Technical/economic/environmental optimal wind generation allocation in power systems

ABSTRACT


INTRODUCTION
With the growing concerns about the need of reducing emissions of greenhouse gas and climate change, wind power has emerged as a clean and renewable source of energy.Unlike fossil fuels, wind energy does not produce any harmful emissions or pollutants, making it a much more environmentally friendly option.Additionally, wind power is a domestic resource that can help countries reduce their dependence on imported oil and gas [1].Furthermore, the cost of wind energy is gradually becoming more competitive with that of fossil fuels, rendering it a desirable choice for both consumers and utility companies.Wind power integration has grown rapidly in recent decades as a result of continued attempts to reduce reliance on fossil fuel resources.As of the end of 2021, the worldwide cumulative installed capacity of wind energy had reached 837 GW [2].Increased wind power penetration poses several obstacles to the energy grid's functioning, spanning from stability to dependability of the system.Some of the most important problems with grid functioning are directly associated with the growing use of wind energy in distribution systems, especially radial distribution networks (RDNs).With the help of competent policymaking and updated regulations, distributed energy resources (DERs) that have a maximum capacity of 50 MW have acquired a lot of traction in power networks as replacements or complementary options to traditional energy sources.The location and sizing of DERs in a distribution network are critical, as failure to do so can result in significant voltage instability, power losses, reliability concerns, financial losses, and increased harmonics [3].Obtaining the desired interconnection of a WF in an RDNs frequently necessitates a complex analysis that includes network data and WF operational capability, as well as other relevant factors such as reverse power flow, frequency regulation, voltage regulation, islanding protection, ISSN: 2088-8694  Technical/economic/environmental optimal wind generation … (Zeinb Abdelhay) 433 prediction of localized solar irradiance for PV.The study employed MCS and was conducted on two actual distribution networks, an 11-bus network and a large feeder in South Australia.A planning framework was recommended for the optimal size and placement of ESS in the distribution networks [17].This framework aimed for minimizing the total cost of energy supply while ensuring network reliability, using the MILP model to optimize DGs placement and sizing.The suggested model was tested on a real 33 kV distribution network in the UK.Similarly in [18], a planning framework was introduced for the optimal size and placement of renewable DG in the distribution networks.The framework aimed for minimizing the total cost of energy supply while ensuring network reliability, also utilizing the MILP model to optimize the placement and sizing of renewable DGs.The study was conducted on a real 33 kV distribution network in the UK.
In 2018, Abad et al. [19] presented an optimization approach for the optimal location and sizing of multiple DGs and ESS in the distribution networks.The approach used the MILP model to minimize the total cost of energy supply while ensuring the reliability of the network.The suggested approach was implemented for a real 33-kV distribution network in the UK.A stochastic optimization approach was proposed in [20] for the optimal placement of multiple DGs in a radial distribution system.The approach was designed to consider uncertainties in load demand and renewable energy generation, and it used the MCS method to generate stochastic scenarios.The optimal placement and size of DGs were obtained through the MILP model.The implemented method was applied in a 69-bus distribution system.
In 2020, Jafari et al. [21] proposed a method for determining the optimal size and placement of switched capacitors which are using the hybrid optimization algorithm.The algorithm consisted of two inner and one outer optimization layer.The outer layer was implemented by a genetic algorithm (GA), while the inner layer was performed by either a GA, PSO, or exchange market algorithm (EMA).The study utilized IEEE 33-bus and 69-bus networks.Jafari et al. [22], an approach was introduced for determining the optimal capacity type and capacity of generation resources for microgrids (MGs) that incorporated renewable energy sources (RESs) such as WTs and photovoltaics (PVs), as well as diesel generators at each bus of the MG.The optimization problem was solved using EMA in MATLAB, with 200 iterations.The mean time for one iteration was approximately 10 seconds, and the overall time averaged around 30 minutes over the course of the study in 2020.
Overall, these studies demonstrate the growing interest in the optimal strategizing and operation of DG and systems of energy in distribution networks.The studies use a variety of optimization techniques, including PSO, MCS, evolutionary algorithms, and MILP.The results show that these approaches can help to improve the reliability and efficiency of distribution networks while promoting the integration of renewable energy sources.In Table 1 compares the mentioned methods according to the objectives and functions that are taken into account.Table 1.Comparative analysis of different methodologies related to optimal location and sizing of wind turbine Reference Economic issues EVI Voltage profile Losses [6], [12], [13], [18], [21]  This paper managed to find the optimal allocation of a WF consisting of two WTs in a transmission network taking into account several objectives associated with economic, losses, voltage profile, and environmental impact represented in the reduction of carbon emissions and maintains four constraints which are transmission line power limits, power flow equations, active power constrain, and bus voltage limits, which to the author's knowledge have not been combined all together on one optimization problem in the literature before.To tackle the optimization problem in its entirety, the PSO algorithm and Newton Raphson method for load flow analysis are employed.In this context, there are two WTs added to the transmission network and a MATLAB was created to assess their performance under different capacities and locations within the system.The validity of the proposed approach was confirmed using the IEEE 14-bus transmission system.The paper is structured as follows: i) Section 2 outlines the problem being addressed; ii) Section 3 describes the methodology used; iii) Section 4 presents the results and discussions; and iv) Section 5 concludes the paper and suggests directions for future research.

