Adequate Operation of Hybrid AC/MT-HVDC Power Systems Using an Improved Multi- Objective Marine Predators Optimizer

This paper presents an Improved Multi-Objective Marine Predators Optimizer (IMMPO) for optimal operation of hybrid AC and multi-terminal-high voltage direct current (AC/MT-HVDC) power systems. The proposed IMMPO incorporates an external repository to conserve the non-dominated preys. Furthermore, fuzzy decision making is employed to select the best compromise operating point for the hybrid AC/HVDC power systems. In these systems, the active and reactive power controllability of the voltage source converters (VSCs) are activated besides the full control in AC grids via the committed generators, transformer tap settings and VAR compensations. The modelling of the VSC losses is integrated in its quadratic function of the converter current. The optimal operation of AC/MT-HVDC power systems is handled as a multi-objective problem for minimizing the total fuel costs, the environmental emissions of the generation units and the total losses over the AC, HVDC transmission lines and VSCs stations. For solving this problem, several recent optimization algorithms are applied on a modified standard IEEE 30-bus. Also, a real part of the Egyptian West Delta Region Power Network emerged with VSC-HVDC grids is considered as a practical case study. The simulation results demonstrate the effectiveness and preponderance of the proposed algorithm with great stability indices over several competitive algorithms. Nevertheless, the proposed IMMPO is successfully extracting well-diversified Pareto solutions while a compromise operating point is effectively produced to satisfy the operator requirements.

Variables and Parameters R ik Resistance of phase reactor and coupling transformer between the converter ''i'' and the AC grid ''k'' X ik Inductance of phase reactor and coupling c transformer between the converter ''i'' and the AC grid ''k'' S ki Total injected apparent power into i th VSCs from the k th AC grid The best position of the preys that achieves the minimum fitness. µ i Membership function for each objective function (J)

