Robust generation expansion planning in power grids under renewable energy penetration via honey badger algorithm

Generation Expansion Planning (GEP) is one of the most relevant problems in the planning of electric energy systems. It addressed the problem of identifying the most adequate technology, expansion size, sitting, and timing for the construction of new plant capacity considering economic criteria and technical power system constraints. However, it is necessary to guarantee that demands will be continuously supplied in all conditions were either an unexpected peak demand is occurred or an important unit fails [1]. The expansion planning criteria can be considered as conditions and limitations based on the decision-making process [2]. They are reflections of the positive features, which the planners would like to have in any future plan [3, 4] and preparing preventive control actions for active power [5] and reactive power issues [6].

Recently, the inclusion of uncertainties with various aspects has been considered in the GEP model as an effective approach to energy efficiency, conservations, CO₂ emission and environmental concerns. Thus, the planning should be investigated to affect by changing in parameters due to uncertainties and its capability to accommodate any changes [7]. In general, uncertainty analysis is critical for assessing the risks of any system that contains any type of uncertainty. The uncertainty which depends on nondeterministic in nature cannot be reduced while the uncertainty, which caused by limited knowledge about the system, is reduced as the search space expands [8]. However, integrating high share Renewable Energy Sources (RESs) within the power system planning had imposed a significant impact of uncertainties. Therefore, ignoring the variability and stochastic nature of RES within the GEP model may result in a lack of robustness of the planning results. Due to the fluctuation and the unpredictable characteristics of wind speed, wind power will have significant impact on the system security, stability, and reliability [9]. Therefore, techniques and approaches for dealing with such wind uncertainties should be more efficient and accurate which can be classified as probabilistic and possibilistic approaches [10]. Besides wind power uncertainty, there are other uncertainty sources such as load growth, fuel price, fuel costs, and the outage of generating units have also impact on expansion plans. Moreover, there are several studies considering wind energy penetration and PV as renewable sources for microgrid system such as [11, 12].

In the planning process, the nature of the GEP problem is nonlinear, mixed-integer, highly constrained, and dynamic. The study of GEP without considering RESs has been introduced such as [13, 14] based on minimizing the total costs and satisfying reliability constraints. In recent years, several studies have been conducted on the reflection of environmental protection by adding emission limit constraints. Also, the impact of integrated RESs in power systems and their resulting uncertainties has been treated in the modeling of GEP problem. Expansion capacity planning requires not only total costs minimization, but also wind power uncertainty analysis and emission control should be handled over the planning horizon [15, 16].

The GEP problem has been solved by several analytical and optimization techniques without considering uncertainty analysis such as a Non-dominated Sorting Genetic Algorithm version II (NSGA-II), Modified Shuffled Frog Leaping Algorithm (MSFLA) that have been used in Refs. [14, 18 and 17], respectively. Also, Loss Of Load Probability (LOLP) has been computed as a reliability criterion in GEP problem which is evaluated based on the cumulative method as [19] where it has been modeled as Mixed Integer Programming (MIP). As a result, a model of least cost generation capacity expansion to control carbon dioxide emissions was presented, taking into account the effects of uncertain load and wind power generation [20, 21]. Moreover, the generation and transmission expansion planning (TEP) has been addressed without considering RESs uncertainty as [22]. The GEP dimensionality is large which the length of a string is equal to the product of the number of planning stages and the number of candidate unit’s types. So that, the Virtual Mapping Procedure (VMP), Penalty Factor Approach (PFA), and the Modified of Intelligent Initial Population Generation (MIIPG) have been accomplished to decrease the GEP problem search space and reduce the computational time [17, 23].

