Transmission Expansion Planning Considering Maximizing Penetration Level of Renewable Sources

Faruk Ugranlı Department of Electrical-Electronics Engineering

Ege University Izmir, Turkey

faruk.ugranli@ege.edu.tr

Engin Karatepe Department of Electrical-Electronics Engineering

Ege University Izmir, Turkey

engin.karatepe@ege.edu.tr

Abstract—Recently, integration of intermittent sources into the power systems has gained most interest in distributed generation environment. Among the others, wind based generation is the most promising renewable based technology. The volatility of these sources requires the careful planning of power systems. This paper proposed a novel genetic algorithm based method to determine the optimal trade-off between wind energy spilled and transmission line investment by deciding the location of new transmission lines. By this way, power system planners can avoid overinvestment of transmission lines while providing maximum usage of wind turbines. The proposed method is illustrated using the IEEE 24 bus reliability test system.

Keywords— Wind power; Genetic algorithm; Transmission investment; Wind energy spilled; Transmission adequacy; DC power flow

I. INTRODUCTION Total penetration of the renewable energy sources based

generations in the power system restructuring has been increasing rapidly and steadily in recent years. According to the American Wind Energy Association, the wind power generation has reached 60,007 MW with increasing capacity by %35 over the past five years in the USA [1]. However, the integration and operation of wind turbines (WT) give rise to new challenges for power system planners and operators. Their volatile characteristic should be included into the planning studies.

Transmission expansion planning (TEP) has been widely investigated to develop new solution methods, objective functions, and treatment of the planning horizon [2]. The objective of this problem is mainly to determine the number and location of new lines to minimize investment cost. The inclusion of the WTs into the TEP problem is also investigated in some studies [3]-[6]. Orfanos et al. propose a Monte Carlo simulation (MCS) based probabilistic TEP to obtain solutions that have acceptable probability of load curtailment by including wind power uncertainty [3]. It is stated that the expansion plan is affected from wind power integration. The impact of wind integration is also considered by taking into account risk cost and congestion cost as well investment cost in the probabilistic framework [4]. However, these studies do not consider the economic dispatch to maximize the usage of WTs. It should be noted that the operational cost of wind power

generation can be assumed zero in the case of economic dispatch formulation [5]. From the point of view of owner and planner, the overall connection costs of WTs are analyzed by using reliability cost/worth analysis to compare different alternatives [6]. Metaheuristic optimization techniques are also applicable to find optimal expansion plan when the WTs are considered. In [7], ant colony optimization is carried out for expansion planning to compare the time step resolution of wind power. In these studies, the effects of WTs are analyzed for classical TEP planning. However, TEP planning should be reviewed by taking into account intermittent characteristic of renewable sources [5].

Energy safety requirements indicate that renewable energy usage is inexhaustible and environmental friendly comparison to the fossil fuels [8]. For this reason, maximization of wind power usage in the power system should be considered in the formulation besides minimizing investment costs of transmission lines. Leite da Silva et al. propose a MCS based methodology to reduce the wind energy spilled (WES) by comparing cost-benefit incremental [5]. Value of the WES is calculated by comparing the economic dispatch results of both with and without line constraints, while the new lines are determined by conservative procedure without using an optimization.

This paper presents a novel genetic algorithm (GA) based method to minimize the total wasted wind energy (TWWE) and investment cost of new added lines by considering the volatility of renewable sources. The main contribution of this paper is to define a new objective function that can handle the TEP problem considering intermittent power sources. By using the proposed objective function, a trade-off is carried out between investment cost of new lines and the cost of conventional sources to compensate TWWE. TWWE is calculated by comparing the installed wind capacity and economic dispatch result considering line limits. Economic dispatch is carried out by using DC-optimal power flow (DC-OPF) considering the load curtailment. The proposed method is implemented into IEEE 24 bus reliability test system and results are discussed.

II. PROBLEM FORMULATION The problem formulation is consisted of three stages that

are generating load and wind data, DC-OPF based economic dispatch, and GA based expansion planning. In the literature,

978-1-4799-0661-1/13/$31.00 © 2013 IEEE

the necessary calculation time for planning problems has been reduced by adjusting the time step resolution of wind and load data [7, 9]. In this study, peak weekly calculation is used to cover annual data to avoid large computational times and all formulations will be developed according to the weekly base. The general structure of the proposed formulation is given in Fig.1 and details of each stage will be given in the following subsections.

DC-OPF based Economic Dispatch

Initial Population

Mutation Crossover

Reproduction

Generating Load and Wind Power Data

1,2,…,52

Sampling Data according to the weekly base

Stag

e I

Stag

e II

Terminate

Result

Stag

e II

I

Fig. 1. General structure of the proposed method.

A. Load and Wind Data Load data of power systems are highly variable with time.

The estimation of these data is carried out by using advanced methods. In TEP studies, the load profile of the IEEE reliability test system have been used, thus the same process is used in this study [10]. Besides the load data, wind speed data is also highly dependent to the weather condition. To include the WTs into the formulation, the wind speed data should be converted to the corresponding power by using the following equations [11]:

⎪⎪⎩

⎪⎪⎨

⎧

≤≤≤

≤≤≤≤

+=

UUUUU

UUUUU

PbUa

P

co

corated

ratedci

ci

rated

k

WT

0

0

0

(1)

where U is the actual wind speed, Uci, Uco and Urated denote cut-in, cut-out and rated speed of WT, Prated is the rated active power of WT and k is an exponential coefficient. a and b can be expressed as follows

krated

kci

kcirated

UUUP

a−

= (2)

krated

kci

rated

UUP

b−

−= (3)

Although the using hourly load data allow us to gather more detailed information, the computational time increases substantially as expected [7]. For this reason, annual load and wind speed data are sampled in the weekly base. For this reason, the hour with the highest wind power production in each week is obtained as

( ) 52,...,2,1,...,,max 16821 == iforPPPMP WTWTWTi

WT (4)

where iWTMP is an 1×52 array which is consist of the peak

wind power production in each week. Sampling process is completed by picking out the corresponding load data of each i

WTMP . At the end of this process, the dataset D is obtained as

[ ] [ ]inb

ij

iiWT dddMPiD ......1= (5)

where ijd represents the load power of jth bus at week i. This

procedure is denoted as Stage I in Fig. 1.

B. DC-OPF based Economic Dispatch DC-OPF can be used to evaluate any objective function by satisfying the power system constraints. System planners are responsible to dispatch economically by considering system constraints. It is clear that the generation of WTs will have maximum value due to the zero average production cost of them. However, transmission line constraints can make the wind energy to be wasted. To calculate the WWE, a DC-OPF based economic dispatch is performed for each week in this study. This section is represented by Stage II in Fig. 1.

Mathematical model of the DC-OPF [12] can be formulated as

Minimize

( ) ∑∑==

+nl

kk

ng

m

mgm rPF

11α (6)

Subject to drPfS g =++ (7)

( ) nbjifornf jiijijij ,...,2,1,0 ==−− θθγ (8)

nbjiforfnf ijijij ,...,2,1, =≤ (9)

gg PP <<0 (10)

dr <<0 (11) where Fm is the cost function of unit m. ng, nl, and nb are the number of generators, number of buses which have load and number of buses, respectively. γij, nij, fij, and ijf represent the susceptance of the line or transformer between buses i-j,

number of line or transformer between buses i-j, the power flow and the corresponding maximum power flow, respectively. It should be noted that the modeling transformer is the similar to the line. Pg is an array with elements m

gP

which is generation in bus m and gP is the corresponding maximum value. S is the branch-node incidence matrix, f represents an array which is consisted of fij, and r is the vector of artificial generations with elements rk. Artificial generation which represents the loss of load is penalized by a cost α ($/MW) in the objective function. This problem is solved by using quadratic programming in this study.

After solution of DC-OPF is obtained, the wasted wind energy (WWE) can be calculated as

52,...,2,1=×−×= iforNPNMPWWE WTsch

WTWTi

WTi (12)

where NWT is the number of installed WTs and schWTP

represents the scheduled power of WT according to the results of DC-OPF. To find the approximate annual TWWE, following equations can be used

⎟⎠⎞

⎜⎝⎛×=∑

= 52873652

1iiWWETWWE (13)

On the other hand, total loss of load should be calculated to be used in the GA optimization. To take advantage of WTs, minimization of TWWE is required. Next section will describe this minimization process by using GA.

C. GA based Optimization Expansion planning is the most critical decision making process to maintain reliable power system operation in the power system. In classical TEP, the cost of new added lines is tried to minimize while the loss of load is kept at the acceptable level, even zero [12]. However, the objective function should be reviewed by the integration of renewable energy. So, the maximization of wind power usage is also desired in the deregulated environment. For this reason, the new lines should be added to minimize the TWWE due to the line flow restrictions. To find the location and number of new lines, GA based optimization is proposed in this study, while minimizing TWWE. The fitness function can be formulated as follows:

Minimize

TLOLTWWECn ij

nb

ji

newij ×+×+∑ αβ

,

(14)

Subject to

newij

newij nn ≤≤0 (15)

where Cij, newijn , and new

ijn are the cost, number and maximum number of lines or transformers to be added between buses i and j. new

ijn is an integer variable. In this formulation, β represents the average production cost of conventional generators that is used to compensate the wind energy to be wasted. The proposed objective function handles the trade-off

between cost of new transmission lines and cost of the non-reduction of TWWE by optimizing the location and number of new transmission lines. It is clear that it will try to minimize the TWWE by adding new lines when the cost of the non-reduction of TWWE is higher than the cost of lines. At the same time, it will try to minimize cost of new added lines. By this way, power system planners can avoid overinvestment of transmission lines while providing maximum usage of WTs.

This optimization problem includes a DC-OPF in the inner loop as can be seen in Fig. 1. For this reason, classical optimization problem cannot be used due to the nonexistence of exact analytic equation. Metaheuristic optimization techniques are powerful tools to solve that kind of problems. One of the most used optimization tool is GA. GA is based on the natural selection and natural genetics [13]. It is a search based optimization algorithm and suitable for solving the unconstrained optimization problems. The differences between the GA and classical optimization methods are as follows [13]: The derivative of fitness function is not needed. The value of it is only used for optimization. This procedure can be applied both discrete and integer programming problems.

III. SYSTEM UNDER STUDY The proposed methodology will be implemented to the

IEEE 24 bus reliability test system [10]. The system under study, as shown in Fig. 2, has two voltage levels which are 138 and 230 kV. There are 10 generator buses and 1 synchronous condenser bus. The branches with lines and transformers are specified in the line data of system [10]. In this study, transformer addition is allowed only to the branches which have already a transformer.

Fig. 2. IEEE 24 bus reliability test system.

Annual peak load of the system is 2850 MW, but it is assumed that the load will be increased 20% [6]. The sampled load data according to the weekly base is given in Fig. 3. It can be seen that the maximum and minimum total load are 2994

MW and 1190 MW, respectively. The generator buses at the low voltage side will be considered as WT locations. Chosen WT has the following specifications; Prated = 1.8 MW, Uci = 3 m/s, Urated = 12.5 m/s, and Uco = 20 m/s. The weekly based active power generation of a WT is obtained as shown in Fig. 4.

Fig. 3. Weekly sampled load data.

Fig. 4. Weekly sampled wind power data.

In the problem formulation, objective function of DC-OPF and fitness function of GA are formed by using two parameters α and β. α is a penalty value to minimize loss of load, so it should be set a high value which is 106 $/MW in this study [3]. On the other hand, as mentioned before, β represents the average cost of conventional generators to compensate the TWWE. Thus, 50 US$/MWh is chosen for β [5]. In this study, all right of ways which already exist are considered to installation of new lines and transformers. Transformers and line branches are specified in the line data of the system. The investment cost of lines and transformers are given in Table I [5].

TABLE I. INVESTMENT COSTS

Type of Equipment Investment Cost 138 kV Line 88,000 (US$/mile) 230 kV Line 130,000 (US$/mile) Transformer 3,000,000 (US$)

IV. CASE STUDY The proposed method to minimize total cost of new lines

and TWWE is evaluated under different scenarios. These scenarios are summarized in the Table II. The reference

scenario is that there is no new line addition. Other scenarios are different WT allocations in the system and different maximum number of new line to be added during the optimization process. This problem is solved by using an integer GA. The parameters of GA are chosen as;

- Population size is 70. - Crossover fraction is 0.8. - Maximum generation is 100.

TABLE II. SCENARIOS

Scenario No.

WT bus (Number of WTs)

Maximum Number of Lines

1 (Reference) 1 (400), 2 (400) - 2 1 (400), 2 (400) 1 3 1 (400), 2 (400) 2

4 (Over investment)

1 (400), 2 (400) 2 lines or transformers are added in each right

of way

5 1 (250), 2 (250),

3 (300) 1

6 1 (250), 2 (250),

3 (300) 2

In the reference scenario, the TWWE is calculated as 5.0199×106 MWh/year as shown in Table III when the 800 WTs are installed at buses 1 and 2. Although, there is no new investment for lines or transformer, the value of fitness function is substantially high. When the second scenario is solved for maximum one new line or transformer in each right of way, the fitness function value is reduced significantly, even approximately 2.3 times, as shown in Fig. 5. The optimum value of fitness function is found to be 1.3311×108 after the nearly 20 generation. It is clear that GA is able to solve this problem efficiently. The GA performance of the other scenarios will not be given because of the space limitation. In the third scenario, maximum allowable line addition is increased to two for each right of way. It is obvious that relaxation of constraint of maximum allowable addition results in the better result in terms of both TWWE and investment cost. The optimum line configurations of both scenarios 2 and 3 are given in Fig. 6. It can be seen clearly that although the number of lines found in scenario 3 is more than that of scenario 2, the investment cost is smaller than the other due to the fact that the length of right of ways are different.

TABLE III. RESULTS OF FIRST FOUR SCENARIOS

Scenario No.

Fitness Function [$]

TWWE [MWh/Year]

Investment Cost [$]

1 2.5110e8 5.0199e6 0 2 1.3311e8 2.2364e6 2.1296e7 3 1.2781e8 2.1531e6 2.0152e7 4 2.3263e8 2.0891e6 2.3814e8

In the fourth scenario, two lines or transformers are added to the each branch without implementing the proposed method to see the effect of overinvestment. In this case, it can be seen that there is an improvement in TWWE in comparison to scenario 3. It means that installing new line and transformer to

the other right of ways has an impact to reduce the TWWE. However, it causes a huge increase in the investment cost as expected. For this reason, one can conclude that construction of new lines and transformers are not a trivial task. TWWE can be reduced significantly by using the proposed method while minimizing investment cost.

Fig. 5. GA performance of the second scenario.

Fig. 6. Optimum configurations of scenarios 2 and 3.

Other two scenarios are formed to evaluate different WT allocations and maximum number of lines or transformers. In these scenarios, the 800 WTs which are used in previous scenarios are allocated to the three buses. The results are given in Table IV and V. The values of fitness function are smaller than the values of scenarios 2 and 3. On the other hand, the investment cost of the new lines is significantly reduced if WTs are allocated more buses. It is found that 3 new lines are enough to minimize TWWE in scenario 5 while 4 new lines should be installed to get better TWWE in scenario 6. It is clear that allocation of WTs have great impact on the optimal solution. These results show that the proposed method has a good ability to deal with the maximization of WTs in the power systems while minimizing investment cost. By this way, power system planners can decide the optimal investments while utilizing the advantages of WTs.

TABLE IV. RESULTS FOR SCENARIOS 5 AND 6

Scenario No.

Fitness Function [$]

TWEE [MWh/year]

Investment Cost [$]

5 1.2163e8 2.3252e6 5.3680e6 6 1.1288e8 2.1220e6 6.7760e6

TABLE V. OPTIMAL RIGHT OF WAYS FOR SCENARIOS 5 AND 6

Scenario No.

Right of Ways (Number of lines)

5 Buses 1-5 (1), Buses 5-10 (1), Buses 7-8 (1) 6 Buses 1-5 (1), Buses 5-10 (1), Buses 7-8 (2)

V. CONCLUSION In this paper, a new method to minimize TWWE and investment cost simultaneously is proposed to determine optimal location and number of new lines to be added. The main contribution of this paper is to define a novel objective function that can handle the TEP problem considering WTs. The proposed method is consisted of three stages; wind and load data preparation, DC-OPF based economic dispatch, and GA based optimization. The results show that optimal right of ways can be determined by using the proposed method by avoiding the overinvestment. Thus, this method can be used as a decision making procedure in the planning centers.

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