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Electric Power Systems Research 104 (2013) 138– 145

Contents lists available at ScienceDirect

Electric Power Systems Research

jou rn al hom epage: www.elsev ier .com/ locate /epsr

eneration expansion and retirement planning based on thetochastic programming

aser Tohidia, Farrokh Aminifarb,∗,1, Mahmud Fotuhi-Firuzabada

Center of Excellence in Power System Control and Management, Electrical Engineering Department, Sharif University of Technology, Azadi Ave., Tehran,ranThe School of Electrical and Computer Engineering, College of Engineering, University of Tehran, North Kargar St., Tehran, Iran

r t i c l e i n f o

rticle history:eceived 3 January 2013eceived in revised form 19 May 2013ccepted 22 June 2013vailable online 26 July 2013

eywords:eneration expansion planning (GEP)

a b s t r a c t

This paper develops a mathematical model based on the stochastic programming for simultaneousgeneration expansion and retirement planning. Retirement decision of the existing generating units isaccommodated since these units are aging more and more. The proposed method is formulated as anoptimization problem in which the objective function is to minimize the expected total cost consisting ofthe investment required for commissioning new units, operation and maintenance costs, the retirementsalvage cost, and the system risk cost. The problem is subjected to a set of generating unit and systemphysical and operational constraints. The modeling of energy limited units is also devised in a proba-

ixed-integer programming (MIP)ncertaintynit retirement

bilistic manner as an underlying requirement in practical studies. The Monte Carlo simulation approachis used to consider the component random outages. A large number of scenarios are simulated and thescenario reduction technique is applied to tailor the computational effort within a tractable range, whichis essential for large-scale problems. Numerical studies are conducted on the IEEE-RTS79 and the per-formance of the proposed model is investigated. As expected, the retirement option could be beneficialparticularly when the contribution of aged units in the system unreliability becomes more severe.

. Introduction

Demand growth in power systems necessitates Generationxpansion Planning (GEP) in which the type, size, location, andommissioning time of new generating units in a planning hori-on are to be determined. The final solution of GEP is based onhe minimum cost and/or optimum reliability taking into accountarious constraints such as capacity of units and lines, operatingonstraints, and budget restrictions. Generally speaking, GEP is aombinatorial large-scale, mixed-integer, and non-linear problem;ccordingly a wide range of heuristic and classical optimizationpproaches have been applied.

The GEP problem has been coped with several heuristic opti-ization approaches among them are genetic algorithm [1,2],

article swarm optimization technique [3], and a combination ofeuristic approaches [4]. However, there is a tendency in formulat-

ng the planning problems as a mathematical optimization models there is no guarantee for optimality of the results in heuris-ic approaches and they request extremely long execution times

∗ Corresponding author. Tel.: +98 21 88769186.E-mail addresses: aminifar@ece.ut.ac.ir, frkh aminifar@ee.sharif.edu,

rkh aminifar@yahoo.co.uk (F. Aminifar).1 Farrokh Aminifar was with Sharif University of Technology.

378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.epsr.2013.06.014

© 2013 Elsevier B.V. All rights reserved.

particularly for real-scale problems. Among classical optimizationtechniques, the Mixed-Integer Programming (MIP) [5] has beenrecognized with a satisfactory performance. MIP method offers agreat flexibility in modeling different aspects of the problem andcould guarantee a solution that is globally optimal or one withinan acceptable tolerance. Decomposition techniques have been alsoemployed in GEP problem to overcome its extreme dimensional-ity. A simple but effective decomposition method for calculatingthe Loss of Load Probability (LOLP) with a strict budget constraintwas elaborated in [6]. Reference [7] investigated the application ofBender’s decomposition technique based on the genetic algorithmto achieve the GEP optimum solution. In [8,9], Bender’s decom-position was exploited in the GEP problem and in the concurrentgeneration and transmission planning, respectively. The GEP prob-lem, although has been primarily defined for the planning of bulkgeneration facilities mainly connected to the transmission level, isalso being applied in the distribution networks for specifying thecapacity, type, and location of distributed generation units [10].

One of the key requirements in the GEP problem is the reliabil-ity concern and its impact on the planning decisions [11]. Inclusionof reliability criteria additionally expands the GEP problem and if

not considered would result in uneconomic overdesign or cost-effective vulnerable schemes. In fact, random nature of powersystem elements has a great effect on the system performance.In this manner, three categories of approaches are identified:

stems Research 104 (2013) 138– 145 139

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2

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END

NS=NS+1

fix ?

