An optimization approach for the assessment of the ... - ACS Publications

Subscriber access provided by - Access paid by the | UCSB Libraries

Process Systems Engineering

An optimization approach for the assessment of the impact of transmission capacity on electricity trade and power systems planning Apostolos Elekidis, Nikolaos Koltsaklis, and Michael C. Georgiadis Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b05159 • Publication Date (Web): 07 Mar 2018 Downloaded from http://pubs.acs.org on March 8, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Industrial & Engineering Chemistry Research

An optimization approach for the assessment of the impact of transmission capacity on electricity trade and power systems planning Apostolos P. Elekidis, Nikolaos E. Koltsaklis1, Michael C. Georgiadis*2

Aristotle University of Thessaloniki, Department of Chemical Engineering, 54124 Thessaloniki, Greece

ABSTRACT This work presents a Mixed Integer Linear Programming (MILP) model for the optimal interconnected power systems planning over a time horizon of one year. The power generation units include thermal units, hydro units and renewable units (wind and solar power plants). Each system can produce power in order to satisfy its demand and/or supply energy to another system via interconnections. The time horizon of interest, consists of a representative day for each month of the year. The model considers the possibility of building new units selected from a set of proposed ones, as well as expanding the capacity of existing renewable energy units (generation expansion planning), stressing the flexibility that electricity trade provides to power systems. The possibility of expanding the existing interconnection capacity between systems is also considered (transmission expansion planning). The proposed optimization model relies on balance, design, operational and logical constraints. Environmental-related constraints for the annual production of a series of emission types including CO2, NOX, SOX and PMX emissions are also taken into account. The main objective is the minimization of the total annualized cost. The applicability of the proposed model is illustrated in several case studies involving different objectives, such as the minimization of the total cost and the minimization of the emissions. Finally, an extensive sensitivity analysis is performed in order to investigate the effects of key input parameters on the final power generation policies.

1 2

Email: [email protected] Corresponding author, email address: [email protected]

1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Keywords: Transmission expansion planning; Generation expansion planning; Environmental impact; Power generation mix; Multi-objective optimization.

1. Introduction The power sector spent around USD 700 billion in 2015 at a global level in order to maintain, upgrade and/or expand power system assets throughout the electricity industry value chain, from generation to end consumers.1 In 2016, global renewable power output increased by an estimated 6% and accounted for around 24% of global power production, while for the first time, renewables represented more than half of new additions to power generation capacity and surpassed coal in terms of world total installed capacity.2 In parallel with that evolution and according to the future projections, electricity demand is expected to report the fastest growth among the final energy sources, enhancing its share in final energy use from 18% to 24% by 2040.3 Power systems planning decision-making is basically classified into three distinct categories based on the range of the planning time horizon, including long-term decisions (capacity, type and number of power generators), medium-term decisions (scheduling of the existing units), and short-term decisions (programming of the power that each committed unit must produce to cover the real-time electricity demand).4 Under this volatile and uncertain environment and the ongoing environmental challenges, power systems expansion planning is of paramount importance for an affordable, secure, and sustainable energy future. More specifically, its aim consists of determining the optimal plan for the construction of new generation and transmission capacity subject to various economic, environmental, technical, and regulatory constraints.5 In that context, Sadeghi et al.6 provided a detailed review of the technical, regulatory, environmental, and economic aspects that influence the generation expansion planning (GEP) decisions, highlighting possible directions for future works. In addition, Soroush and Chmielewski7 presented an overview of how process systems engineering has contributed to the area of power generation through mathematical modelling, control and optimization. The literature is rich with several contribution addressing power planning issues by making use of a variety of modeling approaches. More specifically, Georgiou8 developed a mixed integer linear programming (MILP) model for the optimal GEP of a power system incorporating possible interconnections between mainland and insular systems. The results indicate the potential benefits of such an interconnected power system, in terms of both 2 ACS Paragon Plus Environment