I. INTRODUCTION
In the last two decades, many electrical grids suffered to keep up with the increased electric power demand, especially the emerging countries. Restrictions imposed on the prices of electricity production from conventional sources and higher costs of conventional transmission systems expansions represent one of the obstacles for many electrical networks to meet the increased load demand which reduces systems reliability, security and power quality [1], [2]. Also, after the Paris Agreement of 2015, parties to the UNFCCC reached a landmark agreement to combat climate change. To meet the targets of this agreement a fully decarbonized and sustainable electricity systems by 2050 is the future vision of many countries worldwide [3]. Developed large scale renewable power plants are, usually, far from load centers, which requires modernization of the transmission networks. Similarly, interconnection of power grids of faraway countries to reduce the peak load burden and take advantage of the available renewable resources and running reserves between power grids needs economic and efficient transmission solutions to improve the levels of operational security, as well as maximizing the operational flexibility and reliability [4]. OPF is one of the most conspicuous and integral tools in power systems operation and control, introduced by Carpentier in the early 1960s. The main goal of the OPF is obtaining the most economical combination of power plants to precisely serve the total demand of the system without any load shedding or islanding [5]. It usually seeks to prescribe the most suitable settings of voltages and powers from the generators besides the VAR devices and transformer tap values to attain the key objectives when complying with technological VOLUME 9, 2021 limitations [6]. OPF's key goals are to minimise generation costs, reduce network losses, reduce emissions, optimise loadability, improve voltage quality and improve reliability while preserving various equity and inequality restrictions [7].
Worldwide utilization of VSC based HVDC for transmitting large amounts of electric power over long distances increases day by day because of its advantages. HVDC is an economic solution of transmitting large amount of electric power over long distances such as interconnection of power grids of faraway countries or remote large renewable power stations. Also, HVDC is widely adopted for electric power transmission through undersea/underground cables [8], [9]. The decoupled ability to monitor the VSC active/reactive powers facilitates advanced controls to the interconnected AC sides and independently from the transmitted DC power. MTHVDC grids are built using parallel VSC configurations using modular multi-level converters [10]. The MTHVDC configurations improve the possibilities for combined AC/MTHVDC systems to grow such as Zhangbei project in China which is expected to incorporate large quantities of renewable energy [11].
Power flow within the HVDC networks can be overloaded as it happens in AC grids and conventional OPF cannot control the operation of such integrated MTHVDC grids. In power systems, traditional operational methods of economic dispatching [12], OPF [13] and state estimation [14], etc., must be updated incorporating the interconnected MTHVDC systems. Owing to the OPF role in power system planning and operation, it needs technical and formulation improvements to incorporate combined AC/MTHVDC grids. For this reason, OPF gets much more nonlinear, nonconvex and complicated when extended to combined AC/MTHVDC schemes [15].
Literatures deal with the OPF with several aspects. Refs. [16]- [18] studies the OPF of AC grids with several objectives and with/without renewable power penetration. Refs. [19], [20] studies the OPF of DC grids only. Mathematical formulation of OPF for AC-MTHVDC networks got a great attention in literatures such as [21]- [25]. In these literatures, the DC lines and cables are represented via their equivalent series resistance, resembles that of AC grids. The modelling of the VSCs is more intricate, which can be elaborately modeled as a controlled voltage source considering the transformer, filter, phase reactor, and converter [24]. Refs. [26], [27] study the economic assessment of VSC-HVDC compared to AC alternatives for the connection of the offshore wind farms or connection of bulk networks. In many of these reports, the evaluation of VSC-HVDC technologies was restricted to the setup of two terminals. However, the inclusion of MTHVDC with AC grids raises the complexity of their control and operation [21], [28]. In [29], a hybrid algorithm for the AC/DC transmission expansion has been presented but it lacked the DC power flow modelling for some AC/MTHVDC components. In [30], the AC/MTHVDC system has been handled via the application of SOCP technique while the PDIP method with adjusted Jacobian and Hessian matrices have been utilized in [31]. In [21], IPOPT has used to address this problem with a nonlinear paradigm developed in GAMS software. In [24], an expanded OPF was implemented to accommodate various converter modes of operation. Within these reports, the influence of the VAR compensators and tap transformers inside the Ac system were completely overlooked, while the methods used are highly dependent on the original starting point.
Considering the converter losses, Bardar et al. [30] assumed the converter losses to be proportional to passing active power through the converter. In [2], [32]- [34], the converter losses were represented by a variable shunt conductance proportional to the square of the AC current of the VSC. In [15], [35], the power losses in the converters and their transformers were completely neglected. In the provided study, the modelling of the VSC losses is accurately handled in its quadratic generalized formula which increases the convexity of the optimization problem.
MPO is new algorithm for optimization that is natureinspired from the various strategies that are accomplished by the predators to increase their preys hunting rates [36]. Its high-performance over various algorithms such as GA, PSO, GSA, CSOA, SSO and CMA-ES in solving various benchmark functions [36] motivates this research, at the first time, to adopt the MPO and propose an IMPO for optimal operation of AC/HVDC power systems. The IMPO aims at achieving several objective functions of minimizing the TFC, the TAEE related to the generators and the TPL. In the proposed IMPO, the predator's strategies are merged to consider the random circumstances' occurrence of the environment. Also, it augments a memory saving capability to the preys as well as the top predators.
The goal of the multi-objective model of the optimum operation of hybrid AC/ MTHVDC systems is to achieve technical economic benefits and respecting produced emissions from the generation stations. To achieve these benefits, a novel improved multi-objective MPO (IMMPO) is developed to simultaneously handle bi and tri objectives of the above. The proposed IMMPO commingles an external archive with a specified volume. In this archive, the nondominated preys are conserved whilst Pareto dominance is activated to compare the new and old preys. Nevertheless, the top predator, in each iteration, is extracted from the least congested zone in the archive in a random way through Roulette wheel selection. Furthermore, fuzzy decision making is employed to select a compromise operating solution for the AC/MTHVDC system. The proposed IMMPO is developed in MATLAB language and applied on a modified IEEE 30-bus, and a practical part of the Egyptian system of WDRPN to solve the considered problem in AC/MTHVDC Grids. For such implementations, the suggested algorithm is comparatively assessed with different modern algorithms of BAT [37], [38]; CSOA [39], [40]; DA [41]; MVO [42]; SSO [43]; PSO; GWO [44].
Simulation results that are carried out on two test systems show the capability of the proposed solution methodology in finding diversified Pareto solutions with several possible operating points. The feasibility and efficacy of the proposed IMMPO has been verified by a thorough evaluation of the consistency and robustness of its approach with other recent algorithms. The key contributions of this work could be summed up as follows: Provide an accurate model for the optimal operation of hybrid AC/DC grids. The optimal operation of AC/MTHVDC power systems is handled as single and multi-objective framework for minimizing the TFC, the TAEE and the TPL over the AC, HVDC power systems and VSC stations. The IMMPO incorporates an external repository for the conservation of the nondominated preys while the updated process of the prey's positions in each iteration is changed to be based on the dominance priority.

