Abstract
The objective of this study is to develop a wind farm placement and investment methodology based on a linear optimization procedure. This problem has a major significance for the investment success for the projects of renewable energy such as wind power. In this study, a mesoscale approach is adopted whereby the wind farm location is investigated in comparison with a microscale approach where the location of each individual turbine is optimized. Specifical study focuses on the placement of a wind farm by economical optimization constrained by the power system, wind resources, and techno-economics. Linear optimization is introduced in this context at the power system which is constrained by wind farm planning.
IN addition to the rapid depletion of fossil energy sources, the increasing environmental impact of fossil fuels has led to a proactive search for alternative energy sources. Among alternative energy sources, wind energy comes to the forefront owing to its renewable and rapid installation features. The results of Turkish potential wind power are estimated to be 88000 MW [
A probabilistic load flow methodology considering large-scale integration of wind power was proposed in [
In addition to technical constraints [
Supply reliability regulation of Turkey [
Likewise, the placement of microscale and mesoscale wind farms has also been performed by adopting different optimization techniques, as shown in
To summarize, the list of models and applications in the aforementioned studies used single or multi-objective optimization models. Optimization models for the integration of wind energy systems into the power grid usually aim to capture some of the critical challenges arising from the variable nature of wind energy, multi-objective nature of energy policy formulation, operation issues resulting from the integration of wind energy, and the considerable role of power system characteristics.
This study aims to develop a wind farm placement and investment methodology according to the maximum number of wind farms and minimum installation/production costs under the constraints such as wind potential, power system, and turbine technologies. Within the scope of this study, the original results are listed as follows.
1) The optimization is realized by identifying possible wind areas and shortening the pre-planning time of the wind energy fields.
2) The installation cost components of a power plant are added to the optimization study in detail. Accordingly, the most economical settlement forces of the candidate plants, the connection distances to the energy system, and the costs of these connections are taken into consideration in this study.
3) Economic placement of the system is made by considering not only the regional wind speed, but also its geographical characteristics such as roughness structure and elevation.
4) Using the optimization algorithm, the possibility of selecting the appropriate technology for the region is provided by considering the effects of different technologies on the production cost.
5) When sizing the power plant, the target wind farm is dimensioned for the target region by considering different power options that can be installed in the region.
6) When the energy system constraints are taken into consideration, the questions about how many power plants can be connected to a busbar in economic and technical terms in busbar regions, the total power that can be connected, and the production values upon gaining connection can also be solved with the algorithm.
The remainder paper is organized as follows. In Section II, the theory of the methodological approach is introduced, which is followed by numerical results in Section III and conclusions in Section IV.
As shown in
The objective of the optimization algorithm is to minimize the production and investment costs of the maximum number of wind farms that can be connected to a region within the power system. The optimization algorithm consists of two linear integer optimization blocks. The first one calculates the maximum number of wind farms that can be connected to a power grid. In the second one, the optimal wind power plant placement that can be connected from the first optimization algorithm is obtained by considering the investment cost, production cost, and reliability.
The minimization of production costs given in the objective function equation is defined as a master problem by integer programming. The sub-programs where production values are controlled, and the feasibility and minimized investment costs are defined as linear programming according to the connection configurations determined by the main program. The Bender decomposition algorithm is used to solve the objective function by dividing it into sub-optimization blocks.
The methodology developed in this study is illustrated in

Fig. 1 Flow chart of methodology.
The optimization algorithm given in this study is implemented on an Intel(R) Core(TM) i7-8550U CPU @ 1.80 GHz with 64.0 GB of RAM, and the programs are developed using MATLAB R2014a. Detailed information related to the optimization is provided in the sub-sections.
