A LIFE-CYCLE COST ANALYSIS OF THE PASSIVE HOUSE

“POLITEHNICA” FROM BUCHAREST

The objective of this article is to create a mathematical model based on the

analysis of the life cycle cost of a passive house, including its technical design

variations. In this study we analyzed 14 types of houses derived from the design of the

passive house POLITEHNICA; every house was differentiated by the type of

renewable solution used (EAHX, GHP, solar collectors, PV panels) or by the

insulation thickness, and it was compared with H12, a standard house with classical

HVAC systems and a thermal insulation of 100 mm. The houses were compared

according to criteria of economic performance throughtout their life cycle. It was

found that the additional investment in an energy efficient house can be recovered in

16-26 years, 9-16 years and 16-28 years if the replaced HVAC system is classical gas

fuelled, electric or District distribution. A sensitivity analysis is performed which

revealed the influence of the price of electricity and PV panels. The classification

system made the decision-making process easier for a possible investment in a

solution. This classification system showed that the first three recommended solutions

for investment are the houses H14, H17 and H20.

Keywords: Life-Cycle Cost Analysis, Passive House, Economic Efficiency

Nomenclature

AIRR- Adjusted Internal Rate of Return, [-];

C- Cost [Euro];

ce- unit cost of electric energy, Euro/kWh];

Ce(i)- total cost of the energy in the year i, [Euro];

DPBT- Discounted Payback Time, [Years];

E, Eel, Ei, i=P,S,PHI,PV_HVAC,PV_Storage,N,Grid_balance- total energy, electric energy, energy: primary,

secondary, PassivHaus Institut recommended, PV delivered to HVAC sistem, PV delivered to

storage tank, total delivered by PV, electric network (grid), grid electric balance; [kWh/m2/y];

fgrid- index of bi-directional interaction building-network;

fP-S- Factor of transformation from primary to secondary energy, [-];

FV- Future value, [Euro];

fs- factor of variation of the escalation of the prices from sensitivity analysis;

I0- initial investment, [Euro];

INT()- integer function;

Inv- Investment [Euro];

LCC, LCCbasa case, LCCalternative - Life-Cycle Cost: standard, basic project, alternative project, [Euro];

NS- Net Saving, [Euro];

PV, PVxi- Photovoltaic panels; Photovoltaic panels multiplied by i factor of level of production

PVi, i=Invest,Struct,Ins,NonReimburs,Energy,Subsid,Repl,OM&R,Pers,Taxes,Envir,Residual,Decommis- Present value: investment,

basic structure, insulation, non-reimburs funds of investment, energy, subsidies, replacements,

Operation Maintanance and Repair, Personnel, Taxes, Environmental taxes, Residual cost,

Decommisioning cost;

Qi, i=H,C,walls,fen,solar,vent&leak,int,ground,DHW,P,S,SC,EAHX,GHP - Thermal load: heating, cooling, walls,

fenestrations, solar radiation, ventilation and air leakage, ground, Domestic Hot Water, primary,

secondary, solar collector, EAHX heat exchanger,

ra, ri, rrd, rre, rre,s- rate of actualization, rate of inflation, real rate of discount (interest), real rate of

escalation (of prices), real rate of escalation (of prices) of the sensitivity analysis;

ROOT()- root function;

SIR- Saving-to-Investment Ratio, [-];

1. Introduction

Energy efficient houses began to be widely publicized after the oil crisis of

the 1970s that led to an alarming increase in energy prices.This led to the

development of concepts related to super-insulation, air tightness of the building,

passive design and also the implementation of high efficiency heat recovery. The

passive solar design for buildings was promoted by G. F. Keck with the "House of

Tomorrow" (1933) and by MIT University with "Solar House 1" (1939) and later,

the houses of the 1970s such as "Philips Experimental House" (Germany, 1975),

"DTH Zero-Energy House" (Denmark, 1975), "Lo-Cal House" (USA, 1976), "The

Saskatchewan Conservation House" (Canada, 1977), "Leger House" (USA, 1977)

brought to the forefront issues such as super-insulation "super-glazing" air

tightness, heat recovery ventilation.

In the 1990s, in Germany a series of energy-efficient buildings were built,

beginning with the building "Kranichstein" from Darmstadt as a result of the

concept of "passive house" issued by W. Feist and Bo Adamson. Passivhaus

Institut, founded in 1992 by W. Feist has three basic requirements for the

certification of a passive house: Space Heat Demand (or, Heating Load) ≤ 15

kWh/m2/y (≤ 10 W/m2), Pressure Test n50 ≤0.6 h-1, and Primary Energy Demand

(for all energy services)≤120 kWh/m2/y [1]. In addition to the basic requirements,

some other rules of design are established, including: Average ventilation volume

flow with ACH = 0.30 h-1 at least, indoor design temperature of 20 0C, Heat

recovery efficiency of at least 75%, use of the Ground-sourced Heat Exchanger,

demand for Domestic Hot Water (DHW) to be partially or fully covered by solar

collectors [1].

There is a point up to which intense thermal insulation ensures the

maximum efficiency of the investment, which, if exceeded, leads to over-

investment. In this situation one can calculate whether adding additional electrical

panels to the passive house can be a more effective investment than over-insulation

beyond the optimal point [2].

In 1992, Fraunhofer Institute of Solar Energy Systems (Germany)

completed an "autosufficient house ', a building Off-Grid which produces the entire

electricity it needs by means of PV panels [3]. In 1994 Rolph Disch built in Freiburg

(Germany) the building "Heliotrope" with PV panels capable of producing 4-6

times more energy than necessary; this was among the first "Plus-Energy" buildings

[4]. This new opportunity of increasing the energy efficiency as well as the

economic efficiency of the investment by adding PV panels and by making the

bidirectional connection to the electric network led to the need to develop the

concepts of Plus Energy Building and Net-Zero Energy Building [5, 6].

These types of buildings are taken in consideration in the study of this paper.

In one year a Net-Zero Energy Building produces the same same amount of energy

it consumes [7], while a Plus-Energy House produces more energy than it

consumes, thus offering the opportunity to earn an income. Throughout the year

for these buildings there is a monthly balance network monitored by a Net-Metering

System and the factors taken into account are the weighting factors of import-export

of electricity from the exchanges with the network [8, 9]. The surplus energy

exported to the grid is paid by the network operator [10, 11, 12].

Starting from the targets imposed by international organizations and

international treaties that promote environmental sustainability, the development of

the residential sector is considering the use of renewable resources and the reduction

of emissions of greenhouse gases. Thus, mention must be made of the Kyoto

Protocol which obliged the signatory industrialized countries to reduce the

emissions of greenhouse gases by 5.2% in 2010 as compared to the year of 1990

[13]; for the period 2013-2020 the protocol of Doha (2012) is agreed upon, to be

fully adopted in 2015 [14].

In Europe, buildings consume 40% of the total primary energy and they emit

40% of all CO2 emissions [15]. This percentage is high and there are technical and

legal resources to be significantly reduced. An EU directive issued in 2006 and

approved in 2007 considered the following three goals: for the period 2006-2020 to

reduce the primary energy consumption by 20%, renewables to reach a percentage

of 20% and also for the period 1990-2020 CO2 to be reduced by 20% [16]. The

widespread application of the Passive House concept will significantly contribute

to the achievement of the objectives set at the European level. The European

Climate Change Programme (ECCCP 2006) [17] identified the objectives and

strategies for cost effective solutions, standards and energy efficiency measures for

buildings. At the institutional level several incentives are given to investors in clean

energy, including mechanisms that partially or totally cover the investment by non-

reimbursable funds, green cards that over-pay the unit of clean energy produced,

connection to public facilities, etc. Programs funded with support for energy

efficient buildings catalyze the implementation of the European objectives [18].

