Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland
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Integrated Power Generation and Natural Gas Expansion Planning Clodomiro Unsihuay, Student Member, IEEE, J. W. Marangon-Lima, Senior Member, IEEE, and A. C. Zambroni de Souza, Senior Member, IEEE Abstract—Energy companies and governments have considered alternative solutions over traditional planning problem where electricity, natural gas, oil are treated as an independent problem. The optimization and integration of the energy sources and demands in a common framework is one of the current challenges. New methodologies and tools for system planning and operation that include multiple energy carriers with sufficient topological details are being developed. This paper proposes a method that integrates the natural gas and electricity systems in with the objective of study their expansion together. The natural gas network model includes the natural gas well and pipelines whereas the electrical systems the hydrothermal power generation and transmission systems. The paper describes the main equations associated to the energy transformation between natural gas and electrical energy which links the two structures. A mathematical model of this problem is formulated as a multistage m optimization problem where the objective function is to minimize the integrated gas-electricity investment and operation costs. A simplified example with the Brazilian system is used for testing the proposed methodology. Index Terms— Natural gas systems, pipelines network, hydrothermal system, electricity interconnections, generation expansion planning, natural gas expansion planning.
I. INTRODUCTION
T
he integration of natural gas and electricity sectors has sharply increased in the last decade as a consequence of combined cycle thermal power plants. In many countries such as U.S.A., Russia, Europe and Brazil, gas-fired generation has been a major factor in the overall growth of natural gas consumption [1], [3]. The natural gas consumption should keep growing due to: the great number of unexplored natural gas reserves; its low environmental impact; and, its economic competitiveness compared with other fossil fuels [1], [3]. In Latin America as in other continents, natural gas combined cycle plants have become a clean and low cost alternative for electricity generation [4]. Abundant natural gas resources in Venezuela, Bolivia, Peru, Argentina and Brazil Clodomiro Unsihuay is a PhD candidate in Electrical Engineering at the Federal University of Itajubá, MG-Brazil. E-mail: (
[email protected]) J. W. Marangon-Lima and A.C. Zambroni de Souza are with the Power and Energy Systems Group-GESis, Federal University of Itajubá, MG-Brazil. Emails: (marangon; zambroni) @unifei.edu.br.
978-1-4244-2190-9/07/$25.00 ©2007 IEEE
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have made it attractive in development the gas market. Brazilin government, for instance, decided ten years ago to build gas-fired power plants and pipelines based on the sources at Argentina and Bolivia. The electricity capacity expansion planning (ECEP) problem is designed to determine ‘WHAT’ type of generating units to built and ‘WHEN’ they will be committed over a long-range planning horizon. The main objective of ECEP is to minimize the total investment and operating costs in order to supply the electricity demand following a set of technical criteria. In this traditional concept of power generation expansion model, the fuel supply at the thermal plants is considered as totally independent. Fuels like coal, oil and nuclear are used without constraints either in transportation, in production and storage. The assumption of fuel supply adequacy can be assumed for more mature markets such as coal and oil. These assumptions do not hold for natural gas resources mainly in countries like Brazil where the gas industry is still in the beginning. One example is the recent Bolivian problem where the gas supply was almost cut off.. Moreover, due to the fast growth of the natural gas market, it would be possible that demand outpaces supply and/or transportation investments [3]. It is known that the natural gas pipeline network operation must comply with the natural gas consumption due to its low storage capacity. Consequently, as the thermal plants are the major natural gas consumers, there is a close interaction between the gas supply system operation and expansion and the natural gas power plant operation and expansion, affecting the overall power system operation and expansion. Furthermore, the dispatch and expansion of the natural gas power plants affect the natural gas flows in the pipelines. On the other hand, the pipeline network operational requirements can impose limits on power plant generation compromising the overall power system operation. In this context, models that integrate the operation and expansion of these two systems are very important for security and reliability of both systems [1]-[6]. In the literature, one can find a variety of models dealing eight theses two systems in a desegregated formulation. Very few works can be found considering the integrated approach. In [7]-[9] the authors developed algorithms to solve the problem of optimal operation of a gas pipelines network. A model to compute the maximum power generation of a combined-cycle power plants system considering pipelines
PowerTech 2007
Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland network constraints are presented in [6]. In this paper, the gas distribution pipeline network operation problem was formulated as a minimum cost problem subject to nonlinear flow-pressure constraints, material balance equations and pressure bounds. Similarly, in [1], a methodology was proposed to integrate power generation and natural gas production and dispatch. That approach models the problem as an optimization problem in which the objective function is to maximize the gas-fired power production costs, subject to gas pipeline system and capacities constraints. Reference [2] and [10] deals with detailed steady-state nonlinear power flow equations for natural gas and electricity, since the model is intended to be used for operations purpose. In [11], it addresses the interdependency of gas and electricity; a security constrained unit commitment is used for analyzing the short-time impact of natural gas prices on power generation scheduling. In [12], an interesting approach for combined optimization of coupled power flows of different energy infrastructures such as electricity, gas, and district heating systems are presented. Recently, interesting researches have been published focusing the Brazilian hydrothermal operation and expansion planning. In [3] a linearized model to integrated electricity-gas long-term operations planning in hydrothermal systems is presented. A simplified linearized model is proposed to model the natural gas balance equations the application of the integrated electricity-gas scheduling model is illustrated in case studies with realistic configurations of the Brazilian system. In reference [13] are discuss the technical and economical aspects of the integrated gas-electricity adequacy planning in Brazil. Recently the Brazilian Research Center CEPEL presents a discussion on long-term generation planning modeling and their optimization [14]. This paper presents the premises of modeling and optimization of the new model to long-term generation expansion planning of Brazilian electric sector. That model is name MELP and actually is in developing by CEPEL. Preliminary of MELP modeling and their results can be found in [14], [15] and [16]. This paper follows the guidelines of works [3], [12], [13] [14], [15] and [16]. The contributions of this paper with respect to above papers are: x In this paper is intended modeling the natural gas well and pipelines into a model of long-term generation planning like as MELP model. The model results are integrated model to generation and natural gas long term expansion planning in simultaneous manner. x This preliminary model leads with the deterministic longterm generation expansion model fellows the guidelines of MELP model [14] but in this paper is intended to include the natural gas infrastructure. x In similar to MELP model the gas/electricity expansion model presents in this paper also it is solved using the state-of-art on mixed-integer linear programming: The branch-and-bound based approaches. A didactic study case is presented and their results are discussed. In resume, this proposes integrated gas/electricity expansion planning is formulated as mixed integer linear multi-stage optimization problem where the objective function
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is to minimize the integrated gas-electricity system generation investment and operation costs subject to hydro and thermal power plants constraints, electricity and natural gas interconnections constraints and gas well reserve and capacity constraints. The link between both systems is the gas-fired power plants (simple or combined-cycle plants) which are connected directly to natural gas pipelines network. II. ASPECTS ON INTEGRATION OF ELECTRICITY- GAS EXPANSION The generation expansion models usually take into account a detailed representation of the power system, but do not consider the interaction with production, storage and transportation of the natural gas industry. Expansion planning methods have historically been used for decisions on the construction of generation and transmission assets. In Brazil, hydro generation is the major source of electricity power which has imposed a high integration between generation and transmission due to the long distance between the hydro sources and the loads. With the introduction of the natural gas plants the problem changed because usually such plants may be located close to the loads but the natural gas sources are also far away. Therefore, it is important to analyze the convenience of changing the wires to pipelines. With the development of the natural gas sector and its strong interconnection with the power sector, planning tools should be adapted to consider, among others [13]: (a) decisions to build new gas pipelines;(b) compute natural gas prices as a result of the overall cost of the gas sector (result of decision make process); (c) feedback of the resulting gas prices of step (b) to the planning decisions of the power sector. In a similarly way of power systems operation, the gas is moved from gas producers or wells to end customers at various locations which entails pipelines, underground storages, compressors, and valves. A gas well is commonly located at sites which are far from load centers. In general, pipelines or natural gas interconnections undertake the responsibility of transporting natural gas from wellheads to local distribution companies or directly to large commercial, industrial consumers and thermal power plants. Distribution pipelines generally provide the final link of the delivery chain. Also, there exist several types of natural gas storages: the pipelines themselves, the wells and underground store. The store capabilities of gas structures can provide a better utilization of the pipelines capacities which is not possible using the wires [9]. The connection between gas and electricity systems is the gas-fired power plants (simple or combined-cycle plants) which are connected directly to natural gas pipelines network. Here the concept of energy hub depicted in Figure 1 is applied [12]. It contains an electrical transformer and a gas-fired power plant which converts or transforms the natural gas to electricity. A natural gas-fired fuel plant converts the energy of natural gas energy into electricity at certain conversion rate known as heat rate. In brief, heat rate measures the units of the fuel
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Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland needed for producing one unit of electricity. The lower/higher is the heat rate, named in this paper as gas consumption conversion factor. The heat rate is measured in units of MBTU/MWh where one MBTU represents one million British thermal units and one MWh stands for one Megawatt (MW) hour of electric energy.