To conduct a regional wind analysis, long- and short-term wind speed, wind speed direction data, regional elevation, roughness, and landform information are used. The wind data of Catalca Radar Station from January 1, 2009 to November 1, 2010 are used as reference wind data in the regional wind analysis. This station is at an altitude of 369 m at the coordinates of 41.341185° North latitude and 28.356778° East longitude. For this study, geographic coordinate information is selected on the European side of the city of Istanbul between 41.085° to 41.255° North latitude and 27.929° to 28.784° East longitude. With regard to the scope of this study, surface roughness maps in the data library of the WindPRO/WAsP program are used to calculate natural obstacles without consideration of artificial obstacles [
Firstly, the average wind speeds are calculated to generate regional wind speeds according to the reference wind speeds. The mean wind speeds at different altitudes are calculated by subtracting the friction coefficients for each coordinate and the wind distributions in the region according to the reference wind speeds. To calculate point capacity factors, wind speed-power curves of wind turbines with different technologies are converted into mathematical equations by using the curve fitting method with MATLAB. In addition, wind power information, wind speeds, and belly height friction coefficients based on the mathematical model are obtained from the wind turbine database defined in the WindPRO program [
The input elements of the optimization algorithm are components of the analyzed region (location information and regional geographic map, roughness map, elevation map, long-term wind measurement data, and regional short-term wind measurement data), information of reference wind turbines (nominal power, rotor diameter, tower height, and turbine technologies), power system information (installed plant information, busbar, and transmission lines), network and bus connection restrictions, economic installation and operation data, and optimization constraint information.
A flow diagram of the developed algorithm is illustrated in

Fig. 2 Flow diagram of economic placement algorithm.
The combination of investment and production costs of the maximum wind farms that can be connected to the system and the mathematical equation for this optimization is provided in (1).
(1) |
Minimizing the investment cost is stated in (2) as the main problem. The main problem is to establish power plants in the working area with a minimum installation cost. The investment cost is assigned as .
(2) |
The optimization is based on the establishment of wind power plants. Accordingly, the integer variables that each wind farm can take are defined as 0-1 variables. As an additional constraint, (3) is added, after which the main problem is solved.
(3) |
The primary purpose of these sub-problems is to solve the problem related to production costs. However, it is necessary to check whether the system is operating within safe limits before solving this problem. Therefore, the optimization problem can be solved based on the fact that the candidate wind power generation plants selected according to the annual investment cost in the master problem can meet the loads on the system; in other words, the load shedding value is zero.
As a result of these two optimization processes, cost optimization is performed for the case where the limit values are obtained. If the sub-optimization problems cannot be solved under the existing constraints or if there are infinite solutions, the feasibility and optimality multiples will be calculated and added as a constraint to the main problem. According to the reorganized constraints, the main problem is solved again.
As per the second sub-problem, the objective function is to operate the appropriate solutions at optimal production values from the first sub-problem. In this manner, the maximum number of wind farms that can be installed in the power system is determined. The maximum connection number is reduced by one until the optimum connection number is found when the mixed-integer optimization problem could not be solved in the number of connections given at the beginning. The objective function for the maximum number of wind farms that can be connected to the power system (MG), is given in (4).
(4) |
This step is the production cost optimization. If the optimal value is found as a result of the feasibility optimization, the sub-optimization, where the optimal production value given in (5) is calculated, would be started. The objective of production cost optimization is to minimize the total production cost value. The €/kWh unit obtained from the economic analysis as the production cost value is used by converting €/MWh for production costs. Although the production values of conventional power plants is defined as a parabolic curve under real conditions, it is linearized assuming a constant in this study.
(5) |
The constraints used in the optimization are provided as belows. Accordingly, the maximum number of power plants that can be installed in the system is defined as the sum of the elements whose initial value can be connected to all busbars. In case the optimization at the maximum connection number does not produce appropriate results, the optimization process will be continued by reducing the maximum number until the optimal value is found by using (6).
(6) |
The number of wind turbines defined with different technologies and at different heights shall not exceed the maximum connection number defined for the busbar. To achieve the optimization constraint, wind turbines with the lowest unit production cost are defined for each busbar, as illustrated in (7). In the event where the lowest production cost is not available, the element is converted to the matrix form given in (8).
(7) |
(8) |
The matrix in (9) is obtained by rearranging , which depends on the busbars and turbine technologies.
(9) |
In (9), the matrices obtained for each technology are recalculated according to the target height value of the wind power plants to be established before being converted into (10).
(10) |
The matrices in (10) are collected by (11) and a connection matrix with ns rows and nw columns is obtained for each busbar where the connection and the non-connection values are 1 and 0, respectively.
(11) |
The constraint for the connection matrix is given in (12).
(12) |
The wind farm site is evaluated using multiple technologies, simultaneously. The optimization constraint on the construction of a power plant for the potential farm area is defined in (13).
(13) |
It is checked whether the wind farms are in operation. If the value of the wind farms is enabled, the status is defined as 1, otherwise 0. In (14), the integer changes of the wind farms are defined. Accordingly, it is accepted that wind turbines do not draw power from the power grid.