Page 2 of 40

Page 3 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


operational flexibility and environmental impact. Similarly, Barteczko-Hibbert et al.9 developed an MILP model for the optimal GEP of a national power system, providing specific focus on life cycle costs and environmental impacts (global warming potential). Focusing on the spatial characteristics of the power system, Koltsaklis et al.10,11 presented a generic multi-regional MILP model for the optimal GEP problem of a power system at a national and/or regional level, incorporating also energy resources management aspects. In a subsequent work, Koltsaklis et al.12 developed a Monte Carlo stochastic-based version of the initial approach with the objective of capturing key uncertainties of the inpout parameters, as well as incorporating demand-side management aspects in the GEP decisions. Moreover, Ahmed et al.13 developed a deterministic mixed integer linear model with a goal to minimize the total annualized costs and satisfying simultaneously various CO2 emission constraints. New technologies, including integrated gasification combined cycle (IGCC) and natural gas combined cycle (NGCC) with and without carbon capture and sequestration, are considered in this work. By employing a similar methodological framework, Muis et al.14 presented an MILP model for the optimal GEP of a carbon-constrained power system. Long-range Energy Alternative and Planning (LEAP) System comprises a software tool that is widely utilized in the GEP problem. More specifically, by using that software, Saeed et al.15 provided an assessment of GEP implementation for the country of Iraq, focusing on the utilization of renewable and nuclear energy and the resulting environmental impact, while making use of the same software, Karunanithi et al.16 dealt with the GEP problem investigating the economic and environmental impacts on a power system with high renewables’ penetration, incorporating both demand- and supply-side management strategies. In a similar way, Chang et al.17 made use of an MILP model, built on the LEAP System, for the optimal GEP problem of a given power system. Recently Zhang et al.18 presented a systematic approach to optimize the pathway of China’s power sector under uncertainty using a multi-period superstructure optimization planning model There also exist several works in the literature coping with the GEP problem based on a multi-objective framework. In particular, Aghaei et al.19 proposed a multi-objective GEP model including minimization of cost, CO2 emissions, fuel consumption, fuel price risk, and maximization of system’s reliability. In the same frame of contribution, Gitizadeh et al.20 presented a multi-objective optimization framework for the optimal GEP problem, taking into consideration as objectives the maximization of the project lifetime economic return, as well as the minimization of CO2 emissions, and of the fuel price risk, due to the utilization of 3 ACS Paragon Plus Environment


conventional energy sources. In a similar fashion, Prebeg et al.21 presented a multi-objective approach for the optimal GEP of the Croatian power system, incorporating electric vehicles serving as a battery in a vehicle-to-grid mode. The objective functions considered include minimization of the net present value of the energy system, minimization of the net present value of the energy system normalized by the total amount of energy generated to satisgy demand, and maximization of the share of renewables’ generation to the total. Maroufmashat et al.22 proposed a novel multi-objective approach based on an augmented epsilon constraint technique applied to an urban area in Ontario. A sensitivity analysis conducted, shows that cost is more sensitive to the electricity tariff rate rather than natural gas price. Furthermore, Luz et al.23 developed a multi-objective GEP model with significant penetration of renewables, including as objectives the cost minimization, maximization of system security, and maximization of non-hydro renewable sources. Finally, Guo et al.24 developed a long-term multi-region based model for the optimal planning of China's power sector. A “most-likely” scenario was created considering current energy policies. The results confirm that the development of power transmission infrastructure will significantly influence the regional power generation and transmission profiles. There are several contributions placing emphasis on specific aspects of the power systems’ planning. In order to examine the influence of CO2 emission caps and carbon taxes on the power generation mix of China, Zou et al.25 presented an optimization framework incorporating technological learning curves for solar and wind power. Guo et al.26 introduced a multi-region load dispatch model for China’s electricity sector illustrated in a case study which included a cap-and-trade carbon mitigation scheme to enable direct comparison with previous studies that lacked the temporal element considerations. The results demonstrate how Natural Gas Combined Cycle turbines (NGCC) are well suited to providing peak-demand regulation capability. Additionally, Li et al.27 proposed a scenario-based stochastic linear optimization approach for the optimal GEP problem, incorporating possible climate change outcomes and two objective functions, i.e., total cost minimization and maximum regret maximization. Vespucci et al.28 presented a two-stage stochastic MILP model for the optimal GEP problem under uncertainty in a series of parameters, including units’ production costs, system’s marginal price, price of green certificates and of the CO2 emission permits, as well as potential market share of the producer, and utilizing several risk averse strategies. Sharifzadeh et al.29 developed an MILP model for the optimal GEP problem with the aim of achieving a specific share of renewables’ contribution in the power mix in the future, 4 ACS Paragon Plus Environment

