A SIMULATION TOOL TO BUILD GENERATION EXPANSION PLANS IN COMPETITIVE ELECTRICITY MARKETS

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A SIMULATION TOOL TO BUILD GENERATION EXPANSION PLANS IN COMPETITIVE ELECTRICITY MARKETS

Adelino J. C. Pereira João Tomé Saraiva

ajcp@isec.pt

Instituto Superior de Engenharia de Coimbra Instituto Politécnico de Coimbra Rua Pedro Nunes, 3030-199 Coimbra, Portugal

jsaraiva@fe.up.pt FEUP/DEEC and INESC Porto Campus da FEUP, Rua Dr. Roberto Frias,

4200-465 Porto, Portugal Abstract – This paper describes a long-term simulation

model to help generation companies building expansion plans.

Different from the past, the generation activity is now pro- vided under competition, and investments are affected by uncertainties and by the decisions of other players. This pa- per describes the use of System Dynamics to model the evolu- tion of the demand and of the electricity price along the plan- ning horizon. These evolutions will then be used by individual agents to prepare their own expansion plans. These plans will globally have to comply with general constraints, typically present in Grid Codes, as for instance, a maximum value for an adequacy index as LOLE. This model and the correspond- ing solution algorithm will be illustrated using a Case Study to illustrate the use of the developed approach to build the expansion plans and to conduct sensitivity studies.

Keywords: generation expansion planning, System Dynam- ics, uncertainties, electricity markets, long-term.

1 INTRODUCTION

In the last 20 years, power systems went through a number of changes that, although different from country to country, display some common characteristics. In the first place, traditional vertical companies were segmented typically leading to four main activities as follows – generation, transmission, distribution and retailing. Secondly, generation and retailing are now provided under competition either because the generation and retailing branches of traditional companies originated different agents or because new investors were attracted to the industry. This means there are typically competitive mechanisms in the extreme sides of this new model. Network activities typically remain under the responsibility of monopolies, now regulated by Regulatory Agencies. Apart from these new agents, there are certainly market and system operators, ancillary service providers, brokers and other intermediate agents that, in any case, illustrate a much more decentral- ized model in terms of operation and planning.

The mentioned unbundling of the power industry had several consequences that are relevant for the Generation Expansion Planning problem, GEP. In the first place, the vertical structure prior to the advent of electricity markets was justified considering that the provision of electricity should be done in a natural way by this type of utilities.

This paradigm led to a more centralized way of conducting expansion planning and the decision to build new generation assets was typically taken in an integrated way regarding transmission expansion. Given that all activities were included in the same vertical companies, there was typically little concern with cross-subsidies between activities and in general tariffs reflected average costs. On the other hand, the power industry was a rather stable business in

which key figures and parameters were easily forecasted and investments were remunerated by stable and well known rates, in many cases agreed with state agencies.

With the advent of liberalization and competition, this stable environment changed. Electricity markets determine revenues, generation costs and the demand are no longer easily predicted, as the recent and still on going economic and financial crisis illustrates. On the other hand, the sharp increase of renewables and the forthcoming development of small but numerous generation facilities connected to LV networks imposes new challenges and uncertainties to long-term activities as the GEP.

Apart from these general aspects, each Generation Companie, GENCO, prepares its expansion plan, selecting the most adequate mix of technologies, locations and tim- ing of the investments. The complexity of this new environment in which uncertainties play a key role suggests the development of tools to aid GENCO’s to prepare their plans. Having this in mind, this paper details a model to help GENCO’s building expansion plans as well as to conduct sensitivity studies to evaluate how robust these plans are in view of changes in input data, for instance in investment or fuel costs. Such a tool can also be used in a fruitful way by regulatory agencies to evaluate how the system behaves in the long-term, regarding the security of supply, or to evaluate if, for instance, capacity payments are needed to induce larger capacity investments.

Having in mind these ideas this paper is organized as follows. Section 2 details a number of models and solution algorithms in the literature for the GEP problem. Section 3 briefly reviews the basic concepts of System Dynamics since this is the tool used to model the long-term behavior of the electricity market and the interactions among several variables. Section 4 describes the mathematical formulation of the GEP problem and Section 5 details the algorithm developed to solve this problem. Section 6 presents a Case Study using a generation system with three generation agents and three candidate technologies. Finally, Sec- tion 7 presents the most relevant conclusions.