Scenario reduction

up to NS scenarios

No

Yes

Monte Carlo simulation and

scenario generation

Calculate σ

σ<σ

NS=2

Y. Tohidi et al. / Electric Power Sy

eterministic, probabilistic, and scenario based. In [12], the outageossibility of components is modeled as a deterministic criterion

n expansion planning. Probabilistic approaches for modeling thencertainty are also incorporated in expansion planning in whichtochastic parameters are not described by unique values, butather by probability distributions [13]. Reference [14] assumes

probabilistic distribution function for each stochastic parame-er and solves the problem using genetic algorithm approach. In15], a decomposition method for reliability modeling in expansionlanning is proposed. In [9], the stochastic programming is used toodel the uncertainty. Even though the probabilistic approaches

re more accurate, they put computational burden to the expan-ion planning problem. Scenario based approaches overcome thisifficulty by assessing a selected set of scenarios generated accord-

ng to the probabilistic distribution of stochastic parameters [16].o date, scenario-based techniques have been successfully appliedn the various power system planning problems [17–19]. In theseeferences, a large number of scenarios generated by Monte Carloimulation are reduced in an optimal way to overcome the numer-cal complexities.

A less-investigated issue in the GEP problem is the incorporationf equipment retirement decisions in the problem. As a matter ofourse, power systems are getting older and more generating unitsre facing the aging deficits. Besides, new technologies are of desir-ble features such as the high production efficiency. To the best ofuthors’ knowledge, there is no thorough study emphasizing theging and retirement of generation facilities and their concurrentssessment in the GEP problem. Reference [20] discussed a casetudy conducted in 1999 in which the retirement of a generatorocated in the north region of an island has been discussed. How-ver, the GEP is not covered in the proposed model. As a result ofncreasing operation cost of aged facilities and their significant rolen the system unreliability and risk cost, the retirement of agednits could be an economic option in the GEP problem. Further-ore, owners of retired units could earn more profits with selling

he equipments and/or the field. Generation Expansion and Retire-ent Planning (GERP) is accordingly introduced in this paper as an

pen research area.This paper derives an efficient mathematical model for the GERP

roblem in which all analyses are conducted in a probabilistic wayhrough the stochastic version of MIP. Recourse-based stochasticrograms employ a discrete distribution of the random parametersnd therefore can be solved by effective optimization algorithms.he proposed model is expanded over a number of scenarios whichimulate the random outage of both generating units and trans-ission lines. The scenario reduction, as an essential means for

olving practical large-scale optimization problems, is employedere for decreasing the model size in an optimal way. The pro-osed approach is applied to both Hierarchical Levels I and II (HLInd HLII) [20]. The first level (HLI) focuses on the generation sectornd its adequacy in satisfying the corresponding load. The secondevel (HLII) refers to the composite generation and transmissionystem and its compound ability in delivering energy to the majoroad points. The performance of the proposed model is thoroughlyiscussed based on numerical evidences.

The rest of the paper is organized as follows. Section 2 provideshe uncertainty modeling of generating units and transmissionines. Section 3 presents the proposed methodology and formula-ion. Section 4 elaborates simulations on the IEEE-RTS79 network.oncluding remarks are drawn in Section 5.

. Uncertainty modeling

Over recent decades, deterministic approaches have been grad-ally replaced by probabilistic ones in power system planning

Fig. 1. Flowchart of the scenario reduction algorithm.

studies [20]. Probabilistic approaches, however, bring about heavycomputational burdens on the optimization problem of expan-sion planning. The solution is either to use the parallel processingapproach or to employ the scenario-based technique. The formernecessitates hardware facilities which are not usually accessiblewhile the latter could be generally applicable. This section discussesa scenario-based approach by which component random outagesare effectively taken into account.

Uncertainty modeling initiates with generating a large num-ber of scenarios by the means of Monte Carlo Simulation (MCS).In fact, these scenarios are 0/1 strings that determine the stateof components in each scenario. The number of scenarios in MCSis irrespective of the system size, and this characteristic makes itapplicable in large-scale problems. In its most plain form, SimpleSampling approach is used in MCS with the predefined variance of0.05.

Next, similar scenarios are determined and the probability ofeach scenario is calculated with respect to the number of occur-rences experienced. The final step is to take a scenario reductiontechnique which is essential for solving scenario based opti-mization problems in large-scale power systems. Among variousalgorithms of scenario reduction are fast backward, a mix of fastbackward/forward, and a mix of fast backward/backward methods[21]. Also, several efficient algorithms based on backward and fastforward methods were developed in [22]. In general, these methodsare different from the results accuracy and execution computa-tional time perspectives. For a large number of initial scenarios,the fast backward method is the fastest one, while the results ofthe other two methods are more accurate but at the expense ofhigher computational times.