Page 4 of 40

Page 5 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


considering uncertainty in the demand, as well as in the wind and solar availability. Almansoori and Betancourt-Torcat30 proposed an MILP formulation for the optimal design of the United Arab Emirates’ (UAE) electricity system, considering renewables, nuclear energy and a series of low-carbon options, including carbon capture and storage (CCS), and similarly Betancourt-Torcat and Almansoori31 presented an MILP model for the optimal GEP of the same power system. Finally, in the same context, Koo et al.32 developed an optimization framework for a scenario-based energy planning of the South Korean power system, considering the CCS option and varying CO2 emission allowances prices. The aim of this work is to systematically determine the optimal planning of a power system over a target year, including also the options of combined generation and transmission expansion planning between interconnected systems. The work utilizes a detailed and systematic mixed integer linear programming model which determines the optimal type of power generation technologies, their potential capacity expansion and location that will be constructed considering several technical, economic, regulatory, and environmental constraints. The proposed approach contributes to the relevant literature on the quantification of the impacts of generation and transmission expansion planning options on the evolution of a given power system. Apart from that, it introduces some new elements such as the incorporation of several emission types, with heir corresponding targets, that few works have addressed in the past. More specifically,the main contributions and the key features of our work include: (i) mid-term powers system expansion planning, i.e., combined generation and transmission expansion planning of interconnected systems, providing the transmission expansion as an alternative to supply-side expansion, and highlighting the key role that electricity trade plays in that context, (ii) quantification of the impacts of several environmental criteria in terms of emission types, i.e., in addition to CO2 emissions, the incorporation of several other emission types exert influence in both system’s design and operation, and their role is investigated, and (iii) provision of a multi-objective formulation so as to quantify the relevant value of each specific objective function and its influence on the decision variables, indicating a wide range of alternative planning pathways according to the desired energy policy targets. The manuscript is organized as follows. Section 2 presents the problem statement along with the proposed MILP model. In Section 3, a case study used to illustrate the applicability of the



Page 6 of 40

proposed model, while Section 4 discusses critically the results of the case study. Finally, Section 5 draws upon some concluding remarks.

2. Problem Statement The problem under consideration is formally defined in terms of the following items: •

A set of power generating units ∈ to be installed in each power system ∈ (). This set of power generating units can include thermal power units ℎ ∈ , hydroelectric units ∈ , and renewable (except hydroelectric) units ∈ . The subset of the combined hydroelectric and other renewable units is provided by the subset ∈ . The maximum renewable energy plant capacity expansion potential is represented by the parameter , while there is also a minimum penetration level of renewable energy units (). Each renewable unit, ∈ , is characterized by a specific availability in each hour ∈ and month

∈ given

by !,#,$ . •

The subset which includes the new thermal candidates for construction units is denoted by ∈ . It is characterized by a specific investment cost (subject to a specific capital recovery factor %), while the corresponding subset for hydroelectric units is denoted by ∈ and its investment cost is provided by (subject to a specific capital recovery factor %). The technology type of each power unit, ∈ , belongs to a specific technology type &' .

•

Each power system, ∈ , can be interconnected with other power systems ( ( ≠ ) ∈ according to a specific network structure. Each power system ∈ is characterized by a certain electricity demand in each time period ∈ and month ∈ . There is a nominal interconnection capacity between interconnected power systems ∈ and ( ∈ , ≠ ( , given by the parameter %*+,+, . Each interconnector between the interconnected system is characterized by a specific ramp-up, %, and ramp-down, %-, rate. Its transmission expansion cost is described by the parameter

TC, while there is a maximum transmission capacity expansion value given by . •

The period under consideration is annual and is divided into a set of monthly periods ∈ , through the introduction of specific representative days, each of which is


Page 7 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


split into 24-hour time periods ∈ . The duration of each representative day of each month •

∈ (in days) is represented by the parameter -# .