II. OPTIMAL OPERATION OF AC-HVDC POWER SYSTEMS A. VSC MODEL IN AC-MTHVDC GRIDS
Two types of converters are conventionally used for twoterminals HVDC links, that are VSCs and CSCs. With the development of power electronic devices and converters technologies the MTHVDC systems is suggested as a promising solution for modernization of the transmission networks interconnecting several generating and load centers [30]. What distinguishes the VSCs-HVDC over the CSCs-HVDC is its ability of controlling the reactive power and thus the voltage at the AC side. Fig. 1 shows the simple configuration of the AC-MTHVDC grid, which includes three VSCs interconnected by three DC lines. Each VSC is represented as a controlled voltage source. The phase reactor and coupling transformer between the converter ''i'' and the AC grid ''k'' are represented as an AC line with equivalent inductance and resistance (R ik +jX ik ). The total injected apparent power into i th VSCs from the k th AC grid is given by; The injected current from the k th AC grid to i th VSCs can be calculated as; From (1) and (2), the active/reactive powers on every side of VSC and at the AC connected side can be represented as follow;

B. ECONOMIC ENVIRONMENTAL OPERATION OF AC-MTHVDC GRIDS
As previously mentioned, solution of economic environmental operation problem is a power flow solution that provides the optimum values of the control variables for a particular load situation via optimizing a specific objectives functions while maintaining the operational variables constraints. In the OPF formulation, multifarious objectives can be addressed like fuel costs minimization, environmental emissions reduction of the generation stations and active power losses reduction over the AC, HVDC power systems and VSC stations, etc. while maintaining equality and inequality constraints. Selecting these multiple objectives for solving the proposed problem is very important since they give several benefits. The fuel costs minimization represents an economic dimension, and the emissions reduction of the generation stations represents an environmental dimension whereas the active power losses reduction over the AC, HVDC power systems and VSC stations represents a technical dimension. Based on the above, the proposed problem is considered a multi-objective optimization as it involves more than one objective function to be optimized simultaneously.
The general form of OPF problem can be obtained as; In this paper, the optimal operation of AC/HVDC power systems problem is modeled as a nonlinear, multimodal and multi-objective problem.

1) OBJECTIVE FUNCTIONS
OPF is a nonlinear and nonconvex multi-objectives optimization problem. The first considered objective is the fuel generation costs (F 1 ). Because the steam admission in generation units always subject to the continuous change in steam valves, which is known as the valve point loading effect, the valve point loading effect leads to fluctuations in the fuel cost [45], [46]. Therefore, the fuel cost function, in this paper, is formulated by added rectified sinusoids to the quadratic cost and it is expressed as [45]; Fossil-fueled turbines are the primary cause of atmospheric pollution in electrical systems where Sox, NOx and CO2 are emitted. The total ton/hr emissions (F 2 ) of the pollutants is formulated as follows [47]; The third objective is the TPL (F 3 ) in the AC-MTHVDC grids which are the combination of transmission losses in the AC grid, the combination of transmission losses in the DC grid, and the VSC losses as [21], [22]; F 3 = TP loss = P loss−AC + P loss−DC + P loss−VSC (12) The AC and DC losses are represented in (13) and (14), respectively.
The modelling of the VSC losses can be handled in its generalized formula as a quadratic function of the converter current [21]- [23];

2) CONTROL VARIABLES
For AC-MTHVDC grids, the coupling relationship is employed between the control devices in the AC and HVDC power systems. At first, the AC controls are traditionally performed via the generators output power and voltage, transformers tap settings and VAR injection sources, which can be represented as [47];

3) DEPENDENT VARIABLES
Similarly, the dependent variables of AC grids are generally load bus voltage magnitudes, generator reactive power outputs of the generators, and transmission line loadings, which can be represented as [48]; Additionally, the dependent variables of the MTHVDC side are the DC bus voltage and the power flow though the DC lines.

4) CONSTRAINTS
As equality constraints, the power flow balance in AC grid is usually formulated as [49]; Also, the DC grid power flow constraints must be considered, where power flow through a generic DC line i − k, leaving DC bus i is given as [2]; Added to that, the constraints in Eqs.  [21] in Eqs. (28)- (31). Eqs. (28) and (29) preserve the active /reactive power for the VSC units within the accepted operational limits. In Eqs. (30) and (31), the voltage at ac and dc terminals of the VSC are kept between their allowable limits.
Qvar max Nevertheless, the PQ capability curve of each VSC can be maintained as follows;

III. PROPOSED IMMPO FOR OPTIMAL OPERATION OF AC-HVDC POWER SYSTEM A. MPO
MPO is a new optimizer that is nature-inspired from the various strategies that are accomplished by the predators to increase their preys hunting rates [36]. These strategies are based on Lévy and Brownian movements which are gradually promoted by the ecosystem and the predators can practice for surviving. In MPO, the predators choose the best strategy based on the assessment of the prey's velocity, volume, and the surrounding environment. Based on their velocity ratio and their surrounding life, the predator controls its chasing and hunting strategy. The MPO begins with uniformly distributing and randomly initializing the prey's positions (Y) where their number represents the population size (P S ). Then, the fittest solution is elicited and classified as top predator that are copied in an Elite matrix (E) with P Size like the population. In MPO, the searching journey to catch the prey is passed through three sequential stages so the iterations are divided into three separate and consecutive parts. In the first part of the searching journey, the predator in a reconnoitering process as it makes a military observation of the surrounding region, so it runs with very low speed compared to the prey movement. This exploration scenario is performed in the beginning MPO iterations. In the second part of the searching journey, the predators in a balance between the reconnoitering and chasing processes since they may choose the desirable prey or still search for the target. Thus, the relative speed between the predator and the prey is competitive. This scenario is performed in the middle MPO iterations. The transition may be executed between exploration and exploitation since the population size (P S ) is divided equally as preys for exploration process and predators for exploitation process. In this phase, prey is responsible for exploitation and predator for exploration. In the last part of the MPO iterations, the predator in a hunting process so it runs faster than the prey. This scenario represents the exploitation abilities of the predators in tracking their target prey. These three possibilities can be formulated to update the position (X * ) for each prey (i) as follow, where the symbol ⊗ shows Hadamard product [36]; The dynamic parameter C It is adaptively varied with iteration progress to control the predator locomotion and is formulated as [36]; The equation of updating the prey's positions in (33) describes the various strategies that are accomplished and varied through the iterations. It also includes the Lévy and Brownian movement of the predator during its journey. Firstly, predator is exploring. Then, effective Brownian movement is activated and finally, it follows Lévy strategy. In addition to the previous strategies, the environmental changes like the Fish Aggregating (F A ) effects have been supported. Since the MPs may take longer jumps in indiscriminate dimensions to search for prey distributions in the surrounding environment. On the other side, the existence of fish aggregations may cause in a trapping problem in a local optimum. These two issues are considered in the MPO as a further updating strategy as [36]; After updating the positions of the preys, this fitness (Fit) of each one is estimated, and the Elite matrix (E) is updated as well. This process mimics the memory saving of the marine predators which can be represented as follows [36];

B. PROPOSED IMPO
In this section, an IMPO is developed. In some circumstances, the preys are lost their ways going towards the predators or some predators are more intelligent in hiding and crushing their victims. The division of the iterations into three separate and consecutive parts cancel the chances of these circumstances' occurrence. Therefore, the IMPO includes the  random possibility to merge these stages as; The MPO contains an update strategy for the top predator which provides a memory saving capability to the top predator by comparing the fitness of the Elite with the best fitness of the preys as in (36). Also, a memory saving capability to the preys is augmented as for the MPO as; Thus, the steps of MPO and IMPO are depicted as in Fig. 2.

C. PROPOSED MULTI-OBJECTIVE IMPROVED MARINE PREDATOR OPTIMIZER FOR OPTIMAL OPERATION OF AC-HVDC SYSTEMS
In IMPO, the new positions of the preys are created through one of the strategies that are based on Lévy or Brownian movement of the predator during its journey (37) or even based on the environmental changes' effects (35). Whilst the   (36) and (38), respectively.
The IMMPO handles the multi-objective framework in this section. The proposed IMMPO is evolved incorporating an external repository with a specified capacity. In this repository, the nondominated preys are stored based on Pareto dominance and they are updated two times in each iteration. If this repository is full, an erasing process is executed to remove some of the Pareto solutions in the most congested zones using the roulette wheel option [43]. On the other side, the selection criteria for the top predator in each iteration becomes dependent on several objectives by picking out randomly a nondominated candidate from Pareto set. In this target, the roulette wheel option is applied to give high chances in picking a candidate from the least congested zones. Finally, the updated process of the prey's positions in each iteration (38) is changed to be based on the dominance  priority as follows; (39) Therefore in terms of the goals accomplished, every other new position is contrasted to its counterpart in previous iteration. The new one replaces the previous if it is not dominated by the current one. This approach retains variety and increases the consistency of the solution. A Pareto set is then produced and processed. To release the optimal choice from it, a fuzzy decision-making [1] is applied. For each objective function, a membership function (µ i ) can be assigned as in Eq. (40). Then, a distinguished solution is excerpted using a fuzzy based mechanism which acquires the maximum membership (µ q ) as in (41) where, q, m, and n refer each compromise solution related to each step of W, number of objectives and number of compromise solutions, respectively;

