Energy Conversion and Management 51 (2010) 1230–1241

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Energy Conversion and Management

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Generation planning in Iranian power plants with fuzzy hierarchicalproduction planning

Reza Tanha Aminloei *, S.F. GhaderiDepartment of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 May 2009Accepted 28 December 2009

Keywords:Electricity generation planningFuzzy Hierarchical Production PlanningAnalytical Hierarchy Process

0196-8904/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.enconman.2009.12.034

* Corresponding author. Tel.: +98 09141490515; faE-mail address: ie_tanha@yahoo.com (R. Tanha Am

The Power Plants Generation Planning (PPGP) usually encountered complicated problems. In this paper, anew hierarchical approach is applied for generation planning in power plants. In hierarchical approach,the main integrated problem is separated into some sub problems which could be easily solved by multilevel models. Higher level models include organization total strategy and lower level models is concernedwith detailed accurate planning. When models are broken down into several levels, the solutions ofhigher level could be considered as inputs for the lower levels. In the proposed structure, amount offuture demand is predicted to specify time periods in first level. In the second level, amount of demandfor each aggregate period is allocated to different aggregate methods of electricity generation like; steam,gas, combined cycle and hydro power plants in Iran by using Analytical Hierarchy Process (AHP) andFuzzy Aggregate Production Planning (FAPP). This allocation is carried out according to two criteria of‘‘share of total electricity generated by each type of generation” and ‘‘amount of environmental pollu-tion”. AHP and Fuzzy Disaggregate Production Planning (FDAPP) are applied to determine best utilizingpower plants for generation in the final level. The proposed Fuzzy Hierarchical Production Planning(FHPP) outputs express optimal combination of power plants which contribute for demand satisfaction.

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1. Introduction treating them equally is that problems may be more or less rele-

Electricity production planning which is called generation plan-ning in Power Systems (PS) is divided into: long-terms, mid-termand short-term planning [1]. Planning and operating modern elec-tric PS involves several interlinked and complex tasks. Optimalproduction plan, however, is difficult optimization problem forthermal and hydro power plants, which obviously could be solvedwith proper computer tools.

Long-term energy generation planning is an issue of key impor-tance to the operation of electricity generation companies. It is em-ployed for strategic planning, budgeting, fuel acquisitions and soon to provide a framework for short-term energy generation plan-ning. A long-term planning period (assumed one year) is usuallysubdivided into shorter intervals of weeks or months, for whichparameters like load–duration curve should be predicted, and vari-ables as the expected energy generations of each plant unit mustbe optimized.

The problem of planning the production for the next 10–30 daysis known as the mid-term planning problem in PS management.Production planning problems with up to one week time horizonis known as short-term planning.

The short and mid-term planning problems could be consideredalike principally, except in some specific conditions, the reason not

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vant on variety of time horizons. Since uncertainty exists in predic-tion of electricity demand and also electricity price, the mid-termproblem can be made rough. On the other hand, the short-termmodel can be detailed due to the relatively good predictions thatcan be derived for the next few days. This high level of detail im-plies that a short-term model, in practice, can only implementone district heating system at a time.

Another purpose of the mid-term model is to model therestrictions that connect the different systems. The principalplanning procedure is solving the mid-term problem; outputsof the mid-term problem are used as the inputs to the short-termproblem.

Mathematical optimization algorithmic methods have beenused over the years for many PS planning, operation, and controlproblems. There are many uncertainties in PS problems becausePS are large, complex, and geographically widely distributed. Anoptimization problem is a mathematical model where main objec-tive is to minimize undesirable things (e.g. cost, energy loss, errors,etc.) or maximize desirable things (e.g. profit, quality, efficiency,etc.), subject to some constraints. The main advantages of algorith-mic methods include:

1. Optimality is mathematically rigorous in some algorithms.2. Problems can be formulated to take advantage of the existing

sparsity techniques applicable to large-scale PS.

R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241 1231

3. There are a wide range of mature mathematical programmingtechnologies, such as Linear Programming (LP) and QuadraticProgramming (QP), Nonlinear Programming (NLP), integer andmixed integer programming, Dynamic Programming (DP),et al. [2].

In spite of this advantage, in most of the mathematical optimi-zation production planning, the decisions are made at the sepa-rately models with different time horizon and without afeedback and hierarchical structure. It is important that the deci-sions made at an upper level of planning (long-term) be imposedto the lower level (short-term) as constraints. Also in real prob-lems, exact and sufficient detailed data don’t exist for short-termplanning. But it is possible providing exact data for long-term plan-ning. So upper level of planning is solved and its outputs are usedas a validation criterion for lower level outputs.

Production planning in the electricity industry and PPGP prob-lems are very complex with extensive features. Also, due to the spe-cific condition of respective product, electricity generation planningis mainly different from other production planning problems withspecific characteristics. Some of these characteristics are:

1. Not to be able to suppose the backorder state.2. Generating electricity in a specific period to use it in other peri-

ods in future is not directly possible.3. Considering specific characteristics and exclusive state of this

product, it requires flexible and specific generation planningwhich means it must generated more than predicted to satisfydemand.

An appropriate approach to alleviate this deficiency is to useFHHP by introducing imprecise/fuzzy data along with the soft con-straints, allowing some minor deviations from the outputs of theupper level while making a decision in the lower level.

A rigorous mathematical analysis of Hierarchical ProductionPlanning (HPP) is found in the pioneering work of [3]. Theoreticalwork on the topic has followed [4–6]. Nowadays HPP method isused as a structured method in various fields. In general the essen-tial advantages of using HPP approach are as follow [3]:

1. Planning process complexity decreases due to main problemdecomposition into a series of continuous sub problems. Solv-ing these sub problems is very simple and economical. In hier-archical approach, integrated problem is decomposed into subproblems that need very low calculation and computer mem-ory. Therefore, production planning problem solving is possiblein an acceptable time.

2. In integrated approach, whenever model parameters change dueto the disorders caused by internal or external manufacturingsystem, the planning problem should be solved once again.Whereas in HPP approach, these random events are graduallyabsorbed and considered without any requirement to solve allsub problems. It can be modified with some calculation effortsappropriated to influence of the mentioned events on planningproblem.

3. High levels in hierarchical structure use broad and aggregatedemand information. This aggregate forecasting are more accu-rate and simply to calculate than detailed forecasts which areused in an integrated model. Therefore, long term plans in hier-archical approach are more accurate than long term plans inintegrated models.

4. There is possibility of using proper decision making criteria in dif-ferent levels of hierarchical structure. In industrial applications,different criteria use in different management levels. For exam-ple, worker hire/layoff costs are usually considered in long termplanning level and start up costs are known for scheduling level.