In addition to the above, RES uncertainty is incorporated into generation and transmission expansion planning for a long and short-term planning horizon. In [24], the GEP problem with a certain penetration level of RESs has been solved by dynamic programming, while the wind and solar plants was modeled in Wein Automatic System Planning (WASP-IV).Besides, the effect of renewable energy uncertainties was assessed in the reliability and stability of power system. So that, it is important to develop decision support tools to help generation companies for achieving maximum their profit in a deregulated electricity market as [25, 26]. Also, a coordinated generation and transmission expansion planning in a deregulated electricity market have been addressed with wind power uncertainty analysis as [27]. The wind farm uncertainty was modeled by a normal PDF, and MCS has been utilized to include the uncertainty into the GEP or GEP/TEP problem. The combined GEP and TEP were handled with correlation of load and generation uncertainties that system uncertainties have been modeled with PDF and MCS to generate different random scenarios [28]. Also, Particle Swarm Optimizer (PSO) has been used to solve the TEP problem with reactive power planning and consideration of wind and load uncertainties as [29] while SFLA was performed in [30]. MCS was utilized to simulate the wind output power based on its PDF. Also, a deep learning method is one of the recent methods to deal with time series data such as the long short-term memory (LSTM) network algorithm which have been used for the same problems as in [31, 32]. But it has more steps to create output and consume more time which is not effective for expansion planning. However, the wind power uncertainty has been represented by annual variation of capacity factor based on historical data of wind location where the effect of wind power variation is analyzed at a certain probability of expectation [33]. Furthermore, both long and short-term wind power uncertainties were modeled within the GEP problem. The annual variation of the capacity credit was used to simulate the wind power long-term uncertainty. On the other side, the short-term uncertainty was simulated based on the hourly variation of wind power as [34]. Added to that, reserve margin has been adopted to cope with the uncertainty effect [34], while additional capacities of Pump Hydro Storage (PHS) and Fast Gas Turbine (FGT) have been utilized to cope with short-term uncertainty problems [35]. The problem of short-term uncertainty was modeled using the autoregressive moving average model. The main shortage in [33‐35] is that the forced outage rate (FOR) of generating units was not taken into account at variable cost calculations where the FOR constitutes serious impacts on energy supplied of each generating units and reliability indies.

Furthermore, different battery technologies and demand side management options have been used to cope with the renewable energy uncertainties for off-grid hybrid renewable energy systems [36]. In this paper, the PV and biomass as renewable energy sources have been considered but the wind energy, which has more intermittent and variability of output power and affect the cycling charge of batteries, was not considered. However, the wind energy penetration in microgrid system design is considered in [37, 38], but it was dispatched as a certain value and wind energy uncertainty, and variability was not taken into account that has big effect on the system reliability. Furthermore, For the optimal sizing and techno-economic assessment of the intended hybrid microgrid system consist of solar diesel generator, PV, battery storage, and wind turbine, four dispatch approaches have been unitized: load following, generator order, combined dispatch, and cycle charging strategy while the system reliability study were carried out using Dig-SILENT Power Factory [39, 40]. Also, uncertainty of wind energy was not considered through system reliability calculation. Moreover, the wind speed and power conversions uncertainties are ignored in [41] and the wind power is calculated by specified model not based on a wind site study.

For reliability indies and variable cost calculations, the probabilistic production cost simulation using the Equivalent Energy Function (EEF) [14, 42] and Effective Load Distribution Curve (ELDC) [43] methods shows suitable accuracy with small computational time. Moreover, the RES uncertainties have been handled by the point estimate method for yearly peak loads uncertainties [44] and for distributed GEP in power distribution networks [45]. In [46, 47], the uncertainty of wind power has been modeled as a constraint depending on the wind availability in each hour. Therefore, the adoption of an hourly commitment of generating unit was considered to show the short-term impacts of long-term strategies through the decision-making process. In [15], the GEP analysis with different electricity scenarios for a mixed hydro-thermal and wind plants was performed which have impact in terms of costs and CO² emissions over the planning period. The carbon emissions have been added as an objective function as in [48].

Considering the incorporation of RESs into GEP problem, a whale optimization algorithm was carried out with adjustment strategies to decrease the GEP problem search space such as MIIGP, VMP, and PFA [49]. However, wind and solar output power have been studied at certain scenarios of penetration and emission reduction levels. In [50], differential evolution algorithm was used for minimizing the least cost GEP with certain penetration levels of wind capacity with emission reduction with certain penetration levels of solar power plants as [51, 52]. Also, wind power was considered at only specific capacities through the modeling of GEP problem without discussing varied scenarios [53]. However, there are several wind scenarios which are not considered to lead to negative impact in reliability and security system.