Fig. 1 depicts the flowchart of scenario reduction algorithm. Thenumber of retained scenarios, namely NS, is determined based ona stopping criterion, �fix, which is adopted as the maximum esti-mated standard deviation of loss of load expectation (LOLE) [18],namely �. The formulation of the deviation index, �, is:

� = 1NS

√∑NS (LOLEs − LOLE)2

NS − 1(1)

s=1

Typical values for �fix are of 0.05 or 0.01 [18] and it is assumedhere to be equal to 0.05. Therefore, both the predefined variancefor simple sampling in MCS and �fix are set to 0.05 in this study.

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40 Y. Tohidi et al. / Electric Power Sy

t should be emphasized that the initial number of reduced sce-arios is two, NS = 2, by which the deviation is definable and theumber of retained scenarios should be increased up to the point

n which the stopping criterion over the deviation index, �, iset.The retained scenarios are a subset of initial ones that is clos-

st to the initial probability distribution in terms of probabilisticetrics. Different scenarios and their associated probabilities sim-

late the various probable conditions of the power system and theirorresponding likelihood, respectively.

The mathematical model of scenario reduction along with crite-ion of the reliability index deviation accommodate the stochasticehavior of the system in the planning problem while making surehat the retained scenarios acceptably preserve the accuracy ofeliability measures. By setting an appropriate threshold of theeliability index deviation, �fix, a reasonable compromise betweenhe computational issue and the accuracy of analyses could bechieved. The scenario-based method could encompass the impactsf generating unit and transmission line outages as well as uncer-ainties associated with the system load level. In the current study,he random outages of generating units and transmission lines are

erely taken into account and a multi-level load duration curve isonsidered in the analyses. The more the load level steps, the moreccurate the model is. The system load is assumed to have a fixedmount in each level and the number of load scenarios associatedith each load level is one.

. Generation expansion and retirement planning

Mathematical formulations of the GERP problem are developedn this section. The problem is defined over a long-term horizon, andhe proposed model is hence formed based on a year index. In theroposed model, it is assumed that expansion of the transmissionystem over the planning horizon is known, commonly referredo as the transmission-ready studies. Note as well that all symbolssed throughout the paper are introduced in the Appendix. Thebjective function of the problem is to minimize the summationf yearly discounted costs (2). The cost associated with each years composed of five terms: investment cost (3), salvage cost (4),xpected fuel cost (5), O&M cost save the fuel expenditure (6), andystem risk cost (7). Preserving the MIP format, one may readilynclude the fuel expenditure in O&M cost.

in TC =Y∑

y=1

(ICy + SCy + FCy + OMCy + RCy) (2)

Cy = (1 + r)(1−y)NB∑

b=1

NUn∑k=1

unybk × ICn

yk × r(1 + r)LTk

(1 + r)LTk − 1(3)

Cy = (1 + r)(1−y)NB∑

b=1

NUob∑

k=1

fybk × SCoybk (4)

NS

Cy = (1 + r)(0.5−y)NB∑

b=1

ND∑l=1

tl

y∑s=1

�ys

×

⎡⎣

NUob∑

k=1

stoybsk × FCo

ybk × poyblsk +

NUn∑k=1

stnysk × FCn

yk × pnyblsk

⎤⎦ (5)

Research 104 (2013) 138– 145

OMCy = (1 + r)(0.5−y)NB∑

b=1

×

⎡⎣

NUob∑

k=1

uoybk × OMFo

ybk × poybk +

NUn∑k=1

unybk × OMFn

yk × pnk

⎤⎦

+ (1 + r)(0.5−y)NB∑

b=1

ND∑l=1

tl

NSy∑s=1

�ys

×

⎡⎣

NUob∑

k=1

stoybsk × OMVo

ybk × poyblsk +

NUn∑k=1

stnysk × OMVn

yk × pnyblsk

⎤⎦ (6)

RCy = (1 + r)(0.5−y)NB∑

b=1

ND∑l=1

tl

NSy∑s=1

�ys × VOLLyb × LSybls (7)

To have a precise comparison in the decision making process,the cost terms are scaled to present values based on the interestrate. In this conversion, it is assumed that every cost is in the mid-dle of the year except the investment and salvage costs which aresupposed to be at the beginning of each year. For effective modelingof the investment cost in the planning horizon, it is replaced withthe correlated annual equivalent value as stated in (3). It shouldbe noted that the salvage cost is commonly positive due to thevalue of retired facilities and power plant land; however, it mightbe negative as well.