The European Union Directive on the energy performance of buildings EPBD2010

[19] insists on increasing energy efficiency, by implementing passive heating and

cooling systems and it uses the term "Nearly-Zero Energy" [20, 21] for buildings

that use renewable energy sources in a significant proportion. There are also

requirements to achieve an optimum balance between investment cost and energy

cost savings,a balance should lead to a reduction of the cost over the estimated

economic life cycle, an aspect fully treated in the Supplementing Directive No

244/2012 [22,23,24]. The use of alternative energy is indicated as a way of bringing

the building’s performance at an optimal cost level. Kurnitski et al. [25] and Hamdy

et al. [26] exposed several calculation methodologies for buildings based on

solutions of optimal cost.

Among the requirements of a passive house, three aspects are of interest in

this study and they are related to criteria of cost and energy efficiency: thermal

insulation, renewable energy equipment and energy cost throughout the building's

life cycle. The investment in a project such as a passive house does not mean only

meeting a quality standard, but also meeting the criteria of sustainability (low

energy and as well as energy from renewable resources, cost efficiency, concern

for the impact on the community, environmentally friendly, beneficial ecological

status, and even the use of recycled construction materials). The assessment of a

house only by means of the quality-cost concept is not the most relevant because it

is reduced only to the present time evaluation. The concept of cost throughout the

life cycle of the building brings major contributions to the evaluation of a project

by considering the present cost, the duration of use, the cost of operation, the

interest rate, the escalation of the energy market price, the escalation of price for

various systems and the inflation, in order to update the value of the building. Thus,

it is necessary to underline the advantages of investing in an energy efficient house

involving the cost over a period of the life cycle. The analysis of the life cycle cost

(LCC) is particularly suitable for the assessment of building design alternatives that

satisfy a required level of performance and can be applied to any capital investment

decision where higher initial costs are balanced by future lower operating costs. The

best technical efficiency leads to cost efficiency in operation when the criterion is

energy, but in most cases a further acquisition cost is added and this makes the

analysis based on life cycle methods necessary.

In the studies carried out in the Polytechnic University of Bucharest a

software CYCO-PH in VBA Code has been designed; based on the results of the

balances from PHPP software (delivered by Passivhaus Institut), CYCO-PH is able

to generate an analysis of the life-cycle cost, to make sensitivity analyses for the

main results and to allow risk analyses for alternative projects. It is able to calculate

the heat transfer through envelope based on the outdoor and indoor conditions such

that makes possible sensitivity analysis. In portions of the alghoritms where are

involved the equipments of the house, in its input are used directly the normalized

values of the powers (thermal, electric) obtained from the output of PHPP where

are applied the rigours of Passive House Institute from Darmstadt. Practically, it

comes with an analysis that PHPP does not covers in the domain of economics and

welcomes the European directives that aim to position the buildings in cost-optimal

zones. Climatic data contain monthly normalized values of the temperature and

solar radiation, particularly it was necessary to split the year in two seasons (cold

and warm) and establish the average values for both in order to apply in the

calculation the criterion that in winter to be assured 20 0C and in summer 25 0C (for

at least 90% of the time).

It is necessary to display information about the economic environment as the

latter explains the information about the real conditions of the operation of an

investment. A report by GTM Research for the period 2012-2017 provides a

reduction of 38.8% of the prices of PV panels from 0.5 $/W (0.36 Euro/W) to 0.36

$/W (0.26 Euro/$) [27], a similar trend everywhere, which means an average

reduction of about 17.2% (a negative rate of escalation) from one year to another

for the respective period. If throughout the next 25 years prices varied with a

constant escalation rate of 17.2% that would mean a price of 0.003 $/W at the end

of the period; this value is too low and unsustainable. A more realistic forecast is to

consider that in the next 25 years the price of PV panels will halve from 0.50 $/W

to 0.25 $/W, which means a real average rate of escalation of the price of 0.027

(2.7%) from one year to another. Beyond specific prices $/W or Euro/W what is

important are the trends in time that appear to be about the same for all countries.

The escalation of electricity prices influences significantly the balance of the

costs of an energy-efficient house and this is how the price escalation based on

Eurostat statistics for the period 2007-2012 is considered (an average increase of

0.85% year on year [28]). In this paper are considered prices of fossil fuels (natural

gas) of 0.28 Euro/kWh and also the price for heat from the District Distribution of

0.40 Euro/kWh. The forecast of the rate of energy escalation applies to all types of

energy from industry (a simplification that includes solid fuel, gas fuel, electricity

or mix of energy) and is 0.007 (0.7%) from one year to another for long term periods

(more than 25 years).

Eurostat [29] provides statistics about commercial interest rates (retail interest

rate) which, for the period 2001-2011, was between 0.81% - 4.63% with a multi-

annual average of 2.69%. However, in general, formal values of 3.0-4.0% are

considered, and the most often used value (or required by official procedures) is

3.0%.

Eurostat [30] shows an inflation of 2% in the last 20 years in Europe (in 2013

the inflation was of 1.6%) with a slightly descending trend and the value of 1.5% is

considered the best estimate of the inflation for the next 30 years. In this study are

very important the escalation of the energy price and of PV panels price, which are

strongly related to issues of economic efficiency of the investment; these variables

are kept as such for further use.

2. Literature reviews

There are a number of works in which the method of life cycle cost of

buildings is used. Fuller in [31, 32] provides a set of methodologies for the life cycle

cost analysis (LCCA) of the buildings. Głuch and Baumann (2004) [33] made a

conceptual presentation of the method of LCC and mentioned the support that it

provides for the investment decision and the environmental decision. They insisted

on the essential difference between LCC method and the Life Cycle Assessment

(LCA) method. Among the methods complementary to the life cycle cost analysis

of buildings mention must be made of the method of "life-cycle energy" (LCE)

approached by Cole and Kernan (1996) [34] Sartori and Hestnes (2007) [35]

Huberman and Pearlmutter (2008) [36] Ramesh et al. (2010) [37], where the notion

of energy for traversing and issuing balances of every stage of life of the building

is essential. Feist (1997) [38] also describes the evolution of cumulative primary

energy for various solutions of energy efficient houses, related to a typical standard

house in the 1980s. IEEA [39] gave a comparison of the extra capital cost and of

the cost of passive houses in different countries and in some cases they are very

different from case to case with values even higher than 50%. This suggests the

need for a dedicated analysis for every project, statistics are informative and in

order to interpret them correctly one needs to take into account specific pricing from

country to country and even from region to region. Badescu (2007) [40] studied a

series of alternative heating solutions and he found that for time periods which are

longer than 20 years the GHP solution tends to be the most efficient from an

economic point of view. Audenard et al. (2008) [41] conducted an economic

analysis of a passive house, comparing it with a low energy house and with a

standard house. In that case, if energy cost remains constant the passive house

equals the cost of a standard house in about 29 years and when the cost of electricity

would be with an escalation rate of 5% then the cost equalization period is reduced

to 18 years. Versele et al. (2009) [42] considered the life cycle cost and the payback

period analysis of a retrofitted house in Belgium and he divided the problem into 4

scenarios of fulfillment standard requirements for houses among which the passive

house requirement was included. He found that the additional investment to achieve

a passive house standard was 27% higher than the cost scenario for a standard

house. In a study for a Net-Zero Energy House with a solar combisystem, Leckner

and Zmeureanu (2011) [43] found that the low price of electricity in Montreal made

the full return of the investment in solar technology impossible to be achieved.