RESs uncertainty consideration has a vital role in the planning and operation analysis of power system. Uncertainty analysis has an impact on the reliability and stability of the power system. So that, it is necessary, integrating the RES uncertainty analysis into the expansion planning problems. The presence of wind energy uncertainties is incorporated into the proposed GEP model in this paper. The first step is to assess the impact of long-term wind uncertainties using annual variations in capacity credit at two real-world sites in Egypt, Zafaranh and Shark El-ouinate. The second step addresses each wind site's short-term uncertainties. A PDF is used to model the wind speed uncertainty at each wind site. The wind power curve for each wind site is then used to estimate wind power, and MCS is performed. Sensitivity analysis is used for three, six, and twelve stages as short and long planning horizons to reduce total costs associated with wind energy penetration and emission reduction constraints over planning horizons.

The contributions of this paper can be summarized as follows:

The following portions of this work are organized as follows: Section II presents the conventional GEP model, whereas Section III establishes the proposed GEP model including the wind power uncertainty. Section IV describes the developed HBA for reliability constrained dynamic GEP. Section V defines the discussions and simulation findings. Finally, section VI concludes this paper.

The objective function of the GEP problem is to minimize total costs over the planning period. In this context, the candidate units are responsible for the investment and salvage costs, but the candidate and existing units are jointly responsible for the operation, maintenance, and outage expenses.

Capital investment cost (\(I\left({u}_{t}\right))\) is the cost of purchasing new candidate units that can be provided by

Each generation unit's fixed cost is determined by its capacity, and its variable cost is determined by the anticipated amount of energy that each generation unit will produce at each stage. Therefore, good prediction of the variable costs and reliability indies is essential to provide more precise estimation of the predicted energy produced by each generation unit.

Based on the expected energy not served (EENS), it is possible to calculate the anticipated energy generated by each generation unit. The EENS and LOLP, which are reliability indies, can be calculated by conventional method or PPS method to obtain cost modeling. The established capacity outage probability table, load probability table, and margin between them are the components of the traditional technique, which is used to compute reliability indies [55]. Because of the generous size of the GEP problem, this conventional method is not suitable and takes more computational time. Thus, there are other PPS methods that are more efficient for estimating the variable costs and the reliability indies with smaller computational time. In this context, the EEF method is one of PPS methods, but it depends on the greatest common factor for all adding capacities of existing and candidate units [42, 49]. Also, the ELDC is another method for any additional capacity in the planning [43].

Reliability constraint (LOLP): To continue supplying electricity continuously, both the new and current units need to meet the reliability criterion. A reliability metric called Loss of Load Probability (LOLP) is typically used to show how robust a system is in the face of unforeseen events.

The calculation of expected energy produced by each generation unit, and reliability indices are especially critical issues for solving the GEP problem. For that purpose, PPS methods have been widely used for such calculations. The ELDC is used in this study for LOLP, and EENS calculation. Then, expected energy produced is calculated based on EENS calculation [43]. In the ELDC, the capacity and FOR of the generator \(i\) are equivalent to \({c}_{i}\) and 0 with the fictitious load added to the original load. The sum of the original load and the probabilistic additional load is called effective load as formulated as:

The ELDC is described in Fig. 1 can be calculated as:where \({\Phi }_{{\text{i}}}\left({{\text{LD}}}_{e}\right)\) is the PDF of the ELDC convolved with the PDFs of the outage capacities of the generators, 1st to \(i\)th;\({\Phi }_{i-1}\left({{\text{LD}}}_{e}-{{\text{LD}}}_{{\text{oi}}}\right)\) is the PDF of the ELDC convolved with the PDFs of the outage capacities of all the generator, 1st to N-1. Also,\({f}_{{\text{oi}}}\left({{\text{LD}}}_{{\text{oi}}}\right)\) is the PDF of the outage capacity of the \(i\)th generator. The ELDC can be generated by convolving the load curve and the plant outage capacity which leads to the following:

Using the \({\Phi }_{N}\left(x\right)\), LOLE and EENS can be calculated using ELDC as following:

The expected energy produced \({E}_{i}\) of the \(i\)th generator can be derived as follows:

The probabilistic generated energy \({\Delta E}_{i}\) of the \(i\)th generator can be calculated as following:

Long-term uncertainty of the wind power is embedded into the planning model through the variation of the wind capacity credit of each site. The reliability indices such as LOLP and EENS are calculated based on existing and candidate units by PPS methods. FOR of wind plants are calculated, in this study, by sliding window technique as [49, 50]. It is assumed that FOR values for wind energy are constant over the study period. Based on that technique, the capacity factor of each wind site is estimated by annual wind energy produced divided by the rated capacity. The capacity factor is calculated using Weibull distribution parameters of wind speed [35] which is different for each wind site as follows:

However, the FOR values for wind plant of each site are calculated as follows:

The output of a wind site is related to the output of a single wind turbine, and it scales linearly with the number of wind generators. All wind turbines have similar input–output characteristics since installing different wind turbines in the same wind site is not usual.

