2010 IEEE International Energy Conference
Generation expansion planning in IEEE power system using probabilistic production simulation Abdolazim Yaghooti 1, Ghafur Ahmad Khanbeigi 2 1
Mohammad Esmalifalak 3
2
Amirkabir University of Technology , Member, IEEE Tehran, Iran1, 2 1, 2 E-mail :
[email protected] ,
[email protected]
University of Houston 3 Texas, USA3 3 E-mail :
[email protected]
Keywords— cumulants, Edgeworth series, equivalent load duration curve, expected energy not supplied, generation expansion, gram-charlier series, loss of load probability, transmission expansion
From the viewpoint of power system structures, planning methods can be classified into methods for regulated power systems and methods for deregulated power systems. The main objective of generation and transmission expansion in regulated power systems is to supply the load while maintaining the system reliability. Uncertainties are much more in deregulated power systems than regulated power systems. Probabilistic production simulation is one of the methods used for generation and transmission expansion planning [5]. Equivalent load duration curve (ELDC) is the most important concept in generation expansion. This curve integrates random outage capacity of generation units with random load. In fact ELDC is the same as load duration curve (LDC) in which the effect of forced outage of generators has been taken into consideration. Expansion criteria such as loss of load probability (LOLP), and expected energy not supplied (EENS) can be calculated using ELDC [5]-[6]. In this paper generation and transmission expansion planning of IEEE 300-BUS TEST SYSTEM [8] is investigated. In section II, computing ELDC using the expansion of random distribution series is described. In section III, ELDC is computed for all of the three electricity regions of IEEE 300-BUS TEST SYSTEM. To validate the results, ELDCs are calculated using convolution method [5] in section IV. In section V, expansion planning of IEEE 300-BUS TEST SYSTEM is investigated. Conclusion in section VI closes the paper.
Abstract— In this paper generation and transmission expansion planning of IEEE 300-BUS TEST SYSTEM using equivalent load duration curve is studied. To this end, equivalent load duration curve for each electricity region is calculated for years 1991 and 1996 using the expansion of the probability random distribution series. The criteria loss of load probability, expected energy not supplied, and capacity shortage are computed using equivalent load duration curves. Equivalent load duration curves and the above-mentioned criteria are calculated using convolution method to validate the results. Finally, generation and transmission expansion planning of the system is studied considering the computed criteria.
I. INTRODUCTION
T
o supply electric energy consumption, generation and
transmission should be developed while consumption increases. Expansion costs, reliability, uncertainties, and risk should be taken into account in expansion planning. Generation and transmission expansion planning methods can be classified from different viewpoints. From the viewpoint of uncertainties, expansion planning methods are classified into deterministic and nondeterministic ones [1][2]. In deterministic methods expansion is planned only for the worst system operating point without considering its occurrence probability. In nondeterministic methods, expansion is planned for all possible system operating points considering their occurrences probability. Therefore, nondeterministic methods can take past experiences and future expectations into account. Probabilistic load flow models [3], and probabilistic based reliability criteria [4], take lack of nonrandom reliabilities into account. Analyzing the decision is a suitable way for dynamic planning. Fuzzy decision making takes ambiguous data into account. From the viewpoint of expansion horizon, expansion planning methods are classified into static and dynamic methods [1]-[2]. In static planning, planners attempt to find the optimal expansion plans for a given year in planning horizon.