A. TEST SYSTEMS
In this section, the proposed IMMPO is employed in MATLAB environment and it is applied for the modified IEEE 30-bus, and the practical WDRPN to solve the optimal multi-objective operation of hybrid AC/MTHVDC power systems. The standard IEEE 30-bus system originally consists of 30 buses, 41 lines, 6 generators, 4 on-load tap changing transformers and 9 shunt capacitive sources. Fig. 4 [45].
The AC-MTHVDC test system is the practical WDPN which consists of 52 buses, 108 lines and 8 generators [46], [47] sown in Fig. 5. It is modified with a MTHVDC grid with four VSCs and three DC lines. The VSCs are located at bus 5, 36, 6, and 31, respectively. The DC lines are added between VSCs 1-2, 2-3 and 1-4. VSC 1 is Vdc-Qc control mode whilst the other three VSCs are in Pdc-Vc control mode. The maximum and minimum values for the generator voltage are 1.06 and 0.94 p.u., respectively. The limits for the buses' voltages are ±10%.
Various modern and efficient algorithms are utilized for comparison purposes such as BAT [37], [38]; CSOA [39], [40]; DA [41]; MVO [42]; SSO [43]; PSO; GWO [44].         a tri-objectives of fuel generation costs minimization, the pollutant emissions minimization and the total losses minimization (Case 6). Added to that, three cases are studied for the practical WDRPN to solve the optimal multi-objective operation of hybrid AC/MTHVDC power systems. Case 7 presents the single objective of fuel costs minimization as primary target. Case 8 solves a single objective of losses minimization as primary target. Case 9 optimizes simultaneously the fuel costs and losses In this case, the proposed MPO is introduced for a single objective of fuel cost minimization. The optimal control variables and the corresponding results are tabulated in Table 1 for the proposed IMPO and other techniques  (BAT, CSOA   MPO and manta ray foraging algorithm (MRFO) [50]. As shown, the fuel costs are minimized from 975. 6  The computational burden, in terms of the average time taken for one iteration including the AC/DC load flow algorithm, is estimated, and mentioned in Table 1. This table shows that the associated time for the compared algorithms is different where the proposed IMPO takes the smallest time by 2.748 second. This is essential to the capability to target the search on the best individual obtained in the previous iteration. It is cleared that the IMPO surpasses everyone else to efficiently operate the AC/MTHVDC grid for minimum fuel cost achievement. In addition, the bus voltages in AC and HVDC networks has been substantially enhanced by the proposed methodology as can be seen in Figs. 6 and 7. Fig. 8 indicates the convergence properties of the proposed IMPO and the conventional MPO that shows the higher improvement abilities of the IMPO throughout the iterations.
To assess the proposed algorithm with conventional method of second order cone programming [30] and other algorithms available in the literature such as PSO [51], DE [51] and Equilibrium algorithm (EA) [51]. For this purpose, the IMPO is applied to minimize the fuel generation costs in its quadratic form.   • The converter losses which provide additional nonlinearity were ignored.
• A linearization was performed to the fuel generation costs which is handled as quadratic model ignoring its fluctuations existence due to the valve point loading effect.     even with the progress through the iterations, the proposed technique continues searching for the optimal solution.

3) CASE 3: MINIMIZATION OF THE POWER LOSSES
In Case 3, the proposed technique succeeds in achieving the minimum power losses compared with other methods as in Table 4. The TPL is minimized by 37.37% using the IMPO while its value is reduced by 19.68%, 17.78%, 24.48%,    compromise fuel cost, pollutant emissions and power losses are close to the concerned values in single-objective. In Case 4, several available solutions of compromise solution between TFC minimization (F1) and the TAEE minimization (F2) are attained beginning from F1 at 840.0 $/hr and F2 at 0.2 ton/hr to F1 at 1040.0 $/hr and F2 at 0.55 ton/hr extracting the optimal compromise of F1 about 875.72 ($/hr) and F2 about 0.28416 (ton/hr) as described in Fig. 15. In Case 5, different available solutions of compromise solution between fuel generation costs (F1) and power losses minimizations (F3) are obtained beginning from F1 at 850 $/hr and F2 at 15.8 MW to F1 at 1045 $/hr and F3 at 9.2 MW extracting the optimal compromise F1 = 879.4364 ($/hr) and F3 = 11.80556 (MW).
Eventually, Fig. 17 displays well distributed Pareto alternatives incorporating the best compromise of F1 = 896.55 ($/hr), F2 = 0.25698 (ton/hr) and F3 = 10.622 (MW). In Fig. 15, it is clearly shown that the new positions (as in (39)) improve the diversity and quality of the solution curve where the Pareto set after 100 iterations (yellow circles) becomes finally wider and less values for both objectives are acquired at the end (blue circles). Fig. 16 describes graphically the Pareto repository after each successive 50 iterations. The improvement in the quality of Pareto repository is clearly illustrated since more diversified effective solutions are developed. Table 6 gives the simulation results of the modified WDPN test system with single objective fuel generation costs minimization (Case 7) using the proposed IMPO and other techniques (BAT, CSOA, DA, MVO, SSO, PSO, GWO, and   conventional MPO). Similar to all previous cases, the proposed IMPO gives the best solution, where the fuel costs are minimized by 8.47%. Fig. 18 describes the bus voltages in AC part for MPO, IMPO and the initial case, whereas the bus voltages are inside their specified bounds. The high capacity to find the minimal objective considered and to make significant progress across the iterations in the searching space for the optimum solution of the proposed IMPO is clearly shown in Fig 19. Likewise, the previous cases, the suggested IMPO has been effective in accomplishing the minimum power losses in Case 8 with considerable superiority to the others as shown in Table 7. The TPL is minimized by 48.31 % using the proposed IMPO while its value is reduced by 37 Fig. 20 shows the power losses in AC, DC lines as well as VSCs. Fig. 21 plots the bus voltages in AC part for MPO and IMPO relative to the initial case which demonstrate the verification of the voltages inside their bounds. Fig. 22 displays the convergence characteristics of the proposed IMPO and the conventional MPO for single objective power losses minimization. This figure depicts the fast convergence characteristic and the capability of finding the optimal solution of the proposed technique. For bi-objective functions of Case 9, the obtained solutions of Pareto set are introduced, to identify the capability of the proposed IMPO for searching optimal solutions VOLUME 9, 2021  and compromises the conflicted objectives as show in Fig. 23. Fuel cost can be minimized from 25100 ($/hr) to 23020 ($/hr), while power losses is increased from 48.9 MW to 11.2 MW inversely with fuel cost minimization. Compromised optimal solution can be effectively achieved as shown in Fig. 23.

V. CONCLUSION
This paper has been investigated an Improved Multi-Objective Marine Predator Optimization algorithm for optimal operation of hybrid AC and multi-terminal high voltage direct current grids. It is handled as single and multiobjective framework for minimizing the TFC, the TAEE and the TPL over the AC, HVDC power systems and VSC stations. The proposed optimization algorithm mimics the predator's strategies based on Lévy and Brownian movements for surviving. Also, it is established by integrating external repository to conserve the nondominated preys. Furthermore, fuzzy decision making has been employed to select a compromise operating point for the AC/HVDC electrical power systems. The proposed IMMPO was being validated for nine case studies on modified IEEE 30-bus, and a practical part of the Egyptian system at the West Delta Region Power. The evaluation of the proposed IMPO and IMMPO are performed with substantial enhancements relative to other modern algorithms. The simulation findings indicate the efficacy and superiority of the suggested optimizer with strong robustness indexes over other competitive algorithms in single and multiobjective situations with significant technical and economic benefits. Furthermore, the suggested IMMPO demonstrates high increase in the consistency of the Pareto repository by the creation of more diversified and effective solutions. It can provide distributed and diverse Pareto individuals whereas adequate operating settings are derived for the relevant control and dependent variables to meet the operator's preferences.