2 MODELS TO SOLVE GEP PROBLEMS The GEP problem has long been addressed prior and after the restructuring of the sector. In classic terms, the GEP problem aims at determining a multi-period expansion plan selecting the technologies and capacities to build, their sitting and their commissioning along the planning horizon. From a traditional point of view this problem was for instance addressed in [1, 9]. References [1, 2] present mixed integer problems and [2] considers transmission networks and uncertainties. The models in [1, 3] use Bend-

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ers decomposition profiting from the structure of the GEP problem. The model in [4] uses a multiobjective formulation considering investment, operation and transmission costs, environmental impact and the risk of getting a plan too much exposed to the volatility of the energy price. The solution algorithm builds in the first place a set of non- dominated solutions that are afterwards ranked using Ana- lytical Hierarchy Processes. Finally, [5 - 9] describe ap- proaches using metaheuristics. The use of Genetic Algo- rithms is described in [6 - 9], Simulated Annealing in [6 - 8], ant colonies and particle swarm algorithms [6], expert systems and fuzzy logic [7] and combinations of Genetic Algorithms and Simulated Annealing in [8].

The introduction of competition determined several changes in the industry as briefly mentioned in the Intro- duction. Under the competitive paradigm, reference [9]

describes a two-step approach in which individual generation companies prepare their investment plans that are then submitted to a regulatory agency for global check and approval. Reference [10] follows this idea and describes the use of the Cournot model to get the evolution of the electricity price along the planning horizon. On the other hand, reference [11] formulates the optimisation investment problem to maximize the profit of individual generation companies and the resulting global problem is then solved using Dynamic Stochastic Programming.

Given the long-term aspects of the GEP, recent ap- proaches use System Dynamics. This approach is docu- mented in [12] and Section 3 gives some insight on it.

References [13, 14] illustrate its application to electricity markets identifying the relations between several variables as the demand, the investment and operation costs, the electricity prices and formulate models to represent the long-term evolution of these variables enabling taking more sounded decisions regarding the GEP problem.

3 BASICS ABOUT SYSTEM DYNAMICS System Dynamics is a powerful modeling and simulation tool originally developed in the 60’s, [12], and that is particularly suited to model long-term evolving systems identifying interrelations and dependencies between variables as well as enabling getting a global view of the system. The use of System Dynamics allows simulating in a short-time the long-term evolution of a system, it has a reduced simulation cost, it promotes creativity since different sub models or values of parameters can be easily tested, it has an experimental nature and while modelling and simulating the system one is in fact capturing knowl- edge and representing it in a formal way.

1.a 1.b Figure 1. Examples of casual diagrams.

System Dynamics typically use Casual Diagrams to represent the cause-effect relations between variables as illustrated in Figures 1.a and 1.b showing a positive and a negative cause-effect relation between x and y.

Figure 2 represents another usual diagram termed as diagram of Stocks and Flows. Stocks characterize the state of the system and generate information on which decisions and actions are based. In a certain way, they allow the accumulation of a variable decoupling the amount of inflow from outflow. This means they can be used to model delays and they also represent the memory of the system in the sense it is necessary an inflow larger than the outflow to reduce the level of the corresponding stock.

Figure 2. Diagram of Stocks and Flows.

From a mathematical point of view, this diagram is translated by (1) for continuous models. Inflow(t)and

) t (

Outflow are the functions of the inflows and outflows and Stock(t_o)is the value of the stock at t=t_o.

( ) ( )

∫ − +

= t to

to Stock dt . ) t ( Outflow ) t ( Inflow ) t (

Stock (1)

4 THE DEVELOPED GEP MODEL

4.1 Structure of the problem

Figure 3 details the structure of the developed model. It includes the long-term model of the electricity market using System Dynamics, the coordination analysis and the investment problems solved by each agent. This approach is designed to help generation agents to prepare their own plans while considering the impact of the decisions of other agents and the evolution of fuel costs. As a result, a generation agent obtains its own plan and can run sensitivity studies to evaluate the impact of changing input parameters. This will contribute to gain insight to the problem and to take more sounded decisions. This approach can also be used by regulatory agents to preview the possible evolution of a generation system, or to design specific payments (for instance capacity payments) if that becomes necessary to turn generation investments more attractive.

Figure 3. Global structure of the developed application.