From the above formulation, it is evident that all investment,salvage, fuel, O&M costs as well as the value of lost load (VOLL)have the index of y to offer unequal values in different years, possi-bly due to the inflation. In addition, fuel and O&M costs associatedwith old units might be increasing because of the aging process.The practical capacity of old units has also the index of y to modelpossible decreases in these parameters regarding successive years.

As described in Section 2, the scenario-based method modelsthe stochastic outage of generating units and transmission lines.Accordingly, a summation over the retained scenarios is consideredin (5)–(7). Note that the weighting factor of each scenario s asso-ciated with a given year y is the corresponding probability, �ys,computed after the scenario reduction process. �ys is an implicitfunction of components’ individual Forced Outage Rates (FORs).One crucial point about the scenarios is that the stochastic mod-eling should be executed for each year since the practical capacityand FORs of old units and the system load differ in various years. Theold units aging attributes, i.e. increase in FOR, is accommodated inthe process of scenario generation and reduction associated witheach year. In (5) and (6), known generating unit state values, st,make the fuel and variable operation costs of out of service unitsequal to zero.

Equality and inequality constraints of the problem consist ofcapacity of units (8) and lines (9), and bus-level load balance (11).Eq. (10) calculates line powers in terms of voltage phase angles.Note that the decrease of aged units’ practical capacity is accom-modated in (8.a) by defining po

ybk as a function of year y.

poyblsk ≤ uo

ybk × poybk (8.a)

n n n

pyblsk ≤ uybk × pk (8.b)

−plj ≤ pl

ylsj ≤ plj (9)

stems Research 104 (2013) 138– 145 141

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solution

Solve the optimization

problem

No

Yes

Sce nario reduction

Sce nario generation

New dec ision?

problem and might be very large-scale for real-world applica-tions. In Tables 1 and 2, the number of variables and equality andinequality constraints without/with considering retirement option

Table 1Problem dimension without considering retirement.

Item Size

Binary variables Y . NB . NUn

Y. Tohidi et al. / Electric Power Sy

lylsj = 1

xj

NB∑b=1

Aysbjıybls (10)

ybl = LSybls +NUo

b∑k=1

stoybsk × po

yblsk +NUn∑k=1

stnysk × pn

yblsk −NLy∑j=1

Aysbjplylsj

(11)

In the aforementioned formulation, decision variables uo and un

enote the retirement of old units and the commissioning of newnits, respectively. uo is set to 0 whenever the unit is planned toe retired. In that case, uo in forward years should be kept equal to, expressed by (12.a). un is 1 whenever a new unit is planned toe invested and corresponding variables in forward years are keptqual to 1, stated by (12.b).

o(y+1)bk ≤ uo

ybk (12.a)

n(y+1)bk ≥ un

ybk (12.b)

In order to find the optimum location of new units, a bus indexs added to the new unit binary variables, un

ybk. Hence, for a given

ew candidate unit, the corresponding binary variable is replicatedor all buses while among them, just one variable can be set at 1hich represents the location of the new unit. The correspondingathematical modeling yields the following constraint:

NB

b=1

unybk ≤ 1 (13)

In (4), a flag is incorporated in the formulation to represent theetirement of old unit k at bus b in year y. To activate the flag in theetirement year, the following linear constraint is required:

fybk = (uo(y−1)bk

− uoybk

)

f1bk = (1 − uo1bk

)(14)

The system risk can be represented by a set of indices [20]. Theost common index used to link a probabilistic approach in calcu-

ating risk cost is the EENS. System Minutes (SM) is another indexerived from the EENS as expressed in (15). One SM is equivalento the interruption of system total load for one minute at the timef the system peak load. EENSy is formulated in (16) in terms of sce-ario load curtailment values in a linear manner. The SM should bereserved in an acceptable range during the whole planning hori-on as expressed by (17). It should be noted that as SM is inherently

normalized index, it could be bound with a unique limit during thentire planning horizon and regardless of the load level associatedith any year y.

My = EENSy

Ly

× 60 (15)

ENSy =ND∑l=1

tl

NSy∑s=1

�ys

NB∑b=1

LSybls (16)

My < SM (17)

In practice, some generating units such as fossil-fueled unitsith specific fuel contracts or hydro units with restricted resource

vailabilities are intrinsically energy limited. Inclusion of this limi-

ation needs another inequality constraint on their expected energyupplied which is expressed as below:

ESym ≤ EESm (18)

Fig. 2. Flow diagram of the solution procedure.

where

EESym =ND∑l=1

tl

NSy∑s=1

�ys × peylsm (19)

Obviously, the constraint (18) can be readily expressed for thesummation of expected energy supplied by a set of units associatedwith a specific power plant.

