Assistant Mioara Bãncescu, PhD Candidate
Department of Economic Cybernetics
Academy of Economic Studies, Bucharest, Romania
Lecturer Daniela MARINESCU, PhD
Department of Economic Cybernetics
Academy of Economic Studies, Bucharest, Romania
Professor Dumitru Marin, PhD
Department of Economic Cybernetics
Academy of Economic Studies, Bucharest, Romania
FISCAL POLICIES AND MODELING TECHNIQUES RELATED TO ENERGY
AND ENVIRONMENT PROTECTION
Abstract: This paper consists in a theoretical and applicative approach related to
sustainable energetic systems and global necessity of environment protection. In the first
part of the paper it is reviewed the dedicated literature to sustainable energetic systems.
There are presented the characteristics of past and present models built in this field. The
‘top-down’ category of models and ‘bottom-up’ category of models are described in a
comparative manner. In the end of the first part it is shaped the research perspective in
the field of sustainable energetic systems based on most recent developments. Also, are
presented the implications of externalities on competitive equilibrium and on Pareto
optimality state, being considered some abstract economies.
Keywords: energy, environment protection, research, modeling techniques
1
INTRODUCTION
Many energy – environment models are in current use around the world, from simple
ones to very complex ones. The most important criteria which differentiate one model
against others are:
 economic rationale
 time horizon over which decisions are made
 geographic scope
 level of desegregation of decision variables (degree of detail with which
commodities and technologies are represented)
The first 3 criteria are general applicable for any other research area than energy –
environment, but the last one is more specific for this field. In the following will be
presented more details related to different categories of energy – environment models.
DEDICATED LITERATURE REVIEW
From historic perspective, the models dedicated to energy – environment field can be
largely split into ‘top - down’ models and respectively ‘bottom-up’ models.
Top-Down Models
They represent an entire economy via a relatively small number of aggregate
variables and equations. Usually they are aggregated General Equilibrium (GE)
models. These models are built based on substitutability of production factors.
One characteristic is that the production function parameters are calculated for
each sector, inputs and outputs reproduce a single base historical year.
Also, can be noted that ‘top - down’ models encompass macroeconomic variables
beyond the energy sector proper, such as wages, consumption or interest rates.
Bottom-Up Models
They represent very detailed, technology explicit models that focus primarily on
the energy sector of an economy. Some ‘bottom-up’ models compute a partial
equilibrium, by setting up the objective to maximize the total net surplus – the
consumer surplus plus the producer surplus, while others bring representation of a
system not governed purely by profit or utility maximizing behavior. The first
class mentioned use optimization techniques, and the second one use simulation
techniques.
Each important energy-using technology is identified by a detailed description of
its inputs, outputs, unit costs, and several other technical and economic
2
characteristics. Like this, these models have the capability to track a wide variety
of traded commodities.
For this type of models, the production function of a sector is implicitly
constructed, rather than explicitly specified as in more aggregated models. Such
functions may be quite complex, depending on the complexity of the Reference
Energy System of each sector.
Convergence tendency
Based on recent modeling developments, it can be noticed that distinctions
between bottom-up and top down models tend to be minimized.
On one hand, the top-down models (general equilibrium models), now include a
fair amount of fuel and technology desegregation (i.e. for key sectors such as:
electricity production, oil and gas supply). Such a model example is MERGE
(Model for Evaluating Regional and Global Effects).
On the other hand, more advanced bottom-up models tend to capture some of the
effects of the entire economy on the energy system. Such a model example is
MARKAL model, having in conclusion the following characteristics: technology
explicit, multi-regional, partial equilibrium model, price elastic demands assumed,
competitive markets assumed1, perfect foresight assumed2.
Recent research developments
Numerous advanced have registered lately in energy – environment research area.
Some of them are mentioned bellow:
 Use of innovative policy instruments such as renewable energy or energy
taxation
 Encompass environmental controls
 Modeling the trade with green certificates
 Incorporating decision-making behavior, data uncertainty, asymmetric
information
 Integrated models which to include the global economy, not to be focused
on a specific region or country
 Including corporate culture (i.e. contribution of social sciences) and
interdisciplinary analysis
 Use of software instruments to run the models
 The integration of industrial cogeneration in the energy models
1
Perfectly competitive energy markets are characterized by perfect information and an atomization of the
economic agents [G. Goldstein et all]
2
The perfect information assumption extends to the entire planning horizon [G. Goldstein et all]
3
Data uncertainty is a very important aspect to be incorporated in the models, as the
analysis of an energy – environment system is marked by uncertainties, be it the
specification of demands and prices, or the availability and characteristics of future
technologies, or the emission targets that should be adopted. The traditional models are
linked to a deterministic environment, while the modern ones are rather linked to a
stochastic one, although there are also exceptions.
In the absence of explicit modeling of uncertainties, building models can be approached
trough scenario analysis (i.e. different scenarios of demands, technological development,
or emission constraints). Although this approach is useful, it is also incomplete and will
lead to different recommendations (i.e. in terms of future investment to be done), upon
which one can hardly decide.
The alternative approach is to use stochastic models, where the future event bifurcation is
embedded (i.e. all together the possibilities for demand, technological development, or
emission constraints).
The last approach is the chosen one for the applicative part of the paper - representing
multiple scenarios, each having a possibility of occurring, within a single coherent
formulation.
USING GAMS - GENERAL ALGEBRAIC MODELING SYSTEMS, DECIS
SOLVER
The applicative part of this paper is approached using GAMS - General Algebraic
Modeling Language, one of the most widely used modeling languages.
GAMS is a high-level modeling system for mathematical programming and
optimization. It consists of a language compiler and several integrated highperformance solvers. The software is specifically designed for modeling complex
problems – linear type, nonlinear type or mixed integer optimization type.
GAMS is able to formulate models in many different types of problem classes. That
means switching from one model type to another can be done with a minimum of
effort. You can even use the same data, variables, and equations in different types of
models at the same time. GAMS supports the following basic model types:
Linear Programming
Mixed-Integer Programming
Non-Linear Programming
Mixed Complementarity Problems
Mathematical Programs with Equilibrium Constraints
Constrained Nonlinear Systems
Non-Linear Programming with Discontinuous Derivatives
4
Mixed-Integer Non-Linear Programming
Quadratically Constrained Programs
Mixed Integer Quadratically Constrained Programs
Specifically for this paper, DECIS solver was chosen to be used, which is a large
scale stochastic programming solver developed by Stanford University.
DECIS include parameters that are not known with certainty, but are assumed to be
known by their probability, allowing usage within the model of variables with a
random evolution. It employs Benders decomposition and allows using advanced
Monte Carlo sampling techniques.
For solving linear and nonlinear programs DECIS interfaces with MINOS3 or
CPLEX4.
DECIS employs different strategies to solve two-stage stochastic linear programs.
Either it computes an exact optimal solution to the problem or it approximates the
optimal solution and gives a confidence interval within which the true optimal
objective lies ( i.e. with 95% confidence).
The general form of the two –stage stochastic linear problems DECIS can solve is the
following:
where:




3
4
‘x’ and ‘yω’ denotes the first-stage and respectively the second stage
decision variables
‘c’ and ‘fω’ denotes the first-stage and respectively the second stage
objective coefficients
‘A’ and ‘b’ represent the coefficients and right hand sides of the first-stage
constraints (certainty)
‘Bω’, ‘Dω’ and ‘dω’ represent the coefficients and right hand sides of the
second-stage constraints (uncertainty); they are known by their probability
distribution of possible outcomes
Is a state-of-the-art solver for large-scale linear and nonlinear programs; see Murtagh and Saunders (1983)
Is one of the fastest linear programming solvers available; see CPLEX Optimization, Inc. (1989–1997)
5

‘ω’ – denotes a possible outcome and ‘Ω’ denotes the set of all possible
outcome
The objective is to find a feasible decision x that minimizes the total expected costs,
the sum of first-stage costs and expected second-stage costs.
The paper approaches first the certainty scenario (the deterministic model), when it is
solved ‘the expected value problem’. More specifically, in the first scenario all
random parameters / variables are replaced by their expectation or a particular
realization value.
Then the paper approaches the uncertainty scenario (the stochastic model), when exist
random parameters and variables, expressed by their probability of distribution. In
order to achieve this, the following steps are needed:



the specification of the decision stages (which variables belong to the first
stage and which to the second stage, as well as which constraints are firststage constraints and which are second-stage constraints)
the specification of the random parameters (the distribution probabilities);
NOTE: the number of possible realizations of the discrete random
parameters determines the accuracy of the approximation
setting DECIS to be the optimizer to be used (decomposition iteration
limit and time resource limit can be set directly by the user)
MODEL DESCRIPTION
The application treats the expansion of the thermo sector with a new power plant with
two generators. The reason for choosing this kind of application resides in the
importance of the thermo sector within the energy – environment field.
In Romania, in particular, modernization programs are currently being implemented
in several thermo power plants, aiming at increasing operation reliability and
efficiency, as well as mitigating the impact on the environment. Related to
environment constraints, the programs implemented refer to desulphurization low
NOx burners or NOx removal systems for coal-fired plants.
The objective function considered in the model is to minimize the total costs, having
the following for components:
 investment costs
 operational costs
 unserved demand costs
 pollution costs (taxes)
Model constraints are the following:
 lower and upper limit for the possible capacity of the 2 generators
6



total production (operation level), depending on demand possible levels is
obtained multiplying the availability parameter with capacity of generators
operating level plus unserved demand to be at least the covered demand
emission level depends on production and a specific pollution related
coefficient
The model considered is a linear one.
Case Study – Certainty Scenario
First we consider the deterministic model and we take particular realization states for
all model parameters.
 Availability parameters: for generator no. 1: 69%, for generator no. 2: 65%5
 Minimum capacity: 1000 MW
 Maximum capacity: 10000 MW
 Unit investment cost:
o For generator no. 1  4.4 u.m.
o For generator no. 2  2.9 u.m.
 Unit operating cost, which is depending on demand level:
o For generator no. 1  4.9 u.m.; 2.1 u.m.; 0.5 u.m. (from high to low
demand level)
o For generator no. 2  8.1 u.m.; 4.0 u.m.; 1.0 u.m (from high to low
demand level)
o NOTE: we assume the bigger is the demand level, the more expensive is
to produce (pick periods for energy delivery)
 Expected demand level: 11.26 TWH6
 Unit cost of unserved demand: 10 u.m. (no matter the generator)
 Unit emissions level:
o For generator no. 1  55 tones
o For generator no. 2  76 tones
 Tax on emissions: 0.01 (1%, proportional with operating level)
In conclusion we have chosen the parameters for the 2 generators so that the first
generator to be more expensive to build, but afterwards with inferior operating cost,
as well as inferior emission level while the generator no.2 requires a less investment
level in the beginning, but will produce at a superior unit cost than generator no. 1
and will pollute more, causing like this supplementary costs.
Case Study – Uncertainty Scenario
5
After implementation of a real modernization program starting with 1991 for the 2 biggest Romanian
power plants (Rovinari plant and Turceni plant), the average availability of the 7 units of each power plant
is for Turceni 69% and for Rovinari 65.2% , [Vaida V.]
6
In Romania, the demand level covered by Rovinari plant and Turceni plant is 5.68 TWH for Turceni (with
an installed capacity of 1980 MW) and respectively 5.58 TWH for Rovinari (with an installed capacity of
1320 MW), [Vaida V.]
7
Second, we consider the stochastic model with two decision stages. The split between
1st stage and 2nd stage is as following:
o For variables:
 1st stage: capacity variable
 2nd stage: operation level, unserved demand and emissions
variable
o For constraints:
 1st stage: minimum and maximum capacity
 2nd stage: production equation, demand equation and emissions
equation
We consider that 3 of the total variables evolve random (availability, demand and
emissions) and we consider their probability distributions:
 For availability of generator no.1
Discrete values:
99%
90%
50%
Probabilities:
0.2
0.3
0.4
10%
 For availability of generator no. 2
Discrete values:
99%
90%
70%
Probabilities:
0.1
0.2
0.5
10%
1%
0.1
0.1
 For demand level
Discrete values
(TWH):
9.50
Probabilities:
0.15
0.1
10.00
12.00
14.00
0.45
0.25
0.15
 For emission level for generator no.1
Discrete values
(tones):
67
58
50
Probabilities:
0.4
0.25
0.25
 For emission level for generator no.2
Discrete values
(tones):
81
77
60
Probabilities:
0.4
0.25
0.25
15
0.1
25
0.1
This scenario is linked to the economic reality, taking into account:
 the fact that a power plant, even if a certain quantity was contracted at one
moment, cannot know for sure if will be able to cover it 100%
 the emission level is known for sure only after production when the specific
measurement can be proceeded and not before, when the power plant can
have only expectations based on used production technologies
8
 the availability of the generators at one moment cannot be fixed, but is
depending on several technical random factors, which makes also the
availability variable rather a random one than a deterministic one.
MODEL RESULTS
After running the model using the software described in chapter 3, the following
output is obtained:
 Total cost – optimal value
 Capacity variable for both generators – optimal value
 Emission level for both generators – optimal value
Results – Certainty Scenario
Specifically for the deterministic model, the results obtained are:
Total Cost (u.m.): 28429.64
Capacity for generator no.1 (MW): 1631.8
Capacity for generator no.2 (MW): 1732.3
Emission level for generator no.1 (tones): 61930
Emission level for generator no.2 (tones): 85576
Results – Unertainty Scenario
Specifically for the stochastic model, the results obtained are:
Total Cost (u.m.): 27729.14
95% confidence interval : [26579.18 ; 27847.9]
Capacity for generator no.1 (MW): 1022.0
Capacity for generator no.2 (MW): 2021.9
Emission level for generator no.1 (tones): 41750
Emission level for generator no.2 (tones): 68114
9
Based on distribution probabilities included in a stochastic model, the recommendations
that can be made differ from recommendations that can be made using a deterministic
model. In the example considered: in the certainty scenario, the recommendation is to
build the 2 generators quite close in terms of capacity, while in the uncertainty scenario,
the recommendation is to give an increased role to the second generator, the one which
require less investments costs in the beginning (2021 MW > > 1022 MW). The emission
levels in the second scenario are overall inferior to the ones in the first scenario, so the
recommendation is to build so that to pollute as low as possible in order to minimize total
costs (including the costs with taxes for emissions). Also, by comparing the 2 case studies
results, it can be noticed that overall installed capacity in 2nd case is less than total
installed capacity in 1st case, so the conclusion is that the investments should be directed
also to other energy sources than thermo, such as renewable sources, for which the
environment damages and costs are zero.
Based on the assumption that Pareto optimality state is a desired one in a given economy,
as it ensures the maximization of the social welfare, it will be analyzed in the following
the possibility to restore it when negative externalities are present in an economy such as
the pollution. The theoretical background which will be used in the following is the
Shapley-Folkman theorem related to convex economies, having as applicative aproach
spending an ammount of money in order to reduce the pollution. The paper contains an
algorithm useful to optimally distribute an amount of money invested in pollution
reduction.
COMPETITIVE EQUILIBRIUM AND PARETO OPTIMALITY
The comeptitive equiolibrium in an economy is ensured trough several hypothesis,
among which one is powerful: the characteristic of convexity for all production and
consumption possibilities in the given economy.
What about if exists within the economy at least one non-convex production or
consumption element? Shapley-Folkman theorem can be applied and an aproximative
equilibrium will be obtained. The bigger the number of agents and goods in the economy,
the raughest is the aproximation.
Shapley-Folkman theorem: Let
S
i
i  I  denote a finite crowd and  m , where
i  1,2,..., m, denote the sub-crowds. Then any
vector x  co S i represent the
expression of a sum of the following form: x   xi , where xi  coS i , for all i  I for
which Card i  I xi  S i  m
An example will be considered now: an Arrow-Debreu economy without externalities
  X i , Pi ,Wi , , i i  I 
, Yk k  K  , where: X i - represent the consumption crowd; Yk represent the production crowd, both of them not necessarily convex crowds. In order to
obtain a convex economy, can be used the following transformation: X i into coX i ; Yk
10

into coYk ; each demand  i into  i : S  2 coxi
*
 k * : S  2 coY
k

F

F
, i : S  coi s  ; each offer  k into
*
,  k : s  co k s  .
We will consider a simplified economy, with 2 region/countries, producing 2 goods and 1
consumer. Country 1 produces good 1 in quantity y11  F 1 y 12 , using good 2. On the
other hand, country 2 produces good 2 in quantity y 22  F 2 y12 , y11 . Let U x1 , x2  denote
the utility function for the representative consumer considered, where the arguments
represent the consumption made on the 2 goods. We assume that country 1 generates a
negativbe externality on country 2. Let z denote the pollution level. When no antipullution measures are taken, z  y11 . But, if an amount of money ’d’ is spent to limit the




 


pollution, then z   y11 , d , where  y11 ,0  y11 .
To characterise and determine the Pareto optimality state, the mathematical model is as
following:
Max U  x1 , x 2 
y11  y12  w1  x1  d  0
Availabili ty constraint s
y 12  y 22  w2  x 2  0 

 
Production constraint s
 F  y ,   y , d   0
 y11  F 1 y 12  0
 y 22
2
2
1
1
1
Applying Kuhn – Tucker method to solve the model, will lead to:



 F y     y



L y11 , y 12 , y12 , y 22 , d , 1 , 2 , 1 ,  2  U x1 , x2   1 y11  y12  w1  x1  d  2 y 12  y 22  w2  x2 

 1  y
1
1
1
1
2
2
2
2


 F y , y , d
2
2
1
1
1

11
L
U
0
 1  0
x1
x1
1
L
U
0
 2  0
x 2
x 2
2
L
F 2 

0






0
1
1
2
z y11
y11
3
L
F 1
 0   2  1 1  0
y 12
y 2
4
L
F 2

0




0
1
2
y12
y12
5
L
 0  2   2  0
y 22
6
L
F 2 
 0  1   2
0
d
z d
7 
In the following, using relationships (1) and (2):
U
1 x1

 2 U
x 2
using (5) and (6):
1
F 2
 2
2
y1
using (3) and (4):
1

2
 2 F 2 
F 2 
1

z y11
1 z y11

dF
dF1
1 11
dy 2
dy 12
1   2
using (4) and (6):
2
dF 1
 1
1
dy 2
12
Then, can be noted that:
1

2
1
dF 1 F 2 
dy 12 z y11
dF 1
dy 12
1 F 2 

2
z d
;
and also:
dF 1 F 2 
U
1 1
x1
dy 2 z y11 F 2 
F 2
 2 

U
z d
y1
dF 1
x 2
dy 12
In the last expression, is contained ’d’ at optimum, the theoretical tool used to limit the
pollution level.
We consider for country 1, O1 , O2 ,..., On the pollution sources and their efficiency
measured trough the objectives X k q k  , where q k k  1,2,..., n denote the production
level for Ok .
n
n
k 1
k 1
Total production and consumption will be: q   q k and X   X k q k  .
In most cases, X k function variation is proportional with upper saturation  k :
dX k
  k  k  x k , k  1,2,1..., n
dq k
Solving the equation above leads to:


X k q k    k 1  e   k qk  k  , where  k ,  k ,  k are parameters that can be estimated using
econometric techniques, but is out of the scope of this paper.
We introduce in the system the amount of money ‘d’, distributed proportional with the
production level,  k  a k q k and
n

k 1
k
 d* .
Then, the following model needs to be solved:
13
 n

Max  X k q k 
 k 1

n
a
k 1
k
qk  d *
q k  0, k  1,2,..., n
n
n


The Lagrange function is: Lq1 , q 2 ,..., q n ,     X k q k    d *   a k q k 
k 1
k 1


The optimum conditions are:
L
L
 0, q k
0
q k
q k
k  1,2,..., n
L
L
 0, 
 0,


For q k  0 , is obtained:   k e   k qk  k    k   a k  0 or
k
ak
 k e 
k
 q k  k 
 
To simplify, we consider:
 
l k  ln  k k
 ak
tk 
1
k

   k  k

, a  ln   
I1  k qk  0 and I 2  k q k  0
Then, d *   li  a ai t i or a 
iI1
l a t
iI 2
i
i i
 d*
a t
iI1
i i
So, the problem of optimally distributing the amount ‘d’ to limit the pollution is solved if
the 2 crowds I 1 and I 2 are known. For that, the follwing alghorthm can be used:
Step 1:
tk 
1
k
 
for each Ok , we determine the coefficients l k  ln  k k
 ak

   k  k and

, k  1,2,..., n .
Step 2: reordering the objectives taking into account the relatioships: l1  l 2  l3  ...  l n
14
k
Step 3: computing the expression: E k 
l a t
i 1
i
i i
 d*
k
a t
i 1
i i
Step 4: determening the index for which E p  l p 1
Step 5: for i  p , computing q i  l i  E p t i and for i  p , q k  0

Step 6: computing X i qi    i 1  e   i qi  i 

REFERENCES
1. Brooke, A., D. Kendrick, A. Meeraus, R. Raman (1998), “GAMS – A user’s guide”,
General Algebraic Modeling System - GAMS Development Corporation
2. Goldstein, G., R. Loulou, K. Noble (2004), “Documentation for the MARKAL Family
of Models”, Energy Technology Systems Analysis Programme (ETSAP)
3. Infanger, G. (1999), “DECIS”, General Algebraic Modeling System - GAMS
Development Corporation
4. Laffont, J., (1992), “Economie de l’incertain et de l’information“, Economica, Paris
6. Marin, D., M. Bãncescu (2005), “Benefits from New Technologies for the Sustainable
Energetic Systems”, International Symposium of Economic Informatics
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Bucureşti
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Units in the Context of Interconnected Operation of the National Power System with the
UCTE”, the 6th International Power Systems Conference
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