4.2 Individual optimization problems

In the developed approach a generation agent solves the mixed integer problem (2 – 6) to identify the best expansion plan considering along T years and for M candidate technologies. The decision variables are X^ij_t and they represent the capacity of technology j to start operation in year t by GENCO i. Each technology is characterized by x

+

y x

- y

-

Inflow Stock Outflow

Selection of input parameters

Solution of the optimi- zation problem (2-7) by each generation

Global checking step

Model to simulate the long-term behaviour of the electricity market

• Dynamic Model

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its investment cost, lifetime, fixed and variable operation costs and capacities available to be built.

( ) ( ( ) ) ( )

( ) ( ) ( )

∑













∑ 













∑− −

−

− α

− + α π

=

= =

= −

T 1 t

M 1

j ij

t t tcj

1 k

ij k j t ij

t ij t

ij t ij t ij t t ij t ij t ij t ij t t

i Cfix .X CcapX Ccap.X

. X . Cop Pcap . X . 1 . X . z

max (2)

subj. ∑ ≤

= T 1 t

ij T ij

t MCapI

X (3)

∑∑ ≤

= = T

1 t

i T M

1 j

ij

t MCapI

X (4)

∑∑ ≤ +

= = = T

1 t

iTotal M

1 j

ij i t

0

t X CAcum

CAcum (5)

∑∑ ≤

= = T

1 t

i T j

t M

1 j

ij

t.Cinv CapDisp

X (6)

In this formulation:

T number of stages in the planning horizon;

t stage in the planning horizon (year), from 1 to T;

Tut lifetime of a generation station (year);

tcj construction time of a station of technology j (year);

i GENCO index;

M number of candidate expansion technologies;

j index for candidate expansion technology, from 1 to M;

πt electricity price in year t (€/MWh);

j , i

αt capacity factor of technology j in year t, GENCO i;

j

Cinvt investment cost of technology j in year t (€/MW);

j

Copt variable operation and maintenance cost for technology j in year k (€/MWh);

Pcapt capacity payment (€/MW) in year k;

Ccapj capital cost due to the loan (€/MW.year);

ij

Cfixt fix operation cost of technology j, in year k (€/MW.year);

ij

Xt new capacity of technology j, in year t for GENCO i (MW);

i 0

CAcumt₌ installed capacity owned by GENCO i before the planning period (MW);

i total

CAcum maximum value admitted for the installed capacity owned by GENCO i when the planning horizon ends (MW);

i

CapDispT financial resources available to invest in year t or in all Tperiods, by GENCO i (€);

i

MCapIT maximum capacity that GENCO i can install in all M technologies in year t or in all T periods (MW);

ij

MCapIT maximum capacity that GENCO i can install of technology j in year t or in all T periods (MW).

The objective function (2) corresponds to the maximiza- tion of the profit of GENCO i along the planning horizon.

This profit is computed as the difference between the revenues from selling electricity at price π^t and from the pay- mentPcaptassociated with the capacity not used to pro- duce electricity. These are the two initial terms in the objective function and the first revenue is multiplied by the capacity factor associated with each technology, αⁱ_t^,^j, while the capacity payment term is multiplied by 1−αⁱ_t^,^j. The costs are representing by the third to the sixth terms.

The third and the fourth terms represent the operation and fix costs once the station is in operation. The fifth and the sixth term are associated with financial costs incurred by the GENCO i before the unit starts operation (fifth term) and after that moment (sixth term). This objective function

is constrained by (3 – 7). Constraints (3) represent limitations on the capacity to build of technology j. This limit can be specified by the GENCO itself in terms of its investment policy or can result from a regulatory decision or from an indication of global energy policy to contribute to diversify the technologies in use. Constraints (4) limit the total installed new capacity of GENCO i. This limit can be set for the entire planning horizon as in (4) or can be adapted for specific periods in the horizon. On the other hand, GENCO i already owns capacity prior to the period under analysis. Accordingly, constraint (5) limits the global capacity owned by GENCO i in terms of the old and new capacity. Once again, this limit can be specified by a GENCO itself or can result from a regulatory decision as a way to reduce market power. Finally, constraints (6) en- force limitations on the available financial resources of GENCO i along the entire horizon. It can also be easily adapted to express limits in each stage t or for sets of stages. These limits can be specified by each investor considering their financial resources.