The developed mathematical model is based on the MIP for-mat since it includes both types of binary and continuous variablesand the relation among all variables is in a linear fashion. Oncethe solution is obtained, values of binary variables un and uo revealthe generation expansion and retirement scheme. If the planner isgoing to retire some selected units in specific years, just the respec-tive decision variables should manually be set to 0 by adding somesimple constraints.

The point demanding further attention is that, in the case ofunit(s) retirement or expansion decision, the scenario reductionis executed based on the new condition and the GERP problem issolved again as demonstrated in Fig. 2. In this diagram, the secondblock itself is a separate analysis depicted in Fig. 1. Moreover, itshould be emphasized that the scenario-based MIP model incorpo-rates all retained scenarios concurrently. Thus, in the third blockof the diagram shown in Fig. 2, the stochastic GERP is solved at asingle shot. The iterative process should follow to the point that thesolution doesn’t change any further.

3.1. Problem dimension

As it can be observed from the proposed formulation, the gen-eration expansion and retirement planning model is a complex

Continuous Variables NS . ND . [NUo + NB . (1 + NUn) + NL]Equality constraints NS . ND . (NL + NB)Inequality constraints NS . ND . (NUo + NB . NUn + 2.NL) +

Y . (NB . NUn + NUn + M + 1) − NB . NUn

142 Y. Tohidi et al. / Electric Power Systems Research 104 (2013) 138– 145

Table 2Problem dimension with considering retirement.

Item Size

Binary variables Y . (NB . NUn + NUo)Continuous variables NS . ND . [NUo + NB . (1 + NUn) + NL]Equality constraints NS . ND . (NL + NB)

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Table 4Increase in O&M cost, fuel cost, and unavailability of old units.

Characteristic Increase percentage (yearly)

lines terminating to this bus or its respective area. The similarityof the results in HLI and HLII derives from the immense capacity ofthe bulk transmission system in the IEEE-RTS79 that makes its roleless influencing.

Table 5GEP problem in HLI.

Unit type Size (MW) Energizing year

OC 50 N/AOC 50 6thOC 100 10thOC 100 N/ACC 200 9thCC 200 6thCC 300 2ndCC 300 6th

Table 6GEP problem in HLII.

Unit type Size (MW) Bus no. Energizing year

OC 50 N/A N/AOC 50 15 3rdOC 100 8 10thOC 100 9 3rd

TC

Inequality constraints NS . ND . (NUo + NB . NUn + 2.NL) +Y . (NB . NUn + NUn + NUo + M + 1) − NB . NUn − NUo

s calculated, respectively. In these two tables, NS =∑Y

y=1NSy is theotal number of scenarios considered in the planning horizon andhe number of transmission lines is assumed to be constant overhe years. As presented in these two tables, the number of binaryariables does not grow with the number of scenarios and loadevels. However, the number of continuous variables, equalities,nd the first term in the number of inequalities grow proportion-lly with the number of scenarios. This characteristic makes theroblem dimensionally cumbersome and employing the scenarioeduction technique would be indispensable.

. Simulation results

The IEEE-RTS79 has 38 lines, 24 buses, 17 load buses, and 10eneration buses [23]. The total number of generating units is 32ith the installed capacity of 3405 MW. The system annual peak

oad is 2850 MW and the load duration curve (LDC) is discretizedn 10 steps. The VOLL associated with each load point is extractedrom [24] and increases annually by the rate of inflation rate [25]s happens for the other costs.

The set of new candidate units consists of four open cycle (OC)as fueled units, 2 × 50 MW and 2 × 100 MW, and four combinedycle (CC) units, 2 × 200 MW and 2 × 300 MW. The characteristics ofew candidate units are presented in Table 3. Values in this table areaken from [23] with slight modifications. To model the aging con-ition of existing units, it is assumed that the O&M cost, fuel cost,nd unavailability of those units increase in a manner expressedn Table 4, and their capacity decreases by 3% each year. The plan-ing horizon is ten years considering 3% load growth, 3% inflationate, and 5% interest rate. Six 50 MW hydro units are assumed to benergy limited with the maximum expected energy supplied equalo 150 GWh/yr. SM index as the reliability constraint is limited to7 min. The number of scenarios generated by MCS and associ-ted with different years falls within 3411–4023 for HLI and within348–5906 for HLII. The scenario reduction technique is performednd the number of reduced scenarios in every year varies from 8 to5 in HLI and from 11 to 17 in HLII for the base case.

