Elektrik üretim sistemlerinin optimal planlamasında yeni bir modelleme ve çözüm
Başlık çevirisi mevcut değil.
- Tez No: 9215
- Danışmanlar: PROF. DR. NESRİN TARKAN
- Tez Türü: Doktora
- Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1989
- Dil: Türkçe
- Üniversite: Marmara Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Elektrik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 219
Özet
ÖZET Elektrik, enerjisi üretim sistemlerinde optimal planlama prob leminin temelini, sistemin ekonomik ve güvenilir olarak genişletebilmesi oluşturur. Bu nedenle planlama, başta güvenilirlik olmak üzere, pek çok kritere dayalı olarak sistemi minimum maliyet le gerçekleştirmeyi amaçlayan bir optimizasyon çalışmasını gerekli kılar. Bu çalışmada önce, planlama problemlerine, değişik optimizas yon teknikleri ile çözüm arayan modellerin ayrıntılı olarak karşılaştırması yapılmıştır. Bu tür problemlerin pek çok kritere da yalı biçimde çözümüne olanak veren Karma Tamsayılı Programla ma (Mixed Integer Programming = MIP) modeli en uygun model ola rak seçilmiştir. Ancak bu modelde yapılan bazı değişikliklerle, mode lin temel yapısında bulunmayan periyodlar arası para akışı gerçekleştirilmiştir. Bu işlem, tesislere yapılan yatırımların, tesis ömrü içinde geri kazanılmasını sağlayan sabit miktarlı ödemelerin birbirini izleyen periyodlarda devamı ile sağlanmıştır. Böylece mode lin en büyük kusuru olarak kabul edilen bu soruna çözüm getiril miştir. Ayrıca genel modelde, sabit birim maliyetin çok basit olarak he saplanmasından meydana gelen hataları önlemek amacıyla, kuru luş ve işletme maliyetleri, bunları etkileyen değişik ekonomik faktörler birlikte ele alınarak güncelleştirilmiştir. Modelin uygulaması, Türkiye'de 1990 - 2014 yıllarını kapsayan bir planlama dönemi için gerçekleştirilmiştir. Bu dönem boyunca ge rekli olacak sistem yükü yapılan regresyon analizi yardımıyla elde edilmiştir. Problem, önce genel bir MIP uygulaması olarak daha sonra, modellenen yeni şekliyle çözülmüştür. Sonuçlar karşılaştırıldığında, problemin bu çalışmada uygulanan özgün çözümünde, daha fazla kapasite artışına karşın % 12 ekonomik avantaj sağlandığı görülmektedir.
Özet (Çeviri)
SUMMARY Due to the growth of population and developing technology life styles have changed, thereby increasing the consumption of electrical energy. As a result of this, new techniques have been required to be developed for generation expansion planning in order to provide cheap, reliable and apposite electrical energy. All studies in this area are defined as generation capacity planning in power systems. Capacity expansion problems which previously were solved merely as a minimization of cost problems are now introduced as a function of numerable variables. Due to the energy crisis which arouse at the beginning of 1970's, the problem has become of major importance and starting in the same decade, the solution to the problem is dealt with, by more developed models. Between the years 1970 and 1973 different models which enable Linear Programming (LP), Non Linear Programming (NLP), Dynamic Programming (DP), Mixed Integer Programming (MIP), Simulation and other such techniques to be used have been widely applied. In the first LP model, developed by Masse“ and Gibrat in 1957, the only objective was to minimize the cost. In 1972 Anderson reviewed existing models for electric capacity planning in what is today a well referenced article. His formulation of the investment problem in cost minimization form originated in the earlier works of Masse*, Gibrat, and later Bessiere and is the foundation for many subsequent optimization models. Essentially, the Anderson model minimizes the sum of capital expenditure and operating cost over time, subject to various constraints on demand satisfaction, limits on individual plant output and hydro capacity, reliability assurance, and conservation of energy. NLP models used in capacity expansion planning have brought a solution to the magnitude of the problem; it is generally accepted that the size of this problem is the major shortcoming, however, too many computations are required both for and in the data. DP models, when compared with LP, also decrease the problem size; however, these models are still being worked on, in order to be applicable to more detailed solution techniques. For example, in the past years, DP models which accomodate all shortcomings, from generation to distribution have been developed. On the other hand, simulation models provide detailed information on the system operation and performance. XIFor capacity planners with interest in obtaining precise detail concerning system operation and behavior, the simulation approach provides an intuitively appealling methodology. It has been applied since the initial developement of computers. Based on daily, weekly, or other periodic aggregations of the actions of the generation network, the detailed simulation can model the complex and probabilistic nature of the situation. MIP models are developed for cases where some of the variables, that are desired to take place is the optimum solution table, can be assigned integer values. This model has been highly valuable for many planners since it is very flexible in modeling, has potential to provide highly accuate results, can be pushed for improved computational procedures and requirements, and provides potential opportunity for limited post optimal analysis, eventhough it considers generation cost quite simply. Another important aspect of this model is its providing a sensitivity analysis. Due to the above listed reasons, MIP model has been chosen as a base for this study. In all of the models that are used reliability along with economical optimization have been the main goals. Among all the topics in the generation expansion planning, the main issue is the estimation of the possible changes in energy and/or power demand throughout the planning period. Constructionals