4.3 Coordination analysis

Once all individual investment plans are available, we check if some global constraints are not violated. In the following paragraphs we will mention some of them, but the issues to consider in this phase can easily be enlarged to accommodate specific requirements inserted in grid codes. Having this in mind, the first indicator to check is the reserve margin of the generation system, RMt, for each period t of the horizon. This margin is computed using (7) in which CTinstt is the total installed capacity in period t and Pdemt is the peak demand in period t. Then, the computed reserve margin in each period t is compared with a minimum and with a maximum value (8).

% 100 . Pdem 1 CTinst RM

t

t t 







 −

= (7)

max t t

min

t RM RM

RM ≤ ≤ (8)

Secondly, we compute the Loss of Load Expectancy, LOLE, representing the number of hours per year that the generation system may not be able to supply the demand.

The computation of LOLEt in each period t follows the indications in [15], and its value in each period t is compared with a maximum specified value (9). This evaluation is important to ensure the adequacy of the generation system to supply the demand and the grid codes of several countries specify maximum values for this indicator.

t LOLEmax

LOLE ≤ t=1, …, T (9)

On the other hand, one can also check if the total new capacity of a technology j does not exceed a given pre- specified level for every period t (10). In this constraint,

j

Capmax is the maximum capacity of technology j that can be installed along the horizon and N is number of GENCO’s. This constraint can be used to incorporate information related with national energy policy, namely to diversify the primary resources used in the power sector.

∑ _≤

= N 1 i

j ij max

t Cap

X (10)

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Finally, one can impose that the capacity owned by a GENCO does not exceed a percentage of the total installed capacity using (11). In this expression CAcumⁱ_total_,_tis the total capacity owned by GENCO i till period t,

CapPercmaxis the maximum capacity that can be owned by any GENCO in percentage and CAcumtotal,k is the total capacity till period k. The specification of this maximum percentage can result from a regulatory decision in an attempt to reduce market power in the generation activity.

≤ ∑

= t

1 k

k , total i max

t ,

total . CAcum

100 CapPerc

CAcum for each t and i (11)

If some constraint is violated, then the plans have to be changed or one can adopt strategies to turn capacity investments more attractive. This can be done including the capacity payment term in the objective function (2) or some specific payments directed to some technologies.

Changing these limits or parameters imply that the GENCO´s refresh their plans defining an iterative process that ends when no coordination constraints are violated.

4.4 Long-term simulation of the electricity market using System Dynamics - General Model

The electricity sector displays some characteristics as feed back loops and delays that must be adequately cap- tured to model its long-term behavior. System Dynamics are particularly suited to model these aspects and Figure 4 presents the general cause-effect diagram modelling the long-term behaviour of the generation activity.

Figure 4: Diagram representing the long-term interactions in the market.

According to this diagram, there is a positive cause- effect relation between the installed capacity and the amount of reserves. On the other hand, decommissioning units has a negative effect on the total available power and a demand increase reduces the reserve margin and eventually induces an increase in the electricity price. This diagram also includes a delay, τ, between the decision to build a new unit and its commissioning. This delay is due to the licensing and the building period and it should not be forgotten when modeling the long-term evolution of the electricity price. Finally, there is a feed-back loop between the demand and the electricity price. Departing from an

initial set of investment decisions, it is obtained the evolution of the electricity price using an initial demand rate.

However, the price level will also impact on the demand depending on its elasticity. If there is a capacity shortage or a very dry year, the electricity price tends to increase which can induce a demand reduction. The evolution of fuel costs and the updated electricity prices can then lead to a change in the investment plans because the profitabil- ity of the expansion projects will change.

The sub models of the dynamic model of the generation system will be detailed in the next paragraphs.

4.5 Generation system

The developed Dynamic Model considers thermal and hydro stations (reservoirs and run of river) as well as wind parks. Regarding the thermal stations, their generation depends on a number of factors including the fuel costs and the electricity price. On the other hand, the electricity price is influenced and influences the demand. For each thermal technology we considered normalized marginal generation cost curves in function of the capacity factor.

These curves are obtained by dividing the output power by the installed capacity which allows us to express the marginal generation cost in terms of the capacity factor. On the other hand, these curves were discretized in a number of steps. The Dynamic Model outputs the values of capacity factors (depending on the fuel costs that determine the level of the steps of the generation cost functions and on the electricity price and demand) and this is finally used to compute the active generation of each station.

We admitted that wind parks are paid by feed-in tariffs and so whenever the primary resource exists, this generation has to be considered. In this approach, we considered historic data regarding the capacity factor of wind parks.