5. In the lowest level of hierarchical approach, decisions for eachworkshop plant planning (operational planning) are usuallyperformed by workshop people. Higher levels of decision mak-ing for a factory or a department are made in the proper levelsof management hierarchical structure. This relationshipbetween management hierarchical structure and planning willbe lead to management and organization improvement.

6. One of the advantage characteristic of HPP comparing withintegrated approach is to have a feedback from lower levels tothe higher levels for updating input parameters. In rolling hori-zon approach, higher levels models are again solved by usingnew information that is generated from of lower levels. Thenoutcomes of higher levels are applied as constraints for lowerlevels. In this way production system will have the requiredability and flexibility to repel internal and external changes.

In previous studies for PS, there is very little attention to thehierarchical structure aspects of PS production planning. Also inprevious studies there are missing a proper updating feedback sys-tem for increasing reliability and developing performance of the PSproduction planning. A feedback system allows decision makersnot only to have a very flexible production plans but also to be ablerevise easily the model into different levels with the inputs like‘any unexpected events’, ‘upper manager decisions makers’ and‘actual data which is gained with time lapse’. Moreover in the pre-vious studies, objective functions are used in PS production plan-ning models were cost based and other criteria of powerproduction as environmental pollution, proportion of total capacityand so on, were not considered with economic criterion together.

The main purpose of this paper is to improve the performanceof the PS generation planning structure practically. A feedback sys-tem of FHPP is applied with multi objective functions for powerproduction planning. The imprecise input parameters along withsome soft constraints are introduced in the model formulation in-stead of using the crisp data and imposing hard constraints for pro-viding required consistency between decisions of different levels.The result of production plans through FHPP would be more feasi-ble and compatible in practice.

The rest of the paper is organized as follows: The relevant liter-ature is presented in Section 2. The overall structure of the pro-posed FHPP model along with the corresponding fuzzymathematical models is illustrated in Section 3. In Section 4, theproposed fuzzy HPP structure is elaborated applying appropriatestrategies and the associated fuzzy linear programming modelsare converted into the equivalent auxiliary crisp models. The pro-posed FHPP structure is implemented for a real PS in Iran. The casestudy and the obtained results as well as some managerial implica-tions are provided in Section 5. There is indicated that applyingFHPP as a new approach for PPGP, will conducted toward effectivestructured and efficient PS as concluding remarks in Section 6.

2. Background

Based on the main characteristics of the research problem, ex-plained in more details in the next section, the most relevant andrecent literature in three different but somewhat close streamsof: 1 – production planning in Power Systems, 2 – application ofmathematical optimization (algorithmic) methods in PS produc-tion planning problems and 3 – applications of fuzzy modeling inproduction planning are studied.

2.1. Production planning in PS

The long-term problem is a well-known stochastic optimizationproblem, as several of its parameters are only known as probability

1232 R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241

distributions, such as load, the availability of thermal units, hydro-genation and energy generations from renewable sources ingeneral.

Bloom and Gallant [7] proposed a linear model (with an expo-nential number of inequality constraints) and used an active setmethodology [8] to find the optimal way of matching the LDC ofa single interval using thermal units, in the presence of load-matching and other operational non-load-matching constraints.

The Bloom and Gallant model has been successfully extended tomulti-interval long-term planning problems, using the active-setmethod [9–11] column-generation methods or [12,13] column-generation methods. A quadratic model for formulating the long-term profit maximization of generation companies in a liberalizedmarket has been proposed [14] and column generation procedureshave been employed to solve it [15,16].

Mid-term planning does not frequently appear in the literature.However, the closely related short-term planning, which considerssimilar questions over a time horizon of up to one week, is wellknown. The most common version of the short-term planningproblem, also known as the Unit Commitment (UC) problem, con-siders planning of power producing units in a power grid.

Rong et al. [17] introduced in their paper the DRDP-RSC algo-rithm, which is a dynamic regrouping based (DP) algorithm basedon linear relaxation of the ON/OFF states of the units, sequentialcommitment of units in small groups. Their paper addresses theUC in multi-period Combined Heat Power (CHP) production plan-ning under the deregulated power market.

Currently, the solution approaches to UC of CHP systems arelimited to some general-purpose methods. The research followstwo lines. The first line applies decomposition techniques such asLagrangian Relaxation (LR) [18,19] and (DP) based algorithms[20–22]. The second line treats the overall problem as an entityand resorts to a general solver (possibly with some modifications)such as the Branch and Bound algorithm [23] for solving a MixedInteger Linear Programming (MILP) formulation of the problem.The application of simulation approaches [24,25] and artificialintelligent techniques such as genetic algorithms [26] should beplaced under this category. It is undoubted that the Interior PointMethod (IPM) [27] and the improvement of the formulation forthe UC problem [28] can also be applied to CHP systems. Youakim[29] presented necessary and sufficient conditions for the feasibil-ity of unit combinations that can be checked off-line that is, beforethe start of the UC algorithm, and thus before any economic dis-patches are performed, thereby rendering a very efficient unitscheduling algorithm in terms of computer memory and executiontime. Patra and Goswami [30] a dynamic programming techniquewith a fuzzy and simulated annealing based unit selection proce-dure proposed for the solution of the UC problem.

Jalilzadeh et al. [31] presented a new method with integrationof generation and transmission network reliability for the solutionof UC problem. Gomes and Saraiva [32] described the formulationsand the solution algorithms developed to include uncertainties inthe generation cost function and in the demand on DC OPF studies.The uncertainties are modeled by trapezoidal fuzzy numbers andthe solution algorithms are based on multi parametric linear pro-gramming techniques. Goransson and Johnsson [33] used a MixedInteger Programming (MIP) approach to determine the powerplant dispatch strategy which yields the lowest systems costs. Ku-mar and Naresh [34] an efficient optimization procedure based onReal Coded Genetic Algorithm (RCGA) proposed for the solution ofEconomic Load Dispatch (ELD) problem with continuous and non-smooth/nonconvex cost function and with various constraintsbeing considered.

For the solution of the corresponding optimization problems,several methods have been suggested and implemented, includingalgorithms based on branch-and-bound [35], dynamic program-

ming [36,37], Lagrangian relaxation [38–40] and genetic algo-rithms [41,42]. Surveys are given in [43,44].

2.2. Application of mathematical optimization in PS productionplanning problems

When the objective function and constraints are linear, this givesthe LP [45–47]. LP methods basically fall into two categories: sim-plex and Integer Programming (IP) methods [48–55]. A variety ofIP algorithms have been applied to a number of PS problems, e.g. eco-nomic dispatch, reactive power optimization, PS optimization, andetc. Both the simplex and IP methods can be extended to a linearand quadratic objective function when constraints are linear. Suchmethods are called QP [56,57]. LP has been used in various PS appli-cations, including PS optimal power flow [46], load flow [47], reac-tive power planning [58], active and reactive power dispatch [59,60].

When the objective function or the constraints are nonlinear, itforms NLP. IP methods originally developed for LP can be applica-ble to QP and NLP problem. NLP has been applied to various areasof PS [61], e.g. optimal power flow [62], hydrothermal scheduling[63], et al.

For many optimization problems (e.g. ON status = 1, and OFFstatus = 0), some of the independent variables can take only integervalues; such problem is called integer programming. When someof the variables are continuous, the problem is called mixed integerprogramming. Mainly two approaches, i.e. ‘branch-and-bound’,and ‘cutting plane methods’, have been used to solve integer prob-lems using mathematical programming techniques [64]. Integer/mixed integer programming has been applied to various areas ofPS, e.g. optimal reactive power planning [65], PS planning[66,67], UC [68], generation scheduling [69], etc. DP based on theprinciple of optimality states that a sub-policy of an optimal policymust in itself be an optimal sub-policy. DP has been applied to var-ious areas of PS, e.g. reactive power control [70], transmissionplanning [71], UC [72], etc. The literature review regarding theapplication of mathematical optimization in PS production plan-ning problems reveals the lack of using hierarchical and feedbackstructure in modeling PS production planning. Therefore, in thispaper we develop a novel FHPP model which to the best of ourknowledge, has not been addressed in the literature so far.

2.3. Applications of fuzzy modeling in production planning

Hsu and Wang [71] developed a possibilistic linear program-ming (PLP) model based on Lai and Hwang’s [73] approach todetermine appropriate strategies regarding the safety stock levelsfor assembly materials, regulating dealers’ forecast demands andnumbers of key machines in an assemble-to order environment.Fung et al. [74] presented a Fuzzy Multi-product Aggregate Produc-tion Planning (FMAPP) model to cater different scenarios undervarious decision-making preferences by applying integrated para-metric programming and interactive methods. Wang and Liang[75] developed a fuzzy multi-objective linear programming modelwith piecewise linear membership function to solve multi-productAggregate Production Planning (APP) problems in a fuzzy environ-ment. In another research work, they [76] presented an interactivepossibilistic linear programming model using Lai and Hwang’s [73]approach for solving the multi-product aggregate production plan-ning problem with imprecise forecast demand, related operatingcosts and capacity. Moreover, in mid-term supply chain planningdomain, Torabi and Hassini [77] presented a novel multi-objectivepossibilistic mixed integer linear programming model for a SupplyChain Master Planning (SCMP) problem consisting of multiple sup-pliers, one manufacturer and multiple distribution centers whichintegrates the procurement, production and distribution aggregateplans considering various conflicting objectives simultaneously as

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well as the imprecise nature of some critical parameters such asmarket demands, cost/time coefficients and capacity levels. In an-other research work [78], the authors extended the above model tomulti-site production environments and proposed an interactivefuzzy goal programming solution approach for the problem. Otherrelevant literature may include [79–82]. For a recent review of dif-ferent approaches for dealing with uncertainty in production plan-ning problems especially HPP approach, the interested reader isreferred to [83].

The proposed FHPP which has been stimulated by a real indus-trial case of an Iranian power network is consisted of three deci-sion-making levels. Monthly consumption of the coming year isforecasted in the first level. In second level, forecasted demand isallocated to different methods of electricity generation for anaggregate period. Structure of the proposed Fuzzy AggregateProduction Planning (FAPP) model could be considered as a fuzzylinear programming model which generates an optimal productionplan to satisfy the aggregate forecasted demands of electricity. Theoutputs of this model are comprised of production, amount of un-saved energy unmet reserve requirements, amount of capacity thata zone has reserved for other zone and transit power between twozones at the seasonal period. The two objectives functions are: 1 –minimizing the cost of electricity generation by different methodsof generation and 2 – maximizing the total preference weights ofprojects that are calculated by AHP. In the third level, similar mod-el is applied to determine the production plan at the monthlyperiods.

3. The proposed FHPP model

Because of insufficient or inaccessible data and also the infor-mation acquiring high costs, the modeling parameters for PPGPare usually imprecise in real world. In other words competitivemarket persuades managers to implement precise and reliable pro-duction plans which could not be achieved with inaccurate andfuzzy market data. Also implementation of production plans withimprecise crisp data and crisp models is very difficult. This is oneof the main motivations of this study as fuzziness. This made theobtained results from the proposed FHPP to be more accurate, reli-able and increase the efficiency of production planning. So it willbe convenient to obtain production planning model that couldhandle fuzzy and uncertain data from the market. Fuzzy con-straints should be used to increased efficiency and compatibilityamong different levels of planning. Hence more optimal and feasi-ble results could be obtained.

Fig. 1. Hierarchical structu

Integrated problem of PPGP is divided into three total levels of:1 – demand level, 2 – aggregate level and 3 - disaggregate or allo-cation level Fig. 1.

3.1. First level

The demand forecasting method presented by [84] is applied inthis study. The amount of demand is forecasted for planning thenan optimal planning model is developed to satisfy the demand.

3.2. Second level

The forecasted demand in the first level is allocated to differentaggregate methods of electricity generation for an annual aggre-gate period. Different methods of electricity generation can be di-vided into different features. For example we can divide them inaccordance with technology applied such as Fossil, Nuclear, Com-bine cycle, Small hydro, big hydro, Micro hydro, Wind turbine,PV, Mono crystalline, Multi crystalline and Geothermal. As someof these technologies are not employed in Iran, the most commontechnologies of 1 – Gas, 2 – Steam, 3 – Combine Cycle, 4 – Hydroare considered for electricity generation.

3.2.1. Mixed method of AHP with FAPPAHP is applied to obtain total preference weights for each meth-

od of electricity generation in Iran using Expert Choice software.Then FAPP is applied to maximize total preference weights fordetermining best combination generation method for satisfyingdemand in Iran by using Lingo software for solving the model(Fig. 2).

3.2.2. Assigning score to each generation methodFor each methods of electricity generation in Iran (Gas, Steam,

Combine Cycle and Hydro) a score is given. Two criteria are usedfor scoring each generation method:

1. Amount of environmental pollutions in production procedureincluding SO2, NOx and CO2.

2. The share of each method capacity comparing to total capacity.

Considering defined criteria a score is assigned to each genera-tion method. Forecasted aggregate seasonal demand for the nextyear is assigned to the different methods of generation by applyingheuristic mathematical model. Mentioned criteria are used to rankdifferent methods, in a hierarchical structure (Fig. 3).

re of problem solving.

Net data

AHP

The determined weight of each generation method

FAPP

Amount of generation for each method

Fig. 2. Mixed method of analytical hierarchy process with fuzzy aggregateproduction planning.

Fig. 3. Hierarchical structure for ranking of production methods.

1234 R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241

3.2.3. FAPP of proposed structure to electricity generation planningThe proposed FAPP model is used to provide an optimal aggre-

gate production plan. It can then satisfy the dynamic demands ofelectricity over a given mid-term planning horizon involving out-puts mentioned. The main characteristics and assumptions consid-ered in the FAPP formulation are as follows:

� A four-power plant situation is considered.� There is a seasonal period planning horizon.� Forecasted demand in period ts of zone z and also peak demand

in zone z are assumed fuzzy.� Reliability and balance constraints are assumed fuzzy.

The indices, parameters and variables used to formulate theFAPP model are:

Indices

i Index of aggregate power plant families ði ¼ 1; . . . ;4Þ ts Index of aggregate time periods ðts ¼ 1; . . . ;4Þ z; zp Index of electricity zones of Iran ðz; zp ¼ 1; . . . ;15Þ

Parameters

FCðz; iÞ Fuel cost of power plant i in zone z (Rial/MW) OMðz; iÞ Variable operation and maintenance costs of power plant i

in zone z (Rial/MW)

UE cos tðzÞ Unsaved energy cost per outage (MW) in zone z (Rial/

MW)

UM cos t Unmet reserve requirements cost per MW (Rial/MW) Wzi Total preference weights of projects that are calculated by

AHP (constant)

eDðts; zÞ Electricity demand in zone z in period ts (MW)

eDpeakðzÞ

Peak electricity demand in zone z of next year (MW)

PGLossðz; iÞ

Inner consumption factor of power plant i in zone z (%) PGinitðz; iÞ Total nominal power of power plants i in zone z (MW) PFLossðz; zpÞ Loss percentage between two zones (%) PFinitðz; zpÞ Initial capacity for lines between two zones (MW) Cosh Coefficient of line power that is allocated to active flow (%) RESTHMðz; iÞ Bound of reserve for power plant i in zone z (%)

Variables

PGðts; z; iÞ Production amount of power plant i in zone z and in period

ts (MW)

PFðts; z; zpÞ Transitive power between two zones and in period ts (MW) FMaxðz; zpÞ Capacity that a zone has reserved for other zone (MW) UMðzÞ Unmet reserve requirements in zone z (MW) UEðts; zÞ Unsaved energy in zone z and in period ts (MW)

Based on the above notations, the FAPP model is formulated asfollows:

X4 X15 X4 X4

Min Z1 ¼ts¼1 z¼1 i¼1

PGðts; z; iÞ � ½OMðz; iÞ þ FCðz; iÞ� þts

�X15

z¼1

½UEðts; zÞ � UE cos tðzÞ� þX15

z¼1

UMðzÞ � UM cos t ð1Þ

Max Z2 ¼X4

ts¼1

X15

z¼1

X4

i¼1

Wzi � PGðts; z; iÞ

s:t: PGðts; z; iÞ 6 PGinitðz; iÞ � ð1� PGLossðz; iÞÞ8ts; z; i ð2Þ

PFðts; z; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8ts; z; zp ð3ÞFMaxðz; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8z; zp ð4ÞX4

i¼1

PGinitðz; iÞ � ð1� PGLossðz; iÞÞ1þ RESTHMðz; iÞ

þX15

zp¼1

fFMaxðzp; zÞ � ð1� PFLossðzp; zÞÞg þ UMðzÞ

~PX15

zp¼1

FMaxðz; zpÞ þ eDpeakðzÞ 8z ð5Þ

X4

i¼1

PGðts; z; iÞ þ UEðts; zÞ þX15

zP¼1

PFðts; zp; zÞ

� ð1� PFLossðzp; zÞÞ ffi eDðts; zÞ

þX15

zp¼1

PFðts; z; zpÞ 8ts; z ð6Þ

PGðts; z; iÞ;UEðts; zÞ; FMaxðz; zpÞ; PFðts; z; zpÞ;UMðzÞP 08ts; z; zp; i ð7Þ

3.2.3.1. Objective functions. Minimizing the cost of electricity gener-ation by different methods of generation is considered as the firstobjective, and the second objective function is to maximize the to-tal preference weights of projects which are calculated by AHP.

3.2.3.2. Constraints. For each period, the following constraints areconsidered:

(A) The power plant generation capacity constraints (2)

Production amount of power plant i in zone z and in period ts

should not be greater than amount of total nominal power ofpower plants i in zone z.

Ranking of power plants that produce electricity by a same method

Efficiency Power plant activity in year

Dmnd Rey Bushehr Mashhad Shiraz Lushon

Fig. 5. Hierarchical structure for ranking of power plants that produce electricity bya same method.

R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241 1235

(B) The transmission lines capacity constraints (3)

The amount of exchange that can be transit between two zonesis smaller or equal to installed lines capacity between two zones.

(C) The reserve exchange capacity constraints (4)

In the peak hour, each zone can make part of its capacity as re-serve for other zone named reserve capacity. According to reservedcapacity should be smaller than initial capacity of transmissionlines between two zones. It is necessary to be guaranteed with aconstraint.

(D) The reliability constraints (5)

Reliability constraints guarantee the existence of a suitable re-serve bound between installed capacity and peak period demand.

(E) The Balance constraints (6)

Load balance forces that supply and demand be equal in eachperiod.

3.3. Third level

In this level monthly demand forecasted in the first level is allo-cated to different power plants by using allocation level algorithm.This algorithm is as follows:

3.3.1. Mixed method of AHP with FDPPAHP is applied to obtain total preference weights for each

power plant by using Expert Choice software. Then FDPP is appliedto maximize total preference weights for determining best combi-nation of power plants for satisfying demand in Iran by using Lingosoftware for solving the model (Fig. 4).

3.3.2. Ranking of power plants that produce electricity by a samemethod

For power plants ranking is used of AHP method similar Fig. 5.Two criteria are used for scoring each power plant:

� Efficiency of different power plants.� Power plant activity in year.

After ranking of different power plants by mentioned method,the forecasted monthly demand for a season of the next year is sat-isfied with allocation to the power plants; by using FDPP.

Net data

AHP

The determined weight of each power plant

FDPP

Amount of generation for each power plant

Fig. 4. Mixed method of analytical hierarchy process with fuzzy disaggregateproduction planning.

3.3.3. FDPP of proposed structure for electricity generation planningThe aggregate production plan generated by FAPP model can-

not be implemented in practice because of its aggregate natureregarding both the power plants and time periods. Therefore,in order to develop a detailed production plan, it has to bedisaggregated to provide a master production plan (MPS). Todo so, another fuzzy linear programming model (FDPP) is pro-posed in which its main assumptions and structure are similarto those of FAPP model. FDPP model must be solved separatelyfor each period of FAPP model. It means that we should solveone FDPP model for each season of the year. For example, wesolved FDPP model for autumn (ts = 3). The main characteristicsand assumptions considered in the FDPP formulation are asfollows:

� There is a three-period planning horizon that each period is amonth.

� Forecasted demand in period tm of zone z and peak demand inzone z are assumed fuzzy.

� Reliability and balance constraints and forced constraints (14–16) of aggregate planning level are assumed fuzzy.

The indices, parameters and variables used to formulate theFAPP model are as follows:

Indices

i Index of aggregate power plant families ði ¼ 1; . . . ;4Þ ts Index of aggregate time periods ðts ¼ 1; . . . ;4Þ z; zp Index of Electricity zones of Iran ðz; zp ¼ 1; . . . ;15Þ k Index of Disaggregate power plant ðk ¼ 1; . . . ;niÞ tm Index of Disaggregate period ðtm ¼ 1; . . . ;3Þ

Parameters

FCðz; i; kÞ Fuel cost of power plant k of i family in zone z (Rial/MW) OMðz; i; kÞ Variable operation and maintenance costs of power plant

k of i family in zone z (Rial/MW)

UE cos tðzÞ Unsaved energy cost per outage (MW) in zone z (Rial/

MW)

UM cos t Unmet reserve requirements cost per MW (Rial/MW) Wzik Total preference weights of power plant k of i family that

are calculated by AHP (constant)

eDðtm; zÞ Electricity demand per zone for per season of next year

(MW)

eDpeakðzÞ Peak electricity demand per zone of next year (MW)

PGLossðz; i; kÞ

Inner consumption factor of power plant k of i family inzone z (%)

PGinitðz; i; kÞ

Total nominal power of power plants k of i family in zonez (MW)

PFLossðz; zpÞ

Loss percentage between two zones (%) PFinitðz; zpÞ Initial capacity for lines between two zones (MW) Cosh Coefficient of line power that is allocated to active flow

(%)

1236 R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241

RESTHMðz; i; kÞ

Bound of reserve for power plant k of i family in zone z(%)

Variables

PGðtm; z; i; kÞ Production amount of power plant k of i family in zone z

and in period tm (MW)

PFðtm; z; zpÞ Transitive power between two zones and in period tm

(MW)

FMaxðz; zpÞ Capacity that a zone has reserved for other zone (MW) UMðzÞ Unmet reserve requirements in zone z (MW) UEðtm; zÞ Unsaved energy in zone z and in period tm (MW)

Based on the above notations, the FAPP model is formulated asfollows:

Min Z1 ¼X3

tm¼1

X15

z¼1

X4

i¼1

Xni

k¼1

PGðtm;z; i;kÞ� ½OMðz; i;kÞþ FCðz; i;kÞ�

þX3

tm¼1

X15

z¼1

½UEðtm;zÞ�UEcos tðzÞ� þX15

z¼1

UMðzÞ�UM cos t

MaxZ2 ¼X3

tm¼1

X15

z¼1

X4

i¼1

Xni

k¼1

Wzik�PGðtm;z; i;kÞ ð8Þ

s:t: PGðtm;z; i;kÞ6 PGinitðz; i;kÞ� ð1�PGLossðz; i;kÞÞ 8tm;z; i;k ð9ÞPFðtm;z;zpÞ6 PFinitðz;zpÞ� ð1� PFLossðz;zpÞÞ�Cosh

8tm;z;zp ð10ÞFMaxðz;zpÞ6 PFinitðz;zpÞ� ð1� PFLossðz;zpÞÞ�Cosh

8z;zp ð11ÞX4

i¼1

Xni

k¼1

PGinitðz; i;kÞ� ð1� PGLossðz; i;kÞÞ1þRESTHMðz; i;kÞ

þX15

zp¼1

fFMaxðzp;zÞ� ð1�PFLossðzp;zÞÞg

þUMðzÞ ~PX15

zp¼1

FMaxðz;zpÞþ eDpeakðzÞ 8z ð12Þ

X4

i¼1

Xni

k¼1

PGðtm;z; i;kÞþUEðtm;zÞ

þX15

zP¼1

PFðtm;zp;zÞ� ð1� PFLossðzp;zÞÞ ffi eDðtm;zÞ

þX15

zp¼1

PFðtm;z;zpÞ

8tm;z ð13ÞX3

tm¼1

Xni

k¼1

PGðtm;z; i;kÞ ~PPGðts;z;zpÞ 8z; i; ts ¼ 3 ð14Þ

X3

tm¼1

PFðtm;zp;zÞ ~PPFðts;zp;zÞ 8z;zp; ts ¼ 3 ð15Þ

X3

tm¼1

UEðtm;zÞ ~PUEðts;zÞ 8z; ts ¼ 3 ð16Þ

PGðtm;z; i;kÞ; UEðtm;zÞ; FMaxðz;zpÞ; PFðtm;z;zpÞ; UMðzÞP 0 8tm;z;zp; i;k ð17Þ

3.3.3.1. Objective functions. Minimizing the cost of electricity gener-ation by different power plants is considered as the first objective,and the second objective function is to maximize the total prefer-ence weights of power plants which are calculated by AHP.

3.3.3.2. Constraints. For each period, the following constraints areconsidered:

(A) The power plant generation capacity constraints (9)

Production amount of power plant k of i family in zone z and inperiod tm should not be greater than amount of total nominalpower of power plants k of i family in zone z.

(B) The transmission lines of capacity constraints (10)

The amount of exchange that can be transit between two zonesis smaller or equal to installed lines capacity between two zones.

(C) The reserve exchange of capacity constraints (11)

In the peak hour, each zone can make part of its capacity as re-serve for other zone named reserve capacity. According to reservedcapacity should be smaller than initial capacity of transmissionlines between two zones. It is necessary to be guaranteed with aconstraint.

(D) The reliability constraints (12)

Reliability constraints guarantee the existence of a suitable re-serve bound between installed capacity and peak period demand.

(E) The Balance constraints (13)

Load balance forces that supply and demand be equal in eachperiod.

(F) Forced constraints of aggregate planning level (14)–(16)

The solution of a higher level represents a constraint to be im-posed on the lower level and thus, decisions at each level consti-tute a chain. Moreover, in the HPP problem, solutions of higherlevel consider as inputs of the lower level. Hence it is importantto create suitable compatibility among the levels of HPP. Crisp con-straints reduce flexibility of HPP problems and the probability ofhaving feasible solution in any level. Whereas by using fuzzy con-straints, flexibility of HPP problems increases and it sets a suitablecompatibility between the levels and the probability of having fea-sible solution for the problem [85].

4. Solution procedure

In order to reach a preferred solution for the proposed FHPPstructure, the associated mathematical programming modelsshould be converted into the equivalent crisp ones. In this regard,three main stages are considered as the solution procedure for theproposed FHPP as follows:

� Converting the FAPP model into its equivalent auxiliary crispmodel.

� Converting the FDPP into its equivalent auxiliary crisp model.� Applying an interactive fuzzy programming solution algorithm

to obtain the final preferred solution.

4.1. Formulating the FAPP as an auxiliary crisp model

In order to solve the FAPP model, it should be transformed to anauxiliary crisp model. To do so, we present efficient strategies forconverting the fuzzy objective function and soft constraints intoequivalent crisp equations.

4.1.1. Treating the objective functions of FAPPSince all the coefficients in the objective functions are crisp, it is

sufficient that the multi objective FAPP model be converted into anequivalent single-objective FAPP model.

( )yzst

D⎟⎠⎞⎜⎝

⎛ ,μ

( )ztp

sD , ( )ztm

sD , ( )zto

sD ,

1

Fig. 6. The triangular possibility distribution of fuzzy parameter eDðts ;zÞ .

cμ

a

pb − b pb +

1

Fig. 7. A preference-based membership function of soft equation a ffi b.

R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241 1237

In linear programming for converting the MOLP model into anequivalent single-objective LP model should calculate an aspira-tion level for each objective function and define new objectivefunction based on our minimizing or maximizing objectivesfunction. Then primary objective functions along with free vari-ables and aspiration levels should define as additional con-straints in model [86].

First objective ðZ1Þ is minimizing the cost of electricity genera-tion by different power plants. Aspiration level for Z1 is consideredas follow:A = total annual load �minimum production cost

In other words, all production methods are assumed withminimum production cost. Then two non-negative variables ðd1

and d2Þ are considered in the first objective function as thefollowing:

Z1 þ d1 � d2 ¼ A ð18Þ

Second objective ðZ2Þ is maximizing the total preference weights ofpower plants that are calculated by AHP. Aspiration level for Z1 isconsidered as the following:B = total annual load �maximum prefer-ence weight

In other words, is assumed that total load has been producedwith method which has highest preference. Then two non-negativevariables ðd3 and d4Þ are considered in first objective function asthe following:

Z2 þ d3 � d4 ¼ B ð19Þ

According to the relation of (18), to minimize Z1; d2 should be min-imized. Also according to the relation of (19), to maximize Z2; d3

should be minimized. Therefore we should minimize Z ¼ d2 þ d3

for FAPP problem also consider Eqs. (18) and (19) as constraint inFAPP problem. The new single-objective function defined for FAPPproblem is as the following:

Min Z ¼ d2 þ d3 ð20Þ

Therefore problem is transformed into a FAPP problem with the sin-gle-objective function.

4.1.2. Treating the soft constraintsDue to incompleteness and/or unavailability of required data

over the mid-term decision horizon, the environmental dataand operational parameters are typically uncertain and imprecise(fuzzy) in nature. Therefore, Forecasted demand in period tm ofzone z and peak demand in zone z are assumed to be fuzzynumbers characterized by triangular possibility distribution.These triangular possibility distributions which are determinedusing both objective and subjective data; are the most commontool for modeling the ambiguous parameters due to their com-putational efficiency and simplicity in data acquisition (forexample, see [76–78]). Generally, a possibility distribution canbe stated as the degree of occurrence of an event with imprecisedata. Fig. 6 represents the triangular possibility distribution of

imprecise parameter can be symbolized as eDðts; zÞ ¼ Dpðts ;zÞ;

�Dmðts ;zÞ;D

oðts ;zÞÞ, where Dp

ðts ;zÞ;Dmðts ;zÞ and Do

ðts ;zÞ are the most pessimistic

value and the most optimistic value of eDðts ;zÞ estimated by thedecision maker. The other fuzzy data can be modeled in thesame manner in which:

eDpeakðzÞ ¼ DppeakðzÞ;D

mpeakðzÞ;D

opeakðzÞ

� �

To resolve the vagueness of constraints (5) and (6) which permitthese constraints to be satisfied as much as possible, they can bemodeled by the preference-based membership functions. For exam-ple, a typical membership function of soft equation a ffi b with tol-erance p has been depicted in Fig. 7.

X4

i¼1

PGðts; z; iÞ þ UEðts; zÞ þX15

zP¼1

PFðts; zp; zÞ � ð1� PFLossðzp; zÞÞ

�X15

zp¼1

PFðts; z; zpÞ ¼ Aðts ;zÞðxÞ 6 eDðts; zÞ þ p1ðts ;zÞ; 8ts; z ð21Þ

and

X4

i¼1

PGðts; z; iÞ þ UEðts; zÞ þX15

zP¼1

PFðts; zp; zÞ � ð1� PFLossðzp; zÞÞ

�X15

zp¼1

PFðts; z; zpÞ ¼ Aðts ;zÞðxÞP eDðts; zÞ � p1ðts ;zÞ; 8ts; z ð22Þ

The inequality relation of Eq. (5) can be constructed in the sameway:

X4

i¼1

PGinitðz; iÞ � ð1� PGLossðz; iÞÞ1þ RESTHMðz; iÞ þ

X15

zp¼1

fFMaxðzp; zÞ

� ð1� PFLossðzp; zÞÞg þ UMðzÞ �X15

zp¼1

FMaxðz; zpÞ

¼ BðzÞðxÞP eDpeakðzÞ � p2ðts ;zÞ; 8Z ð23Þ

where the p1ðts ;zÞ and p2

ðts ;zÞ denote the associated allowabletolerances.

Regarding the constraints (21)–(23), we should now comparethe fuzzy right-hand sides with the crisp left-hand sides. An effi-cient approach to deal with such fuzzy constraints is to convertthem to their equivalent crisp ones by obtaining crisp representa-tive numbers for the corresponding fuzzy right-hand sides. To doso, we apply the well-known weighted average method [76,87]and [78]. This approach seems to be the simplest and most reliabledefuzzification method in converting the fuzzy constraints intotheir crisp ones. In this regard, we also need to determine a mini-mal acceptable possibility level, b which denotes the minimumacceptable possibility level of occurrence for the correspondingimprecise/fuzzy data. So, the equivalent auxiliary crisp constraintscan be represented as follows:

Aðts ;zÞðxÞ6w1Dpðts ;zÞ;bþw2Dm

ðts ;zÞ;bþw3Doðts ;zÞ;b�p1

ðts ;zÞ; 8 ts;z ð24ÞAðts ;zÞðxÞP w1Dp

ðts ;zÞ;bþw2Dmðts ;zÞ;bþw3Do

ðts ;zÞ;b�p1ðts ;zÞ; 8 ts;z ð25Þ

BðzÞðxÞP w1Dppeak;bðzÞþw2Dm

peak;bðzÞþw3Dopeak;bðzÞ�p2

ðts ;zÞ; 8 Z ð26Þ

where w1 þw2 þw3 ¼ 1, and w1;w2 and w3 represent the weightsof the most pessimistic, the most possible and the most optimisticvalue of the related fuzzy demands, respectively. In practice, the

1238 R. Tanha Aminloei, S.F. Ghaderi / Energy Conversi

suitable values for these weights as well as b are usually deter-mined subjectively by the experience and knowledge of the deci-sion maker. Based on the concept of the most likely valuesproposed by [73] and considering several relevant works [76,87]and [78] we set these parameters to: w2 ¼ 4=6;w1 ¼ w3 ¼ 1=6and b ¼ 0:05 in our numerical experiments.

4.2. Formulating the FDPP as an auxiliary crisp model

Recalling the FDPP model, regarding the objective functions (8)along with the constraints (12) up to (16), we can apply the sameapproaches as used in the FAPP model.

4.3. Applying an interactive solution algorithm

In the previous section, we described that how the original FAPPand FDPP models could be replaced with an equivalent crisp sin-gle-objective LP model, respectively. Generally, to solve the LPmodels, there are different techniques in the literature amongthem; the fuzzy programming approaches are being increasinglyapplied due to their ability in determining the satisfaction degreeof each objective function explicitly. Thus, the decision makercan take her/his final decision by choosing a preferred efficientsolution according to the satisfaction degree and preference (rela-tive importance) value of each objective function. Here, we proposean interactive solution algorithm for implementation of the pro-posed FHPP as follows:

Step 1: Determine appropriate triangular possibility distributionsfor the imprecise parameters and formulate the FAPP andFDPP models.

Step 2: Transform the FAPP model into its equivalent singleobjective LP crisp model.

Step 3: Transform the FDPP model into its equivalent singleobjective LP crisp model.

Step 4: Solving the above-mentioned crisp models.

To solve the single-objective APP model is used of the Warnerfuzzy programming method as follows:

I. Suppose that ZU is the high bound of objective functionwhich has gained of below model (APP) solving:

Min ZU ¼ d2 þ d3 ð27Þ

S:t:X4

ts¼1

X15

z¼1

X4

i¼1

PGðts; z; iÞ � ½OMðz; iÞ þ FCðz; iÞ�

þX4

ts

X15

z¼1

½UEðts; zÞ � UE cos tðzÞ� þX15

z¼1

UMðzÞ

� UM cos t þ d1 � d2 ¼ A ð28ÞX4

ts¼1

X15

z¼1

X4

i¼1

Wzi � PGðts; z; iÞ þ d3 � d4 ¼ B ð29Þ

PGðts; z; iÞ 6 PGinitðz; iÞ � ð1� PGLossðz; iÞÞ 8ts; z; i ð30ÞPFðts; z; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh8ts; z; zp ð31Þ

FMaxðz; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh8z; zp ð32Þ

Aðts ;zÞðxÞ 6 w1Dpðts ;zÞ;b þw2Dm

ðts ;zÞ;b þw3Doðts ;zÞ;b 8ts; z ð33Þ

Aðts ;zÞðxÞP w1Dpðts ;zÞ;b þw2Dm

ðts ;zÞ;b þw3Doðts ;zÞ;b 8ts; z ð34Þ

BðzÞðxÞP w1Dppeak;bðzÞ þw2Dm

peak;bðzÞ þw3Dopeak;bðzÞ 8Z ð35Þ

PGðts; z; iÞ;UEðts; zÞ; FMaxðz; zpÞ; PFðts; z; zpÞ;UMðzÞP 08ts; z; zp; i ð36Þ

II. Suppose that ZL is low bound of objective function which has

gained of below model (APP) solving:

on and Management 51 (2010) 1230–1241

Min ZL ¼ d2 þ d3 ð37Þ

S:t:X4

ts¼1

X15

z¼1

X4

i¼1

PGðts; z; iÞ � ½OMðz; iÞ þ FCðz; iÞ�

þX4

ts

X15

z¼1

½UEðts; zÞ � UE cos tðzÞ� þX15

z¼1

UMðzÞ

� UM cos t þ d1 � d2 ¼ A ð38ÞX4

ts¼1

X15

z¼1

X4

i¼1

Wzi � PGðts; z; iÞ þ d3 � d4 ¼ B ð39Þ

PGðts; z; iÞ 6 PGinitðz; iÞ � ð1� PGLossðz; iÞÞ 8ts; z; i ð40ÞPFðts; z; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8ts; z; zp ð41ÞFMaxðz; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8z; zp ð42ÞAðts ;zÞðxÞ 6 w1Dp

ðts ;zÞ;b þw2Dmðts ;zÞ;b þw3Do

ðts ;zÞ;b þ p1ðts ;zÞ

8ts; z ð43ÞAðts ;zÞðxÞP w1Dp

ðts ;zÞ;b þw2Dmðts ;zÞ;b þw3Do

ðts ;zÞ;b � p1ðts ;zÞ

8ts; z ð44ÞBðzÞðxÞP w1Dp

peak;bðzÞ þw2Dmpeak;bðzÞ þw3Do

peak;bðzÞ � p2ðts ;zÞ

8Z ð45ÞPGðts; z; iÞ;UEðts; zÞ; FMaxðz; zpÞ; PFðts; z; zpÞ;UMðzÞP 08ts; z; zp; i ð46Þ

III. Determine of membership function for the objective func-tion and constraints of APP.

Membership function for objective function is defined asfollows:

lZðd2 þ d3Þ ¼1 if d2 þ d3 < ZLd2þd3�ZL

ZU�ZLif ZL 6 d2 þ d3 6 ZU

0 if d2 þ d3 > ZU

8><>: ð47Þ

Membership functions for constraints (24)–(26) are defined asfollows:

If: w1Dpðts ;zÞ;b þw2Dm

ðts ;zÞ;b þw3Doðts ;zÞ;b ¼ M

If: w1Dppeak;bðzÞ þw2Dm

peak;bðzÞ þw3Dopeak;bðzÞ ¼ N

l1Dðts ;zÞðAðts ;zÞðxÞÞ

¼

1 if Aðts ;zÞðxÞ < MMþp1

ðts ;zÞ�Aðts ;zÞðxÞ

p1ðts ;zÞ

if M 6 Aðts ;zÞðxÞ 6 M þ p1ðts ;zÞ

0 if Aðts ;zÞðxÞ > M þ p1ðts ;zÞ

8>>><>>>:

ð48Þ

l2Dðts ;zÞðAðts ;zÞðxÞÞ

¼

1 if Aðts ;zÞðxÞ > MAðts ;zÞðxÞ�M�p1

ðts ;zÞp1ðts ;zÞ

if M � p1ðts ;zÞ 6 Aðts ;zÞðxÞ 6 M

0 if Aðts ;zÞðxÞ < M � p1ðts ;zÞ

8>>><>>>:

ð49Þ

lDpeakðzÞðBðzÞðxÞÞ

¼

1 if BðzÞðxÞ > NBðzÞðxÞ�N�p2

ðts ;zÞp2ðts ;zÞ

if N � p2ðts ;zÞ 6 BðzÞðxÞ 6 N

0 if BðzÞðxÞ < N � p2ðts ;zÞ

8>>><>>>:

ð50Þ

R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241 1239

IV. Having membership functions for fuzzy constraints andobjective function, the APP problem can be transformed intoa crisp optimization system as follows:

Maxk ð51ÞS:t: k 6 lZðd2 þ d3Þ ð52Þ

k 6 l1Dðts ;zÞðAðts ;zÞðxÞÞ 8ts; z ð53Þ

k 6 l2Dðts ;zÞðAðts ;zÞðxÞÞ 8ts; z ð54Þ

k 6 lDpeakðzÞðBðzÞðxÞÞ 8z ð55ÞPGðts; z; iÞ 6 PGinitðz; iÞ � ð1� PGLossðz; iÞÞ 8ts; z; i ð56ÞPFðts; z; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8ts; zp; z ð57ÞFMaxðz; zpÞ 6 PFinitðz; zpÞ � ð1� PFLossðz; zpÞÞ � Cosh

8z; zp ð58ÞPGðts; z; iÞ;UEðts; zÞ; FMaxðz; zpÞ; PFðts; z; zpÞ;UMðzÞP 08ts; z; zp; i ð59Þ

0 6 k 6 1 ð60ÞTo solve the single-objective DPP model is used of the Warner fuzzyprogramming method similar above manner.

Step 5: To solve the above-mentioned crisp models for APP andDPP, the required parameters including the minimalacceptable level of satisfaction of soft constraints, a, theminimal acceptable possibility degree of imprecise data, band also the tolerances of soft constraints, should be givenby the decision maker. Moreover, if the decision maker issatisfied with the current efficient compromise solution,stop. Otherwise, provide another efficient solution bychanging the value of some controllable parameters say aand b.

5. Implementation of FHPP model for electricity generationplanning in Iran

The proposed model has been implemented for Iran using Ira-nian Electricity Industry Statistic, energy balance of Iran and Tava-

Table 1Amount of power plants production in each month of autumn season of next year.

Steam power plants (i = 1) in zone = 1 Power plants pro

October ðtm ¼ 1Þ

k1 142.1482 0

Gas power plants (i = 2) in zone = 11 63.4242 0.1323 99.7

Combine cycle power plants (i = 3) in zone = 11 02 0

Hydro power plants (i = 4) in zone = 11 21.312 3.1563 12.987. . . . . ..

Steam power plants (i = 1) in zone = 151 0

Gas power plants (i = 2) in zone = 151 96.8062 0

Combine cycle power plants (i = 3) in zone = 151 402.4986

Hydro power plants (i = 4) in zone = 151 0

nir Co. data by using Lingo version 8 software. The output of themodel is presented in a table that illustrates the amount of eachpower plant production monthly. In Table 1 the amount of powerplants production has been presented briefly only for each monthin autumn. The results indicate a very close relation between thereal load trend and our model outputs.

The advantages of the addressed new approach (FHPP) are asfollow:

� Attention to the hierarchical structure aspects of PS productionplanning.

� The proposed model decrease complexity of problem using dis-aggregation of the problem to different levels.

� The proposed model is a proper updating feedback system forincreasing reliability and developing performance of the PS pro-duction planning.

� By applying proposed approach PS production planning problemwill be solved in less time and with less computer memory.

� FHPP is very consistent with changes, due to its high flexibility.� Weakness of using imprecise data is solved appropriately by

fuzzy theory and increased reliability of model’s solutions.� Accurate planning is done and blackout problems will be nearly

solved.� By using of AHP technique, those technologies would be chosen

for electricity generation which is unpolluted and efficientbeside economical views for electricity industry.

6. Conclusion

Usually, HPP is applied in production systems with same situa-tions. In this paper FHPP has been applied as a new approach forPPGP. The proposed approach converts complex electricity genera-tion planning problem to small sub-problems which could be eas-ily solved and need less computer memory. This approach isrelatively more effective than traditional approaches are used inIranian power plants planning system. Besides the feedback sys-

duction in each month of autumn PGðtm , z, i, k) MW

November ðtm ¼ 2Þ December ðtm ¼ 3Þ

505.852 0603.2 0

0 059.4 00 0

344.0605 00 0

21.318 03.156 012.987 0. . . . . .

0 0

0 00 119.16

402.4986 402.4986

0 0

1240 R. Tanha Aminloei, S.F. Ghaderi / Energy Conversion and Management 51 (2010) 1230–1241

tem increases the flexibility of the system and dynamically allowsthe model to be well-suited with changes. Unexpected consumerbehavior makes uncertainty for demand prediction hence the outputs of demand models are not accurate. This is a very importantissue for electricity generation planning. Fuzzy theory can solvethis weakness appropriately and increase reliability of model’ssolutions. Therefore accurate planning could be done and anyshortage in electricity demand satisfaction could nearly be solved.In this research also combined AHP and linear programming modelapplied to considered environmental pollution, efficiency, propor-tion of total capacity and power plant activity in year criteria inaddition to the previous cost based models has been developed.

Acknowledgement

The authors are grateful for the valuable comments and sugges-tion from the respected reviewers which have enhanced thestrength and significance of our paper. The authors would also liketo acknowledge the University of Tehran for the support under theresearch Grant No. 619/3/1087 and No. 617/3/989.

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