(14) |
The permissible load shedding limits for the reliability requirement considered for the constraint in each busbar are given in (15). If the intention is always meeting all loads in a busbar, the total value of (15) will be assumed to be equal to zero.
(15) |
The constraint is Kirchhoff’s first law, which is shown in (16), and accordingly, the equality of total production in a busbar to total consumption is defined.
(16) |
Kirchhoff’s second law, which is considered in the constraint, is given in (17). Meanwhile, the load flow on the power transmission line is defined as the ratio of the phase openings of the busbars, to which the power transmission line is connected.
(17) |
In the constraint, it is defined that other plants already established in the system should operate between the minimum and maximum production limit values given in (18).
(18) |
According to the constraint, the candidate wind farms in the system should operate between the minimum and maximum limit values given in (19).
(19) |
According to the constraint, the transmission lines in the system must operate between the minimum and maximum limit values given in (20).
(20) |
The busbar angles in the system must operate between the minimum and maximum limit values given in (21).
(21) |
The maximum number of wind power plants that can be connected is determined by changing the conventional power plant production values as a result of the obtained optimization. Additionally, the maximum number of wind farms determined by the number of wind farm connections are defined as the new bus constraint, which is a subset of the initial bus constraint vector.
New busbar constraints and maximum connectable wind farms are sent as inputs to the Bender separation method. The purpose of the first sub-optimization problem () is to ensure that all loads in the working zone operate within the specified load shedding values in (22). As per the scope of this study, it is intended that the needs of load energy can be met and load shedding values are accepted as zero.
(22) |
The constraint functions of the first sub-optimization problem consist of (15)-(21), which are used to define the DC load flow constraints and the maximum and minimum limits of the variables in the power system. In the first sub-optimization, (21) is rearranged and transformed into (23) and (24).
(23) |
(24) |
The first dual sub-optimization factors of wind farms, and , are defined as the amounts of production cost reduction in the case of an increase of 1 MW power generation. They are used in the feasibility layer calculation to be added in non-feasible cases, as given in (25). The calculated feasibility level is subsequently added as a constraint to the main optimization problem given in (1).
(25) |
If there is no optimal result of the second sub-optimization problem, the calculated optimal coefficient in (28) will be added as a constraint to the main optimization problem given in (1). The equation constraint functions of the second sub-optimization consist of (15)-(21).
(26) |
(27) |
The multipliers and represent the dual factors of the optimality of wind farms, and are defined as the amounts of reduction in production costs versus a 1 MW increase in power generation. The constraints of the optimization problem are listed in the following items. The upper optimization limit y is calculated using the formula given in (1), whereas the new lower limit (Z) is defined in (28).
(28) |
The difference between the lower and upper limits is expressed as optimization termination criteria [
(29) |
In power system analysis, it is very difficult to analyze the national grid in its entirety. For this reason, selecting the region directly affected by the work and performing the analyses related to the selected region will increase the intelligibility while reducing the calculation time. In this study, the power system section, including the Ikitelli (B1), Buyukcekmece (B2), Catalca (B3), Silivri (B4), Trakya Elektrik (B5), Botas (B6), and Akcansa (B7) busbars in the first transmission system connected to Turkish National Energy Transmission System, is selected as the working area. The coordinates of the selected busbars on the geographical system (35 time zones) are listed in
The lengths of transmission lines between the busbars, the electrical parameters of the transmission lines, the nominal power of the transformers, and the maximum and minimum generation values of the generators were used to model the selected region [
The single-line diagram of the section within the first transmission system, which is taken as a reference for the modeling of wind energy systems in the Turkey National Electricity Network, is illustrated in

Fig. 3 Single-line diagram of the 7-bus system connected to the first transmission line.
In accordance with the scope of this project, the model belonging to two different wind farm manufacturers, as shown in
The lowest cost busbar is selected considering the the coordinate information of the connection point, the transmission line distance to the busbar, the total investment, reduced investment, and unit energy generation values. In the calculations made with a resolution of at a height of 70.0 m, 440 wind areas are found, and each area is calculated based on energy generation, reduced annual energy, and unit energy costs, as depicted in
In

Fig. 4 Distribution of wind farms with a resolution of according to busbars in the test zone.
In the maximum connection optimization, the number of initial wind farms that can be connected to all busbars is calculated to be 30. After the maximum connection optimization process, the number is 11 due to power system constraints. The distribution of the 11 wind farms to the busbars is shown in
According to the obtained results, the total number of wind farms that can be connected to each bus is arranged as the initial constraint of Bender decomposition optimization. Accordingly, the most economical connection model of the 11 wind farms is calculated in accordance with the configuration, as given in
As a result of the third iteration shown in

Fig. 5 Convergence of algorithm optimization.
Wind power plant located within the boundaries of B4 is found to be the plant with the highest capacity value in the area. It is also the wind farm with the lowest energy generation cost among the selected turbines, as shown in

Fig. 6 Representation of busbar-based power plant locations on the map.
By analyzing the potential wind power of a region without consideration of the technical and economic aspects of power system components, it can lead to significant errors in the target planning. As an evaluation result of regional wind data alongside power system components in this study, the endeavor is to obtain more realistic results in determining the connectable regional potential wind power as well as to increase long-term planning accuracy. Through utilizing this developed optimization, the maximum number of wind farms that can be connected to a region as well as the capacity factor of these wind farms and unit energy production costs are obtained.
Thus, in the regional energy planning process, priority comparisons can be calculated as to which power plant can be installed or which regions can receive priority analysis.
Although 50 MW power plants are used as a base, the algorithm, optimization, and functions can be used within different power values.
The effects of different sized wind power plants can be examined. In this manner, the impediments to the use of wind power resources at higher power values can be partially overcome. In this study, the wind turbines with different technologies are considered and compared.
According to both cost and turbine power generation values, the regional potential wind power is analyzed for tower heights of 74.5, 89.5, and 94.0 m, respectively. It is observed that the most suitable height is 94.0 m, and the most suitable technology is the PMSG. When the region is divided into areas with 50 MW power plants, there are 440 potential areas. When the recycling and system connectivity of these candidate plants are technically and economically optimized, it is calculated that 50 MW wind farms in 11 regions can be built and the total annual cost of the wind farm is 268.38 M€. This study specifically focuses on the placement of mesoscale wind farms by economical optimization constrained by power systems, wind resources, and techno-economics. However, the proposed methodology can also be used to optimize large-scale or microscale wind farms. Although wind is used as the energy source in the optimization process prepared in this study, it has an easily adaptable structure for planning other energy sources, especially solar energy.
Nomenclature
Symbol | —— | Definition |
---|---|---|
—— | The first sub-optimization dual factor of wind farm | |
—— | Limit dual factor of the optimality of wind farm | |
—— | Busbar degree | |
—— | Desired difference | |
max | —— | Representation of maximum value |
min | —— | Representation of minimum value |
—— | Permitted cut-off value | |
—— | Unit cost of energy production | |
—— | Number of wind turbines that can be connected to the busbar | |
—— | Turbine technology and busbar | |
—— | Wind turbines with the lowest unit production cost defined for each busbar | |
—— | Target height value of the wind power plants to be established before being converted into the matrix form | |
—— | Connection matrix in which the wind power plants can be connected to each busbar according to location technology, and heights within the region | |
—— | Capacity factor | |
—— | Annual investment cost for wind power plants | |
—— | Annual production cost for wind power plants | |
—— | Annual production cost for installed power plants | |
—— | Vector of load for busbars | |
—— | Power flow on transmission line between busbars m and n | |
—— | Power generated by the planned wind farms | |
—— | Wind farm area index | |
—— | Iteration index | |
j | —— | Wind power plant technology index |
—— | Available tower height index of selected wind farm technology | |
—— | Busbar index | |
—— | Bus number | |
—— | Total number of farm areas | |
—— | Total number of technologies | |
—— | Total number of installed power plants | |
—— | Total number of installation heights of wind turbine tower | |
—— | Total number of available busbars | |
—— | Power plant index | |
—— | Representation of busbar and transmission lines | |
f | —— | Vector of load flow |
—— | Annual maintenance and repair cost | |
—— | Matrix of production plants in busbars | |
—— | The lowest generation value of the power plant g | |
—— | The highest generation value of the power plant g | |
—— | Power generated by installed power plant q | |
—— | The highest carrying capacity of transmission line | |
—— | Vector of the accepted load shedding value for each bus | |
—— | Calculated load cut-off value for each bus | |
Xmn | —— | Reactance of the transmission line between the busbars m and n |
—— | Integer variable of optimization (0-1) | |
—— | The upper limit of optimization | |
—— | The lower limit of optimization |
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