Values available for Portugal indicate that this factor ranges from 20 to 30% of the installed capacity. In the Dynamic Model, we considered a time step of 1 hour and for each period we sampled values in this range to get the capacity factor of wind parks. Hydro stations were grouped in run of river and in reservoirs. Historic data indicated that the capacity factor for run of river stations was in average of 30% and for reservoirs was 20%. Then we used stochastic processes with different parameters to model their electricity generation along the year.

If necessary, the application can easily be adapted to consider other technologies, as solar. If these are paid according to feed-in tariffs as wind parks mentioned above, they would treated in a similar way. If in the future, they are eventually subjected to market conditions, then some sort of cost function should be derived in order to incorporate solar panels in the investment decision problem as any other technology.

4.6 Electricity demand

The casual diagram used to model the evolution of the electricity demand is represented in Figure 5. The sub model on the right side of Figure 5 uses the annual growth rate as input. This variable was modeled by the Mean Re- verting Process in [16] and formulated by (12 - 15).

+

+ + -

- - -

Solution of investment problems by individual

GENCO’s Installed capacity

Reserve

Long-term evolution of the electricity price

τ

Long-term evolution of fuels

and coal prices.

Forecast of investment and maintenance costs

Evolution of the electricity demand Decommission of

generation units

Forecast of expected costs

along tine

Dynamic model to get the evolution of the electricity price

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Electricity market price

evolution Mean Reverting

Process

Information to Model Electricity market price Price elasticity of

demand

Demand

Demand change Reference demand

Reference electricity market price

Anual growth rate

dx

Initial growth rate

FDP_normal Volatility

dz

Reversion strenght Speed of reversion

Long-run growth rate

Figure 5: Dynamic model to simulate the demand evolution.

In this formulation, tannualdemand, tLP,t0and are the annual growth rate, the long-run growth rate, the initial growth rate (%/year), ε_t is a normally distributed variable with 0 mean and standard deviation, sd, of 1, ηis the speed of reversion, δ is the volatility of the process, FR is the reversion strength and T is the horizon, in years.

(

t t

)

. . t

F_R= _LP− _annualdema_nd η_t∆ (12)

t . .

d_z=ε_tδ ∆ (13)

z R

x F d

d = + (14)

∫ +

= ^T

0 0 nd

annualdema t dx.dt

t (15)

The Dynamic Model of the demand also uses a reference demand in the year prior to the simulation period,Dref₀, the initial electricity price,π^t⁰, and its evolution along the horizon,π^t. The initial price is specified by the user and its evolution results from the Dynamic Model in a way there is a feed-back loop with the demand. There- fore, the mathematical model used to represent the demand evolution is given by (16 - 17) where tannualdemandis the annual growth rate (%/year), E_DPis the demand elasticity to the price and T is the planning horizon in years.

. 0 EDP t

D Dref πt

π

 

=  

  (16)

0 0

0

. .

T

annualdemand

Dref =Dref +

∫

t Dref dt ⁽¹⁷⁾

4.7 Electricity price

Figure 6 details the Dynamic Model used to get the evolution of the electricity price. It uses the values obtained from the models associated with the generations and with the demand evolution and it plays a key role because it outputs the evolution of the electricity price as a result of the interaction of different sub models. The corresponding mathematical formulation is given by (18, 19).

∫∆π + π

=

π ^T

0 t 0 t

t .dt (18)

AF . 1 D

P . D ^G

t

t 



 



 − π

= π

∆ (19)

In this formulation, D is the electricity demand (MWh), P_G is the electricity generation (MWh), AFis an adjustment factor and ∆π^tis the electricity price variation (€/MWh). The AF factor allows simulating delays reflect- ing deviations between the demand and the generation to

the electricity price. This means that if AF is larger than 1.0, unbalances between the computed values of generation and demand will not immediately impact on the price.

Forecast Electricity Price

Electricity Price

Chande Electricity price Adjustment time

Production of Thermal Power Plants Grid Loss

Availability annual average of Thermal Power Plant Capacity factor of Thermal Power Plant

Total Capacity of Thermal Power Plant Total Production

Production of Hydro Power Plants

Total Capacity of Hydro Power Plants

Stochastic simulation Hydro Power Plants

Availability annual average of Hydro Power Plants Production of Wind

Power Plants Total Capacity of Wind Power

Plants

Stochastic simulation Wind Power Plants

Availability annual average of wind Power Plant

Figure 6: Dynamic model to simulate the electricity price.