PROBLEM STATEMENT
The location of WTs in the electrical grid is a critical and important aspect that should be taken into consideration during the setup of any WF.There are many problems faced the integration of wind energy in the grid when wind turbines are not optimally allocated such as reduced energy production, increased costs, environmental impacts, and community opposition.The annual wind speed variation is represented using the Weibull distribution [23].The probability density function   () and the cumulative distribution function   () of the Weibull distribution are defined as ( 1) and (2).
In the formula, where  represents the scale parameter,  represents the shape parameter, and  represents the Weibull random variable (wind speed) [23].Characteristics of wind speed vary depending on wind direction, according to measurements.These equations explain how the probabilistic wind speed model integrates the correlation between the speed and direction of the wind.Annual wind data (typically collected hourly) at a single location is divided into   intervals according to ongoing direction.Afterward, a Weibull distribution is applied to represent the values of wind speed grouped for each interval, along with a frequency measure that indicates the proportion of the ten wind directions in this interval concerning all intervals [24], [25].Consequently, the model defines the probability density function of the speed of wind for a specific location as (3).
Where   is the overall number of direction intervals, and   is the frequency of  ℎ interval.
There are various factors, including wind speed, rotor blade size and shape, and generator efficiency, that affect the amount of energy that can be harnessed by a WT and converted into electrical energy.Usually, the amount of energy that a WT can capture increases as wind speed increases, but there is a limit to how much energy a WT can capture based on the maximum output of the generator and the rotor blades design.If the wind speed is too low, the WT may not generate enough energy to be economically feasible, while if the wind speed is too high, the WT may need to be shut down to prevent damage to the equipment.Thus, WT operators continuously monitor wind speed and alter the rotor blades direction to optimize energy generation while maintaining safe operating conditions.The energy available in the wind is transformed into a practical type of energy by WTs.The power output of a WT based on wind speed is given as (4).
The formula includes the parameters   ,   , and   which represent the output power, rated power, and rated speed of the wind turbine, respectively.To initiate power generation, the wind velocity must exceed the critical cut-in speed   , and the turbine will discontinue its operation at wind speeds that exceed the cut-off speed   to avoid damage and stop power production [25].The probability of zero output power can be evaluated as the total probability of wind speeds being either below the cut-in speed or above the cutoff speed [26].Where  is a small positive number.

METHOD
This study primarily aims to find the optimal location and size of WF consisting of two WTs in a power system, considering several technical objectives.The objectives that this work takes into account are operation cost, power losses, voltage profile, and environmental impact.Newton Raphson method is used for load flow analysis and PSO is used for solving optimization problems.The PSO algorithm [9] is a method of population-based optimization that utilizes a group of particles to find the optimal solution.Each particle represents an individual and the clusters of particles are known as a swarm.One of the advantages of PSO is that it is easy to implement and does not require knowledge of gradients.The problem's solution space is transformed into a search space in PSO, with each point in the search space representing a potential solution.The particles work together to locate the best position (optimal solution) within the search space (solution space).Each particle's movement is determined by its velocity [27].
PSO is an optimization algorithm, that differs from MFO, GWO, and WOA even enough all of them are metaheuristic optimization methods [28]- [33].PSO uses a velocity-based search strategy, where each particle's velocity is updated based on its own position and the swarm's best position.PSO uses a set of empirically determined equations to update the particle velocities and positions.The PSO algorithm can have a variable number of iterations depending on the problem being solved, the size of the search space, and the convergence criteria.In general, PSO iterations continue until a stopping criterion is met, such as a maximum number of iterations being reached, a minimum error threshold being achieved, or the fitness value no longer improving.A typical number of iterations for PSO can range from a few hundred to several thousand.However, the optimal number of iterations for a given problem can be determined through experimentation and tuning until we get to the best values of hyperparameters [34].The PSO parameters used in training our model were as follows: a maximum number of iterations = 1000, population size (swarm size) = 100, inertia weight W = 0.8, inertia weight damping ratio (wdamp) = 0.9, personal learning coefficient c1 = 1.5, global learning coefficient c2 = 2, number of WFs = 2, WFs _max.Size = [300, 250], and WFs _min.Size = [10,40].

The objectives
In general, objectives refer to specific goals or targets that an individual, organization, or project aims to achieve.Objectives provide a clear and measurable direction for action and help to focus efforts toward a desired outcome.The objectives that this paper takes into account are mentioned below.

Operation costs
The operation cost of generators is a critical objective that must be taken into account.The generation cost of thermal generators is expressed as in (6).
Where:   ,   , and   are the thermal generation cost coefficient.The used generation cost coefficients of five generators are illustrated in Table 2. Due to the variability of available RES at any given point in time, the model should account for factors that may cause overestimation or underestimation of their availability.The reason for the overestimation factor is straightforward: if the model assumes a particular amount of renewable energy power will be available at a specific time, but it is not, alternative sources of power must be utilized or the demand for power must be reduced.In the case of an underestimation penalty, if more renewable energy power is available than expected, the surplus energy may go to waste, and the system operator may charge the RES power product for the loss of capacity.Typically, excess renewable energy is sold to neighboring utilities or quickly redistributed.If neither of these options is feasible, load resistors may be connected to "consume" the excess power.A clearly, a straightforward minimization penalty cost function may be used to model these activities as shown in [23]: (  ) =   ƒ  (   )  +  . (   −   ) +  . (  −    ) (7) where   is the total cost of WF generators ($),   is the cost coefficient of WF generators ($/MW), ƒ  (  )  the Weibull  of WF generator,  . is the cost coefficient of WF generators because of over-generation ($/MW),   is the scheduled output of WT generators, and  . is the cost coefficient of WF generators because of under-generation ($/MW).The cost coefficients of WF are calculated as ( 8) and ( 9) [23]:

Maximizing annual WT generation
The relation in (10) presents an optimization problem aimed at identifying the optimal solution for the WF allocation issue.The goal is to maximize the total annual power generation expected from the chosen locations while complying with the regulations set by the transmission system operator.As a result, the objective function (  ) to be maximized is defined as (10) [35].
()) × 8760 (10) In the context of the optimization problem, (  ) denotes the total annual power generation from the WFs, while N represents the total number of possible WF locations that meet the established criteria.  () is the cumulative distribution function (CDF) of the power output for the WF at the  ℎ site, and   represents the capacity of the WF at the  ℎ site.

Reducing total losses
Either the load flow software running on the system or using the B-coefficient method can be used to calculate the transmission losses.The first one is used in this study based on the following expression of transmission losses as (11) [23].
Where   is the conductance of the transmission line that connects bus i and bus j.   ,   are the voltage levels of bus i and bus j, respectively   is the difference in voltage phase angle between bus i and bus j.

Improving voltage profile
The voltage constraints will be as follows: In order to achieve the desired voltage level at a particular bus in the network, automatic voltage regulation is employed, which involves controlling multiple components in the system, such as the reactive power generation in synchronous generators.This control is achieved through the use of complementary constraints that generate a discrete function as described in [36].To obtain a continuous approximation of this behaviour, a sigmoid function is used, which has been finetuned for this purpose.
Where   and  are the voltage set point and a tuning parameter that determines the sensitivity of the control function, are both used in the process [ 37 ] .Also mentions the use of the sigmoid function for voltage regulation.The following are the required limitations for generator voltage control: where  1 and  2 are two auxiliary variables with the continuous interval [0 1] as their bounds.Given that the generator's reactive power output is restricted by   and   , the reactive power produced by the generator will be constrained and eventually reach one of the following states.

Maximization of the environmental index (EVI)
Evi is a parameter that measures environmental considerations proposed in [38] and expressed as (17).
It is assumed that producing 1 MWh of energy from fossil fuels releases around 0.93 metric tons of greenhouse gases.

Solution space constraints 3.2.1. Transmission line power limits
According to (18), where |   | and  ,  are the absolute and maximum power transmitted through the distribution line connecting nodes  and , respectively.It`s one of the primary factors that limit transmission line power is the maximum current that the line can handle.The amount of current that can flow through a given transmission line is limited by the line's physical characteristics, as well as the surrounding environment, including temperature, humidity, and wind speed.

Power flow equations
According to (19) and (20), where   and   represented the active and reactive powers that are injected,   and   are the voltage magnitude and phase angle at  ℎ bus.Also,   and   are the magnitude and phase angle of the branch admittance connecting  ℎ and  ℎ buses.Power flow analysis is essential for power system planning and operation.By analyzing the power flow in a network, potential problems can be identified, such as overloaded transmission lines or voltage instability, and take corrective actions to ensure that the power system remains stable and reliable.

Active power constraints of the WPG
According to (21), where  ,, and  ,, are the minimum and maximum permissible power of the  ℎ WTG.Active power constraints are typically implemented to ensure that the power system remains stable and reliable.When the amount of active power being generated or consumed exceeds the system's capacity, it can lead to voltage instability, frequency fluctuations, and even power outages.

Bus voltage limits
According to (22), where   and   are the minimum and maximum allowable magnitudes for the bus voltage.Bus voltage limits are important because excessive voltage can damage equipment, while low voltage can cause equipment to malfunction or even fail.In addition, voltage levels that are too high or too low can lead to instability in the power system, which can cause power outages and other problems.

RESULTS AND DISCUSSION
The proposed method has been tested on the modified IEEE 14-bus transmission system [38].The data for a system based on 100 MVA.The range of acceptable voltage magnitude and phase angle is between 0.95 p.u. and 1.05 p.u.The discussion can be made in several sub-sections.The wind speed is unstable and changes throughout the day, Figure 1 shows minimum, maximum, and mean speed all day long.

Cost
After optimization, the optimal costs of five generators are 630.14, 472.33, 393.6, 423.6, and 748,236$.So it can be said the total cost of generators improved from 13,300$ to 2,668$.Figure 2 shows the improvement that occurred in the cost of generators after optimization.

Power losses
By using Newton Raphson load flow analysis, without optimization real and reactive losses respectively are 7.6011 MW and 29.5488 MW and total losses are 30.75125MW.After running 50 iterations and optimization by PSO real and reactive losses respectively become 6.0005 MW, 23.4639 MW, and total losses are 24.390863MW.In summary, optimization has minimized total losses, and the minimum achievable loss is 24.390863MW.This occurs when the optimal location and size of the two WTs at bus 3 and bus 14 and the optimal size are 300 MW and 250 MW respectively.Figure 3 shows the total losses of the system before and after optimization, and Figure 4 shows the active power of the turbine during the day.

Voltage profile
The voltage profile improved in the system after PSO optimization generally and especially at bus 3 from 1.01 to 1.03 p.u. and bus 14 from 1.017 to 1.05 p.u. Bus 3 and bus 14 have been identified as the optimal locations based on the voltage profile analysis.Figure 5 shows the improvement of the voltage profile and active power.

EVI
Figure 6 shows that EVI without PSO optimization is 531.7 and after optimization 639.4.So, it can be said that EVI is improved and the optimal EVI is 639.4.Although the model is active, it has also limitations.It may be inefficient to find the global optima if the search space gets enamors or is very complicated that is why we choose to optimize a selected number of objectives and we applied the complete Int J Pow Elec & Dri Syst ISSN: 2088-8694  Technical/economic/environmental optimal wind generation … (Zeinb Abdelhay) 439 iteration for each objective separately.Also, the PSO algorithm suffers from a major limitation regarding finding the global optimum solution, it is known that PSO like other population-based optimization techniques, is susceptible to premature convergence, which can result in suboptimal solutions and to overcome this limitation we were careful to initialize the PSO hyperparameters with values that were proven to perform ideally in previous work [34].Also, the model was very consuming regarding computational resources and memory requirements.And we do not believe that the model could be scalable to larger populations.Table 3 presents the improvement achieved in each objective before and after optimization.

CONCLUSION
An innovative multi-objective planning methodology for identifying the optimal location and size of a WF consisting of two WTs in a transmission system based on operation cost, losses, voltage profile, and the environmental index has been proposed in this work.The used optimization method is PSO and Newton Raphson method for load flow analysis.The total cost improved from 13300$ to 2668$, so the percentage of improvement is 79.94%.Total losses improved from 30.75125 MW to 24.390863 MW, and the percentage of improvement is 20.68%.The voltage profile improved at bus 3 from 1.01 to 1.03 p.u., and at bus 14 from 1.017 to 1.05 p.u. EVI is improved from 531.7 to 639.4, and the percentage of the environment is 20.26%.So it can be said that the optimal allocation of two WTs is at bus 3 and bus 14 where optimization of all objectives occurs on it.These results are shown in Table 3. Future research should consider extending this study to various WTs.Additionally, it might be explored whether adding energy storage would have any effects on the dependability and financial aspects.

Figure 5 .Figure 6 .
Figure 5. Voltage profile of the system before and after optimization

Table 3 .
Comparison of objectives before and after optimization