J it, j
D it
operation costs of thermoelectric j at subsystem i at stage t; amount of energy generated by thermoelectric j at subsystem i at stage t; electricity deficit cost at subsystem i at stage t;
wit
electricity deficit at subsystem i at stage t;
I git, j
E it
investment costs of natural gas exploration project j at subsystem i at stage t; investment costs of natural gas interchange project that connect the subsystems i and j at stage t; operation cost of natural gas well j at subsystem i at stage t; amount of natural gas extracted by gas well j at subsystem i at stage t; natural gas deficit cost at subsystem i at stage t;
sit
natural gas deficit at subsystem i at stage t;
kit, j
I pit, j D it, j Fig. 1. The hybrid energy hub
git, j
III. INTEGRATED GAS-ELECTRICITY EXPANSION PLANNING (IENGCEP) FORMULATION As discussed in the previous section, electricity capacity expansion and operation costs (ECEOC) and natural gas capacity expansion and operation costs (NGCEOC) need to be computed together. The objective is to minimize the present value of both investment and operation costs. Thus, it can be formulated as follows.
B. The Constraints of IENGCEP x
Project construction constraint :
1
¦ (1 W )
Min
t 1
Where: ECEOC
t 1
¦
xhit, j d 1 ; i 1,..., I ; j i
(4)
¦
xkit, j d 1 ; i 1,..., I ; j i
(5)
t 1,..,T
A. The Objective Function of IENGCEP: T
( ECEOC NGCEOC )
t 1,..,T
(1)
¦
xz
d 1 ; i 1,..., I ; j i
(6)
¦
xgit, j d 1 ; i 1,..., I ; j i
(7)
d 1 ; i 1,..., I ; j i
(8)
t i, j
t 1,..,T
¦ Ih
t i, j
.xhit, j
i 1,..., I ji
¦J
t i, j
NGCEOC
t i, j
.xhit, j
i 1,..., I ji
.kit
i 1,..., I ji
and,
¦ Ih
¦ Iz
t i, j
.xzit, j
i 1,..., I ji
¦ G .w t i
t i
t 1,..,T
¦
(2)
I g it, j .xg it, j
i 1,..., I ji
D it, j .g it
xp
xhit, j , xkit, j , xzit, j , xgit, j , xpit, j {0,1}
i 1,..., I ji
¦
t i, j
t 1,..,T
i 1,..., I
¦
¦
I pit, j .xpit, j
x
E it .sit
ji
(3)
(9)
Supply of electricity energy constraint:
¦h
i 1,..., I ji
¦
3
t i, j
¦ kit, j ¦ (K tji z tj ,i zit, j ) wit t 4ik Eik ji
ji
(10)
; i 1,..., I ; t 1,...T
i 1,..., I
Where: Where: i, j , t index for subsystems, projects and stage of planning; T, I total number of stages in the planning horizon and of subsystems; W discount rate; I hit, j investment costs of hydroelectric project j at subsystem ii i at stage t; I kit, j investment costs of thermoelectric project j at subsystem i at stage t; I zit, j investment costs of electricity interchange project that connect the subsystems i and j at stage t; hydroelectric project j at subsystem i at stage t; xhit, j xkit, j
xz
t i, j
electricity energy production of hydroelectric j at subsystem i at stage t; electricity energy interchange from subsystem i to subsystem j at stage t;
hit, j zit, j
Kit, j 4ti
loss factor of electricity energy interchange from subsystem i to subsystem j at stage t; electricity load-duration curve at subsystem i at stage t;
Eik
electricity load at subsystem i at stage t;
thermoelectric project j at subsystem i at stage t;
x
¦g
ji
interchange project that connect the subsystems i and j at stage t;
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Supply of natural gas constraint: t i, j
¦ (V tji p tj ,i pit, j ) ¦\ it, j kit t ) ik N ik ji
ji
; i 1,..., I ; t 1,...T