5 SOLUTION ALGORITHM

5.1 Individual optimization problems

Since the number of available capacities is typically discrete, the problem (2 – 6) has a combinatorial nature suggesting the use of Genetic Algorithms. On the other hand, several input parameters can be subjected to uncertainty as for instance the operation and investment costs.

The Evaluation Function, EF, of an element of the population of the Genetic Algorithm is given by (2) plus penalties on the violated constraints. To consider uncertainties, we sampled a large number of values of the uncertain data from their probabilistic functions to characterize each element of the population by the expected value of EF. The number of samples to take was controlled along the sampling procedure using an uncertainty coefficient that indi- cates if the current estimate of the expected value of EF is already of good quality in terms of being sufficiently stable to enable stopping the sampling procedure. This algorithm was detailed in [10].

5.2 Long term simulation of the electricity market

The long term Dynamic Model of the electricity sector was formulated using the PowerSim software tool [17].

This tool uses the 4^th order Runge-Kutta method to inte- grate differential equations using a step of 1 hour. We also used Microsoft Excel to supply data to the applications developed in MATLAB and in the PowerSim as well as to receive the results and to treat them is a graphical way.

6 CASE STUDY 6.1 Data

In this Case Study we considered a planning horizon of 15 years, three GENCO’s and three candidate technologies. Table 1 presents the generation mix at the starting year. The FOR values of the wind parks, hydro stations and cogeneration are not indicated because their generation depend on stochastic processes considering average historic values for their capacity factors. These stations are owned as follows: GENCO_A 27,15%, GENCO_B 23,18

%, GENCO_C 22,52 % and other GENCO’s 27,15 %.

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no. units Technologies Inst. capacity (MW) FOR

5 coal_1 1.000 0,02

2 coal_2 600 0,02

3 Gas turbine 500 0,02

6 CCGT 1.500 0,02

2 Oil 200 0,02

6 Wind parks 1.000 -

8 Hydro reservoires 750 -

6 Hydro run-of-

river 1.500 -

Cogeneration 500 -

Table 1: Characteristics of the existing technologies.

We considered the following decomissioning plan. In the 5^th year are decomissioned 300 MW of coal type 1 and 200 MW of CCGT. In the 10^th year are decomissioned 500 MW of gas turbines, 300 MW of coal type 1, 300 MW of coal type 2 and 200 MW of wind parks. In the 15^th year are decomissioned 400 MW of CCGT and 200 MW of wind parks. The remaining thermal stations and wind parks in Table 1 are decomissioned in the 20^th year. We admitted that the life-time of the hydro stations is equal to the period considered in the simulation. As described in Section 4.5, for each thermal technology we considered curves relating their marginal operation cost with their capacity factor.

Figure 7 illustrates this type of curve for coal Type 1.

Figure 7: Normalized marginal cost for coal type 1 stations.

The value of the peak power in the starting year is 4750 MW and the annual demand is 30,64 TWh. We admitted that the annual load duration curve was discretized in 6 steps as follows: 100% of the peak power during 5 % of the year, 90% for 20 % of the year, 80% for 45 % of the year, 70% for 65 % of the year, 60% for 85% of the year and 50% of the peak power during 100% of the year.

Along the planning horizon we admitted that the annual demand increased as determined by the Dynamic Model but the above discretization remains unchanged.

Regarding the candidate technologies, Table 2 has the data for the available capacities, the investment cost, the fix operation and maintenance cost, the cost of capital and the FOR. The life-time and the construction period were assumed as 30 years and 2 years for the three technologies.

The construction time can be set at different values for different technologies but 2 years seems well adjusted for instance for combined cycle stations.

Type of technology

Available capacities (MW)

Investment cost (€/MW)

Fix operation and mainte-

nance cost (€/MW.year)

Cost of capital with the loan (€/MW.year)

FOR

Tech_1 100 or 150

or 200 450.000 6000 42230,40 0.02 Tech_2 100 or 200 550.000 6137 44133,40 0.02 Tech_3 100 or 200

or 250 800.000 7655 49666,72 0.01 Table 2: Characterization of the candidate technologies.

On the other hand, GENCO_1 is interested in the three technologies. In the first 5 years he has 1000 million € to invest and 1000 million € more in the last 10 years.