Marszal and Heiselberg (2010) [44] made an analysis of the life cycle cost of a

multi-floor building Net-Zero Energy for a period of 30 years and found that

investing in a heat pump is more advantageous than using the district heating grid.

3. Method

A general model of the life cycle cost includes a number of factors of

varying economic conditions (variability of bank interest rates, inflation, price

escalation); every cost is considered updated at the present value:

𝐿𝐶𝐶 = 𝑃𝑉 = 𝑃𝑉𝐼𝑛𝑣𝑒𝑠𝑡 − 𝑃𝑉𝑁𝑜𝑛𝑅𝑒𝑖𝑚𝑏 + 𝑃𝑉𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑃𝑉𝑆𝑢𝑏𝑠𝑖𝑑 + 𝑃𝑉𝑅𝑒𝑝𝑙 + 𝑃𝑉𝑂𝑀&𝑅

+𝑃𝑉𝑃𝑒𝑟𝑠 + 𝑃𝑉𝑇𝑎𝑥𝑒𝑠 + 𝑃𝑉𝐸𝑛𝑣𝑖𝑟 − 𝑃𝑉𝑅𝑒𝑠𝑖𝑑 + 𝑃𝑉𝐷𝑒𝑐𝑜𝑚𝑚 (1)

A reduced form of the equation (1) of LCC is found in [31,32]. Aspects of

utilities, staff, tax, residual value, decommissioning are not taken into account in

this analysis, as they are not relevant to the purpose of the study. At the same time,

they tend to have the same values throughout the change of the design of the houses

involved. To highlight the issue of economic efficiency of the building, the

following components will be considered arbitrary in equation (2):

𝐿𝐶𝐶 = 𝑃𝑉𝐼𝑛𝑣𝑒𝑠𝑡 + 𝑃𝑉𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑃𝑉𝑆𝑢𝑏𝑠𝑖𝑑 + 𝑃𝑉𝑅𝑒𝑝𝑙 + 𝑃𝑉𝑂𝑀&𝑅

= (𝑃𝑉𝑆𝑡𝑟𝑢𝑐𝑡 + 𝑃𝑉𝐼𝑛𝑠 + 𝑃𝑉𝐸𝑞𝑢𝑖𝑝) + 𝑃𝑉𝐸𝑛𝑒𝑟𝑔𝑦 − 𝑃𝑉𝑆𝑢𝑏𝑠𝑖𝑑 + 𝑃𝑉𝑅𝑒𝑝𝑙 + 𝑃𝑉𝑂𝑀&𝑅

(2)

Simplifications are made by ignoring the costs involving fixed funds such as

national or international grants (we considered only subsidies for the production

process), taxes, environmental taxes, residual value, the cost of decommissioning

at the end of life cycle. This is done in order to explore the key factors of economic

interaction throughout the economic life cycle of a house.

PV panels are considered extensively with a life cycle of 25 years, OM&R

costs (operation, maintenance and repair) are considered annually as 0.1% of the

entire investment. There are considered in calculation government subsidies in

Green Certificates (4 Green Certificates=4x0.027 Euro/kWh=0.108 Euro/kWh)

which are given for the first 15 years of operation and production, thereby

improving cash flow and reducing the period of payback.

Further on, for the calculation we considered the inflation rate ri, the real

rate of escalation (of energy or equipments such as PV panels) rre and the discount

rate in order to convert the future values FV into present values PV by an overall

actualization rate ra:

𝑃𝑉 = 𝐹𝑉1

(1+𝑟𝑎)𝑛= 𝐹𝑉

(1+𝑟𝑖)𝑛(1+𝑟𝑟𝑒)𝑛

(1+𝑟𝑟𝑑)𝑛= 𝐹𝑉

(1+𝑟𝑖)𝑛(1+𝑟𝑛𝑒)𝑛

(1+𝑟𝑛𝑑)𝑛 (3)

where n is the n-th year in the evaluation, and the overall actualization rate ra is:

𝑟𝑎 =(1+𝑟𝑟𝑑)

(1+𝑟𝑖)(1+𝑟𝑟𝑒)− 1 (4)

This approach includes all three terms (discount rate, inflation rate and

escalation rate) with their proper variation generalizing the two approaches

"constant dollars/ currency" (which uses real rates) and "current dollars/currency"

(which uses nominal rates).

In this study the rate of inflation is not considered. In order to get more

relevant results from a technical point of view we will keep constant the purely

economic conditions related to inflation because they are more appropriate for the

analyses which insist on aspects of the financial market.

The fact that money is the common element of all goods gives us the

opportunity to analyze heterogeneous solutions and their combinations. The

analysis of the economic efficiency may use one or more of the criteria in Table 1.

Economic efficiency is met for the situations of the minimum Life-Cycle

Cost (LCC), maximum Net Saving (NS), maximum Saving-to-Investment Ratio

(SIR), maximum Adjusted Internal Rate of Return (AIRR) and minimum

Discounted Pay-Back Time (DPBT). Thus, we obtained the necessary information

on whether the additional value of the investment is eligible or not.

Table 1 Specific variables of evaluation of the economic efficiency of a project Variable Expression Required

LCC

∑ ∑ 𝑃𝑉𝑖𝑗

𝑁

𝑖=0

𝑀

𝑗=1

= ∑ ∑𝐹𝑉𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=0

𝑀

𝑗=1

= 𝐼0 + ∑ ∑𝐹𝑉𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=1

𝑀

𝑗=1

(5) Minimal

NS 𝐿𝐶𝐶𝐵𝑎𝑠𝑒 𝐶𝑎𝑠𝑒 − 𝐿𝐶𝐶𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 = −∆𝐼0 − ∑ ∑∆𝐼𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=1

𝑀

𝑗=1

+ ∑ ∑𝑆𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=1

𝑀

𝑗=1

(6) >0, Maximal

SIR ∑ ∑ 𝑆𝑗𝑖/(1 + 𝑟𝑎,𝑗)

𝑖𝑁𝑖=1

𝑀𝑗=1

−∆𝐼0 − ∑ ∑ ∆𝐼𝑗𝑖/(1 + 𝑟𝑎,𝑗)𝑖𝑁

𝑖=1𝑀𝑗=1

(7) >1,

Maximal

AIRR (1 + 𝑟𝑟)𝑆𝐼𝑅1/𝑁 − 1 (8) >rd, Maximal

DPBT ≈ 𝐼𝑁𝑇 {𝑅𝑂𝑂𝑇 [𝑖, −∆𝐼0 − ∑ ∑∆𝐼𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=1

𝑀

𝑗=1

+ ∑ ∑𝑆𝑗𝑖

(1 + 𝑟𝑎,𝑗)𝑖

𝑁

𝑖=1

𝑀

𝑗=1

= 0]} (9) <LC,

Minimal

where i=0...N is the year number, j=1...M is the component of the investment, I0 is the initial investment, ΔI0 is the difference of investment of the alterntive project related to the base case, Sji is the saving from the component j in year i in operational

costs of the alternative project related to base case, ΔIji is the additional investment from the component j in year i of the

alternative project related to base case.

After the payback at the end of Discounted Pay Back Time or at the end of

life-cycle there is a period when the investor has a remanent value.

In order to quantify the increase of the energy efficiency by reducing the

energy consumption or by the production of electricity (which can be economically

exploited by the bi-directional electric energy exchange with the public grid through

a metering system and by starting a commercial relationship with the District [10,

11, 12]), a period of operation of the house for 30 years is predefined. This is

necessary in order to close the time loop algorithm for the system performance

evaluation by considering a life cycle which in this case is the usual period of 30

years and in some results periods of up to 60 years will be included.

Two approaches are basic in the evaluation of economic systems: the

simplest economic conditions, where all variations are neglected in the economic

environment (inflation, bank interest rates, escalating prices) as a most conservative

approach; economic conditions considered the most probable based on the existing

information (from published statistics), and they imply "the most likely" specific

values of the economic environment derived from a forecasting analysis. This paper

uses both hypothesis of economic conditions in order to present the things in a rough

view (by considering simplest economic conditions) and also in a more balanced

evaluation (by considering the best forecasted economic conditions for the future

period of evaluation). As result, it is obtained a complete picture of the way the

project could follow.

The techniques for analyzing the variable economic environment involve

deterministic approaches (which are used in this study) considering in analysis the

variation of one or of combinations of variables around the predicted point. Another

technique is the probabilistic one where a probability factor is added to every value

considered; however, in order to proceed to such an analysis it is necessary to

process and correlate large amounts of statistical data.

4. Technical data of the Passive House “POLITEHNICA”

The building “POLITEHNICA” is built at University POLITEHNICA of

Bucharest at the follwing coordinates: 44.4380N Latitude, 26.0470E Longitude and

76.6 m Altitude. It contains two houses: the “East House” and the “West House”

that are placed in a common external envelope. Table 2 shows the geometric

parameters of the houses and of the building as a whole, highlighting its high

compactness which characterizes a great spaciousness at a minimal external surface

with the overall effect of reducing the heat losses.

Table. 2 Geometry information of the Passive House [46] Geometric Indicator Indicator value for each case

“East House” “West House” Overall

Treated floor area [m2] 140 140 280

Envelope area [m2] 481.6 481.6 797.2

Indoor air volume [m3] 435.3 435.3 870.6

Compactness C=V/S [m3/m2] 1.628 1.628 1.967

Table 3 gives information about the envelope of the building and about the thermal

properties of its parts.

Table. 3 Envelope information of the Passive House [46]

Envelope Component Geometric

indicator

Thermal

indicator

thk [mm] Stotal [m2]

Uvalue [W/m2/K]

Walls

Vertical

wall

Bricklayer 250 188.8 0.122

Thermal insulation layer 300

Roof

Roof Concrete Layer 130

188.8 0.107 Roof Thermal Insulation Layer 120

Roof Thermal Insulation Layer 120

Floor Floor Thermal Insulation Layer 150

188.8

Floor Concrete Layer 120 0.105

Windows

3x Glass layers+2x Argon 90% layers 44 64.04

0.800 Frame 86

Doors 70 3.78 0.800

The Passive House characteristics have been processed through certified

PHPP software (Passivhaus Planning Package) of the Passivhaus Institute from

Darmstadt (Table 4). On the south-facing roof angled at 15 degrees are mounted 26

PV panels (PVx1) that generate the specific space energy of 37.5 kWh/(m2y); also

are mounted 2 solar collectors with the power of 2.5 kW each.

Table. 4 Certification parameters of the Passive House Indicator Indicator value for each case

Required East House West House Overall

Specific Space Heat Demand, [kWh/m2/y] 13 13 12.5 ≤15

Specific Space DHW Demand, [kWh/m2/y] 18 18 18 -

Specific Space Electric Energy Consum., [kWh/m2/y] 45.8 30.5 38.1 -

Total Specific Primary Energy Demand, [kWh/m2/y] 119 79 99 ≤120

The “East House” has an Earth-to-Air Heat Exchanger (EAHX) (Fig. 1a)

with a maximum ventilation rate of 0.5 h-1. The "West House" has a geothermal

heat pump (GHP) (Fig. 2b) with the thermal load of 5.4 kW and it is based on a

drilling of 80 m depth [46, 47].

An evaluation of the balance between the electric energy production and the

electric energy consumption results in approximately equal values and suggests that

the Passive House “POLITEHNICA” is a Net-Zero Energy Building (Net-ZEB).

The parameters are based on the evaluation of PHPP and at present measurements

are being taken throughout an entire year in order to obtain real data. Stutterecker

pointed out that it is important whether the definition is based only on design data

or also on valid monitoring data [11].

Fig. 1 Thermal instalations of the “POLITEHNICA” building: a) “East House”, b) “West House”

[46, 47, 48] a)

1 – Solar Collector, 2 – Cold Water Inlet, 3 – Hot Water

Tank, 4 – Domestic Hot Water Outlet, 5 Electric Resistance

Heater, 6 – Heat Recovery Unit (HRU), 7 – Water-Air Heat Exchanger, 8 – Pumps Station, 9 – Geothermal HEat

Exchanger, 10 – Passive Cooling Heat Exchanger, 11 –

Hydronic Radiant Panel

b) 1 – Solar Collector, 2 – Cold Water Inlet, 3 – Hot Water

Tank, 4 – Domestic Hot Water Outlet, 5 Electric

Resistance Heater, 6 – Heat Recovery Unit (HRU), 7 – EAHX By-Pass, 8 – Condensate Drain Well, 9 – Earth

To Air Heat Exchanger (EAHX), 10 – Electric Radiant

Panel

Heat Recovery Units (HRU) of the system of ventilation have an efficiency

of 90%. The efficiency of the equipments corelated with factors of utilization are

translated in heat gains that are processed by PHPP software.

The ocupancy is considered as per the one indicated by Passive House

Institut, 1 person/35 m2 [1] . Temperature setpoint of the indoor air is 20 0 C in the

winter and 25 0 C in the summer for a balanced evaluation while the design

temperature is 20 0 C.

In [49], Feist has provided some valuable rules of efficient design of the

buildings such as passive houses and he has also built an argument accompanied by

an energy diagram for the limit case when the dedicated heating system of the

building would be removed, still keeping a minimum level of thermal comfort. He

believes that by applying the principles of "superglazing" and "superinsulation" a

quantity of heat required for heating of the house still exists but its level is so low

that it can be neglected at the limit. Fig. 2 [50] shows the costs diagram (for a life

cycle of 30 years) based on information from the passive house POLITEHNICA

mainly related to the thermal insulation thickness and has an analogy with the

diagram presented by Feist in [49].

Fig. 2 Diagram of specific space cost considering removing the dedicated heating systems when

the passive house standard is met [50]

5. Model of analysis

The interest is to find the economic benefits of a passive house with all the

technical variations over a life cycle, relative to the base case of a standard building.

The choice of a particular investment project among its alternatives should be

explained on the basis of economic criteria.

The economic information of the passive house POLITEHNICA allowed

the reproducing of its economic behavior at theoretical level, and further,

investigation was made extending to other alternatives derived from its basic core.

We explored the variation of equipping the house ( generating H13-H25)

while the same thermal insulation is maintained (300 mm as in the design case of

the passive house "Politehnica"), the same air tightness. The applied

abstractizations and limitations facilitate to determine the differences by economic

performance criteria. The house is compared with the standard insulation house

H12 which is also derived from the design of the house POLITEHNICA but has a

thermal insulation thickness of 100 mm.

All variables that are used are expressed in specific space energy and

specific space heat calculated for a year in terms of primary energy. If one wants to

express variables in secondary energy (electricity), then the following

transformation can be used:

𝑓𝑃−𝑆 =𝐸𝑝

𝐸𝑆=

𝑄𝑝

𝑄𝑆= 2.6 𝑘𝑊ℎ/𝑘𝑊ℎ (10)

The values of thermal loads for the passive house POLITEHNICA are

evaluated by the PHPP software required by the Passivhaus Institut for certification.

Balance of heating in the cold season:

𝑄𝐻 = (𝑄𝑤𝑎𝑙𝑙𝑠 + 𝑄𝑓𝑒𝑛 − 𝑄𝑠𝑜𝑙𝑎𝑟 + 𝑄𝑔𝑟𝑜𝑢𝑛𝑑 − 𝑄𝑖𝑛𝑡 − 𝑄𝑣𝑒𝑛𝑡&𝑙𝑒𝑎𝑘) (11)

Balance of cooling in the warm season:

𝑄𝐶 = (−𝑄𝑤𝑎𝑙𝑙𝑠 − 𝑄𝑓𝑒𝑛 − 𝑄𝑠𝑜𝑙𝑎𝑟 − 𝑄𝑔𝑟𝑜𝑢𝑛𝑑 − 𝑄𝑖𝑛𝑡 + 𝑄𝑣𝑒𝑛𝑡&𝑙𝑒𝑎𝑘) (12)

Table 5 provides information about the thermal loads extracted from PHPP

in order to be used in the equations of thermal balance of the passive house and its

derivatives. Those loads are design values with a degree of redundance that it is

able to cover partial loads derived from the variation of the weather, situational

consumptions, overlaping of the processes, etc.

Table. 5. Thermal loads of the Passive House POLITEHNICA “East” House “West House

Thermal Load Cold Season Warm Season Cold Season Warm Season

QH [kWh/m2/y] 12 - 13 -

QC [kWh/m2/y] 8.1 - 7.9

QDHW [kWh/m2/y] 18 18

Qwalls [kWh/m2/y] 17.8 11 17.8 11

Qfen [kWh/m2/y] 13.4 8.6 13.4 8.6

Qsolar [kWh/m2/y] 19.3 19.3 18.1 18.1

Qvent&leak [kWh/m2/y] 7.7 40.4 7.5 39.1

Qint [kWh/m2/y] 10.3 10.3 10.3 10.3

Qground [kWh/m2/y] 2.7 1 2.7 1

The information on thermal loads can also be obtained by processing models

in platforms such as TRNSYS, EnergyPlus, Simulink that can further perform

balances of them. In this study a VBA programming code was created in order to

achieve a conservative balance of the thermal loads (supplied by PHPP) by using

conditional, Boolean logic functions and threshold functions.

The equations that certify the passive house as per Passive House Institute

criteria [1] and also verify the thermal/electrical loads are presented below:

𝑄𝐻 , 𝑄𝐶 ≤ 𝑄𝑃𝐻𝐼 = 15 𝑘𝑊ℎ/𝑚2/𝑦 (13)

𝐸 = 𝑄𝐻 + 𝑄𝐶 + 𝑄𝐷𝐻𝑊 + 𝐸𝐸𝑙 ≤ 𝐸𝑃𝐻𝐼 = 120 𝑘𝑊ℎ/𝑚2/𝑦 (14)

where (13) checks the heating/cooling load and (14) the total primary energy

consumed in the house.

Balance equations of heating and hot water storage of the “East House”:

𝐸𝑃𝑉_𝐻𝑉𝐴𝐶1 + [𝑄𝐸𝐴𝐻𝑋 − 𝑄𝐻1 − 𝑄𝐶1]− = 0 (15)

𝐸𝑃𝑉_𝑆𝑡𝑜𝑟𝑎𝑔𝑒1 + [𝑄𝑆𝐶1 − 𝑄𝐷𝐻𝑊1]− = 0 (16)

where [ ] _ extracts the negative value of the expression, and when the expression

is positive then the result is null. This operator is used to describe the electric power

supply that comes in only when the thermal systems of renewable energy are over-

loaded by the thermal load requirements.

The electricity needed for the house with an EAHX system is:

𝐸𝑁1 = 𝐸𝑃𝑉_𝐻𝑉𝐴𝐶1 + 𝐸𝑃𝑉_𝑆𝑡𝑜𝑟𝑎𝑔𝑒1 + 𝐸𝑃𝑉_𝐸𝑙1 = −[𝑄𝐸𝐴𝐻𝑋 − 𝑄𝐻1 − 𝑄𝐶1]− − [𝑄𝑆𝐶1 − 𝑄𝐷𝐻𝑊1]− + 𝐸𝑃𝑉_𝐸𝑙1

(17)

Balance equations of the heating and the hot water storage of the “West House”:

𝐸𝑃𝑉_𝑆𝑡𝑜𝑟𝑎𝑔𝑒2 + [𝑄𝐺𝐻𝑃 + 𝑄𝑆𝐶2 − 𝑄𝐻2 − 𝑄𝐶2 − 𝑄𝐷𝐻𝑊2]− = 0 (18)

The electricity needed for the house with GHP system is:

𝐸𝑁2 = 𝐸𝑃𝑉_𝑆𝑡𝑜𝑟𝑎𝑔𝑒2 + 𝐸𝑃𝑉_𝐸𝑙2 = −[𝑄𝐺𝐻𝑃 + 𝑄𝑆𝐶2 − 𝑄𝐻2 − 𝑄𝐶2 − 𝑄𝐷𝐻𝑊2]−

+ 𝐸𝑃𝑉_𝐸𝑙2

(19)

Situational peak loads can give an influence on the balances, but for this

study that is pursuing only an economic and global evaluation of the energy status

of the building the conservative balances (that use averaged values along of a year)

give good results.

The total required (necessary) energy is:

𝐸𝑁 = {

𝐸𝑁1 + 𝐸𝑁2, if the building solution is 𝐸𝐴𝐻𝑋 + 𝐺𝐻𝑃2𝐸𝑁1, if the building solution is 𝐸𝐴𝐻𝑋𝑥2 2𝐸𝑁2, if the building solution is 𝐺𝐻𝑃𝑥2

(20)

For a Plus-Energy house the following relation occurs:

𝐸𝑃𝑉 − 𝑓𝑔𝑟𝑖𝑑 ∙𝐸𝑁

𝑓𝑃−𝑆= 𝐸𝑔𝑟𝑖𝑑_𝑏𝑎𝑙𝑎𝑛𝑐𝑒 (21)

where fgrid ≈ 1.01 is an index of the energy interaction building- network [7]

monitored through a metering system. The following criteria may be established:

𝐸𝑔𝑟𝑖𝑑_𝑏𝑎𝑙𝑎𝑛𝑐𝑒: {< 0, for Traditional, Standard or Nearly-ZEB Building≈ 0, for Net-ZEB > 0, for Plus-EB

(22)

The amount of money paid to or resulting from the export of energy will be

𝐶𝑒(𝑖) = 𝑐𝑒 ∙ 𝑖 ∙ 𝐸𝑔𝑟𝑖𝑑_𝑏𝑎𝑙𝑎𝑛𝑐𝑒 (23)

where ce [Euro/kWh] is the cost per unit of energy, and i is the i-th year of the start

of operation. This case is available by not considering actualization rates (simple

and constant economic conditions).

A house is a set containing heterogeneous elements. In order to carry out

the analysis we proceeded to a theoretical decomposition of the passive house in its

parts, thus providing a diversification of the options (something like puzzle pieces)

with a level of granularity and scalability. The main components of the passive

house considered in the model are the concrete structure (walls, foundation, etc.),

the thermal insulation, the glazing, the renewable energy systems (or

conventional/classical HVAC systems), the heat recovery system, a solar collector

system with a DHW storage tank, and the photovoltaic PV panels system.

Scalability is especially related to some specific variation of a component -

for example, in the study [50] after the thermal insulation was extracted as a part

from the assemble of the passive house, a variation of the thickness was performed

for a comparative study. The granularity of the variation is related to the magnitude

of the steps of variation. In this study scalability is mainly related to the variation

of the solution of the renewable energy system (EAHX + GHP, EAHXx2, GHPx2)

and of the number of PV panels. This treatment of a heterogeneous system finds the

solution due to the fact that the common denominator of all components is money.

Accepting an additional cost for a building only for its properties of super-

insulation is not enough. A passive house involves greater complexity than super-

insulation, it also includes renewable energy equipment such as EAHX or GHP,

solar collectors, solar photovoltaic panels, etc. which add extra cost to the

investment.

Table 6 shows the details of the design solutions for a range of houses (H12-

H25) with their facilities of renewable energy equipments. The solution H19 of the

passive house "POLITEHNICA" is "highlighted" and it has EAHX in the "East

House" and GHP in the "West House", two solar collectors (SC), and a photovoltaic

system of 26 PV panels (PV panels PVx1 = 26 ↔ 37.5 kWh/m2/y).

Table 6 Classification of the houses energy efficiency by adding equipments of renewable energy

House

Ins.

thick.

of the

walls

[mm]

Glazing

Classic

Heating

system/

Cooling

System

Solar Coll.

/PV Panels

Equipent of

Ground

Sourced Energy

Heating Load/

Cooling Load

[kWh/m2/y]

Energy Classification

Treshold value/ Description

[kWh/m2/y]

H12 100 2 Pane yes/yes No/No No 58.2/34.9 ≤65, Standard Energy

H13 300 3 Pane yes/yes No/No No 13.5/8.0 ≤15, Super-Insulated Bld.

H14 300 3 Pane No/No SCx2/PVx1 EAHXx2 13.5/8.1 ≤15, Passive,Nearly-ZEB

H15 300 3 Pane No/No SCx2/PVx1 GHPx2 13.5/7.9 ≤15, Passive,Nearly-ZEB

H16 300 3 Pane No/No SCx2/PVx1 EAHX+GHP 13.5/8.0 ≤15, Passive,Nearly-ZEB

H17 300 3 Pane No/No SCx2/PVx1 EAHXx2 13.5/8.1 ≤15, Passive, Net-ZEB

H18 300 3 Pane No/No SCx2/PVx1 GHPx2 13.5/7.9 ≤15, Passive, Net-ZEB

H19 300 3 Pane No/No SCx2/PVx1 EAHX+GHP 13.5/8.0 ≤15, Passive, Net-ZEB

H20 300 3 Pane No/No SCx2/PVx2 EAHXx2 13.5/8.1 ≤15, Passive, Plus-EB

H21 300 3 Pane No/No SCx2/PVx2 GHPx2 13.5/7.9 ≤15, Passive, Plus-EB

H22 300 3 Pane No/No SCx2/PVx2 EAHX+GHP 13.5/8.0 ≤15, Passive, Plus-EB

H23 300 3 Pane No/No SCx2/PVx5 EAHX+GHP 13.5/8.1 ≤15, Passive, Plus-EB

H24 300 3 Pane No/No SCx2/PVx5 EAHXx2 13.5/7.9 ≤15, Passive, Plus-EB

H25 300 3 Pane No/No SCx2/PVx5 GHPx2 13.5/8.0 ≤15, Passive, Plus-EB

The information shown in Table 6 calls for explanations on the energy

classification of houses solutions in order to give a synthetic picture of the status of

each. Thus, the following terms are used: "Super-insulated building", a house with

a corresponding level of insulation comparable to a passive house (as understood

by the Passivhaus Institut) with a conventional/classical heating system; Nearly-

Zero Energy Building (Nearly-ZEB) which is a building in accordance with the

requirements of the EPBD 2010/31/EU [19] and which also meets all the

requirements of the Passivhaus Institut from Darmstadt; Net-Zero Energy Building

(ZEB-Net) which is an on-grid building capable of producing as much energy as

it consumes throughout one year ; Plus-Energy Building (Plus-EB) which is an on-

grid building capable of producing more energy than it consumes thoughout one

year.

6. Results

Fig. 3 shows the diagram involving the cost investment in solutions H12-

H25 by adding different combinations of renewable energy systems including PV

panels at different power envelopes (1x, 2x and 4x relative to the solution of the

minimum number of panels 1x = 26 PV panels which basically obtained the status

of net-zero energy for "POLITEHNICA" house).

Fig. 3 Specific Space Cost of investment in different solutions of houses H12 to H25

H12 is the standard building and the simplest solution with a thermal

insulation thickness of 100 mm, and the other solutions (with insulation thickness

of 300 mm) meet the passive house standard (and Nearly-ZEB principles), and Plus

Net ZEB-EB. The latter have specific costs associated with their systems (Fig. 3).

If the building is based solely on a geothermal heat pump solution (GHPx2),

then the cost is particularly high especially because these systems are generally

more suitable for large buildings. The EAHXx2 alternative is the cheapest in terms

of initial investment, followed by the combined solution EAHX + GHP. However,

in the design execution of the passive house "Politehnica" the combination of two

different solutions was preferred, a heterogeneous approach which does not provide

the most effective combination but which is chosen on the grounds of challenges of

the research and of diversified teaching.

The starting point is the initial investment and the end point of the economic

cycle is usually reached after 30 years, but the analysis can be extended to 60 years

or more. Fig. 4 shows the total cost of the houses involving life cycles of 24 years

(even before the end of the operation of PV panels), 30, 40, 50 and 60 years.

a) b)

Fig. 4 Specific Space Life Cycle Cost LCC on time spans of 24, 30, 40, 50, 60 years: a) Life Cycle

Cost in the simplest economic conditions; b) Life Cycle Cost in the best forecasted economic

conditions

The longer the period of the life cycle cost, the more obvious the disadvantage

of the standard house H12. Some more defined results that allow a more direct

analysis solution versus solution are those derived from the "break-even" diagram

of cost equalization.

The "break-even" analysis of cost equalization (fig. 5) is made for the houses

H12-H25 in which H12 is the base case (or the standard reference). Fig. 5b also

shows a reduced list where houses H13, H16, H19, H22 and H25 are considered;

these houses have the same renewable EAHX + GHP system as the passive house

POLITEHNICA (H19) does, in order for us to have a comparative view of the

results. The life cycle cost of standard house H12 is matched by other alternatives

in 16-33 years in the simplest economic conditions (a conservative case) and in 16-

26 years if the best forecasted economic conditions are considered. The "break-

even" analysis of the simplest economic conditions (with the exclusion of the

escalation of prices of energy and PV panels) and in the most probable economic

conditions (average negative escalation of prices of the PV panels of -2.7% per year

and an annual escalation of energy prices of +0.7%) shows the moments when the

energy efficient solutions H13-H25 are able to recover the additional investment

against the standard house H12.

a) b)

c) d)

Fig. 5 Break-even analysis of the cost: a) extended list of houses in the simplest economic

conditions; b) reduced list of houses in the simplest economic conditions; c) extended list of

houses in the best forecasted economic conditions d) reduced list of houses in the best forecasted

economic conditions

The graphs of Cumulative Cash Flow or Net Saving (fig. 6) are related to

the base case H12. They complement the information in Fig. 5 to show the evolution

of the recovered amount over time due to improved efficiency after initially

investing more money.

a) b)

c) d)

Fig. 6 Specific Space Discounted Cash Flow or Net Saving: a) extended list of houses in the

simplest economic conditions; b) reduced list of houses in the simplest economic conditions; c)

extended list of houses in the best forecasted economic conditions d) reduced list of houses in the

best forecasted economic conditions

Table 7 shows the situation when the heating and DHW systems of the

standard house H12 based on the natural gas fuel are replaced. Hypothetical

replacement is made by systems of heating and DHW based on electricity (when

the cost of investment is the same as in the classical case but with a higher operating

cost) or District Distribution (when the investment in facilities for heating and

DHW is almost zero but the operation is cheaper than the classic case of fuel gas)

respectively.

Also are seen major differences in the duration of the recovered amount,

electrical heating system being the easiest to be replaced by the renewable energy

equipment while the option of District Distribution is the most difficult to be

replaced by the alternatives.

Table 7 Discounted Pay-Back Time (DPBT) for different references of heating and DHW systems

in the best forecasted economic conditions

Heating & DHW Systems H13 H14 H15 H16 H17 H18 H19 H20 H21 H22 H23 H24 H25

Gas Fuel System - DPBT [years] 20 16 24 20 18 26 21 16 21 19 16 19 18

Electric System- DPBT [years] 13 9 14 12 11 16 14 12 15 14 13 15 14

District Distribution- DPBT [years] 20 19 27 23 20 28 23 18 27 21 17 26 19

In comparison with the District distribution case, particularly H15, H18, H21,

H24 have a higher DPBT recovery period because the initial investment for the

solutions with GHPx2 is bigger and amplify the delay of the money recovery. At

the same time, the change of the PV panels after 25 years makes the Net Savings

(NS) become negative for a gap of several years, and then they become definitively

positive.

A sensitivity analysis is carried out in order to evaluate the solutions of

houses in hypothetical economic conditions. This analysis takes into account the

life cycle cost, net savings, the savings to investment ratio and the internal rate of

return, the payback time.

If multiple variables of evolution of a system are forecasted, then around the

point of maximum probability the response of the system to the excitation of one

variable is studied when the other variables are maintained constant at their

maximum probability (the average point for normal distributions).

𝐶(𝑥1, … , 𝑥𝑖 , … , 𝑥𝑛) = 𝐶(𝑥1, … , 𝑥𝑖, … , 𝑥𝑛) +𝜕𝐶

𝜕𝑥1𝑑𝑥1 + ⋯ +

𝜕𝐶

𝜕𝑥𝑖𝑑𝑥𝑖 + ⋯ +

𝜕𝐶

𝜕𝑥𝑛𝑑𝑥𝑛

≈ 𝐶(𝑥1, … , 𝑥𝑖, … , 𝑥𝑛) + (𝜕𝐶

𝜕𝑥1)

𝑥1

(𝑥1 − 𝑥1) + … + (𝜕𝐶

𝜕𝑥𝑛)

𝑥𝑛

(𝑥𝑛 − 𝑥𝑛)

(24)

The limits of the variations are established in the equation (25):

𝑚𝑎𝑥, min[𝐶(𝑥1, … , 𝑥𝑖, … , 𝑥𝑛)] = 𝑚𝑎𝑥, min[𝐶(𝑥1, … , 𝑥𝑖 , … , 𝑥𝑛), … , 𝐶(𝑥1, … , 𝑥𝑖, … , 𝑥𝑛)]

(25)

The real escalation rate is modified by the factor of variation fs that comes in order

to do sensitivity analysis:

𝑟𝑟𝑒,𝑠 = (1 + 𝑓𝑠)𝑟𝑟𝑒 (26)

Sensitivity analysis and interaction between the influences of variables

gives the main path of variation of the implied function. The biggest interest in this

kind of analysis is on buildings that imply the combination of the renewable energy

systems EAHX+GHP because they are more correlated with the house

POLITEHNICA. Fig. 7 shows the influences of the rate of escalation of the prices

of PV panels and of the energy around their best forecasted point. H16 does not

have its own production of electricity and LCC increases with the price of energy.

H19 is able to produce its own necessary energy. H19 is able to produce its own

necessary energy; in this way LCC remains constant with energy prices. The

descendent trend with the factor of variation of the price of energy is ascertained in

cases of H22 and H25 that are Plus-Energy houses able to export their surplus.

a)

b) c)

d) e) Fig. 7 Specific Space Life Cycle Cost (LCC) with sensitivity analysis

Net Savings shew a similar trend of variation for H16, H19, H22, H25 when

the price of energy is taken into consideration, but mention must be made of an

increase of the values by accentuating the negative price escalation factor of the PV

panels. The range of the values is radically influenced by the price of PV panels,

especially for Plus-Energy houses.

The Adjusted Internal Rate of Return, AIRR is applicable especially when the

investment is made by a company, but in any other situation it is a rigorous

parameter for the determination of the efficiency of a project and has to be as high

as possible in comparison with the rate of discount.

In general, the rate of discount used in calculations in projects is of 3% and

in the case of analyzed houses the values of the AIRR of 4-4.5% are obtained, a

percentage which is higher than the base value. For the domestic projects of natural

persons, this rate value is reasonable, but for companies it is still low, but at least it

meets the minimum requirements.

In order for these projects to be much more appealing, besides the gains

arising from improving the efficiency, they should also be able to obtain a certain

quota of the initial investment from authorities.

An important evaluation involves Discounted Pay-Back Time (DPBT) (fig.

8) which is determined by people’s tendency to recover as quickly as possible the

extra charges added to an investment. After this period, when the value is recovered,

a remanent time is considered when the benefits arise from the full ownership of

the project which eventually became free of arrearages.

a)

b) c)

d) e)

Fig. 8 Discounted Pay-Back Time (DPBT) with sensitivity analysis

Table 8 shows the global situation of the additional investment specific for

the houses H13-H25; it also shows five decision criteria through a simple

classification system where the best project receives 14 points and the worst 1 point.

In addition, a global classification that integrates all 5 criteria gives an overview on

the economic sustainability of the project. The terms of the pair LCC and NS, SIR

and AIRR correlate as score with 100%, while DPBT has a nonlinear dependence

on NS. The economic techniques make it possible to obtain final results that are

able to simplify the decision through rigorous algorithms while uncertainty is

reduced.

