Introduction

The European Union (EU) climate and

energy policy, including its long-term vision

of striving for EU climate neutrality by 2050

and regulatory mechanisms stimulating the

achievement of effects in the coming de-

cades, has asignificant impact on shaping

the national energy strategy. Achieving the

EU’s 2020 and 2030 climate and energy

targets is key to alow-carbon energy transi-

tion. In line with the EU’s ambition to decar-

bonise the European Union, in December

2020 the European Council approved

a binding EU target to reduce net green-

house gas emissions by 2030 by at least

55% compared to 1990 levels. Thus, the

40% reduction target was increased. The

new EU ambition has been defined as

acollective goal for the entire EU, i.e. imple-

mented on the basis of contributions of

Member States, taking into account national

conditions, specific starting points, reduction

potential, the principle of independence in

shaping the national energy mix, the need to

guarantee energy security; in the most cost-

effective manner possible in order to main-

tain affordable energy prices for households

and the competitiveness of the EU, as well as

taking into account the principle of fairness

and solidarity. Following the dynamically

accelerating EU climate and energy trends

will be ahuge challenge for Poland. [1]

The base point on the path of energy

transition are the 2020 targets. In 2009,

aregulatory package was adopted setting

out three headline targets for counteracting

climate change by 2020 (the so-called

3 x 20% package), with Member States

participating in accordance with their ca-

pabilities. Poland is obliged to:

o increase energy efficiency by saving

primary energy consumption by 13.6

Mtoe in 2010-2020 compared to the

forecasts of demand for fuels and en-

ergy from 2007;

o increase the share of energy from re-

newable sources in gross final energy

consumption to 15% by 2020;

contribute to the EU-wide reduction of

greenhouse gas emissions by 20% (com-

pared to 1990) by 2020 (in terms of 2005

levels: – 21% in the EU ETS sectors and –

10% in non-ETS). [1]

The key importance for current policies

and activities is the so-called the Paris

Agreement concluded in December 2015

at the 21st Conference of the Parties to the

United Nations Framework Convention on

Climate Change (COP21). It results in the

need to stop the increase in the average

global temperature below 2°C compared

to the pre-industrial levels, and try to be

that it was not more than 1.5°C. During the

24th conference (COP24) in December

2018, during the Polish Presidency, was

signed the so-called Katowice climate

package implementing the Paris Agree-

ment. Particular attention has been sub-

jected to that the transformation resulting

from the Paris Agreement must be carried

out in afair and solidarity manner.

In 2019, the work on the Clean Energy

for All Europeans regulatory package,

which was ongoing at the EU forum, was

completed the package indicates how to

operationalise the EU’s 2030 climate and

energy targets and is intended to contrib-

ute to the implementation of the Energy

Union and the construction of the EU’s sin-

gle energy market. The Polish government

1/2025 www.informacjainstal.com.pl

Ź ródła ciepła i energii elektrycznej/Sources of heat and electricity

Energy transformation towards climate neutrality

in Poland

Transformacja energetyczna Polski wkierunku neutralności klimatycznej

RAFAŁ NOWAKOWSKI

DOI 10.36119/15.2025.1.1

The paper presents the idea of modelling of rational energy mix in Polish Power System with multicriteria assessment

methods. Desired generation stack can be predicted correctly in simplified manner under condition of choosing correct

input parameters for modelling. Thus the different assumption for Polish future energy mix were discussed as well as

investment assessment methods for modelling of power generation in the future in Poland under UE legislation

requirements regarding decarbonisation goals up to 2050.

Keywords: EU regulations, climate neutrality, energy sector, power strategy development, assessment methods for

development modelling

Dokument przedstawia pomysł modelowania racjonalnego miksu energetycznego polskiego systemu elektroenerge-

tycznego zwykorzystaniem multikryterialnych metod oceny. Docelowy stos źródeł wytwarzania może być popraw-

nie zaprognozowany wuproszczony sposób pod warunkiem wyboru właściwych danych wejściowych do modelo-

wania. Wzwiązku ztym, wartykule, omówiono różne założenia przyszłego miksu energetycznego Polski, jak rów-

nież różne metody oceny do modelowania przyszłego majątku wytwórczego wPolsce, biorąc pod uwagę wyma-

gania regulacji UE dotyczące celów dekarbonizacji do roku 2050.

Słowa kluczowe: regulacje UE, neutralność klimatyczna, sektor energetyczny, rozwój strategii energetycznej,

metody oceny do modelowania rozwoju

Rafał Nowakowski M.Sc.Eng.; Ph. D. ‒ candidate of Gdańsk University of Technology. Adres do korespondencji/ Corresponding author:

rafal.j.nowakowski@gmail.com

www.informacjainstal.com.pl

1/2025

Źródła ciepła i energii elektrycznej

took an active part in shaping the final

wording of the provisions, as these regula-

tions strongly affect the functioning and

determination of the future of the energy

market model in Poland.

In the future, it is assumed that the key

EU regulations concerning the energy sec-

tor will be further revised, which will refer to

the goals and tools of the European

Union’s energy and climate policy in atime

horizon that goes beyond the 2030 frame-

work. This applies particularly to the deci-

sions regarding the long-term vision of re-

ducing greenhouse gas emissions in the EU

until 2050.