(11)
Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland
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IV. STUDIES CASE RESULTS
Where: natural gas interchange from subsystem i to subsystem j at stage t;
pit, j
A. Description of study case The modeling of the integrated electricity and natural gas V loss factor of natural gas interchange from subsystem capacity expansion planning presented in this paper is novel. i to subsystem j at stage t; Then, in the literature no exist test case about it problem. \ it gas consumption conversion factor for thermal plant j Thus, to show results of the proposed model in more didactically possible, a hypothetically and very simplified at subsystem i at stage t; natural gas load-duration curve at subsystem i at stage study case is presented in this paper. However, some ) ti aggregated data are extracted of Brazilian power system and t; of natural gas importation from Bolivia. natural gas load at subsystem i at stage t; N ik Fig.1 shows the diagram for the study case considered in this paper. The proposed projects and in-operation projects of x Bounds on hydroelectric, thermal generation and hydroelectric, thermal plant and electricity interconnections electricity interchange: are visualized and located at thee subsystems. The subsystem t SO represents the Bolivian gas wells with the natural gas hit, j d ¦ xhim, j 4ti H imax ; i 1,..., I ; j i; t 1,...T (12) ,j connections with the subsystem SE which is a natural gas load m 1 center. The gas-fired thermal plants are at the subsystem SE t which represents São Paulo and Rio de Janeiro load centers hit, j t ¦ xhim, j 4ti H imin ; i 1,..., I ; j i ; t 1,... T (13) ,j m 1 Finally there is also represented the Brazilian southern t subsystem (S). Data of the study case is presented in the max t m t ki , j d ¦ xki , j 4i K i , j ; i 1,..., I ; j i; t 1,...T (14) appendix. t i, j
m 1 t
kit, j t ¦ xkim, j 4ti K imin ; i 1,..., I ; j i; t 1,...T ,j
(15)
m 1 t
zit, j d ¦ xzim, j 4ti Z imax ,j
; i 1,..., I ; j i; t 1,...T
(16)
m 1
zit, j t 0 ; i 1,..., I ; j i; t
0 d w d Wi t i
x
max
1,...T
(17)
; i 1,..., I ; t 1,...T
(18) Fig. 2. Illustration of study case considered in this paper.
Bounds on natural gas extraction and natural gas interchange: t
git, j d ¦ xgim, j ) ti Gimax ,j
; i 1,..., I ; j i; t 1,...T
(19)
git, j t ¦ xgim, j ) ti Gimin ; i 1,..., I ; j i; t 1,...T ,j
(20)
m 1 t
m 1 t
pit, j d ¦ xpim, j ) ti Pi ,max j
; i 1,..., I ; j i; t 1,...T
(21)
m 1
pit, j t 0 ; i 1,..., I ; j i; t
0ds dS t i
max i
1,...T
(22)
; i 1,..., I ; t 1,...T
(23)
The integrated optimal electricity and natural gas expansion planning proposed model is a mixed-integer linear multi-stage optimization problem, which in this paper it is solved using the commercial software TOMLAB/CPLEX [14]. The Tomlab/CPLEX is released by Tomlab Optimization Inc. [14], and provides a MATLAB© [15] interface to the world leading optimization commercial software CPLEX from ILOG Inc. [16]. ILOG CPLEX Mixed Integer Optimizer employs a branch-and-bound technique that takes advantage of innovative, cutting-edge strategies. It provides fast, robust solutions to the most difficult mixed integer programs, please see [16] for details.