With regard to the hydroelectric units ∈ , there is a minimum (maximum) daily electricity generation from all hydroelectric units ∈ provided by the parameter 9 (9 ). The same rule applies also to the new candidate for construction hydroelectric units, i.e., minimum (maximum) daily electricity generation from all new candidates for construction hydroelectric units ∈ , given by the parameter (-9 ) 9 .

•

Each power generating unit ∈ is identified based on specific technical characteristics including: (i) technical minimum (maximum) of each power unit ∈ , &' (&' ), and (ii) ramp-up (down) rate of each power unit ∈ , ' (-' ). Each thermal unit, ℎ ∈ , is characterized by a specific thermal efficiency *$: , CO2 emissions rate coefficient %;$: , NOX emissions rate coefficient ;$: , SOX emissions rate coefficient ;$: , and PMX emissions rate coefficient &$: . Each thermal unit ℎ ∈ has a specific fuel cost *%$: , other variable costs ;%$: , while there is also a specific conversion factor of fuel to energy !$: .

•

The environmental standards of the studied power system, it includes: (i) Upper annual CO2 emissions limit %, (ii) Upper annual NOX emissions limit , (iii) Upper annual SOX emissions limit , and (iv) Upper annual PMX emissions limit &U.

The key decisions to be determined by the mathematical include: Total

output

of

each

power

unit

∈

in

each

time

period

∈ ,

&',#,$ , which for the candidate for installation units ∈ is subject to the decision for their construction or not, ,#,$ , accounting for the quantity of power capacity block of the energy offer function of each power unit cleared in time period ∈ . Electricity flow between interconnected power systems ∈ and ( ∈ , ≠ ( in each

time

period

∈ ,

provide

by

*+,+, ,#,$ .


the

non-negative

variable


Page 8 of 40

Expansion Capacity of renewable energy sources units, provided by the non-negative variable , and subject to the decision for their construction or not, ? . Expansion Capacity of transmission grid between power systems ∈ and ( ∈ , ≠ ( , provide by the non-negative variable %+,+, , and subject to the decision for its construction or not, +,+, . The objective of the proposed model is to minimize the total annual cost for the underlying power systems expansion planning problem considering several technical, economic, environmental, and regulatory constraints, in order to fully meet the total electricity demand.

3. Mathematical formulation 3.1. Objective function The objective function (3.1) consists of five terms which determine the operating costs of all production units and systems. In particular, the first term expresses the variable cost that depends on the output power of all thermal units over the examined period. The second term refers to the annualized construction cost of all the new units which are decided to be constructed. Similarly, the next term represents the annualized expansion cost of each RES power unit under expansion. The next two terms refer to the interconnection grid between the energy systems. The first term describes the total electricity flow between the energy systems and the last term quantifies the cost of the transmission grid expansion. Operational Variable Cost  644444444444 47444444444444 8   FCth + COth ⋅ CC + OCth  Pi , m ,t ⋅ DRm + min  ∑ ∑ ∑  m∈M i∈I t∈T HVth ⋅ 0.277778 ⋅ EFth   New Units ' Construction Cost and RES Units ' E xpansion Cost 644444474444448   + CR ⋅  ∑ Yn ⋅ IN n + ∑ X ren ⋅ IRren  + ren∈REN  n∈N  Transmission Expansion Cost Transmitted Power Cost 6447448  6444474444 8  + ∑ ∑ ∑ ∑ ( Fs , s ', m ,t ⋅ TF ) + ∑ ∑ E s , s ' ⋅ TC 2  s∈S s '∈S m∈M t∈T s∈S s '∈S 

3.2 Model constraints 8 ACS Paragon Plus Environment

(3.1)