In 2019, the European Commission

published a communication on the Euro-

pean Green Deal, i.e. a strategy whose

ambitious goal is to achieve climate neu-

trality by the EU by 2050 – as a world

leader in this field. Poland supported this

goal, however, working out aspecific na-

tional derogation, due to the difficult start-

ing point of the Polish transformation and

its socio-economic aspects. In the last

dozen of years Poland has made great

strides in reducing the environmental im-

pact of the energy sector, through the

modernisation of generation capacity and

diversification of the energy generation

structure. Our dependence on carbon fuels

is still much higher than that of other EU

Member States, which is why afair transi-

tion is so important, which means consider-

ing the starting point, the social context of

the transformation and counteracting the

uneven distribution of costs between coun-

tries, which is more burdensome for econo-

mies with high use of carbon fuels. It should

be noted that the costs relate to both the

regions of coal (mining and energy pro-

duction), as well as entire economies,

which in abrief time incur expenditures for

new capacity, often immature economi-

cally more expensive technologies, net-

work infrastructure, which is also reflected

in the price of energy.

In 2020, the world was hit by the coro-

navirus pandemic, affecting all global

economies. This emergency situation also

highlighted the important role of the energy

sector, including energy security, for the

functioning of the economy of Poland and

other European countries. In the coming

years, the energy sector will face anumber

of post-COVID challenges related to, inter

alia, the reconstruction or substitution of

supply chains in order to conduct invest-

ments, mobilise financial resources in bud-

gets strained by the effects of the epidemic,

and sometimes – verification of investment

plans and accumulation of funds for key

projects. It is important that investment de-

cisions are made taking into account the

aspect of green and low-carbon economic

recovery. Post pandemic recovery efforts

are designed to create arapid and effec-

tive growth impulse and create new op-

portunities for the national economy. In

addition to protective tools and activities

mobilising domestic public funds, EU sup-

port will be used.

The energy transformation will require

the involvement of many entities and incur-

ring capital expenditure. In the years

2021–2040 their scale may reach ap-

prox. PLN 1,600 billion. Investments in the

fuel and energy sectors will involve ap-

proximately PLN 867-890 billion. The

projected outlays in the electricity genera-

tion sector will amount to PLN 320-342

billion, of which approx. 80% will be al-

located to zero-emission capacities, i.e.

renewable energy and nuclear energy. As

aresult of transformations in the fuel and

energy sector, energy costs may increase.

Numerous investments may obtain finan-

cial support (operational and capital),

which enable changes to take place as

quickly as possible and on alarger scale.

It is important that the way in which the

transformation is carried out ensures so-

cially acceptable energy prices and does

not intensify energy poverty.[1]

On 27

of June 2022 EU Council

agreed on Fit for 55 to set higher target for

RES and energy efficiency. The Fit for 55

package is aset of proposals to revise and

update EU legislation and to put in place

new initiatives with the aim of ensuring that

EU policies are in line with the climate

goals agreed by the Council and the Euro-

pean Parliament. Fit for 55 refers to the

EU’s target of reducing net greenhouse gas

emissions by at least 55% by 2030. The

proposed package aims to bring EU legis-

lation in line with the 2030 goal.

The package of proposals aims at pro-

viding a coherent and balanced frame-

work for reaching the EU’s climate objec-

tives, which:

o ensures ajust and socially fair transi-

tion;

o maintains and strengthens innovation

and competitiveness of EU industry

while ensuring alevel playing field vis-

à-vis third country economic opera-

tors;

o underpins the EU’s position as leading

the way in the global fight against cli-

mate change [2].

Yet another recent regulation is taxono-

my agreen classification system that trans-

lates the EU’s climate and environmental

objectives into criteria for specific economic

activities for investment purposes.

It recognises as green, or ‘environmen-

tally sustainable’, economic activities that

make asubstantial contribution to at least

one of the EU’s climate and environmental

objectives, while at the same time not sig-

nificantly harming any of these objectives

and meeting minimum social safeguards.

The Taxonomy Regulation establishes

six environmental objectives [4]:

1. Climate change mitigation;

2. Climate change adaptation;

3. The sustainable use and protection of

water and marine resources;

4. The transition to acircular economy;

5. Pollution prevention and control;

6. The protection and restoration of biodi-

versity and ecosystems.

A first delegated act on sustainable

activities for climate change adaptation

and mitigation objectives was published in

the Official Journal on 9 December 2021

and is applicable since January 2022.

Asecond delegated act for the remaining

objectives was published in 2022.

Thus, the energy transformation will re-

quire the involvement of many entities and

incurring capital expenditure and several

scenarios to meet the EU environmental

goals and Polish electricity demand in cost

effective manner.

Doing research through the scenarios

and methodism of forecasting energy mix for

Poland there is acommon approach of using

the tools based on mathematic models, very

deeply based on fundamentals and future

environment. Those works need alot of data

and are very time consuming. The paper Is

about to propose novel approach based on

setting several criteria for the future energy

mix based on AHP, DEA or other similar

models. If the results are convergent, it will

confirm the truth of assumptions.

Problems which are presented in this

paper regard power generation in Poland

and are based on the realistic research

data.