The numerical case studies are conducted in the following twoases without and with considering the units’ retirement option.lso, the studies are performed in both HLI and HLII to reflect

he effects of the transmission system. In HLI, the only source ofncertainty is the availability of generating units and the adopted

eliability index is assessed excluding the impacts of transmissionetwork. However, for uncertainty modeling in HLII, the availabil-

ty of transmission lines and network’s constraints are considereds well.

able 3haracteristics of the new candidate units.

Unit type O&M cost

Fixed ($/kW/Yr) Variable ($/MWh)

Open cycle 50 MW 0.085 4

100 MW 0.05 3

Combined cycle 200 MW 1.15 0.6 1300 MW 1 0.5 1

O&M cost 10Fuel cost 3Unavailability 2

4.1. Excluding the retirement

In this study, binary variables of old units are manually set to 1,i.e., the retirement of old units is not allowed and we have the GEPproblem. This study is necessary to demonstrate the beneficial roleof old unit retirements.

Tables 5 and 6 show the obtained results for the GEP in HLI andHLII, respectively. As it can be seen, the CC units are commissionedfirst, which reveals that they are economical investments. The keyreason of this conclusion regards the relatively smooth standardLDC and characteristics of units. CC units, compared to OC units,have higher investment and smaller operation costs. These unitsare hence more beneficial when their operating periods are longer,and this situation is exactly what we have with the smooth standardLDC.

Comparing Tables 5 and 6, commissioned units and their ener-gizing years are identical in HLI and HLII except the followings: (i) inHLII, a 100 MW gas unit is added to bus 8 in the 3rd year, and (ii) inHLII, a 50 MW unit is commissioned three years earlier. Installationof one 100 MW gas unit in bus 8 is due to the insufficient gener-ating capacity around this bus and rather congested transmission

CC 200 10 9thCC 200 10 6thCC 300 15 2ndCC 300 13 6th

Investment cost (M$) Fuel cost ($/kWh) Availability Life (Yr)

1.5 2.6 0.98 202.5

1.0 1.5 0.95 305.0

Y. Tohidi et al. / Electric Power Systems Research 104 (2013) 138– 145 143

Table 7GEP problem in HLI with modified LDC.

Unit type Size (MW) Energizing year

OC 50 7thOC 50 5thOC 100 2ndOC 100 3rdCC 200 10thCC 200 8thCC 300 1stCC 300 5th

Table 8GEP problem in HLII with modified LDC.

Unit type Size (MW) Bus no. Energizing year

OC 50 11 3thOC 50 11 4thOC 100 8 1stOC 100 9 2ndCC 200 9 10thCC 200 10 8thCC 300 15 1stCC 300 13 5th

Table 9GEP problem in HLI with modified VOLL.

Unit Type Size (MW) Energizing Year

OC 50 N/AOC 50 8thOC 100 10thOC 100 N/ACC 200 10thCC 200 6thCC 300 2ndCC 300 7th

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Table 10GEP problem in HLII with modified VOLL.

Unit type Size (MW) Bus No. Energizing Year

OC 50 N/A N/AOC 50 15 5rdOC 100 8 5rdOC 100 9 10thCC 200 10 10thCC 200 10 6thCC 300 15 4ndCC 300 13 8th

Table 11GERP problem in HLI: new commissioned units.

Unit type Size (MW) Energizing year

OC 50 8thOC 50 6thOC 100 10thOC 100 N/ACC 200 9thCC 200 6thCC 300 2ndCC 300 6th

Table 12GERP problem in HLI: old retired units.

Unit Retirement year

5 × 12 MW 4th

Table 13GERP problem in HLII: new commissioned units.

Unit Type Size (MW) Bus no. Energizing year

OC 50 15 8thOC 50 15 3rdOC 100 8 3rdOC 100 9 10thCC 200 10 9thCC 200 10 6thCC 300 15 2ndCC 300 13 6th

Table 14GERP problem in HLII: old retired units.

Unit Retirement year

invested in the 8th year. These decisions improve the cost func-tion with the value of $3.5 million in HLI. In HLII, comparingTables 13 and 14 with Table 6 reveals that just two of 12 MW units

To further digest the impact of load profile on expansion plan-ing, LDC is modified so that loads greater than 95% of the peak

oad are multiplied with 1.1. Indeed, this modification imposesome severe fluctuations in LDC. The new version of GEP problems solved and obtained results are presented in Tables 7 and 8. Itan be observed that, in contrast with the preceding study, all unitsre commissioned, which is due to heavier loading of the system.oreover, OC gas units are invested in early years, which is due to

he system higher peak load. Referring to Tables 7 and 8, OC gasnits are planned earlier in HLII, indicating more significant effectsf network constraints in peak load conditions.

Depending on the acceptable level of the reliability criterion,ay the SM index adopted here, the reliability constraint mightffect the final results or may be unrestrictive on the most econom-cal solution. In this regard, another pair of simulations in HLI andLII is fulfilled. In these studies, the VOLL of buses is decreased by0%, while all other parameters are kept as before. In other words,he optimal point of the problem is shifted but the reliability con-traint remains unchanged. The original standard LDC is considereds well. The new problem is solved and Tables 9 and 10 presenthe unit expansion scheme. Comparing the obtained results withhose presented in Tables 5 and 6, one can categorize the new unitsn twofold classes (i) some are invested like before, and (ii) somethers are commissioned later. The key conclusion drawn here ishat the former class is being added to the system due to the reli-bility requirement, while the latter class consists of units whosenstallation has economic outcomes.

2 × 12 MW 3rd and 4th

4.2. Considering the retirement

In this study, the binary variables of the existing units are setto 1 in the first year to prevent their retirement in the beginningof the study. The reduced scenarios fulfilled in the preceding studyare also used here as the initial set. The salvage costs associatedwith retired units are assumed to be zero. The simulation resultsobtained in this study include both unit expansion and unit retire-ment plans. The results are given in Tables 11 and 12 in HLI and inTables 13 and 14 in HLII.

Comparing Tables 11 and 12 with Table 5, it is observed thatby considering the retirement option in HLI, five 12 MW units areretired in the 4th year, while, an additional new 50 MW unit is

144 Y. Tohidi et al. / Electric Power Systems Research 104 (2013) 138– 145

Table 15Salvage values of old units.

Unit type Unit size Salvage value (M$)

Fossil–oil 12 0.2100 0.6197 0.8

Fossil–coal 76 0.5155 0.7350 1

Combustion turbine 20 0.2Hydro 50 0.8

Table 16GERP problem with salvage cost in HLI: new commissioned units.

Unit Type Size (MW) Energizing year

OC 50 8thOC 50 5thOC 100 10thOC 100 N/ACC 200 9thCC 200 6thCC 300 2ndCC 300 6th

Table 17GERP problem with salvage cost in HLI: old retired units.

Unit Retirement year

5 × 12 MW 3rd20 MW 5th

Table 18GERP problem with salvage cost in HLII: new commissioned units.

Unit Type Size (MW) Bus no. Energizing year

OC 50 15 8thOC 50 15 3rdOC 100 8 3rdOC 100 9 10thCC 200 10 9thCC 200 10 6thCC 300 15 2nd

atmsuf$tcc

uvso4iTTa

Table 19GERP problem with salvage cost in HLII: old retired units.

Unit Retirement year

2 × 12 MW 2nd and 3rd20 MW 5th

Table 20Execution Time and Cost of Simulated Cases.

Simulated Case Execution Time (h) Cost (M$)

Base Case (HLI) 0.1 62Base Case (HLII) 0.2 68Modified LDC (HLI) 0.1 63.6Modified LDC (HLII) 0.2 69.8Modified VOLL (HLI) 0.1 61.2Modified VOLL (HLII) 0.2 66.7Retirement (HLI) 0.2 58.5

ularly when the new cost-effective capacities are inadequate in

CC 300 13 6th

re decided to be retired in the 3rd and 4th years, while, an addi-ional new 50 MW unit is invested in the 8th year. The reason for

aintaining three 12 MW units in HLII is that they are needed forupplying the loads around bus 15 that cannot be served by othernits due to the network constraints. The improvement of the costunction in HLII, drawn by enabling the retirement option, is about1 million. As the salvage cost is assumed zero in these simulations,he retirement decisions of some old units are due to either theirostly operations (including fuel and O&M costs) or their significantontributions in the system unreliability.

As expected, either positive or negative salvage cost of retirednits could change the solution of GERP problem. Unlike the pre-ious study, it is assumed here that the system old units havealvage values as given in Table 15. These values are equal to 20%f the investment cost of similar units and salvage values of two00 MW units are assumed to be zero. The GERP problem is accord-

ngly solved and the results in both HLI and HLII are outlined in

ables 16–19. Comparison of the new results with those shown inables 11 and 14 demonstrates that more units and in earlier yearsre to be retired when positive salvage values of retired units are

Retirement (HLII) 0.4 67Retirement with Salvage (HLI) 0.2 54.4Retirement with Salvage (HLII) 0.4 66.6

incorporated. In other words, positive salvage values make the unitretirement a more beneficial decision. A comprehensive sensitiv-ity analysis on the salvage cost value provides worthy informationabout the economic impacts of retirement option on the GEP solu-tion and leads to compromised decisions. This issue is an appealingresearch topic and is under study by the authors.