The gas/electricity conversion factor of the natural gasfired thermal power plant T1 and T2, in this paper is considered equal to 13.8 MBTU/MWh, and their lower heating value of natural gas is 26.8 m³/MBTU, then converting it to Mm³/MMh (million of cubic meter of gas by million of Watts hour) it results 0.00370 Mm³/MWh (370 m³/MWh). A value of 12 % of discount rate is considered in this study case. The loss factors of electricity and natural gas interchange is 1 (i.e. the power and gas losses are neglected). The operation cost of natural gas at gas wells G1 and G2 is considered similar to cost of the currently (in 04/2007) Bolivian natural gas, it is 5 US$/MTBU or in its equivalence in US$/m3 is 0.18 US$/m³. From the above data, is noted that the natural gas price that the gas-fired plants T1 and T2 have to buy from gas wells is 66.6 US$/MWh (0.18x370). However assuming an additional cost due to the transmission charges of 3.4 US$/MWh and others cost it become 75 US$/MWh. In the proposed model this 66.6 US$/MWh since it is being take into account in the expression (3). Then, in (2) for all natural gas-fired plants (T1 and T2 in this example) their operation cost is only their revenue minus their natural gas cost, it is 8.4 US$/MWh (7566.6). In other words for the objective function considered in this paper for all natural gas-fired plants their net operation cost are their revenue minus their natural gas cost.
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Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland B. Results Simulations were carried out of study case and the main results are described in Table I. The expansion cost and operation to meet the demand growing in the natural gas and electricity sector during the five year of planning horizon is 4.9744e+05 MUS$ (million of dollars). TABLE I RESULTS OF ELECTRICITY AND NATURAL GAS EXPANSION Investment Cost Operation Cost Total Cost CPU time (MUS$) (MUS$) (MUS$) (s) 2.7165e+5
2.5853e+5
5.3018e+5
0.031250
5
This example supports the notion of the need of developing an energy capacity expansion planning in an integrated manner. This extreme situation may justify the need of electricity generation diversification for reducing the dependence of electric power systems on natural gas or on hydroelectric power searching for other sources of energy. Figure 4 shows the natural gas supply versus the natural gas demand. Notice that the average gas consumption at gas-fired power plants is 5 Mm³; which represents only 5% of the total of natural gas well capacity. In this case, the low natural gas consumption is only due the capacity constraint of gas-fired power plants.
TABLE II RESULTS OF ELECTRICITY AND NATURAL CAPACITY EXPANSION Project
SE/H2 SE/T2 S/H4 S/T3 SE-S/EI1
Hydro Thermal Hydro Thermal Electricity Interconnect. Natural gas extraction Natural gas Interconnect.
SO/G2 SO/GI2
It will be Implemented? yes Yes Yes Not Not
Stage of implement. Year 3 Year 2 Year 2 -
Yes
Year 4
Fig. 4 . Natural gas Supply versus natural gas demand.
yes
Year 3
Fig. 5 shows the complementary effects between natural gas and the hydrothermal systems at subsystem S in the case where exits a reduction of water inflows in hydroelectric power generation. From Figs. 5 and 6, one can clearly note that at stage two the hydroelectric generation deficit is balanced using more natural gas (10 Mm³) consumption at gas-fired power plants (10 GW).
Hidrothermal CapacityExpansion(MW )
Table II summarizes the expansion capacity of the hydro, thermal, natural gas wells and their respective interconnections. Notice that natural gas-fired plant T2 will be implemented at stage 2 (year 2) of planning horizon, also the gas well G2 and the pipeline GI2 must be built at stage 4 and 3 respectively in order to satisfy the natural gas demand and the natural gas consumption of gas-fired power plants. Figure 3 shows the capacity expansion of the base case where the hydroelectric project H4 isn’t considered in the expansion plan because at subsystem S it was forecasted a drought period at planning horizon. The capacity of the gasfired plants was duplicated to compensate the lack of rain. From Figure 3, it is observed that the thermoelectric participation increased compared with the base case. The deficit of electricity energy is mitigated because of the availability of natural gas. In case where a drought period and a lack of natural gas coexist in the expansion horizon it will result in electricity deficit, provoking an energetic crisis (load-shedding). 14
x 10
Fig. 5. Natural gas Supply versus natural gas demand 3
x 10
4
2.5 2 M W h
Subs./Name
Hydro Thermal Demand
1.5 1 0.5 0 1
4
2
3 Year
4
5
Fig. 6. Hydro and thermal power plant supply versus electricity demand in subsystem S
12 10 8
Total demand Hydro: base case Thermal: base case Hydro: dry water Thermal: dry water
6 4 2 0 1
2
3 Year
4
5
Fig. 3 Hydrothermal capacity expansions in case base and dry water case.