changes that may arise in energy and/or consumption, out to be considered in parallel with the expected economical changes. With the aid of demand or load estimations that are already developed, demand levels for different time intervals are estimated. The closer this estimation is to the actual values, the closer one gets to the optimal values. The estimation techniques, which are being used, have been developed to forcast the future loods as values. Load estimation techniques used in power system planning are based on the use of extrapolation, correlation or both. Extrapolation is the technique to estimate a curve which will reflect the tendency to expand, in accordance with the given values of the past. In correlation, relations between system loads and different economical and public factors are determined. Generally, in energy demand estimation first individual estimations since the consumers have different characteristics, are made and then they are synthesized to obtain a final estimation. Generation expansion planning problem involves system reliability along with economical optimization as one of its main goals. Reliability involves stability of the system, its continuation and adequacy. Evaluation of system reliability and its application to planning decisions are important issues. The measures taken up in reliability evaluation are very difficult to set exactly. As a usult of this, in different reliability evaluations four qualities have been developed for use as basis. They are: XII- adequacy, - being relatively easy to compute, -mathematical consistency, - being easily interpretable and understantable for the planners. Reliability evaluation is made, based on probable estimation of power demand and system capacity. There are many methods that are used in reliability evaluation. Among these the one that is used the most for constant load values is the Loss of Load Probability (LOLP). Besides this, there are many techniques which have been classified into probability, duration and expectation approaches. Since generally in this study, generation expansion planning problem in electrical power systems is dealt with in accordance with a MIP model, reliability is inserted as a reserve capacity coefficient. In electrical power system planning, as the accomplishment of optimal stability from the point of view of being economical and reliable, the planner considers choices whic have high techical reliability. The choices are made based on basic concepts of engineering economy. Engineering economy studies are mainly comperative, therefore decisions are always in terms of alternatives. The primary condition for a healthy comparison and the choice of the best alternative is the closeness and even congruency of the technical properties of the compared alternatives: The methods of engineering economy can only be applied to a situation that has been brought up to this point. With the aid of these methods many-time relation may be found. The different economical values of investment materials can be calculated and protection by allowing an amortization can be planned. After all this technical and economical information is obtained, reliability must be maintained and a model which will minimize the generation cost must be set. A general MIP model, developed for generation expansion planning, which contains an objective function that will simultaneously minimize the capital and operational costs consist of some constraint inequalities, as follows: MinimizeZ=2cjxj + 2ZZ Çt^^ J 1 J t Subject to y] ajtXj Uj £Pti d+m) for every t, i (1) (2) 2! yjtf - pti for everv *» * o) 0 < yjti < ajti xj uj for every j,t,i (4) xj < uj for every j (5) xj e { 0,1 } for every j (6) xmwhere j : index for units; there is a ”unit“ for every combination of generation class and year of commisioning t : index for time periods i : index for segments of each time period x; : Zero-one integer variable indicating whether or not unit j is to be constructed yjti '. Power output of unit j in increment i of the load duration curve for period t (MW) C; : discounted capital costs for project j; Cj = 0 for existing units ($) % : discounted marginal cost associated with production by unit j for year t ($/MWh) wj : time span represented by interval i of each time period (h) P^ : power demand requirement during segment i of the time period t (MW) au : availability of unit j in period t; equal to zero when plant j not yet commisioned m : margin of spare available capacity required to meed demands above mean expectation uj : upper bound on expansion capacity for unit j (MW) In the general model, the C; is a value which is determined as a different constant for every type all plant. But this cost does not stay constant, due to the changing economical and technical conditions during the 20-25 years of planning time. For this reason, in this study, v = 1,2,... V are the mid-point years of the planning periods and assuming the investements to be made during this time, then the capital costs are defined as Cjv. For the same reason xj, for this coefficient, is changed to xjv. Also xjv, in the model, is not merely a variable that can adopt zero-one values and show whether capacity addition is made or not as in the initial model, but also shows the magnitude of the addition made. fu, unit operational cost in the objective function has been defined as f;^ for the same reason. Since this coefficient also involves the product of cost and lenght of the period it is calculated in terms of ($/MW). As a result, wj that gives each time periods in hours is removed from the equation. In the objective function, ws which gives the lengths of the segments in load duration curves as a percent of the total time in stepped demand function at every period, has replaced W£. Similarly, variable y^ of the operational cost coefficient is defined as yjtvs, which it shows how much of the demand at tth period, vth year and ”s“ rationed demand step will be provided by the j type plant. And thus, the objective function denoted by (1) equation in the general model has become xivJ V J T V S Z=ZZCjvxjv + ZZZZfJtvyjtvsW8 j=l v=l j=l t=l v=0 s=l,”v The same adaptations have been made for the desicion variables in the constraint inequalities. Also the upper limit values of the u; addition capacity that takes place in (2) and (4) is removed from this constraint inequalities. In the algorithm used in the solution of the model, since it is given as data to the problem for each period. After this changes are made (2), (3), (4) inequalities are formed in the sequence shown below. Within a reserve margin the total available capacity must meet the maximum power demand J T 22>jtV8>Pte for every t, s (® j=lv=0 ands = l The necessity of total generations of the units in operation, at spesific time, to meet the power demand for the same period, is given as J T 2 2 yjtvs ^ Pts for every *» s o) j=l vM) The generation of every unit in operation is limited by its available capacity yjtvs - ^jv xjv for every j» *» v» s (10) Uj in equation (5) has been changed to Xjmax showing the upper limit of the possible capacity from a certain plant during the whole planning period. Here, Xjmax is determined taking into consideration natural resources, economical and technological conditions of the country. So inequality (5) is rewritten as J 2 5v ^x.ax for every j (11) v=l Inequation (6) is removed from the model since x:v variables are revised to show not only whether the plant is established or not, but also the amount of the increase in its capacity. In the place of (6), S 2 vjtvs ws * !j xjv It (wx + w2 ++ w“ ) for every j, t, v (12) s = l xvas a new constraint to maintain the condition that the energy generated by the plant in a period can not be greater than what the available capacity can generated during the same period, is inserted in the model. Here lj is the load factor of the j type plant and 1|. is the lenght of period t, in years. Since ws is defined as a ratio; considering 2ws =1, this constraint is expressed as s 2 yjtvs ws ^ \j xjv k for every j, t, v (13) 8=1 The last constraints arise from the nature of the model and are related to the condition that the decision variables can not adopt negative values. These are defined as xjv»vjtvs^° for every j, t, v, s (14) After the model is set, the variables in the model are determined. In order to makes up for shortcomings that arise due to the simple computation of the generation cost, which is considered as the main detect of MIP modes, a lot of factors are considered in determining especially capital costs. Due to the economic conditions in Turkey being unstable, in order to cancel the negative effects that will be reflected on the calculations, factors such as interest, discount, inflation, escalation are based on U.S. $. Also since the plants are generally established with credit, for the amortization to every plant within its economical life, capital recovery factor is included in capital cost. Additional cost factors to avoid enviromental pollution are also evaluated. Capital and operatinal cost are up-dated taking into consideration effective interest and escalation rates. All other coefficients in the model are determined both in accordance with their average values available in publications and with the conditions in Turkey. Using regression analysis, regression equation y = 42 x2 + 330.5 x + 10064.5 determined. By referring to this equation, load forcasting for the planning period in Turkey can be made. In this study the problem is solved in two different ways. First one is, the traditional method, which solves the problem in two equal periods and does not allow currency flow beetween the periods. In the second method, applied and explained in this study for the first time, the planning period is first divided into three equal periods which are subsequently redivided into equal subperiods. Funds and payments for an investment made in one of the three periods are allowed to be xvicarriedover, from period to period. Also, the solutions found in the one of the main periods are used as data for the following periods. Both methods are used to find solutions to the problem of optimal planning when a comparasion between the two models is made, the following results favoring the second model have been observed. 1. The distribution of the capacity increases, over the years is actualised in a more homogenous and more rational style. 2. The second method allows a more economical expansion planning to meet the same increase in demand. The solution reached by this method compared to the traditional method, has an average % 12 economical advantage. 3. This new method actualized, allows a more capacity increase during the planning period. However, the reason of its being more economical is its minimizing both the capital and operational costs together in objective function. 4. The actualization of more suitable capacity distribution according to different plant types in meeting peak load and base load and reserve capacity in the installed power increase, thus, decreases the total cost. 5. The gas turbines which are high in cost, have an important shore in meeting peak and base load in solution with the tradional method. However, in the solution with the new method, the same high cost plants have only the function of meeting the peak load and reserve capacity. This is in accordance with the principle ”the high cost energy plants, should be used less". 6. In the solution with the tradional method, to meet the peak load, the hydro plants are used; whereas, in the solution of the new method, the hydro plants are rather used as base load plants as it is in general. 7. Using the other plant types, solutions of both methods, result the same in general. This shows the validity of the new method. xvn
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