Page 9 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Capacity constraints

Pi,m,t ≥ PLi,m,t ⋅Ui,m,t

∀i ∈I ,m∈M,t ∈T,TPi ≠ 4

(3.2)

Pi,m,t ≤ PUi,m,t ⋅Ui,m,t

∀i ∈I ,m∈M,t ∈T,TPi ≠ 4

(3.3)

Pren,m,t = AVren,m,t ⋅ (PUren + Xren )

∀ ren ∈ REN , m ∈ M , t ∈ T

(3.4)

Constraints (3.2) and (3.3) express the maximum and minimum amount of power that can be generated by each power unit i. According to the constraint (3.2), the minimum output of each power unit, when it is under operation (',#.$ = 1), is given by the parameter &' while constraint (3.3) guarantees that the output cannot exceed the maximum unit capacity, expressed by the parameter &' i. Constraint (3.4) states that the output power of RES units is always equal to the product of the maximum capacity and parameter!,#,$ , which expresses the availability of RES per period of time. The maximum capacity is the sum of the installed capacity and the additional capacity added by a potential extension of the RES units. According to the constraint (3.4) all the available power that the RES units can produce, is fully utilized by the system. It is noted that the production from the Renewable Energy Sources (RES) and the production of the hydroelectric units are introduced as a matter of priority in the system because it is mandatory to utilize this energy, regardless of the price at which it is offered. Since their variable cost is considered zero, they enter the system with priority, and thus the net load, i.e., total load minus mandatory hydro and renewables’ generation, is going to be met by the conventional power units. Note also that energy storage options are not considered in the current approach. Ramp-up and down limits of power units

Pi,m,t − Pi,m,t −1 ≤ RUi,m,t ⋅ 60

∀i ∈I,m∈M,t ∈T,typei ≠ 4

(3.5)

Pi,m,t −1 − Pi,m,t ≤ RDi,m,t ⋅ 60


(3.6)

Constraints (3.5) place limitations on the ramp-up rates of the output of each unit at time period . According to constraints (3.5), the difference in the value of the power output between two consecutive hours cannot be greater than a number equal to the product of ' with 60. A parameter ' expresses the unit's ramp-up rate and it takes into account 9 ACS Paragon Plus Environment


Page 10 of 40

the technical characteristic of the units. Since the ramp rate is usually given in MW/min, the constant 60 accounts for a 60-minute period. Similarly to constraints (3.5), constraints (3.6) place limitations on the ramp-down rates of the output of each unit at time period . These constraints express again the maximum power difference between two consecutive hours. This difference cannot be greater than the product -' ∙ 60, where -' accounts for the ramp-down rate of the unit. Units’ power output constraints

∀i ∈I, f ∈F,m∈M,t ∈T,typei ≠ 4

0 ≤ Bi, f ,m,t ≤ BLi, f

∑B

i , f ,m,t


= Pi,m,t

(3.7) (3.8)

f ∈F

Each power unit provides power to the network in the form of power blocks, each of which is characterized by a specific price-quantity pair of the submitted offer. Note that successive prices should follow a strictly non-decreasing trend. Constraints (3.7) specify that the sum of the total power of these blocks should be equal to the total power output of each unit for each time period . Constraints (3.8) define the minimum and maximum values of the continuous variable E',>,#,$ . This variable takes a zero value (the unit does not provide power from that block), while its maximum bound is provided by the parameter =',> . All units provide power starting from the block with the lowest electricity generating marginal cost. Power demand balance

∑P

i ,m,t

i∈IS

+

∑F

s ', s ,m,t

= Ds,m,t +

s '∈INT

∑F

s , s ',m,t

∀s∈S,m∈M,t ∈T,TPi ≠ 4

(3.9)

s '∈INT

Constraints (3.9) represent the energy balance of the problem. The first term refers to the total power generated by all units at each time period ∈ , while the second term refers to the total imported energy in the system ∈ from the all the other interconnected options. The third term represents the demand of each system ∈ at each time period ∈ , while the fourth term refers to the total power exporting from a system ∈ to the other interconnected power systems. Power Adequacy Constraint