GENCO_2 is interested in Tech_1 and Tech_2. In the first 5 years he has 450 million € to invest, 450 million € more to invest from the 6^th to the 10^th year and 450 million € more in the last 5 years. GENCO_3 is interested in the three technologies. In the first 5 years he has 600 million € to invest, 600 million € more to invest from the 6^th to the 10^th year and 600 million € more in the last 5 years. In each year of the horizon each agent can not install more than 300 MW in Tech_1, 300 MW in Tech_2 and 400 MW in Tech_3 and shall not own more than 40% of the installed capacity. The total new capacity shall not exceed 600 MW in Tech_1, 600 MW in Tech_2 and 800 MW in Tech_3. The reserve margin should range from 20 to 40%

and the maximum value admitted for LOLE is 2h/year.

The capacity factor of wind parks was modelled by a stochastic process using a Normal FDP with mean 25%

and sd of 5%. Along the planning horizon we admitted there are new additions of wind parks with a total capacity of 3000 MW. The hydro stations are modeled in two groups: run of river and reservoirs. Their outputs are modelled by stochastic processes using Normal FDP’s. For run of river units the mean value is 30% and the sd is 5% and for the reservoirs the mean value is 20% and the sd is 5%.

6.2 Results of the expansion planning exercise

Tables 3 to 5 detail the plans for GENCO’s 1, 2 and 3.

Stage Tech_1 (MW) Tech_2 (MW) Tech_3 (MW)

1 100 200 200

2 100 200 200

3 - 100 -

6 100 200 200

7 100 200 200

8 - - 200

Table 3: Generation expansion plan obtained for Genco_1.

1 100 200 -

2 100 200 -

3 - 100 -

6 100 200 -

7 100 200 -

8 - 100 -

11 100 200 -

12 100 100 -

1 100 200 200

2 - 100 200

6 100 200 200

7 - 100 -

11 100 100 200

12 - 100 -

At the end of the horizon, the distribution of the new capacity per technology is as follows: 21,31% for Tech_1, 49,18% for Tech_2 and 29,51% for Tech_3. The distribution of the new capacity per GENCO is as follows: 37,70%

for GENCO_1, 31,15% for GENCO_2 and 31,15% for GENCO_3. These results indicate that there is a larger concentration of investment in the first half of the horizon

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due to the available financial resources and also due to the larger values of LOLE in the initial years (maximum value of 1,67 h/year in year 2 and minimum of 0,97 h/year in year 9). The impact of new additions can also be seen in the evolution of the annual average electricity price, Figure 8. In the first two years the price increases since the construction period of the new stations is 2 years. The investments decided in year 1 will then only be in operation in year 3, contributing to reduce the price and LOLE.

Figure 8: Evolution of the electricity price along the horizon.

Finally, Figure 9 presents the evolution of the capacity factors of the three candidate technologies. They tend to decline namely due to the increasing share of wind parks in the generation mix paid according to feed in tariffs and the resulting decline of the electricity price in the market. In any case, Tech_3 has the largest capacity factors since it is the technology having lower marginal operation costs.

Figure 9. Evolution of the capacity factors.

6.3 Sensitivity analysis – variation of operation costs Finally, we admitted that the operation cost of Tech_1 reduced by 20% regarding the value used before. The results obtained clearly indicate that Tech_1 is now more attractive for all generation agents. Now, the percentual distribution of the new capacity per techonology is as follows: 44,83% for Tech_1, 32,76% for Tech_2 and 22,41%

for Tech_3. In the previous simulation the share of Tech_1 was 21,31 and now more than doubled to 44,83% while the shares of Tech_2 and Tech_3 reduced.

7 CONCLUSIONS

This paper described a long-term approach to help generation companies to develop investment plans in new capacity or to conduct sensitivity studies to build more robust plans. This approach can also be used in a fruitful way by regulatory agencies to anticipate the possible evolution of the sector or to adopt new market designs, eventually to turn capacity investments more attractive. The main feature of this approach is the use of System Dynam- ics to capture the long-term characteristics of the problem and to model it in a more realistic way. Real generation

expansion studies consider a number of other aspects as fuel availability and economic growth. These are considered in an indirect way in the developed approach since fuel availability will be reflected on fuel prices and economic growth will impact on the future electricity demand.

This means that the developed approach has the potential to be used by several agents in a profitable way while considering a large variety of situations and factors.

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