Consequently, the wind power from two Egyptian wind sites (Zafaranh and Shark El-Ouinate) is added to candidate units in the base case. The long-term uncertainty of the wind power is imposed into the planning model through the variation of the wind capacity credit of each site. The traditional objective function of GEP model described in Eq. (7) is updated by adding the costs of investment \({{\text{in}}v}_{w}\), operating \({{\text{oper}}}_{w}\), and fixed \({{\text{fix}}}_{w}\) terms of each wind site as follows:

Also, additional constraints related to the two wind sites should be merged which are the wind level penetration and emission reduction constraints over all planning period as follows:

For ease of the construction and manpower, two wind sites should not be selected in the same stage which is represented in the following constraint:

The MCS is used to include wind short-term uncertainty in the problem. Each site of Zafaranh and Shark El-ouinate has different mean and variance wind speed which affect the output capacity of it. Therefore, Weibull distribution parameters are assessed individually for each site. Moreover, there are two main sources of uncertainties related to wind RESs: wind speed forecast uncertainty and the wind-electrical power conversion curve [8]. The wind speed uncertainty is simulated by accurate estimation of Weibull parameters, while the wind speed power conversion curve is selected based on each wind site characteristics. The scenario-based MCS is a commonly used tool to deal with wind speed uncertainty in the problem [56]. For each scenario of MCS, the wind speed is a randomly generated based on its Weibull PDF which is characterized by the following equation [57, 58]:where v is the wind speed.

The most efficient model for each site is applied based on the minimum error of energy density for Zafaranh \({g}_{z}\left(v\right)\) and Shark El-ouinate \({g}_{s}\left(v\right)\) sites, respectively [59] as follows:

The general form can be represented as the following equation:

The objective function of the proposed GEP model with short-term uncertainty \({({\text{ob}}}_{{\text{sc}}})\) is defined as adding the costs of adding units \({({\text{ob}}}_{{{\text{add}}}_{{\text{cap}}}})\) to the base case \(({\text{ob}})\) and wind costs \({({\text{ob}}}_{w})\) as follows:

For each scenario, all constraints for the base case and long-term uncertainty are examined. The addition of new FGT and/or PHS units under a wind power violation scenario could alter the system's fuel mix ratio Eq. (10) and overall emission Eq. (25). Therefore, whenever a new unit is added, those constraints need to be checked again.

HBA is an entirely novel meta-heuristic technique that is based on how honey badgers hunt for their prey in an intelligent way. It is brave and prefers to spend time alone in self-made burrows, only meeting other badgers to mate. To access bird nests and beehives for food, it can also climb trees. A honey badger finds its prey through sniffing, digging, or following a honey guide bird, which can find beehives but cannot obtain honey. Exploration and exploitation phases are developed from the honey badger's dynamic search behavior using digging and honey-finding methods [60]. Firstly, an initial population is generated based on the number of honey badger and their respective positions as follows:

The intensity (\({{\text{In}}}_{i}\)), which is related to concentration, prey strength, and the distance between the prey and the honey badger, is then specified. The motion of the prey will be fast at high smell intensity and vice versa. The intensity is defined as follows:

The density factor \(\left(\alpha \right)\) is specified and updated which controls time varying randomization to ensure a smooth transition from exploration to exploitation phase. So that, this factor decreases with iterations to decrease randomization with time as follows:

A flag (F), which alters the search direction, is generated to enhance escaping from local to optima regions. The positions of the agents are then updated, and \({x}_{new}\) is modified in accordance with the two stages of the digging phase and the honey phase as follows:

Then, the positions of agent’s \({x}_{new}\) are updated via digging and honey phases A. The honey badger's digging phase resembles the shape of a cardioid, which can be simulated by doing the following:where \(\beta\) is the ability of the honey badger to get food which is greater than or equal to 1 (default = 6).