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II. COMPUTING THE ELDC USING THE EXPANSION OF RANDOM DISTRIBUTION SERIES Random variables in power system are mostly dependent on load changes and random outage of generators. Random phenomena can be modeled by their distribution functions. Each probability distribution function can be described using its moments, central moments, or cumulants. We can suppose that random variable x is equal to xi with probabilityܲ . , order moment of random variable x, is defined as follows: J ൌ σ୧ ୧ ୧ J (1) Cumulants of different orders of random variable x can be calculated from the following recursive relation [5]: ଵ ൌ ଵ Jିଵ J െ ͳ J ൌ J െ σ୧ୀଵ ቀ ቁ Jିଵ ൈ ୧ ǡ J ʹ (2)
769
where ߛܭis order cumulants of random variable x. If x and y are two independent random variables, then: ሺ ሻ ൌ ሺሻ כሺሻ ሺ͵ሻ ሺሻ is probability density function of random variable x, and כis convolution operator. In order to reduce the amount of computation the following summability property of cumulants can be used: J ሺ ሻ ൌ J ሺሻ J ሺሻ (4) ሺ where ܭJ ሻ is J order cumulant of . Expansion of random distribution series such as GramCharlier Series or Edge Worth series expansion can be used to calculate the probability density function or ELDC. ELDCs can be expanded using Gram-Charlier and Edge Worth series. Expansion series are as follows respectively [5]: ஶ
ଶଷ
ଷ ସ ͳͲ ൈ ሺሻ ൌ න ሺሻ ሺതሻ ቈ ଶ ሺതሻ ଷ ሺതሻ ହ ሺതሻ ͵Ǩ ͶǨ Ǩ ୶ ଶ ൈ ͳͲ ൈ ଷ ͵ͷ ൈ ସ ൈ ଷ ହ ሺതሻ ሺതሻ Ǩ Ǩ ଶ ଼ ͷ ൈ ହ ൈ ଷ ͵ͷ ൈ ସ ሺതሻ ǥ ǥ ൨ ሺͷሻ ͺǨ ஶ ଷ ସ ͳͲ ൈ ଶଷ ሺሻ ൌ න ሺሻ ሺതሻ ቈ ଶ ሺതሻ ଷ ሺതሻ ହ ሺതሻ ͵Ǩ ͶǨ Ǩ ୶ ହ ͵ͷ ൈ ସ ൈ ଷ ʹͺͲ ൈ ଷଷ ସ ሺതሻ ሺതሻ ଼ ሺതሻ ͷǨ Ǩ ͻǨ ͷ ൈ ଷ ହ ହ ሺതሻ ሺതሻ Ǩ ͺǨ ʹͳͲͲ ൈ ଶଷ ସ ଽ ሺതሻ ͳͲǨ ସ ͳͷͶͲͲ ൈ ଷ ଵଵ ሺതሻ ǥ ǥ ǥ Ǥ ൨ ሺሻ ͳʹǨ
Where ୶ିρ ത ൌ ,
(7)
V
ഥሻ ൌ ሺ ஓ ൌ
ಋ ಋ
ଵ ξଶV
ൌ
ಋ ಋ
మమ
షሺ౮షρሻమ మಚమ
,
ߙJ ൌ
ൌ ܭJ
(15) ሺ୧ሻ ܭJ
are J order cumulants of unit i, J where, J , ܭJ , and order cumulant of the loads, and J order cumulants of the equivalent load after considering the forced outage of the unit i, respectively. D) Computing ELDC using the expansion of random distribution series When equivalent load cumulants were calculated, ELDC can be calculated using the expansion of random distribution series. For this purpose, the amount of x is increased from zero to ݔ௫ ܥ௧ step by step. ܥ௧ is the installed total capacity, and ݔ௫ is the peak of the load curve. Coefficients of series are calculated using relations (7) to (10) in each step, and then the amount of ܮሺሻ is determined using (5) or (6).
(12)
ܺ ሺሻ ൌ ൈ ܺ ሺିଵሻ ݍൈ ሺܺ ሺିଵሻ ୧ ሻ
A) Computing moments of load and forced outage capacity of each unit Load moments and forced outage capacity of generators can be calculated as follows:
J ೞ σே ௦ୀଵ ܲ௦ ܥ௦
ሺሻ
ܭJ
(11)
ష౮మ
(10) ୬ ሺሻ ൌ ሺെͳሻ୬ మ మ ୢ୶ The algorithm of calculating the ELDC, using the expansion of random distribution series, is as follows [5]:
ȽJ ൌ σ୧ ୧ ୧ J
ܭJሺ୧ሻ ൌ ܭJሺିଵሻ ܭJ
Fig. 1 shows the final ELDC and the amount of LOLP and EENS [5]. In order to calculate the capacity shortage, typical ELDC is given in Fig. 2 [5]. According to Fig. 2 peak of ELDC is equal to ሺܺ௫ +ܥ௧ ) then the shortage capacity is equal to ሺܺ௫ +ܥ௧ )െܥ௧ ൌ ܺ௫ . This method is very conservative and expensive to cover capacity shortage. In fact the total capacity should be two times higher than the peak load in the worst condition, i.e. where capacity outage is equal to ܺ௫ which is a very rare condition. In this paper expected value of capacity shortage is calculated and used as a criterion for expansion planning. Expected load duration curve (XLDC) is defined as follows:
(9) ౮మ ୢ
Generating units are ordered and numbered in an ascending manner according to their generation cost. Therefore units take load according to their generation cost. Unit outage is equivalent to the load increase amount to the forced outage capacity. So, the equivalent load is equal to the system's load plus forced outage capacity of generators. Therefore, using the summability property of cumulants, cumulants of equivalent load is calculated as follows: ሺ୧ሻ ܭJ ൌ ୪J σ୧୨ୀଵ ୨J (14) Equation (14) can be written as:
E) Computing loss of load probability, expected energy not supplied, and capacity shortage
(8)
,
C) Computing cumulants of equivalent load
where, ߙJ ǡ ߙ݅J are J order moment of the load and outage capacity of unit i. Load is equal to xi with probability୧ . ܰ௦ is the state number of unit i. Outage capacity of unit i is equal to ܥ୧ୱ with probabilityܲ୧ୱ . For dual-state units, moments of forced outage capacity of generators is calculated as follows: J ȽJ ൌ ୧ ୧ (13) where, ݍ୧ is the forced outage rate (FOR) of unit i.
(16)
Expected value of maximum load and expected value capacity shortage (EVCS) is computed as follows: ሺ୧ሻ
ሺ୧ିଵሻ
ሺ୧ିଵሻ
ൌ ൈ ୫ୟ୶ ൈ ሺ୫ୟ୶ ୧ ሻ ቊ ୫ୟ୶ ሺ୧ሻ ൌ ୫ୟ୶ െ ୲
B) Computing cumulants of load and forced outage capacity of each unit Cumulants of load and forced outage capacity of each unit can be calculated using (2).
770
(17)
9000 EVCS = -344 MW
8000
Ct= 7398 MW
7000
LOLP = %0 TIME(hour)
6000 5000 4000 3000
Fig. 1- Typical load duration curve [5]
2000
FOR that is calculated by XLDC almost equals to FOR that is calculated by ELDC.
1000 0
ܲ
0
1000
3000
4000 5000 LOAD(MW)
6000
7000
8000
Fig. 3- load duration curve of system 3 in 1991
1 ሺͲሻ
݂ሺ݊ሻ (ࣲ)
10000
(ࣲ)
8000 TIME(hour)
݂
LOLP EENS 0
2000
ݐܥ
ࣲ ܥ௧ ࣲ௫
Edgeworth Series
Ct= 7398 MW
6000
LOLP= %3
4000
EENS= 97425 MW.h
2000 0
Fig. 2- Typical equivalent load duration curve [5]
0
5000
10000
15000
LOAD(MW) (a)
III. CALCULATION OF ELDC FOR IEEE 300-BUS TEST SYSTEM- SYSTEM 1, 2, 3 ELDC of each electricity region is calculated regarding its consumed load and the capacity of its generators [8], assuming the power input/output to other electricity regions is zero. In this section calculation of ELDC for system 3 is investigated. LDC for the year 1991 has been drawn in Fig. 3. Load hourly data, i.e. 8760 data, in 1991 have been used to draw this curve. This figure shows that maximum consumption power is 7054 MW in 1991, assuming forced outage rate equals zero. Since the installed capacity of the total system is 7398MW [8], EENS=0MW.h, LOLP=0% and EVCS=-344MW. There are about 16 generators in SYSTEM 3 [8]. In Fig. 3 cumulative capacity of generators has been shown with points on horizontal axis. If FOR of these units are considered in LDC, then ELDC will be obtained. To this end, at first, generators are ordered in ascending manner based their weighted bid during the year 1991 [8]. Then using the relations described in section II, ELDC is calculated. Using the expansion of Edge Worth and Gram-Charlier series, the calculated ELDC is illustrated in Fig. 4. It is assumed that the FOR of all units is equal to 0.1. Considering the calculated ELDC using the expansion of Edge worth series (Fig. 4) and considering that the total generation capacity of system 3 is 7398MW in 1991, LOLP = 3%, EENS = 97425MWh and EVCS = 395MW.
TIME(hour)
10000 8000
Ct= 7398 MW
6000
LOLP= %3
Gram-charlier series
EENS= 95663 MW.h
4000 2000 0
0
5000
10000
15000
LOAD(MW) (b)
Fig. 4- ELDC of system 3 in 1991, computed using (a) Edgeworth (b) Gram-Charlier series
In order to determine the generation and transmission expansion in system 3, ELDC is calculated for 1996. Energy consumption growth in IEEE 300-BUS TEST SYSTEM is assumed about 7% per year. So, the load of different hours of the year 1996 can be defined as follows: ܲଵଽଽ = ܲଵଽଽଵ × ሺͳ ͲǤͲሻହ
(18)
Following the above-mentioned method, and assuming that the number of generators, forced outage rate and their capacities are constant, ELDC for the year 1996 is calculated. Fig. 5 shows ELDC for the year 1996. Installed capacity of the total system has been specified by a vertical line in Fig. 5. Considering this figure, EENS and LOLP in 1996 are 3819225MWh, 41% respectively and considering Fig. 6 EVCS is 3235MW. Table II shows LOLP, EENS and EVCS for each electricity region in the years 1991 and 1996.
771
10000
9000 Edge worth series
TIME(hour)
Ct= 7398 MW
8000
LOLP= %41 5000
Ct= 7398 MW
EENS= 3819225 MW.h
7000 LOLP = %40 6000
0
2000
4000
6000
8000 10000 LOAD(MW) (a)
12000
14000
16000
EENS = 4052484 MW.h
1800
TIME(hour)
0
10000 TIME(hour)
Gram-charlier series Ct= 7398 MW
5000 4000 3000
LOLP= %41
5000
2000
EENS= 3836415 MW.h
1000 0
0
2000
4000
6000
8000 10000 LOAD(MW) (b)
12000
14000 16000
1800
0
Fig. 5- ELDC of system 3 in 1996 computed using (a) Edgeworth (b) Gram-Charlier series
V.
TIME(hour)
4000
6000
8000 10000 12000 14000 16000 LOAD(MW)
18000
SUGGESTION FOR GENERATION AND TRANSMISSION EXPANSION OF IEEE 300-BUS TEST SYSTEM
Ct= 7398 MW
7000
EVCS = 3235 MW
6000
LOLP = %41
5000 4000 3000 2000 1000 0
2000
Fig. 7- ELDC of system 3 in 1996, computed using convolution method
9000 8000
0
0
2000
4000
6000 LOAD(MW)
8000
10000
1200
A) Table II shows that all electricity regions except System 2 will be faced with generation shortage in 1996. Therefore, transmission expansion will not be able to resolve the problem of capacity shortage. To some extent, system 2 can supply its neighbor region, System 1 shortage, if there is enough available transmission capacity (ATC) from System 2 to System 1. Hence, since extra capacity of System 2 cannot cover the whole shortage of these regions, it is needed to expand the generation of these regions too. For generation in these regions we consider the probabilistic analysis of lifetime discounted costs of electrical energy if produced in coal-fired, gas-fired and nuclear plants. The cost of electricity generation was given by the following formula [9]:
Fig. 6- XLDC of system 3 in 1996
భ
ೝ σసభ
൫భశ ൯
ܿ =
IV. COMPARING THE RESULT OF CONVOLUTION AND RANDOM DISTRIBUTION SERIES METHOD
ቀభశ ቁ ష ା ା଼ ቌ మళళǤఴആ ାೡ ቍ భష൫భశ ൯
σసభ
ఴళలబಽ
൫భశ ൯
ቀభశ ቁ ఴళలబ ቌ మళళǤఴആ ାೡ ቍ ೝ ൫భశ ൯
σస
Table III shows the results obtained from convolution method. Comparison of table II and table III shows that the calculated LOLP using convolution, Edge worth series, and Gram-charlier series are almost same. But calculated EENS by convolution method does not have enough accuracy, because in this method trapezoidal approximation with a great step is used [5]-[6]. Calculated EENS using the Edge worth series is more accurate than Gram-charlier series [7]. Using random distribution series in comparison with convolution method needs much less computation load and time to calculate ELDC. But in using random distribution series, if incorrect amount (one or more load data) is inserted in hourly load data mistakenly, ELDC will contain fluctuation and leads to false values for LOLP and EENS, while such a problem does not arise in convolution method. Fig. 7 shows ELDC of System 3 for the year 1996, computed using convolution method.
+
ቆ σసభ
ఴళలబಽ ቇ
(19)
൫భశ ൯
where ܥ is the cost of produced electrical energy US$/kWh, ܥ the constant operational and maintenance cost US$/kWyear, ܥ௩ the variable and operational and maintenance cost US$/kWh, ܥ the overnight specific investment cost US$/kW, ܥ the fuel cost US$/GJ, the plant efficiency, ܮ the load factor, ݊ the years of loan repayment, ݊௧ the years of plant life, ௗ the discount rate, the average interest rate for loan repayment, the average rate of foreseen fuel price change during plant life time [9]. Each of the indicated cost parameters is characterized by an uncertainty range and distribution within the range as given in table IV. The results of electricity cost calculation generated by analyzed plants by using the probabilistic method. The distribution of discounted cost of electricity generation for the combined cycle gas plant is the range 4.58 USܿ݁݊ݏݐΤܹ݄݇, with a most probable value of about 5.8 USܿ݁݊ݏݐΤܹ݄݇. For coal-fired plants the corresponding
772
9000
B) From the viewpoint of EENS the priority for generation expansion is as below respectively System3, System1, System2.
6000 TIME(hour)
values are 4.5-6.3 USܿ݁݊ݏݐΤܹ݄݇ and 5.2 USܿ݁݊ݏݐΤܹ݄݇. Most favorable is cost for nuclear power plant with distribution in the range 4.2-5.8 USܿ݁݊ݏݐΤܹ݄݇ and a most probable value of about 4.8 US ܿ݁݊ݏݐΤܹ݄݇ [9].
C) From the viewpoint of EVCS the priority for generation expansion is as below respectively System1, System3, System2.
8000
EVCS = 2495 MW
7000
Ct= 7398 MW LOLP = %23
5000 4000 3000 2000
D) From the viewpoint of LOLP the priority for generation expansion is as below respectively System3, System1, System2.
1000 0
0
1000
E) Since EENS is more important criterion than both EVCS and LOLP, the priority of EENS should be regarded.
4000 5000 6000 LOAD(MW)
7000
8000
9000
10000
VI. CONCLUSION In order to develop generation and transmission of IEEE 300-BUS TEST SYSTEM for the years 1991 and 1996 are calculated. Then loss of load probability, expected energy not supplied, and expected value for capacity shortage. All of the three electricity regions have been computed. Suggestion for generation and transmission planning of IEEE 300-bus test system are made based on the computed planning criteria in each region which has been calculated regarding its capacity shortage.
H) System 3, 2 electricity regions have a low load factor (LF), LF= 63.70%, LF=63.23% respectively, their neighbor, System 1, has a higher LF, LF=71.25%. If transmission lines between two regions (System 2, System 3) has been exist and are reinforced then these two regions can be aggregated and considered as one region. ELDC of aggregated System 2 and System 3 and aggregated System 1 and System 2 and System 3 are shown in Fig. 9. Fig. 9 shows that if transmission lines between these two regions are reinforced, total EENS will decrease from 3828125 MWh to 221130 MWh. Reduction of FOR of generators is much less effective on EENS reduction if transmission lines between these two regions are reinforced. If transmission lines are not reinforced and FOR of generators are reduced from 0.1 to 0, the total reduction of EENS of System 2 and System 3 is equal to 1396704MWh. If transmission lines are reinforced and FORs are reduced from 0.1 to 0, the total EENS is more decreased. If transmission lines between three regions are reinforced then these three regions can be aggregated and considered as one region. Total EENS will decrease from 7261844 MWh to 0 MWh.
773
TABLE I- COMPARISON PLANNING CRITERIA FOR TWO DIFFERENT FOR IN THREE ELECTRICITY REGIONS FOR=0.1 FOR=0 System 1 System 2 System 3
LOLP %26 %0.21 %.41
EENS 3433719 8900 3819225
EVCS 3395 -1842 3235
LOLP %11 %0 %23
EENS 961281 0 1396704
EVCS 2776 -2868 2495
10000 Edge worth series
Ct= 17657 MW TIME(hour)
G) If generation expansion is not economic in an electricity region or with the presence of some limitations, generation expansion of these electricity regions should be accomplished on electricity region that has no limitations for generation expansion with enough ATC between sink and source electricity regions. If ATC is not enough, transmission should be expanded. To reduce the total costs an optimization should be done to find the optimal place for generation expansion considering the generation and transmission expansion costs.
3000
Fig. 8- XLDC of system 3 in 1996, assuming FOR 0
LOLP= %3 5000
0
EENS= 221130 MW.h
0
0.5
1
1.5 2 LAOD(MW) (a)
2.5
3
3.5 4
x 10
10000 TIME(hour)
F) If FOR of generators is reduced, EENS, LOLP and EVCS will noticeably be reduced. Table I compares the planning criteria for three regions for FOR=0.1 and FOR=0. This table shows that reduction of FOR from 0.1 to 0 will reduce the EVCS from 3235 MW to 2495 MW in System 3 electricity region that has been shown in Fig. 8.
2000
Ct= 29855 MW
Edge worth series
LOLP= %0 5000
0
EENS= 0 MW.h
0
0.5
1
1.5
2
2.5 3 LOAD(MW) (b)
3.5
4
4.5
Fig. 9- (a) ELDC of aggregated System 2 and System 3 electricity region, (b) ELDC of aggregated System 1 and System 2 and System 3 electricity region in 1996, computed using Edge worth series
5 4
x 10
TABLE II- COMPARISON PLANNING CRITERIA FOR YEARS 1991 AND 1996 IN DIFFERENT ELECTRICITY REGIONS
Electricity Region System 1 System 2 System 3
Peak load (MW) 10676 5270 7054
ܥ௧ ሺܹܯሻ 12198 10259 7398
THE YEAR 1991 LOLP EENS (%) (MWh) %0 0 %0 0 %3 97425
EVCS (MW) -302 -3963 395
LOLP (%) %26 %0.21 %.41
THE YEAR 1996 EENS EVCS (MWh) (MW) 3433719 3395 8900 -1842 3819225 3235
TABLE III- COMPUTED LOLP AND EENS USING CONVOLUTION METHOD
LOLP (%) System 1 System 2 System 3
The year 1991 EENS (MW.h)
%0.7 %0 %3
LOLP (%)
682 0 98896
The year 1996 EENS (MW.h)
%25 %0.2601 %40
3646806 10984 4052484