Table 8 Overall balance and ranking of the additional investment solutions

Minimum

Inv Minimum LCC

Maximum

NS Maximum SIR Maximum AIRR Minimum DPBT

Overall

Classif.

Value

[Euro/m2]

Score

(Rank)

Value

[Euro/m2]

Score

(Rank)

Value

[Euro/m2]

Score

(Rank)

Value

[-]

Score

(Rank)

Value

[-]

Score

(Rank)

Value

[Years]

Score

(Rank)

Score

(Rank)

H12 707.8 14(1) 1178.4 1(14) 0.0 1(14) 0.0 1(14) 0.000 1(14) 30 14(1) 32 (13)

H13 869.3 13(2) 1083.6 4(11) 94.8 4(11) 1.6 10(5) 0.046 10(5) 20 9(6) 50 (6)

H14 875.2 12(3) 993.1 11(4) 185.3 11(4) 2.1 14(1) 0.056 14(1) 16 3(12) 65 (1)

H15 974.1 9(6) 1095.0 3(12) 83.4 3(12) 1.3 5(10) 0.039 5(10) 24 12(3) 37 (10)

H16 926.0 11(4) 1045.5 7(8) 132.8 7(8) 1.6 11(4) 0.046 11(4) 20 9(6) 56 (4)

H17 946.9 10(5) 1011.6 9(6) 166.8 9(6) 1.7 13(2) 0.048 13(2) 18 5(10) 59 (2)

H18 1045.9 6(9) 1113.5 2(13) 64.9 2(13) 1.2 2(13) 0.036 2(13) 26 13(2) 27 (14)

H19 997.8 8(7) 1064.0 5(10) 114.4 5(10) 1.4 6(9) 0.041 6(9) 21 11(4) 41 (9)

H20 1018.7 7(8) 962.0 12(3) 216.4 12(3) 1.7 12(3) 0.048 12(3) 16 3(12) 58 (3)

H21 1117.7 4(11) 1063.9 6(9) 114.5 6(9) 1.3 3(12) 0.038 3(12) 21 11(4) 33 (12)

H22 1069.6 5(10) 1014.4 8(7) 164.0 8(7) 1.5 8(7) 0.043 8(7) 19 7(8) 44 (8)

H23 1234.1 3(12) 894.9 14(1) 283.4 14(1) 1.5 9(6) 0.045 9(6) 16 3(12) 52 (5)

H24 1333.0 1(14) 996.8 10(5) 181.5 10(5) 1.3 4(11) 0.039 4(11) 19 7(8) 36 (11)

H25 1285.0 2(13) 947.4 13(2) 231.0 13(2) 1.4 7(8) 0.042 7(8) 18 5(10) 47 (7)

The criterion of initial investment (Inv) obviously brings the choice of H12

(the base case or standard solution) as the cheapest solution and disagrees the most

with H24 (with GHPx2 and PVx5), which is the most expensive. The life cycle cost

LCC and net saving NS recommend H23 solution which gives a combination of a

relatively cheap investment in EAHXx2 system coupled with the version of most

PV panels (PVx5) that significantly reduce the final cost by producing and selling

electricity. Parameters SIR and AIRR recommend the cheapest solutions H14, H17

and reject H18. However, an overall comparison recommends solutions H14, H17

and H20.

7. Discussion

A fact to be discussed is that the solutions Plus-Energy are not placed on the

top of the list and an explanation can be found for this. The costs for PV panels are

still big as initial investment. An encouraging fact is that most companies that invest

in renewable energy systems obtain from the Government of their country apart

from operating subsidies, also non-reimbursable credits that cover totally or

partially the initial investment in PV panels or renewable energy systems. Many

investments in the European Union have compensations of 50% or even 100% if

they are made in the field of renewable energy. A separate study can be dedicated

to the impact that certain facilities granted at the European or national level can

have, but it is appreciated that if the initial investment was compensated by 50%

then the Adjusted Rate of Return would increase to values above 7.5% in the

assessment of 30 years, a value which would meet even the usual exigencies of the

commercial companies.

One thing that may not be predictable is the fact that governments change and

financing policies can be significantly affected. The latter will still exist, under the

form of facilities granted for sources of renewable energy, considering that every

EU country has important objectives related to sustainable development.

A sensitivity analysis involving a reduction in the cost of the initial

investment in PV panels is needed; the state can give grant funds for the initial

investment, and this can be a topic for future analysis. An inverse problem can also

be formulated: how much of the initial investment should be covered by grant funds

in order for investors to consider it a really attractive business? Anyway, in this

study we presented investments based on the real market, investments that show

that throughtout the life cycle of 30 years the initial investment is recovered and

positive net savings are obtained.

Another problem is the high variability of the price of investment from

country to country depending on that country's policy for renewable energy. This

variability can easily reach 30%, compared to the average acquisition cost for

countries with market economies. This issue can also be studied; such a study

should aim at establishing what list of countries from trade statistics for investment

may be preferred, given several initial requirements. By using the published

statistics, comparative studies can be made for EU countries; for example, 3-5

countries involving a variety of prices for equipments, energy - this is a kind of

analysis made by international corporations when they study the possibilities of

investment in some countries and choose the best for a given opportunity.

Sometimes, on short term, investors look for answers to the question whether it is

sustainable to invest at present in a given country or to wait for 1-2 years for a

predicted improvement of the economic conditions. Clearly, in order to achieve a

level of efficiency sought by companies (in which AIRR ≥ 7.5%) partial or total

grants for specific equipments of production of clean and renewable energy are

required.

8. Conclusions

This paper reproduces the economic model of the Passive House

POLITEHNICA of Bucharest at the parametric level; the latter allowed subsequent

technical variations by adding and removing equipments that affect the final energy

consumption.

The software CYCO-PH was built at University POLITEHNICA during

this study. This software is specialized in analyzing heterogeneous solutions of

investment projects in buildings that include renewable energy systems, particularly

PV panels for the production of electricity, solar collectors, heat pumps, etc.

A comparative analysis of a range of solutions of houses, among which are

a standard house (H12) and the Passive House POLITEHNICA (H19), was made

by means of several criteria of cost that are significantly influenced by energy

efficiency. All these criteria were finally abstracted in a classification system that

helps investors to choose the best solution for their purpose.

We concluded that the recovery of the additional investment in alternative

and energy-efficient solutions in comparison with a standard house can be achieved

in 16-33 years by a conservative assessment or in 16-26 years when the best

forecasts of the economic conditions are considered.

The base case itself influence accordingly the results of evaluation: if

standard house have the solution of heating and DHW based on gas fuel then

payback time is achieved in 16- 26 years; if heating and DHW is based on electricity

then payback time is achieved in 9-16 years; if heating and DHW is based on

District Distribution then payback time is achieved in 16-28 years. As noted, the

District Distribution system remains the most difficult to be replaced by renewable

energy systems applied to the buildings.

The sensitivity analysis with the deterministic approach has imposed

scenarios of variation from the uncertainty of the economic environment, sketching

possible ranges for the monitored parameters (LCC, DPBT). This analysis can be

completed in the future through an approach that includes risk analysis.

The price variations from country to country and also from year to year are

wide (for renewable energy systems in general and for PV panels in particular) and

this can be a special research topic.

Beyond the interpretation of the results of this research paper, every investor

may prepare its own decision based on its goals. The life-cycle cost method used in

this study was able to provide useful information and a new approach to potential

investors (individuals, institutions, companies) that can be used in their projects.

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