Scenarios for Power Sector

Development in Poland

– general overview

Polish Energy Policy 2040 [1], [2]

Polish Energy Policy 2040 (PEP2040)

is the Government Policy published in

2021 and establishes the framework to-

wards the energy transformation in Poland.

It contains strategic decisions regarding the

selection of technologies for building

a low-emission energy system. PEP2040

describes the state and conditions of the

energy sector. Afterwards it indicates three

pillars of PEP2040, on which the eight

specific objectives of PEP2040 were

1/2025 www.informacjainstal.com.pl

based, along with the activities necessary

for their implementation, and strategic

projects. Presents territorial approach and

identified sources of funding EPP2040.

The scenario is based on Polish Energy

Policy to 2040 which is based on three

pillars [1]:

o Pillar I– Just transition – means provid-

ing new development opportunities for

the regions and communities most neg-

atively affected by the low-emission

energy transition, while creating new

jobs and building new branches of in-

dustry that participate in the energy

sector transition. Activities related to the

transition of coal regions will be sup-

ported with funds amounting to ap-

prox. PLN 60 billion. In addition to the

regional approach, the transition will

involve individual energy consumers,

who on the one hand will be shielded

from the increase in energy prices and

on the other hand will be encouraged

to actively participate in the energy

market. This will ensure that the energy

transition is conducted justly and that

everyone – even small households –

can participate. The transition will use

national competitive advantages, cre-

ate new development opportunities

and initiate broad modernisation

changes, allowing to create up to 300

thousand new jobs in high-potential

industries, in particular related to RES,

nuclear power, electromobility, grid

infrastructure, digitalisation, thermal

modernisation of buildings, etc.;

o Pillar II – Zero emission energy system

– it is along-term direction in which the

energy transition is heading. Decar-

burisation of the energy sector will be

possible through the implementation of

nuclear power and offshore wind en-

ergy, increasing the role of distributed

and civic power generation, but also

through the involvement of industrial

energy, while ensuring energy security

through transitional use of energy tech-

nologies based, among others, on

gaseous fuels;

o Pillar III – Good Air Quality – this goal

is one of the most noticeable signs of

moving away from fossil fuels; thanks

to investments in the district heating

sector transition (system and individu-

al), electrification of transport and pro-

motion of passive and zero-emission

houses using local energy sources, air

quality will visibly improve, which has

an impact on the environmental health;

the key result of the transition, which

will be noticed by every citizen, will be

ensuring clean air in Poland.

The targets for PEP 2040 are [1]:

o No more than 56% of coal in electric-

ity production in 2030;

o At least 23% of RES in gross final en-

ergy consumption in 2030;

o Implementation of nuclear energy in

2033;

o 30% reduction in GHG emissions by

2030 (compared to 1990 – baseline

of Kyoto Protocol);

o 23% reduction in primary energy con-

sumption by 2030 (compared to the

PRIMES2007 projection).

Development Plan for Transmission

System 2023-2032 [5]

Development Plan for Transmission Sys-

tem (DPTS) is the plan of power transmission

system development. It predicts the set of

investments in transmission grid based on

fundamental analysis of power transmission

system environment and internal constraints

development scenarios. This work has been

done to point out such investments that

would give the input in safety of final cus-

tomers supply in all possible conditions.

The investments in the plan aim to sup-

port:

o Poland’s commitment to fulfil the share

of RES obligation in the final energy

consumption;

o Government’s plan of offshore wind

farms construction on the Baltic See;

o Government’s plan of nuclear power

plants construction;

o Connection of new power units ac-

cording to the results of capacity mar-

ket auction between 2023 and 2026.

Power supply improvement including

minimisation of grid bottle necks. Particularly

in parallel with RES development in northern

Poland, both onshore and offshore.

The Plan brings first great technological

revolution in the investment approach with

significant share of RES in the energy mix.

The novel solution in the Polish grid will be

construction of HVDC line connecting to

areas of Poland – south and north. The

goal of this investment is to get the possibil-

ity to transmit energy produced from RES

(offshore and onshore wind farms) in the

north of Poland to the south of the country

where most of the heavy industry (power

consuming) is located in Poland.

Second approach for long-term plan-

ning of power transmission network opera-

tion is a proposal of construction of pro-

duction resources made by transmission

system operator. The idea behind that is to

have units in the system ready for interven-

tional needs or for improvement of network

operation in case if the set of production

units available for operator is not sufficient.

Polish Energy sector up to 2050 [6]

The aim of this document is to analysis

four scenarios of development of Polish

energy sector up to 2050, taking into ac-

count economic, social and environmental

aspects of its realisation and the impact on

country’s economy. The proposal of that

solution is four scenarios of power sector

development [6]:

o Coal scenario – based mainly on coal

fired units, it covers new investments in

coal mining both hard and lignite. The

RES share is 17%;

o Diversified scenario with nuclear pow-

er plants – it brings diversified technol-

ogy mix along with nuclear power

plants instead of lignite power plants.

The share of RES in 2050 accounts of

38%;

o Diversified scenario without nuclear

power plants – it is close in assump-

tions to the previous one, but in the

substitution of nuclear power plants the

natural gas fired power plants enters in

place together with RES, which share

constitutes 50% in 2050;

o RES Scenario – it assumes coal-out.

The RES production increases up to

73% and gas fired cogeneration units

close the production balance.

Polska NET-ZERO 2050 [7]

The study analysis possible directions

of the transformation of electricity and dis-

trict heat generation sectors in Poland and

in the EU. The scenarios consider important

from the point of view of challenges lying

ahead, taking into account risks associated

with fuel market turbulences in the current

geopolitical situation [7]:

o The reference scenario (BASE) that as-

sumes 60% reduction of emissions in

2050 vs. 1990, excluding Land Use,

Land Use Change and Forestry (LU-

LUCF) sector;

o The neutrality scenario (NEU) that as-

sumes 90% reduction of emissions by

2050 vs. 1990 and net-zero emissions

from all sectors, including LULUCF by

the same date;

o The neutrality scenario with high fuel

prices (NEU_HPRICE) that assumes the

same GHG reduction targets and tech-

nological potential as the NEU sce-

nario, but assumes higher prices of

fossil fuels;

o The neutrality scenario with lower po-

tential of offshore wind installations

(NEU_LWIND) that assumes the same

GHG reduction targets but lower

potential of sites suitable for the con-

struction of offshore wind installations.

Changes in the power sector will have

www.informacjainstal.com.pl

1/2025

Źródła ciepła i energii elektrycznej

asignificant influence on all sectors of the

economy, including transport, heating and

industry. Meanwhile, the decarburisation

process in these sectors will impact the

functioning of the power system by gener-

ating additional demand for electricity,

which will require increase in production.

The realisation of ambitious targets of cli-

mate policy and decarburisation of the

economy leads to adeep reconstruction of

Polish power sector. Modernisation of the

sector will be incentivised by afast-grow-

ing prices of emission allowances for the

sector.

The report presents needed techno-

logic changes in the power production

sector that are necessary of fulfil goals in

following regulations:

o European Green Deal;

o Fit for 55 together with the package of

legislation acts.

The scenario also covers the present

geopolitical situation resulting from Russian

aggression on Ukraine that has begun in

2022.

KPRM Report up to 2060 [8]

The energy mix is defined as the ener-

gy carriers that supply the final energy for

industry, households and public facilities.

As the optimal model it was assumed the

energy mix that provides:

o Sufficient power supply in national

power grid;

o The lowest possible cost of power sup-

ply of all power carriers in the project-

ed period.

The presented model has the charac-

ter of linear optimisation and is focused

on fuel technology changes that is con-

verted to electric energy. The goal of the

model is to set out the optimal model with

the cheapest energy mix with the break-

down on technologies together with as-

surance of sufficient power reserve in the

grid and realisation of binding goals for

Poland that comes from European Energy

Package.

The report presents the optimal energy

mix structure to 2060 but is calculated up

to 2090 to avoid end of the World effect.

The idea is to set the technologies that have

longer turnover period than 40 years and

the economy of those could have negative

impact on the technology choice due to

depreciation and construction period. The

energy sector will not stop its production in

2060. It can occur that the cheapest mix

up to 2060 will not be the cheapest in the

longer period and on the contrary the

cheapest energy mix in the short time will

not be economy optimal in longer period

of time.

PEP 2040 with increased storage

capacity in hydro-pump power plant

This scenario is based on PEP2040 but is

extended by the big scale energy storage

plants in form of hydro-pump storage power

plants. Presently, in Poland there is roughly

about 5% energy storage of total installed

capacity. The safety and reliability level pres-

ents that sufficient level of energy storage

should be at the level of around 10% for the

current Polish energy mix [5]. The scenario

should confirm or not the need of new invest-

ment and extension of big scale reliable

power accumulators like hydro-pump stor-

age power plants. The hydro pump storages

characterises the lowest carbon footprint

among other available similar storage tech-

nologies, that is presented in Fig. 1.

Moreover HPS technology has the

lowest total cost of energy storage (LCOS)

as shown on Fig. 2.

For the moment in Polish government

plans there is potential of construction

about 3 GW in hydro-pump power plants.

Two in South regions and one in North re-

gion of Poland.

The planned hydro pump storages

(HPS):

o HPS Tolkmicko with power capacity of

1040 MW;

o HPS Mloty with power capacity of

1050 MW;

o HPS Roznow II with power capacity of

700 MW.

EC has noticed in its documents “The

future role and challenges of Energy Stor-

age” and “Study on energy storage –

Contribution to the security of the electric-

ity supply in Europe” [11], that increasing

share of intermittent sources of energy like

PVs, windfarms will emphasis the role of

energy storages. If the RES (Renewable

Energy Sources) share will achieve 15% to

20% of total energy consumption, the

electricity network operators will not man-

age to compensate the outages of unsta-

ble RES generation. Higher share of RES

needs support of energy storages. This

support is arange of services like: balanc-

ing power, frequency stabilisation, reac-

tive power compensation, black start. The

energy storage will also play significant

role for stabilization of operation of new

nuclear power plants in Poland. First nu-

clear power station will start operation in

2033 with first unit installed capacity of

1-1,5 GW [12].

The RES share above 25% (depending

on energy system) would need support of

energy storages in two situations:

Fig. 1.