Table 20 summarizes the execution time and cost of all simu-lated cases. This table reveals the trivial computation burden of theproposed method; however, larger numbers of reduced scenariosdrastically increase the execution time.

5. Conclusion

This paper introduced a mathematical model based on thestochastic programming for simultaneous generation expansionand retirement planning. The proposed model includes the retire-ment decision of aged generating units in the GEP analysis. Thisdecision might be beneficial since old units are being operated atincreased costs and decreased practical capacities. Additionally, theavailability of these units is deteriorated with passing the time,which in turn enforces greater load curtailment or reserve provi-sion expenses. A scenario based approach was used for uncertaintymodeling. Even though various sources of uncertainty could beincluded in the proposed model, the stochastic outages of gener-ating units and transmission lines were considered in the currentstudy. Expanding the model for inclusion of other sources of uncer-tainty could be a future work. Decisions drawn for the units’expansions and retirements were justified by analyzing the net-work under study. The simulation results revealed the efficientperformance of the developed model. It was shown that the rev-enue gained because of the retirement option could be remarkable,and it is greater in HLI compared to HLII since network constraintsimpose more restrictions on the problem. When the LDC of thesystem is smoother, the CC units become more beneficial sincetheir operating periods last longer. On the contrary, the OC gasunits are better options for short period operations as they havelower investment costs. The effect of the reliability constraint wasdemonstrated with simulations with various VOLLs. It was shownthat some portion of the generation expansion is due to the eco-nomic revenues and some is to preserve the system reliability levelwithin the desired range. Simulations illustrated that the congestedtransmission system could restrict the retirement options, partic-

the congested area. Moreover, numerical evidences verify that theretirement option becomes more beneficial with positive salvagevalues.

stems

A

A

E

EEFF

F

f

II

LLL

LLLMNNNNNNNOO

O

O

O

p

ppp

p

p

p

RrSS

Ss

s

Ttu

u

[

[[

[

[

[

[

[

[

[

[

[

[

[

Y. Tohidi et al. / Electric Power Sy

ppendix. List of symbols

ysbj element of network incidence matrix in year y in scenarios, 1 when bus b is the sending end bus of line j, −1 whenbus b is the receiving end bus of line j, and 0 otherwise

ESym expected energy supplied by energy limited unit m in yeary

ESm upper bound of EESym

ENSy expected energy not supplied in year yCy fuel cost in year yCn

ykfuel cost of new unit k in year y

Coybk

fuel cost of old unit k at bus b in year y

ybk flag indicating the retirement of old unit k at bus b in yeary

Cy investment cost in year yCn

ykinvestment cost of new unit k in year y

y peak load in year y

ybl load value in load level l at bus b in year ySybls load shedding (curtailment) in load level l at bus b in year

y in scenario sOLE loss of load expectation in reduced scenariosOLEs loss of load expectation in scenario sTk life time of new unit k

number of energy limited unitsB number of busesD number of load levelsLy number of lines in year ySy number of reduced scenarios in year yUn number of new candidate unitsUo number of old unitsUo

bnumber of old units at bus b

MCy operation and maintenance (O&M) cost in year yMFn

ykfixed O&M cost of new unit k in year y

MFoybk

fixed O&M cost of old unit k at bus b in year yMVn

ykvariable O&M cost of new unit k in year y

MVoybk

variable O&M cost of old unit k at bus b in year ylj capacity of line jnk capacity of new unit koybk capacity of old unit k at bus b in year yeylsm

continuous variable of power generation of energylimited unit m in load level l in year y in scenario s

lylsj

continuous variable of power flow of line j in load level lin year y in scenario s

nyblsk

continuous variable of power generation of new unit k inload level l at bus b in year y in scenario s

oyblsk

continuous variable of power generation of old unit k inload level l at bus b in year y in scenario s

Cy risk cost in year y interest rateCy salvage cost in year yCo

ybksalvage cost of old unit k at bus b in year y

My, SM system minutes index in year y and its upper boundtnysk

state of new unit k in year y in scenario stoybsk

state of old unit k at bus b in year y in scenario sC total cost of GERP problem

l duration of load level lnybk

binary decision variable of new unit k at bus b in year yoybk

binary decision variable for retirement of old unit k at busb in year y

[

[

Research 104 (2013) 138– 145 145

VOLLyb value of lost load at bus b in year yxj reactance of line jY planning horizonıybls voltage phase angle of bus b at load level l in year y and

scenario s�ys probability of scenario s in year y�, �fix standard deviation of LOLE and its predefined value

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