V. CONCLUSIONS This paper proposes a model to integrate gas and electricity industries not only in terms of operation but also in terms of expansion planning. It was shown the methodology and the main variables that should be included in the mixed-integer optimization problem. A simple example was used to illustrate the advantages of applying the proposed integrated gaselectricity operation and expansion planning model.
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Paper accepted for presentation at 2007 IEEE PES PowerTech Conference, July 1-5, Lausanne, Switzerland
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APPENDIX: DATA OF STUDY CASE
ACKNOWLEDGMENT
Table III shows the operation and expansion characteristics of electricity generation plants. Table IV shows the operation and expansion characteristics of electricity interconnections. Table V shows the operation and expansion characteristics of natural gas wells. Table VI shows the operation and expansion characteristics of natural gas interconnections. Table VII shows the natural gas and electricity demand in each stage of planning horizon. The load growth was set equal to 10% a year.
The authors would like to thank the support of the Brazilian institutions CAPES (project #023/2005) and CNPq. REFERENCES [1]
[2]
TABLE III CHARACTERISTS OF OPERATION AND INVESTMENT OF ELECTRICITY GENERATION PLANTS
Type
State
Bound
Subs./Name
SE/H1 SE/H2 SE/T1 SE/T2 S/H3 S/H4 S/T3 S/T4
Hydro Hydro Therm. Therm. Hydro Hydro Therm. Therm.
Oper. Proj. Oper. Proj. Oper. Proj. Oper. Proj.
Min (MW) 0 0 0 0 0 0 0 0
Max (MW) 80000 20000 5000 5000 20000 10000 5000 5000
Oper. Cost US$ MWh
Investment Cost MMUS$
2 5 75 75 2 5 75 80
30000 5000 20000 5000
TABLE IV CHARACTERISTS OF OPERATION AND INVESTMENT OF ELECTRICITY INTERCONNECTIONS Subs. FromTo
Name
SE-S SE-S
EI1 EI2
State
Bound Min MW
Bound Max MW
Oper. Proj.
0 0
1000 3000
Oper. Cost US$ MWh -
Invest. Cost MMUS$ 3000
[3]
[4] [5] [6] [7] [8] [9] [10]
CHARACTERISTS OF
TABLE V OPERAION AND INVESTMENT
OF NATURAL GAS WELLS
Subs./ Name
Type
State
Bound Min (Mm3)
Bound Max (Mm3)
SO/G1 SO/G2
Onshore Onshore
Oper. Proj.
0 0
30 50
TABLE VI CHARACTERISTS OF OPERAION AND INVESTMENT OF Subs. From-To
Name
SO-SE SO-SE
GI1 GI2
Oper. Cost US$ m3 0.18 0.18
NATURAL GAS
Invest. Cost MMUS$ 5000
[12] [13]
INTERCONNECTIONS
State
Bound Min Mm3
Bound Max Mm3
Oper. Cost US$ m3
Invest. Cost MMUS$
Oper. Proj.
0 0
30 40
-
5000
NATURAL GAS
[11]
[14]
[15]
TABLE VII AND ELECTRICITY DEMAND
[16] Stage or year
loadduration curve (h)
1 2 3 4 5
8760 8760 8760 8760 8760
Gas Demand (Mm3) SO SE
Elec. Demand (MW) SE
S
0 0 0 20 22
85000 89250 93710 98390 103300
20000 21000 22050 23150 24110
25.00 27.50 30.25 33.27 36.60
[17] [18] [19] [20]
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