 0.65

Other coefficients t eprice discount rate Brazilian currency

monthly hours (US$/kWh) % (BRL/US$)

66 0.46 8.44 3.21

Table 2 - Values of coefficients

[46] [39] [46] [44] [47]

ACCEPTED MANUSCRIPT Table 3 - Parameters values for association with triangular functions and yes-no probability functions

Parameters for association with triangular functions DG case parameters NG case parameters Minimum Likeliest Maximum Minimum Likeliest Maximum Investment per rated power 900 1000 1100 612 680 748 (US$/kW) Mean energy fee 0.41 0.46 0.51 0.41 0.46 0.51 (US$/kWh) b (L/kWh) ou (m³/kWh) 0.225 0.250 0.275 0.250 0.278 0.306 a (L/h) ou (m³/h) 0 0 1 1.279 1.422 1.564 Diesel price (US$/L) 0.84 0.93 1.03 NG price (US$/m³) 0.72 0.80 0.88 GHG emission (kgCO2/L) 2.84 3.15 3.47 0.36 0.40 0.44 Carbon credit price 9 10 11 9 10 11 (US$/tCO2)

θ

Parameters for association with yes-no probability functions Yes probability No probability Yes probability 0.4 0.6 0.4

No probability 0.6

Abstract This paper aims to evaluate the owners' economic risk of purchasing an electric generator in order to provide energy during the peak time. The study considers different rated powers of diesel and natural gas-based generators as well as cases with and without an extra expense due to the carbon credit (CCr), which is a cost generated by the emission of greenhouse gases (GHG). Net Present Value (NPV) is used as a method for the economic feasibility analysis while Monte Carlo Simulation (MCS), a stochastic approach, is performed to evaluate the economic risk. A Brazilian university project is taken as a case study and the campus is assumed to be an investor of an electric generator. The analysis has shown that diesel and natural gas-based generators are able to guarantee a low risk of return on investment to investors and such risk is truly dependent on the generator rated power. Diesel generators present a narrow range of rated powers with a high probability of positive NPV whereas natural gas-based engines show a wide range of them with a null risk of an unprofitable purchase. The carbon credits costs have no high sensitivity in the risk analysis.

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Highlights  Diesel and natural gas-based generators' projects evaluated economically  Both diesel and natural gas-based generators are cost-effective  The generators' rated power highly influence the economic risk of the project  A profitable business depends on ranges of rated power values  The carbon credit has not a significant impact to the risk analysis