In the honey phase, a honey badger follows the honey guide bird to reach beehive which is simulated as follows:

The flowchart diagram of the HBA is shown in Fig. 2. Therefore, a honey badger performs search closed to prey location, and the searching process is influenced by time varying (\(\alpha\)). Also, the HBA performance is significantly affected by two user-defined parameters (\(\beta and Ch\)) so that these parameter values should be selected carefully. In this context, the best parameter values (\(\beta =6,\mathrm{ and Ch}=2\)) of the proposed algorithm are taken from [60].

The proposed GEP problem is a high large dimensional problem with multiple conflicting objectives, uncertainty analysis and nonlinear constraints which represents a complex optimization problem. Thus, some modifications are proposed to enhance the HBA to deal with this problem. VMP, PFA, and MIIPG improve the effectiveness of the meta-heuristic algorithm as follows [23, 49]:

Figure 3 describes the evaluation of the expected total costs with short-term uncertainty representation based on scenarios of MCS. As shown, each scenario is checked for the constraints and other generating units of PHS and/or FGT can be added as referred in block (D), in some cases, to meet the constraints. Then, the objective function of the current scenario is calculated, which is saved and MCS is reiterated. After convergence of MCS, the meaning of all expected values of scenarios is evaluated. For each scenario, the objective function is calculated after adding the costs due to addition capacities. Then, the mean value of all scenarios is considered as the objective function for this particle.

The test system consists of 15 existing generation units (Oil, Liquid Natural Gas (LNG), coal and Nuclear) is tabulated in Table 1. Five different new generation technologies are selected as candidate conventional units (Oil, LNG, Coal, and Nuclear) as in Table 2. The forecasted peak load is illustrated in Table 3, with initial peak load of 5000 MW, and other data of existing and candidate generation units are taken from [14, 23, and 61]. In this study, the discount rate is taken 8.5%; LOLP criterion at each stage is considered of 0.01. The lower and upper limits for reserve margin are set at 20 and 50%, respectively. EENS cost is assumed to be 0.05 $/kWh. The bounds of capacity mixes by fuel types are 0% and 30% for oil-fired power plants, 0 and 40% for LNG-fired, 20 and 60% for coal-fired, and 30 and 60% for nuclear, respectively. The emission coefficient for oil is 0.85, LNG is 0.5, and coal is 1.05 while the reduction in total emission is considered as 10% of base case [49, 50, and 62]. The cost of unserved energy, or EENS, which is calculated by ELDC method, is set at 0.05 $/kWh. The initial period is set as two years while the economic and technical characteristics of the additional units are listed in Table 2 as [35].

The candidate wind sites, in this study, are Zafranah, and Shark El-ouinate wind farm sites. The first site, Zafaranh wind farm, is in the Suez Gulf which is approximately 200 km southeast Cairo. While the second site, Shark El-ouinate, is in depth southern Egyptian desert. The operational data of wind turbines and their descriptive statistics, which are considered in this study for the two sites, are recorded in Table 4. Added to that, the time series data of the wind speed for the year 2019 in hourly basis of Zafranah, and Shark El-ouinate wind farm sites are taken from [63]. As shown in Table 4, the mean wind speed value of Zafaranh site is greater than its value for Shark El-ouinate site. But the variance and standard deviation for Zafaranh site are less than it values for Shark El-ouinate. Thus, most values of the generated wind speed scenarios based on PDF for Zafaranh site will be around the corresponding mean and below its maximum speed other than Shark El-ouinate site which reaches maximum speed values with a smaller number of scenarios. So, studying each wind site with its characteristics is especially important for the reliability, and security of the power system.

HBA is used to solve the GEP problem as base case and wind energy uncertainty analysis based on the considered three policies planning horizon as follows:

Two cases are considered in the first two polices in this paper. The first case study is performed using the proposed framework, and results are compared with different other techniques in the literature. This case study is the base case in which the original problem is solved without wind energy penetration and emission reduction constraint. Then, the second case study is implemented for solving the GEP problem which includes wind energy uncertainty analysis and emission reduction objective function. Added to that, an extra scenario that aims at minimizing the total GHG emission as an objective function: