Energy 50 (2013) 74e82
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Risk based multiobjective generation expansion planning considering renewable energy sources Mohsen Gitizadeh*, Mahdi Kaji, Jamshid Aghaei Department of Electronics and Electrical Engineering, Shiraz University of Technology, Shiraz, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 May 2012 Received in revised form 27 November 2012 Accepted 29 November 2012 Available online 3 January 2013
Generation expansion planning is defined as the problem of finding the technology type, number of generation units, size, and location of candidate plants within the planning horizon. In the deregulated environment rather than the traditional system which considered the cost minimization as the main objective function in generation expansion planning problem, the major objective is to maximize the Project Lifetime Economic Return. In this paper, the problem is solved considering three objectives, simultaneously (i.e. maximization of the Project Lifetime Economic Return, minimization of CO2 emission, and minimization of the fuel price risk due to the use of non-renewable energy sources). Furthermore, due to the extensive use of renewable energy sources, e.g., onshore wind, offshore wind, solar, etc, the effect of these power plants has been investigated in this paper. In order to make the problem more compatible with the real world, some of the most common incentive systems (i.e. carbon tax, emission trade, quota obligation, and feed-in-tariff) have been considered for the problem formulation. The problem is solved using Modified Normal Boundary Intersection method using General Algebraic Modelling System. Finally, a case study is designed to assess the efficiency of the proposed scheme. 2012 Elsevier Ltd. All rights reserved.
Keywords: Generation expansion planning (GEP) Renewable energy sources (RESs) Multiobjective optimization Modified normal boundary intersection (MNBI) Green certificate
1. Introduction The generation expansion planning (GEP) has historically addressed the problem of determining what generation technology to be commissioned, when the units to commit online, and where the units to be installed. By the time the electricity industry throughout the world was mainly dominated by vertically integrated utilities, the main objective of GEP was to minimize the total cost (including investment and operating cost), to meet the expected demand growth. After mid-1980 by liberalization of the electricity industry, energy producers had no more open access to the grid and had a competition with other Generating Companies (GENCOs) to sell their produced energy. In this case, for a price taker GENCO, it is not guaranteed that its cost be covered and thus, the main objective of the GENCO would be maximizing the Project Lifetime Economic Return (PLER) rather than minimizing the cost. As it was mentioned, GEP is one of the earliest problems in power systems industry and numerous techniques have been applied to solve the problem. In Ref. [1] dynamic programming and
* Corresponding author. Tel.: þ98 711 7264121; fax: þ98 711 7353502. E-mail address:
[email protected] (M. Gitizadeh). 0360-5442/$ e see front matter 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2012.11.040
in Ref. [2,3] linear programing were used to solve the problem. In Ref. [4] the Wien Automatic System Planning (WASP) is used to solve GEP problem minimizing the cost of plan. More recently the problem has solved by means of artificial intelligent methods. Chuang et al. used genetic algorithms in Ref. [5]. In Ref. [6], the Evolutionary Programing (EP) technique with Gaussian mutation is used, and in Refs. [7e11] Particle Swarm Optimization (PSO), Simulated Annealing (SA), Tabu Search (TS), Ant Colony Optimization (ACO), and Genetic Algorithm (GA) are applied to solve the GEP problem. The electricity industry is one of the most important parts of the countries’ economy and is a significant source of greenhouse gas emissions. Moreover, its economic and environmental role is growing in coming years. On the other hand, over the past decades, the demand for electricity has steadily increased and is expected to rise in the upcoming years. Thus, many governments around the world have worked on the issue of global warming and environmental protection. As the result they have agreed to Kyoto protocol [12,13], which commits the countries to reduce their greenhouse gas emissions. In Ref. [12] and [13], in order to cope with Kyoto protocol, the level of CO2 emission is considered as a constraint in GEP formulation. Nelson et al. [14] has carried out the power system planning by considering various CO2 pricing scenarios
M. Gitizadeh et al. / Energy 50 (2013) 74e82
Nomenclature
Sk,t
at Indices t n
index corresponding to years of the planning horizon index corresponding to a generation technology available for planning
gc
hn
ufn,t Constants T number of years in the planning horizon d discount factor (rate of return) per-unit time on investment investment cost(V/MW) for the installation of In,t a generating unit of technology n in the tth year pet average price of electrical energy in the tth year (V/MWh) pgc green certificate price in the tth year (V/MWh) t 2 εCO n
old
En;t
FTn,t Pn
rate of CO2 emission releasing by the nth generating unit (ton/MWh) maximum energy (MWh) that can be produced in the tth year by the set of units already installed in the year 0, belonging to technology n. feed-in tariff for technology n in the tth year rated power of generation units based on technology n
75
expected coefficient of variation in prices of the fuel type k in period t percentage of energy produced and must be balanced by green certificates in the tth year coefficient for assigning the green certificates to the renewable technology n corresponding to 1-MWh generation utilization factor
Variables amount of energy sold in the tth year (MWh) Ets ex amount of energy produced by the existing units En;t (MWh) new amount of energy produced by the new generating En;t units (MWh) number of selected plants in the tth year Un,t un,t number of units based on technology n benefiting from renewable energy incentives in year t Gst ðGbt Þ tradable Green Certificate (TGC) sold (bought) in the tth year Sets Nex Nnew Jk
set of existing generating units set of candidate units set of unit fuel types
in order to make the planner use renewable energy sources. Careri et al. [15] have modelled several incentive systems to evaluate their application effect in the age of green economy. To the best of our knowledge, the contributions of this paper with respect to the previous researches in the area can be listed as follows:
Integer Linear Programming (MILP). Section 3 introduces a framework based on NBI method to solve the multiobjective problem. In Section 4 simulation results are presented and the results obtained by the application of the methodology are thoroughly discussed to highlight the efficacy of the proposed approach. Some relevant conclusions are drawn in Section 5.
(i) The generation expansion planning problem is solved using a multiobjective mixed integer linear optimization model by a GENCO in the restructured power system. The proposed optimization framework includes maximization of the GENCO’s PLER, minimization of CO2 emission, and maximization of the energy price risk. In addition, a simple risk model has been implemented that can quickly and efficiently evaluate the fuel price volatility for the GEP problem. (ii) Renewable Energy Sources (RESs) have been considered in the proposed GEP problem. Also, to motivate GENCOs to employ these kinds of technologies, financial incentives have been implemented in the proposed framework including feed-in tariffs and green certificate trading schemes. (iii) In the conventional multiobjective optimization methods, the range of the objective functions constructed based on the payoff table may not be optimized. Consequently, it is not guaranteed the resulting Pareto set be an efficient or nondominated Pareto set. Therefore, the lexicographic optimization is proposed here to calculate the payoff matrix to be used in the NBI method. Accordingly, the Pareto optimal solutions of Multiobjective Generation Expansion Planning (MOGEP) are identified using the Modified Normal Boundary Intersection (MNBI) method.
2. Multiobjective generation expansion planning problem formulation
The model is implemented in the General Algebraic Modelling System (GAMS), using CPLEX solver and applied to a hypothetical GENCO [15]. The reminder of this paper has been organized as follows: In Section 2, the mathematical multiobjective generation expansion planning problem formulation is introduced in the form of a Mixed
RESs decrease the pollution production rates; contribute to the attainment of the Kyoto Protocol climate change mitigation goals, permit countries to develop security of energy supply by decreasing fossil fuel dependency and offer several socioeconomic opportunities such as investment, development and job creation. The model presented here, includes several RESs and CO2 reduction measures. In this model three objectives are optimized in the viewpoint of a GENCO, while the previous models mostly consider only one objective. In comparison with single objective optimization techniques, the Pareto-based multiobjective optimization methods have a number of advantages including the ability of having enough flexibility to deal with conflicting objectives [16]. 2.1. Objective functions 2.1.1. Maximization of PLER This objective function is defined as the overall present value sum of revenues minus the total present value of costs.
new 3 2 e s P P ex þ pt Et ln En;t Ftn;t ln En;t X ex new n˛N n˛N 6 7 f1 ¼ ð1þdÞ1t 4 P 5 gc In;t Un;t Pn þ pt Gst Gbt t˛T
(1)
n˛N new
In this formulation, FTn,t represents the feed-in tariff for technology n in the tth year of the planning horizon. A feed-in tariff is a policy mechanism designed to speed up investment in renewable energy technologies. This aim can be attained by offering long-term
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M. Gitizadeh et al. / Energy 50 (2013) 74e82
contracts to renewable energy producers, classically based upon the cost of generation of each technology [17]. Besides, Gst ðGbt Þis the Tradable Green Certificate (TGC) sold (bought) in the tth year. Green tags or green certificates stand for cost-efficient tools to stimulate electricity production from RESs. These certificates can be traded or used, and can be sold together with the electrical energy or separately to it. The other costs of each technology are considered as multiplying the amount of produced energy by l. This coefficient is variable cost of per-unit of energy which is as the variable unit cost (per MWh) of a payment stream that has the same present value as the total cost of building a generating plant over its life. Here it includes decommissioning costs (Dn,t), fuel costs (Fn,t), and maintenance costs (Mn,t) as follows [15]:
PT
t¼1
ln ¼
Dn;t þ Fn;t þ Mn;t
PT
t¼1
ð1 þ dÞt1 En;t
for all n:
(2)
ð1 þ dÞt1
2.1.2. Minimization of environmental impacts Despite the previously mentioned benefits, renewable energy competes with conventional electricity on an imbalanced playing field amid a failure to internalize the negative externalities associated with conventional energy production. In other words, in order to make the applications of RES more justifiable, the party responsible for environmental pollution (e.g. air pollution) must be in charge of paying for the negative impacts caused. In this case, it is said that the external costs have been internalized and thus, the market mechanism will not fail to secure an optimal allocation of resources. Furthermore, the carbon dioxide emissions from fossil-fuel plants should be minimized because of their danger for the global warming (greenhouse). Therefore, the second objective is considered as the minimization of the environmental effects by minimizing
f2 ¼
" X X t˛T
2 ex εCO n En;t
n˛Nex
X
þ
# 2 new εCO n En;t
(3)
n˛Nnew
Moreover, more polluting gases such as NOx and SOx can be considered if necessary. It should be noted that by minimizing CO2 emission, the released NOx and SOx will be minimized. 2.1.3. Minimization of energy price risk (volatility) A key feature in the price of the electrical energy is the fuel price in conventional energy sources. Fuel price changes dramatically due to numerous reasons over time and thus, it is desired for a GENCO to control the risk of employing units using different types of fuels. The following equation contributes the vulnerability of energy price changes to the expansion plan model. More specifically using this equation the fuel price volatility is to be minimized.
2 3 X X X F 4 f3 ¼ Sk;t En;t 5 t˛T
k˛F
(4)
n˛Jk
2.2.1. Energy balance This equality constraint shows the balance between the amount of energy by all units (existing as well as new ones) and energy sold at the market in year t.
Ets ¼
X
X
ex En;t þ
n˛Nex
new En;t
(5)
n˛N new
2.2.2. Sold energy constraints The amount of energy that the GENCO wants to sell at the market is limited by proper bounds as follows.
Ets min Ets Ets max
(6)
2.2.3. Quota obligation This constraint stands for the mechanism of the quota obligation for RESs. This obligation forces the electricity supply companies to produce a specific part of their energy from RESs. Furthermore, their green certificate will be tradable, and each GENCO can buy or sell its right to other GENCOs upon its needs.
X
!
at Eknew þ Ekex
¼ Gbt Gst þ
X
gc
new hn En;t
(7)
n˛N new
k˛F
The right hand side of Eq. (7) is a specific fraction of the total produced energy from conventional sources, which must be balanced with the green certificate bought (sold) Gbt ðGst Þ and produced energy from renewable energy sources. 2.2.4. Generation limits Energy output of the units should be limited by the following inequalities: new En;t 8760 uf n;t un;t Pn;t
(8)
old ex 8760 uf n;t Pn;t Un;t un;t þ En;t En;t
(9)
In Eq. (9) un,t > 0 by the time the incentive period is not expired. After that, the unit is shifted from new units to existing ones. 2.2.5. Maximum construction time These physical constraints reflect the maximum number of yearly construction capability of various types of units to be committed in the planning horizon.
0 Un;t U n;t
(10)
0 un;t un;t
(11)
2.2.6. Maximum investment limit This economic constraint stands for the maximum amount of investment which will be made by the GENCO. T X
" 1t
ð1 þ dÞ
X
# In;t Pn Un;t Imax
This risk measure in prices is simple but original in multiobjective models [18].
t ¼1
2.2. Constraints
2.2.7. Non-negativity constraints The following variable should be positive in the problem.
In this multiobjective problem nine sets of constraints have been applied as described below.
new ex Gbt ; Gst ; Un;t ; un;t ; Ets ; En;t ; En;t 0
(12)
n˛Snew
(13)
M. Gitizadeh et al. / Energy 50 (2013) 74e82
77
3. Solution methodology Generally, in Multiobjective Optimization Problem (MOP), it should be dealt with several conflicting objective functions, causing to have more than a single optimal solution. In this case, the Decision Maker (DM) should find the most preferred optimal solution among all the obtained ones. In such problems, the efficient solution (Pareto Optimal) is the one optimal solution which cannot be improved in one objective unless at least one of the other objectives deteriorates. In this paper, in order to find the Pareto surface the NBI method is used, which is shown to be more effective comparing to other methods when dealing with non-linear and mixed integer problems [19]. The Normal Boundary Intersection (NBI) [20e22] method uses a geometrically intuitive parameterization to produce an even distributed set of points on the Pareto surface, even for poorly scaled problems. In this method, in spite of the advantages, the objective functions over the efficient set should be optimized. Thus, lexicographic optimization technique is used here. where
3.1. Multiobjective mathematical programming In mathematical terms, for a general Multiobjective Optimization Problem (MOP):
h iT min F X ¼ f1 x ; f2 x ; .; fp x
(14)
In which X ˛ U, p 2 andU ¼ fx˛Rp : hðxÞ ¼ 0; gðxÞ 0; a x bg. Here the feasible area is denoted by U and x is the decision variable of the problem. For a MOP, a point x* ˛ U is said to be optimal (or Pareto optimal) if and only if there is no x ˛ U such that fi(x) fi(x*) for all i ¼ 1, 2, ., p with at least one strict inequality. The first step in the application of NBI method is the preparation of the payoff matrix. In order to form this matrix with p different objective functions, each objective (fi) should be optimized individually. The optimum value of fi(x) is denoted by fi (x*i ) in which x*i indicates the vector of decision variable corresponding to the optimal solution of the objective function fi. In the next step, by the achieved value of x*i other objective functions f1, f2, . fi1, fiþ1, ., fp are calculated, and represented by f1(x*i ), f2(x*i ), ., fi1(x*i ), fiþ1(x*i ), ., fp(x*i ). The procedure will be continued until the last objective function be optimized, individually. Consequently, the payoff table can be achieved in the following form:
0
f * x* B 1 1 B B « F ¼ B B fi x*1 B B « @ fp x*1 0
/ 1
/
f1 x*i
/
fi* x*i fp x*i
1
fii
1
f1 x*p
1
1 /
C C C C fi x*p C C C A fp* x*p
(18)
Furthermore, as it is shown in Fig. 1 another point will be defined as pseudo nadir point which is in the feasible region.
h i f SN ¼ f1SN ; .; fiSN ; .; fpSN i h fiN ¼ max fi x*1 ; .; fi x*i ; .; fi x*p
(19)
Another point generally outside the feasible region at which all objectives are at their ideal optimal value is called utopia point. It is denoted by f U in Fig. 1 and can be expressed as:
h i h i f U ¼ f1U ; .; fiU ; .; fpU ¼ f1* x*1 ; .; fi* x*i ; .; fp* x*p (20) Convex Hull Individual Minima (CHIM) is defined as the line connecting anchor points in the normalized space. It can be expressed as the following
( H ¼
4:wk : bi
˛Rp ;
p P i¼1
)
bi ¼ 1; 0 bi 1
(21)
Generally, in MOP each objective function has its own physical interpretation with different order of magnitude. Hence, based on the defined terms (utopia and pseudo nadir points) all the objective functions will be transformed as follows.
1
C C fip C C A
fiN ¼ maxfi x ; x˛U
wk ¼ b1 ; b2 ; .; bp
f11 / f1i / f1p
B « B ¼ B B fi1 @ «
Fig. 1. Graphical description of multiobjective reference points.
(15)
fp1 / fpi / fpp
fi x fiU f i x ¼ SN fi fiU
(22)
This transformation normalizes each objective function and maps them into the [0 1] interval. Here, the bar expressed the normalized value of variables. Therefore, in the normalized space each point can be shown as:
A few remarks should be presented here, before enhancing the NBI method to the modified MOP solution. As it is shown in Fig. 1 there is a point in the space at which all the objective functions are at their worst value, this point is called Nadir Point. In mathematical form it can be written as:
P @b1 ; .; bp A ¼ 4 «
h i f N ¼ f1N ; .; fiN ; .; fpN
where
(17)
1
0
2
b1 411 þ . þ bp 41p bp 4p1 þ . þ bp 4pp
Pp i¼1
bi ¼ 1and0 bi 1.
3 5
(23)
78
M. Gitizadeh et al. / Energy 50 (2013) 74e82
Table 1 Existing plant data.
Table 3 Obtained results from the first scenario for all objective functions.
Technology
Energy (GWh)
Rated power (MW)
Utilization factor
On-shore wind Coal/steam Oil/CT Oil/steam CCGT
480 4440 2000 1200 21,280
100 600 400 500 400
0.19 0.68 0.49 0.47 0.57
Case Case Case Case
The distance between the Pareto surface and CHIM can be achieved as
2
3 2 3 b b1 411 þ . þ bp 41p f 1 x n 6 17 5 D4 « 5 ¼ 4 « bp n bp 4p1 þ . þ bp 4pp f p x _
_
_
Cases
I II III IV
Case V
Case VI
(24) Case VII
T
In this equation n ¼ ½n 1 ; .; n p represents the normal unit vector to the CHIM and FðxÞ ¼ ½f 1 ðxÞ; .; f p ðxÞT shows the coordinates of the crossing point between Pareto surface and normal to the utopia line [23]. In this case the optimizing the objective function (14) can be achieved by solving a set of single objective problems (25) in which the distance between the Pareto surface and CHIM will be maximized.
maxD _ s:t: : 4:wk þ n D ¼ F x hðxÞ ¼ 0; gðxÞ 0
Coal/steam Oil/CT Oil/steam CCGT Nuclear On-shore wind Off-shore wind Geothermal Biomass Waste Thermal solar
I
b3
1 e e 0.4 0.5 0.6 0.4 0.5 0.6 e e e 0.2 0.33 0.4 0.4
e 1 e 0.6 0.5 0.4 e e e 0.4 0.5 0.6 0.4 0.33 0.2 0.4
e
mkiði¼1Þ
f3 (MV)
total 2803.506 e e 2158.380 2305.360 2403.400 2168.870 2411.600 2551.620 e e e 604.750 1853.640 1896.240 1952.920
1 e e e 0.6 0.5 0.4 0.6 0.5 0.4 0.4 0.33 0.4 0.2
e
e
e e e 0.559 0.574 0.581 0.887 0.903 0.811 0.804 0.880 0.824 0.698 0.815 0.767 0.490
2043.440 e 169117.609 216733.915 251818.994 e e e 2291.799 2143.948 2099.037 69081.078 74516.508 121439.729 146694.047
0.051 e e e 5.688 11.926 46.418 0.067 0.071 0.098 20.419 22.084 36.335 71.544
mkiði¼1Þ
¼
> fiSN fiU > > > :1
mkiði¼2;3Þ ¼
8 > > >1 > < f k f SN i i > fiSN fiU > > > :0
fiU
fik fiU fik fiSN fiSN fik
fiU
(26)
fik fiU fik fiSN fiSN fik
(27)
The fuzzification procedure described in (26) and (27) is used for the objective functions that should be maximized and minimized, respectively [24]. The total membership function (total degree of optimality) of each Pareto optimal solution is computed considering the individual membership functions and the relative importance of the objective functions (ui values) as follows:
mk ¼
3 X i¼1
ui mki
(28)
Table 4 Number of chosen candidate plants in the first scenario.
Table 2 Candidate plant data. Generation technology
b2
8 > > 0 > > < f k f SN i i
3.2. Fuzzy Decision Making Much of a decision making in the real world takes place in an environment in which the goals, the constraints and the consequence of possible actions are not known precisely. To deal quantitatively with imprecision, we usually employ the concepts and techniques of fuzzy logic. By means of the Fuzzy Decision Making (FDM) the most desired solution between the Pareto optimal solutions can softly be chosen. After obtaining the Pareto-optimal solutions by solving the optimization sub-problems, it is necessary for the decision-maker too choose one the best compromise solution according to the specific preference for different applications. Hence, for each objective function in the Patero optima solution, a linear membership function is calculated. This function measures the relative distance between the value of the objective function from its values in the respective utopia and pseudo nadir points. The closer value of the
b1
f2 (ton)
objective function to its utopia value (farther from its pseudo nadir) results in the higher membership function (higher degree of optimality) for the objective function in the Pareto optimal solution. The mathematical formulation of these membership functions is as follows:
(25)
By solving (25), for w sets, wk ðk ¼ 1; 2; .; Nw Þ the Pareto surface can be obtained in a point-wise estimation. More details on the production of w sets can be found in [23].
f1 (MV)
Importance
Tconstruction Tlife
P
N
l
S
MV/MW Year
Year MW
Hour V/MWh V/MWh
1 0.39 0.39 0.47 2.5 1.2
4 3 3 2 7 2
25 25 25 25 45 20
6000 33.96 4300 124.8 4100 124.8 5000 72.46 7800 13.95 1700 44.79
2.8
3
25
100 2700
3.5 2.35 4 5
3 2 2 3
20 15 20 25
100 20 50 10
600 400 500 400 1200 100
12.7 870.4 870.4 28.9 0.003
hgc
0 0 0 0 0 1
60.57
1.6
7700 32.82 6100 146.74 5000 58.31 2000 72.41
1.8 1.5 1.9 2
Cases
Coal/steam
Oil/CT
Oil/steam
CCGT
Nuclear
I II III IV(1) IV(2) IV(3) V(1) V(2) V(3) VI(1) VI(2) VI(3) VII(1) VII(2) VII(3) VII(4)
5
4 2
5 1 1
5 5 5 1
2 4 2 1
2 4 4 5 5 5 5 5
4 4 4 4 4 4 4 4 4 4 4 4 3 4 4 3
5 5 4 5 4 5 5 3
5 1 3 4
3 5 2 4 4 1
4 4 4 3
1 1 4 4 1 3
2 5
M. Gitizadeh et al. / Energy 50 (2013) 74e82
6
x 10
5
0.25
5
0.2
4
Risk (M€)
Emission (ton)
79
3
0.15
2 0.1
1 0 1600
1800
2000
2200 PLER (M€)
2400
2600
0.05 2000
2800
2100
2200
2300
2400 2500 2600 Emission (ton)
2700
2800
2900
Fig. 4. Emission and fuel price volatility (Risk) Trade-off in the first scenario.
Fig. 2. PLER and Emission Trade-off in the first scenario.
The best planning scheme is determined by ranking the schemes based on value of mk which is represented in (28). In this paper, the importance of objective functions is the same as w values which was introduced in Eq. (25).
4. Simulation results and discussion The proposed framework of the GEP problem is applied on a hypothetical GENCO for a 14-year planning horizon. The energy market price is supposed to increase linearly from 90.1 V/MWh (year 2012) to 108.3 V/MWh (the last year of planning horizon). This price is considered to be deterministic and its stochastic nature is ignored in this study. As in [15], the annual price of green e certificates can be obtained bypgc t ¼ 180 pt . The main characteristics of the existing technologies are presented in Table 1 which represents the initial conditions of the expansion plan [15]. The technology of coal-fired power plant is super-critical pulverised coal (SCPC). In this table, the technology of Oil/CT power plant is based on the combustion turbine and CCGT shows the combined cycle gas turbine. In order to calculate the present value of the first objective function (i.e. PLER) a 5% discount rate is considered (r ¼ 0.05). Table 2 consists of 11 different types of plants including non-RESs (for instance, nuclear plant) and RES-based technologies [15]. Here I is the capital cost of each technology, and l is the variable cost of different candidate plants. P shows the rated power of generation units based on technology n, Sk,t is the Expected coefficient of
variation in prices of the fuel type k in period t, and N is the utilization hours per year. In this table, coefficient hgc is to assign green certificate to renewable energy source to be compatible in the market. The construction time of each plant is also considered as a constraint in this problem. To have better illustration of the proposed framework features, two scenarios have been studied in the following subsections. 4.1. Scenario I: GEP without considering RES-based technologies In order to analyse the effects of RES-based technologies in the proposed MOGEP problem two scenarios are analysed here. In this scenario, the candidates are coal, oil, combined cycle gas turbine, and nuclear power plants. Using the MNBI method for the proposed formulation of the MOGEP, the payoff table obtained. According to the payoff table (F) the ideal and anti-ideal points of objective functions f1 to f3 is determined as the minimum and maximum values of rows 1 to 3, respectively.
2
473:08 2043:44 0:21
2803:50 F1 ¼ 4 506421:20 15:43
3 535:51 2883:20 5 0:05
The results of the first and third rows in terms of million euros are related to the PLER and fuel price volatility (risk), and the second row in ton corresponds to the emission. The main diagonal of the payoff table F1 shows the result of the individual optimization of the objective functions (the utopia point).
150
100
Risk(M€)
Risk (M€)
150 100 50
50 0 6 4
0 0
5
500
1000
1500 2000 PLER (M€)
2500
3000
Fig. 3. PLER and fuel price volatility (Risk) Trade-off in the first scenario.
2
× 10
Emission (ton)
0
-2000
0
2000
4000
6000
PLER (M€)
Fig. 5. PLER, Emission, and fuel price volatility (Risk) trade-off in the first scenario.
80
M. Gitizadeh et al. / Energy 50 (2013) 74e82
Table 5 Obtained results from the second scenario for all objective functions.
Case Case Case Case
I II III IV
Case V
Case VI
Case VII
f1(MV)
Importance
b1
b2
b3
1 e e 0.4 0.5 0.6 0.4 0.5 0.6 e e e 0.2 0.33 0.4 0.4
e 1 e 0.6 0.5 0.4 e e e 0.4 0.5 0.6 0.4 0.33 0.2 0.4
e e 1 e e e 0.6 0.5 0.4 0.6 0.5 0.4 0.4 0.33 0.4 0.2
f2(ton)
f3(MV)
mkiði¼1Þ
4769.120 e e 4466.372 4498.703 4593.382 2941.861 3604.525 4060.827 e e e 793.416 2092.370 2561.210 2693.990
e
e e 0.013 e e e 1.134 1.278 1.655 0.027 0.034 0.042 2.001 1.594 1.654 1.791
405.609 e 107955.756 131415.621 158952.942 e e e 424.415 421.282 418.143 112800.703 98023.348 102360.317 101842.444
e e e 0.592 0.297 0.270 0.640 0.707 0.194 0.630 0.608 0.586 0.358 0.528 0.557 0.578
Table 3 shows the value of each objective function in seven cases where b represents the importance of each objective and m is the total membership function value. The first three cases are the single-objective ones, Cases IV, V, and VI are two-objective problems and the Case VII is the three-objective optimization problem. In this table, f1, f2 and f3 show the amount of PLER, emission and fuel price (volatility) risk, respectively. As it can be observed in Table 3, cases I, II, and III show the best values of each objective. In these cases, the single objective problem is solved and the values attained are the most optimum ones comparing to other cases which is because the other conflicting objectives do not have an effect on the results. By increasing the value of b in other cases, the value of f1, f2, and f3 seek to reach to their optimum values. The conflicting nature of all objective functions is realizable here. For instance, in case V by increasing the importance of the PLER, the amount of the second objective function increases which means in this case more CO2 is produced. This change in the emission production can be respected to the combination of the chosen candidate plants. The comparison of chosen plants and their effect on the objectives can be done by considering Table 4. This table shows the number of different chosen plants in planning horizon. It is expected that the selected plants be based on the importance of the objectives, which is when the risk objective plays the most important role, the number of candidates having a higher value of risk function, S, be less than before. In the same way, when
x 10
2.5
total
Emission (ton)
Cases
5
3
2 1.5 1 0.5 0 4200
4300
4400
4500 4600 PLER (M€)
4700
4800
Fig. 6. PLER and Emission Trade-off in the second scenario.
the PLER objective is the most important one, the plants having lower investment and operational cost should be chosen. Considering Tables 2e4, it can be said that in case I when the PLER is to be maximized, nearly all the plants have their maximum allowable number. By changing the priority of the objectives, it can be seen that in case II, the use of a coal unit as the one having the highest value of CO2 emission rate is completely stopped, and besides the number of oil units with the higher CO2 emission rate than the nuclear and CCGT plants, is also decreased. The same analysis can be done for Case III where the use of oil units is limited compared with the Case I. It can be recognized that in other cases where the problem is solved as a multiobjective one, the number of chosen candidates are more than the units discussed in cases II and III. The conflicting nature of the objectives is obvious and is shown in Table 3, and Figs. 2, 3, and 4 which show the Pareto front of two-objective cases IV, V and VI, respectively. It should be noted that in Figs. 2 and 3 when PLER enhances, the other objectives deteriorates which is in the opposite direction of its optimum value. Fig. 5 shows the three-objective case corresponding to the case VII of Tables 3 and 4. 4.1.1. Scenario II: GEP considering RES-based technologies In this scenario, six different RESs including on-shore wind, offshore wind, geothermal, biomass, waste, and thermal solar are considered as the candidate plants of MOGEP problem in addition to conventional technologies mentioned in the first scenario. Table 5 shows the value of the objectives in seven different cases.
Table 6 Number of chosen candidate plants in the second scenario. Cases
Coal/Steam
I II III IV(1) IV(2) IV(3) V(1) V(2) V(3) VI(1) VI(2) VI(3) VII(1) VII(2) VII(3) VII(4)
5
2 4 5 5
Oil/CT
Oil/Steam
CCGT
Nuclear
1
4 4
1 2 2 2
5 4 4 4 4 4
1 1 1 5 2 2 2
2
2 1
4 2 3 2
On-shore wind
Off-shore wind
Geo-thermal
Biomass
Waste
4 3 4 4 4 4 4 4 4 4 4 4 1 4 4 4
1 1 4 1 1
4
5 5 3
4 1 2 4
3 5 5 5 5 2 5 5 5
1 4 4 4 4 4 2 3 4 4
Thermal solar
4 4 4 4
2 3
4
2
2 1 4 4
2 1 1
3 1 1 2 4 1 1
M. Gitizadeh et al. / Energy 50 (2013) 74e82
81
2.5
6 Risk (M€)
Risk (M€)
2 1.5 1
4 2 0 3
0.5
2 5
0
1
× 10 0
1000
2000 3000 PLER (M€)
4000
5000
Emission (ton)
0
0
1000
2000
3000
4000
5000
PLER (M€)
Fig. 9. PLER, Emission, and fuel price volatility (Risk) trade-off in the first scenario. Fig. 7. PLER and fuel price volatility (Risk) Trade-off in the second scenario.
Although, the part of discussion on the number of selected units and the objectives’ behaviour is almost the same, comparing Tables 3 and 5, shows the noticeable role of RESs. Moreover, in this scenario the Eq. (7), i.e., green certificate trading scheme, was used which affects the GENCO’s PLER. As an example, the value of PLER in case I in the second scenario has a 70% increase while the level of the produced emission in the planning horizon in case II decreased 80%. The later can be easily realized by assessing the combination of selected units provided in Table 6. It is noteworthy that the nonzero value of the emission is due to the conventional power plants existing in the initial condition of the problem. The same remark applies on case III where no thermal power plant is selected among the candidates. In this case the value of the risk corresponding to the fuel price variations is decreased down to 0.013 million euros which is 25% of the first scenario. In the two objective optimization cases, it can be seen that the selection of RESs leads to higher PLER and lower values of risk and emission which can be found in Figs. 2e9. Another interesting observation which can be inferred from Figs. 8, 9 and Eqs. (3) and (4) is that in both equations the amount of produced energy is multiplied with coefficients S and εCO2 . But as it is shown in Table 2, these values have different behaviour ratios. In other words, while the value of coefficient S for Coal/Steam unit is smaller than Oil/CT, Oil/Steam, and CCGT, it has a higher emission production rate than the others which in turn leads to conflicting manner of the objectives f2 and f3. This point beside Table 6 helps to clarify the behaviour of the objective functions shown in Fig. 9.
0.07 0.06
Risk (M€)
0.05
2
4769:12 F2 ¼ 4 270360:24 4:33
792:35 405:6 0:07
3 792:70 445:6 5 0:01
5. Conclusions In this paper, a new multiobjective framework for GEP problem has been introduced. The proposed MOGEP model, owning MILP formulation, includes cost function, emission and risk of fuel prices as the competing objective functions. Furthermore, the results show the trade-off between the presented objectives. Therefore, the decision maker is able to choose the best combination of the plants upon its needs. To cope with the MOGEP problem, a new multiobjective framework named MNBI, composed of lexicographic optimization (for the calculation of a more effective payoff table) and NMI method, has been proposed. Because of the extensive plans for using RESs, several renewable sources are considered as the candidate plants of the GEP problem. Moreover several mechanisms are included in the model to speed up the use of RESs. The suggested framework is implemented on the multiobjective generation expansion planning problem in the viewpoint of a GENCO. Further work is on track in order to add the uncertainty of different parameters (e.g. energy price, the amount of energy produced by RESs, etc.) to extend the proposed deterministic scheme to a stochastic framework. Also, different risk indices including operational, credit and political and regulatory risks of energy technologies in the proposed multiobjective GEP framework can be considered as an extension to this work in the future research. References
0.04 0.03 0.02 0.01 405
By comparing the payoff table obtained for the second scenario (F2) with F1 the effect of incorporating RESs and green certificate trading scheme is observable on the utopia point.
410
415
420
425 430 Emission (ton)
435
440
445
Fig. 8. Emission and fuel price volatility (Risk) Trade-off in the second scenario.
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