Page 11 of 40 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Α1 ⋅

∑

PU th + Α 2 ⋅

th∈ IS

∑

PU ren +

ren∈ IS

∑ PU

j

+ Α 3 ⋅ ( CFs , s ' + C s , s ' ) ≥ (1 + MR ) ⋅ D s , m , t

j∈ IS

∀ i ∈ I , j ∈ J , ren ∈ REN , m ∈ M , t ∈ T , s ∈ S

(3.10)

Constraints (3.10) ensure the adequacy of power for each period of time t. It has the form of a reserve margin, i.e., strategic reserve, constraint and its aim is to satisfy the long-term capacity adequacy of the studied system. Particularly, the percentage of the guaranteed availability of the thermal units’ capacity &$: expressed as A1 and the percentage of the guaranteed availability of the RES units’ capacity, & expressed through parameter 2 plus the proportion of guaranteed available import capacity, expressed by parameter 3 must be greater than or equal to the predicted demand rate -+,#,$ plus a percentage expressed by the parameter . The above rates of availability are estimated by taking into account any possible damages or blackouts that may happen into the network. Transmission Constraints

Fs,s ',m,t ≤ CFs,s ' + Cs,s '

∀ s ∈ S , s ' ∈ S , m ∈ M , t ∈ T , s' ≠ s

(3.11)

Constraint (3.11) guarantee that the power transmitted between two systems, s and s', can not exceed the sum of the network’s existing capacity, %*+,+( ’, and the possible network ‘s expansion, %+,+( .

Fs,s,m,t = 0

∀s ∈ S , m ∈ M , t ∈ T

(3.12)

Equation (3.12) determines that there is no energy flow from a system to itself.

Cs,s' ≤ Es,s' ⋅TR

∀ s ∈ S , s ' ∈ S , s' ≠ s

(3.13)

Cs,s' = Cs',s

∀ s ∈ S , s ' ∈ S , s' ≠ s

(3.14)

∀s ∈ S

(3.15)

Cs,s = 0

The above constraints (3.13) and (3.14) refer to the expansion of the interconnection line. According to constraint (3.13), the expansion of the interconnection network has an upper limit, expressed by parameter . Constraint (3.14) also ensures that the expansion between two systems s and s' takes place simultaneously in both directions. Thus, when the transmission capacity from system s to s’ increases, a corresponding increase in transmission



Page 12 of 40

capacity from system s' to s also happens. Constraints (3.15) ensure that the transmission expansion from a system to itself has a zero value.

Fs,s',m,t − Fs,s',m,t −1 ≤ CM ⋅ Fs,s ',m,t −1

∀s ∈ S , s ' ∈ S , m ∈ M , t ∈ T

(3.16)

Fs,s ',m,t −1 − Fs,s ',m,t ≤ CD ⋅ Fs,s ',m,t −1

∀s ∈ S , s ' ∈ S , m ∈ M , t ∈ T

(3.17)

The constraints (3.16) and (3.17), corresponding to the constraints (3.4) and (3.5), indicate that both the increase and the decrease of the transmitted power between two hours, should be lower than the two percentages, expressed by parameters, % and %-, respectively. Maximum and minimum penetration of RES

∑∑ ∑ P

renall ,m,t

renall m

t

∑∑ ∑ renall m

≥ RL ⋅ ∑∑ i

m

i

i,m,t

(3.18)

Pi,m,t

(3.19)

t

Prenall ,m,t ≤ RM ⋅ ∑∑

t

∑P

m

∑ t

The penetration rate of renewable energy units, including hydroelectric power units, has to be between two percentages, expressed by parameters and . New units construction and RES units expansion constraints

Un,m,t ≤ Yn

∀n ∈ N , m ∈ M , t ∈ T

(3.20)

Constraints (3.20) ensure that a new candidate for construction unit can be operated only if it has already been decided to be constructed. Particularly, the binary variable corresponding to the operation of a unit n, ,#,$ takes the value 1 only if binary variable

An optimization approach for the assessment of the ... - ACS Publications

Recommend Documents