TABLE IV-ESTIMATED COST DATA AND THEIR EXPECTED RANGES AND DISTRIBUTION [9] Plant type Overnight specific investment cost-ࢉ US$/kW Distribution: End values: Constant operational and maintenance cost (no fuel)-ࢉࢉ US$/kWyear Distribution: End values: Variable operational and maintenance cost-ࢉ࢜ US$/kWh Distribution: End values: Fuel cost-ࢉࢌ US$/GJ Distribution: End values: Plant efficiency- Distribution: End values: Load factor-ࡸࢌ Distribution: End values: Years of loan repayment- ࢘ Distribution: End values: Years of plan life time-࢚ Discount rate-ࢊ Distribution: End values: Average interest for loan repayment- Distribution: End values: Average annual rate of fuel price increase-ࢌ Distribution: End values:
Nuclear Triangular 1900
Coal 2100
Triangular 1400
Flat 100
120
Flat 0.15
0.25
Five-point 0.45 0.475(0.7)
2000
0.5(1.0) 0.525(0.7)
Flat 0.32
Triangular 0.6
Flat 15
0.7
1600
Triangular 500
Flat 30
40
Flat 10
20
Flat 0.30
0.40
Flat 0.15
Flat 0.25
Five-point 1.8 1.9(0.7)
0.55
0.34
Flat 0.38
0.8
Triangular 0.5
20
Flat 15
40
Combined cycle gas
1500
2.0(1.0) 2.1(0.7)
0.6
2.2
Five-point 4.0 4.25(7.0)
0.42
Flat 0.54
0.7
Triangular 0.4
20
Flat 12
35
600
4.5(1.0) 4.75(o.7)
0.62
0.5
8%
Flat 5%
8%
Flat 5%
Flat 5.5%
7.5%
Flat 5.5%
7.5%
Flat 5.5%
Flat 0.8%
1%
Flat 1%
2%
Flat 2%
REFRENCES [1] G. Latorre, R. D. Cruz, and J. M. Areiza, “Classification of
[2] [3] [4]
[5] [6]
[7] [8] [9]
Abdolazim Yaghooti (b.1983) received the bachelor degree in Electrical Engineering from the Shahrood University of Technology, Iran (2003-2007). His topics of research include electricity markets modeling and simulation, and expansion planning of restructured power systems.
Ghafur Ahmad Khanbeigi (b.1986) received the bachelor degree in Electrical Engineering from the Semnan University, Iran (2009). His topics of research include electricity markets modeling and algorithms.
Mohammad Esmalifalak (b. 1982) received the Master degrees in Electrical Engineering from the Shahrood University of Technology, Iran (20052007). Presently he is PhD student in University of Houston. His topics of research include electricity markets modeling and simulation, and expansion planning of restructured power systems.
774
5.0
0.6
15
30
Flat 5%
publications and models on transmission expansion planning,” Presented at sIEEE PES Transmission and Distribution Conf., Brazil, Mar. 2002. M. Oloomi Buygi, H. M. Shanechi, G. Balzer and M. Shahidehpour, “Transmission planning approaches in restructured power systems,” in Proc. 2003 IEEE PES Power Tech Conf., Italy B. Borkowska, “Probabilistic load flow,” in Proc. 1974 IEEE PES Summer Meeting & EHV/UHV Conf., pp. 752-755. M. J. Beshir, “Probabilistic based transmission planning and operation criteria development for the Western Systems Coordinating Council,” in Proc.1999 IEEE Power Engineering Society Summer Meeting, Vol. 1, pp. 134-139. X. Wang, and J. R. McDonald, Modern Power System Planning, McGRAW-HILL, International Edition, 1994. M. Oloomi-Buygi, A. Yaghooti, and J. Amirfakhrian, “Generation Expansion planning in Iran's Network Using Equivalent Load Duration Curves,” the 15th Iran's Conference on Electrical Engineering, Tehran, 2007 (Persian). Wikipedia. “Edge worth series” available on "http://en.wikipedia.org/wiki/Edgeworth_series" IEEE 300-BUS TEST SYSTEM available on http://www.ee.washington.edu/research/pstca/ D. Feretic, and Z. Tomsic, “Probabilistic analysis of electrical energy costs comparing: production costs for gas, coal and nuclear power plants”, 2005 ELSEVIER. Energy Policy 33.
700
8%
7.5%
5%
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