Comparative LCA (Life Cycle Assessment) of GHG (Green-House-Gas) emissions including stages of

construction, operation, decommissioning on example of energy mix for Canada. PHS (Pumped

Hydroelectricity Storage), aconventional C-CAES (Conventional Compressed Air Energy Storage),

the adiabatic compressed air storage A-CAES (Adiabatic Compressed Air Energy Storage) [10]

Rys. 1. Analiza porównawcza LCA (Ocena Cyklu Życia) emisji GHG (Gazów Cieplarnianych) uwzględ-

niająca etapy budowy, eksploatacji, likwidacji na przykładzie miksu energetycznego Kanady. PHS

(elektrownia szczytowo-pompowa), konwencjonalna C-CAES (konwencjonalny magazyn energii

sprężonego powietrza), A-CAES (adiabatyczny magazyn energii sprężonego powietrza) [10]

Fig. 2.

Range of LCOS for hydro pump storage in comparison to other storage technologies [10]

Rys. 2. Zakres LCOS (zdyskontowane koszty magazynowania energii) dla elektrowni szczytowo-

-pompowych wporównaniu zinnymi technologiami magazynowania [10]

1/2025 www.informacjainstal.com.pl

l when RES generation is high and there

is surplus of generation over demand,

the network disturbances may occur

(frequency, voltage, reactive power)

and network overload. These prob-

lems can be solved by storing of sur-

plus of energy;

l when RES generation is low, the short-

age of power my occur in relations to

demand. The support from energy

stored during surplus generation would

be asolution in such situations.

Assessment methods [13]

The evaluation of the effectiveness of

investing under market conditions would

better rely on amultiparameter and multi-

variate analysis, taking into account di-

verse conditions of execution and exploita-

tion than on classic simplified static ways

without considering time factor or dynamic

ways through comparison by means of

discount technique. Basic differences be-

tween static and dynamic methods consist

in the fact that in simple methods not the

whole investment period is taken into con-

sideration. Research focuses only on arep-

resentative year or afew years. Moreover,

calculations are made on nominal data,

which means that all income and expendi-

ture to be analyzed are not discounted. In

dynamic methods, however, the whole

construction and exploitation period and

the time factor are taken into account as

well as future income and expenditure are

calculated at present values [14], [15].

The following methods of investment

effectiveness evaluation are called simple,

because they do not consider change of

value money over time:

l cost comparison CC;

l profit comparison PC;

l yield Y (accounting rate of return ARR,

return on investment ROI, return on

equity ROE);

l payback period comparison PBPC

(payback period PBP);

l profitability account PA;

l break-even point analysis BEP.

The dynamic methods of investment

effectiveness evaluation take into account

change value over time, for example

through discount calculus (see Fig. 3):

l net present value NPV;

l present value annuity PVA;

l internal return rate IRR;

l modified internal return rate MIRR;

l annuity AN;

l profitability index PI;

l discount payback period DPBP.

While technological reasons beyond the

expected (projected) level of energy de-

mand are objective, economic situations,

however, being of dynamic nature, have

a significant impact on the risk and uncer-

tainty of investing in the power energy sector.

Therefore methods which are able to

meet modern market demands must be

sought [16].

In an investment process, the decision

maker usually has to confront asituation in

which there is acouple of opposite (discor-

dant) objectives e.g., profit maximisation

or minimisation of total direct costs.

The essence of amulti-dimensional de-

cision problem lies in the fact that individual

investment projects can be evaluated from

different viewpoints, using both quantitative

and qualitative criteria. The final choice,

however, should be in terms of quantity,

which means that the decision maker has to

receive answers which projects are effective

from the point of view of different aspects.

All methods from this procedure class

are in general strongly formalised and fre-

quently require mathematical apparatus

for which special software is needed. This

group comprises appealing application

methods for assessing the effectiveness of

an investment in power engineering, such

as [13]:

l nonparametric boundary estimation;

l hierarchic problem analysis;

l artificial neural networks;

l multi-criteria ranking methods.

These methods, via the decision maker’s

preference modelling, allow taking into ac-

count various decision situations, including

risk and investment uncertainty.

Non-parameter Estimation of Edge

Values

Data Envelopment Analysis (DEA),

which is a nonparametric method, was

elaborated by Charnes, Cooper and

Rhodes (1978) [17]. In general, the method

relies on two types of data analysis. In par-

ticular, aset of investment options – Deci-

sion Making Units (DMU) – is investigated.

The core issue is to obtain the effectiveness

of the evaluated investment variants (op-

tions) in accordance with the so called ef-

fectiveness curve. The DEA method is alin-

ear programming methodology to measure

the efficiency of DMUs when the production

process presents a structure of multiple in-

puts and outputs, “costs – effects”. It is

based on the conception of productivity

measure f (productive efficiency) formulated

by Farrell (1957), defined as [18]:

(1)

where:

E – effects;

J – costs;

r = 1,2, ..., s:

p = 1,2, ..., q;

s – effect number;

q – cost number;

µr – effect weights;

vp – cost weights.

This method does not require the

knowledge of weights because weights

maximising effects and minimising costs

are sought for each researched object.

In general, since the appearance of

DEA, there have been other methods mod-

ifying and expanding it, which, due to their

orientation, may be classified into three

basic models as follows [18]:

l cost-oriented;

l effect-oriented;

l non-oriented.

Two of the above group models (due

to scale effects) come in the following ver-

sions:

l with fixed scale effects;

l with variable scale effects;

l with non-increasing scale effects.

Non-oriented models come in the fol-

lowing versions:

l non-oriented with fixed scale effects;

l multi-plicate with variable scale ef-

fects;

l additive with variable scale effects.

The former focuses on expenditures

and is known in the literature as the CCR

model, its name originates from the first let-

ters of its inventors’ family names: Charnes,

Cooper, Rhodes. The latter enables aclas-

sification of objects to be evaluated in term

of effectiveness, which allows applying it in

investment effectiveness assessment.

The extended DEA model can be used

in the evaluation of investment options in

power engineering in order to rate them.

Fig. 3.

Economic investment evaluation methods [13]

Rys. 3. Ekonomiczne metody oceny inwestycji

[13]

www.informacjainstal.com.pl

1/2025

Źródła ciepła i energii elektrycznej

This necessarily entails making additional

assumptions which allow compiling arat-

ing list that creates aranking list of effective

options. It is assumed that in the process of

the optimisation of t objects, the analysed

i-th object is not taken into account in the

linear combination being created, which

causes that the effectiveness of the object is

not restricted by the value 1. Then, the cal-

culated measures of effectiveness enable

rating effective objects [18].

In general, the most important element

in an analysis of investment effectiveness

by means of the DEA method is the choice

of appropriate expenditures (input values)

and effects (output values), used in the

evaluation process.

The DEA method has its advantages

and disadvantages [18]. The former are as

follows:

l the possibility of taking into account the

supply (expenditure) and the demand

(effects) in the research; the knowledge

of the functional relation between ex-

penditures and effects is not necessary;

l the possibility of applying in the evalu-

ation objects using more than one ex-

penditure to create more than one ef-

fect;

l expenditures and effects can be ex-

pressed in different units, not necessar-

ily in monetary units;

l the possibility of discovering extreme

values, which are invisible in other

methods due to data averaging – in

the analysed method a polyhedron

based on extreme data is constructed

unlike in other methods where regres-

sion curves fit mean values;

l the possibility of achieving effective-

ness results in a suitable form of the

relative effectiveness of the investigat-

ed investment options.

Disadvantages of the method result

mainly from the lack of an easy way of

providing an absolute measure of effective-

ness. Only the effectiveness of the whole

group of the investigated objects is mea-

sured, excluding or eliminating one object

from the investigated group can have an

impact on the effectiveness coefficients of

particular objects. In order to calculate the

effectiveness of a new object, calculations

must be repeated. Moreover, for each in-

vestigated object, an individually formulat-

ed linear programming task must be solved,

which can be time-consuming if a great

number of investment options must be evalu-

ated. At the same time, the DEA method

shows great sensitivity to erroneous data.

Since the effectiveness curve is constructed

not due to the estimation of parameters but

only on the basis of empirical data, one er-

roneous datum can significantly change the

results of calculations [19].

The conclusions that should be empha-

sised is that the main advantage of the DEA

method is the possibility of making amulti-

criteria evaluation of investment options.

What is more, in the same decision-making

model there may be variables which differ

in terms of economic categories, which is

very important in the process of amulticri-

teria evaluation of effectiveness.

Hierarchic problem analysis

The analytic hierarchy process method

(AHP) is amulticriteria analysis method of

decision-making, which is used to solve

problems to whose analysis more than one

criterion is needed [18]. The method allows

presenting adecision-making problem in

the form of a hierarchical structure, and

assigning measures to the applied criteria

(attributes) of evaluation. This results in or-

dering a multicriteria decision-making

problem, which in turn enables rating the

investigated objects – investment options.

The analytic hierarchy process method

(AHP) is based on amultistage, multicrite-

ria decision-making analysis which en-

ables arranging investment options in the

form of a tree structure (1st stage) and

evaluating them (2nd stage).

Assigning weights to particular crite-

ria/attributes plays an important role. Ac-

cording to [21] and [19], [23] the follow-

ing assumptions must be made:

l decision-making is hierarchical process;

l particular decision-making options are

characterised by many criteria;

l there can be numerical or linguistic at-

tributes;

l weights can be assigned to particular

attributes;

l at particular decision-making levels

there may be different groups of ex-

perts taking part in decision-making

(the so called group decision-making)

or individual experts.

In general, a decision-making matrix

D, in which the rows correspond to op-

tions/alternatives and the columns to attri-

butes (criteria), is the basis for decision-

making at each level.

Taking into account the number of op-

tions, multiattribute decision-making (finite

number of criteria) and multitarget deci-

sion-making (infinite number of criteria) are

distinguished. It is worth emphasising that

in the case of multiattribute decision-mak-

ing, the number of defined options is rela-

tively small [19], [21], [23].

After rating the investment options be-

ing evaluated, an initial matrix, in which

the rows correspond to options and the

columns to attributes, is the basis of adeci-

sion-making process.

An initial matrix X has the following form:

(2)

where:

Xij – matrix element in numerical or lin-

guistic form.

The columns of an initial matrix X are

ordering vectors of options with respect to

particular attributes, they can be expressed

by different measures. Weight coefficients

for particular options are elements of an

ordering vector. They determine a prefer-

ence ordering. Ordering vector compo-

nents can be expressed in numerical form

(quantitative data) or linguistic form (quali-

tative data). It is also worth emphasising

that particular orderings can have non-ho-

mogeneous orders (in the sense of an or-

dering relation in the set of real numbers),

i.e., in one ordering ahigher value and in

another ordering alower value may cor-

respond to abetter option from the deci-

sion-maker’s point of view. Moreover, par-

ticular attributes may have weights which

show their importance [19], [21], [23].

Weight factors are given in the form of

avector w::

w = [w

··· w

] (3)

In a special case, weight coefficients

can be equal, which means that the prob-

lem at this level is considered to have no

weight.

An element of amatrix shows what the

evaluation of an option from acertain cri-

terion/attribute viewpoint is.

The AHP method became very popular

in ashort period of time, and many works

were written about it. Until the end of the

nineteen eighties of the last century, it was

applied in many fields of economy, namely:

l economics and finance management;

l transport;

l logistics;

l forecasting;

l investment programming;

l issues of choice and technology trans-

fer.

As it frequently happens, despite its

enormous popularity, the AHP method

was severely criticised in later years. It was

shown that the AHP method in its form had

numerous disadvantages [21]. Firstly, it

cannot be directly applied when there are

missing data. Another thing is that the solu-

tion depends on the scale inversion. More-

over, when anew variant is added, there

can appear the so called loss of impor-

tance phenomenon, which means that the

ordering obtained earlier is changed in the

sense of the ordering relation in the set of

real numbers. One can also obtain solu-

tions dependent on the order of aggrega-

tion operations and on determining the or-

dering. It means that the solution obtained

as aresult of aggregating afew evaluation

matrices, and calculating the ordering

then, will be different from the one ob-

tained as aresult of calculating the order-

ing for particular matrices first to be fol-

lowed by aggregation [21]. Awide discus-

sion of some disadvantages of the AHP

method can be found in Barzilai’s newest

works – from the years 1997 – 2001.

The AHP method can be applied in re-

search on the effectiveness of investment

options in power engineering. Traditional

methods used to solve the problem of effec-

tiveness, in spite of the fact that they are

popular with decision-makers, do not al-

ways allow taking into account market con-

ditions. The AHP method, due to an inte-

grated approach to the analysis and evalu-

ation of options, can be arational tool which

aids strategic investment management.

In general, an evaluation procedure

by means of the AHP method consists of

three main stages, namely:

l creating a model for analysis and

evaluation, which takes into consider-

ation information concerning intended

investment strategies;

l conducting a comparative evaluation

of strategies using the model con-

structed earlier, which leads to asyn-

thetic evaluation and partial evalua-

tions of the investigated options;

l conducting a strategic analysis, which

results in an evaluation of decisions and

the formulation of recommendations.

Artificial Neural Networks

Artificial Neural Network (ANN)

method helps to choose the most favour-

able investment variants/options, which

allows evaluating investment effectiveness

in power engineering. It results in decision-

makers freeing themselves form time-con-

suming and mathematically advanced

classical models of decision-making.

The conception of the ANN applica-

tion assumes, first, determining, on the ba-

sis of earlier research, atraining set which

is amatrix of initial parameters and results.

Next, the artificial neural network must be

taught to compare its responses to the ini-

tial data with the results of the research.

Then, coefficients characteristic for the net-

work, called weight vectors, must be cor-

related so that the difference between the

network response and the results of the re-

search was smaller than the assumed error.

Taught in this way, the neural network,

which is often amultilayer structure called

perceptron, allows programming ataught

phenomenon. The conception assumes

aphenomenological approach to the in-

vestigated phenomenon, in this case to in-

vestment processes, by means of the so

called black box method, i.e., by describ-

ing values of input/output parameters

without investigating the phenomenon’s

nature and mechanisms [24], [25], [26].

The subject of research is the evalua-

tion of investment variants-options. Eco-

nomic and technological parameters of the

variant would be the initial data, the ef-

fectiveness of the variant, expressed e.g. as

the ratio of the profit to the expenditures or

as a simple relation of the effects to the

expenditures, would be the result.

An analytical technique based on an

artificial neural network would be a tool

supporting an investment decision, concern-

ing the choice of the best investment option.

On the basis of an investment and effect

analysis concerning real investments in pow-

er engineering, amultidimensional base ma-

trix B of the following form can be achieved:

(4)

where:

i=1,2,...,t;

j=1,2,...,k.

The matrix B is composed of initial data

in the form of a subset of initial features

(characteristic of arespective variant – e.g.

realisation costs) and a subset of output

data in the form of results (effectiveness

coefficients – e.g. the expected profits). The

data of an entry matrix will hence be aba-

sis for two sets:

l training set;

l verifying set.

These sets will be exploited after an

appropriate neural network have been

created for teaching and verification pur-

pose. Once satisfactory results have been

achieved, the neural network will then be

used for an investment option analysis.

Artificial neural networks are analytical

techniques modelled after the neural func-

tions of the human brain and are capable

of forecasting new observations (specified

variables) on the basis of other observa-

tions (made on the same or different vari-

ables), after conducting alearning process

on the basis of existent data.

The subset of the basis matrix B consti-

tutes training data for teaching a neural

network which consists of e.g., two hidden

layers (with 8 neurones in each layer), at

error tolerance.

The learning process of a neural net-

work can sometimes lead to solutions in

avery short period of time, but at another

time it may require several thousands of it-

erations [27]. However, it always runs au-

tomatically, not absorbing the human be-

ing who is looking for specific solutions.

The method of investment effectiveness

evaluation using artificial neural networks

may be applied in power engineering pro-

vided the researcher has an appropriate

teaching database. The use of the method is

fully justified when design offices with along

tradition apply it because they have data-

bases that have been created for years.

The way of determining investment ef-

fectiveness presented above could provide

an opportunity of afast initial evaluation of

the usefulness of aparticular strategy and

of choosing the appropriate way of action.

However the method probably would

need to be confirmed by other method of

investment effectiveness calculation even if

the results obtained during a simulations

performed by artificial neuronal network is

positive. In fact it is not known in detail how

the thought process is carried out.

Multicriteria Ranking Methods

(MRM)

Multicriteria ranking methods allow

choosing the best variant of an investment

project from the point of view of different

evaluation criteria. Because the above

methods stem from the Electre method (Élim-

ination et Choix Traduisant Réalité – in

French), in the literature they are often re-

ferred to as the Electre methods. The way

they are used to evaluate investment effec-

tiveness is described below [28], [29], [30].

In general, it is an interesting decision-

making situation in which a finite set of

projects X={X1,X2,…,Xt} is going to be

evaluated from the point of view of

K={k1,k2,…,kk} criteria. These criteria

can be both quantitative and qualitative.

However, the final evaluation should be

quantitative, expressed in terms of acertain

order of “goodness”. In order to compare

criteria, a common evaluation scale may

be adopted in which particular criteria,

expressed by numbers, have been as-

signed the following labels: bad, satisfac-

tory, medium, good etc. Any object XiÎ{X}

should be evaluated by means of the crite-

ria. This will result in digraphs meeting par-

ticular criteria. The final general evaluation

Źródła ciepła i energii elektrycznej

will be shown by means of a synthetic

graph representing acompromise between

evaluations obtained due to applying the

criteria.

Basic problems, with which the deci-

sion-maker has to cope with, are as fol-

lows: non-convergence of criteria i.e., de-

sire to bring together things which are to-

tally unlike in their nature and formulating

one-element decisions regarded as the

most justifiable. It is also important so that

the decision-maker will not be influenced

by the magic of numbers, formalisations,

where in the in the suggested procedures

there were clearly determined and ex-

plained decision-maker’s preferences, not

obscuring the nature of the problem [29].

It is worth noticing that in multi-criteria

situations, every limitation of the choice of

an effective solution (optimal in the Pareto

sense) means introducing additional infor-

mation about the decision-maker’s prefer-

ences, and as arule they are subjective.

Methods like Electre, PROMETHEE-II

and similar from that group are character-

ised by a high calculation complexity,

which involves the necessity of using spe-

cialist software [18]. The application of this

methods require use of complicated math-

ematical apparatus and a high level of

subjectivism (e.g. the subjective choice of

the type of fuzzy preference and the

weights of particular criteria).

Conclusions

For the purpose of assessment methods

for calculation of rational energy mix in Pol-

ish Power System the variable parameters

have key importance for the value of the

results. All of above presented scenarios

from different sources have slightly different

prognosis of electric energy demand curves

that depend on power intensity of Polish

economy. According to Polish Energy Law

there is anecessity to keep certain margin of

power reserve in the power system.

Availability of country’s natural sources

of energy are important as well as import

capacities for modelling energy sources

based on conventional power plants. Fur-

ther on the carbon emission of fuels should

be added like biogas, biomass, hard coal,

lignite, natural gas, uranium, hydrogen. In

addition the potential of renewable re-

sources needs to be taken into account like

biogas and biomass.

Generation technologies should cover

investment preparation, construction period,

life cycle of power generations units, capital

expenditures (CAPEX), operational expen-

ditures (OPEX), technical power potential of

each technology, technology efficiency.

Further, criteria are effective operational

time for each technology in one period, that

depends on maintenance, time to achieve

optimal operational parameters, weather

conditions, own consumption for the pur-

pose of electricity generation.

Models should cover environmental

issues like carbon emissions and share of

renewables that depend on the SRMC

(short run marginal cost). Finally assess-

ment methods needs to be filled with im-

ports capacities from neighbouring coun-

tries, legal constraints, social criteria’s.

Having analysed potential modelling

methods the preferred method for model-

ling the power generation mix for Poland

based on various available power devel-

opment scenarios in Poland is analytical

hierarchy process (AHP) as the method al-

lows presenting adecision in clear, hierar-

chical structure, and assigning measures to

the applier criteria of evaluation that result

in rating investigated options. The method

has its disadvantages like lack of resistance

for the lack of data, dependency on the

scale inversion, new added variants may

cause disturbances, to point some of them.

Nevertheless other analysed methods

like DEA, ANN, MRM have also disadvan-

tages like in DEA method sensitivity for er-

rors that have significant impact on calcula-

tion results, generalising of data in form of

presentation of the investment effectiveness

for the whole group of invested objects, time

consuming calculations. The ANN method

results should be confirmed by other method

of investment effectiveness calculation, even

if the simulations performed by ANN pres-

ent positive results. Finally MRM method in-

volves use of specialist software and has

high calculation complexity.

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