Optimal Power Flow of Power System with Unified Power Flow Controller Using Moth Flame Optimization with Locational Marginal Price

: Consideration of transmission line capacity and the optimal power flow (OPF) determines the locational marginal price (LMP), which in turn determines the performance and profitability of a producing unit. Reducing the total cost of the generators can lead to a drop in the market price of electricity. It is recommended to use numerical and repetition-based approaches for solving power flow equations due to their nonlinear nature. In order to achieve the ideal power flow at an affordable price, this paper employs a Moth Flame Optimization (MFO) to solve the equations. We then enhance the MFO’s structure to make it more effective at performing the simultaneous calculations of power passing through transmission lines. Flexible AC transmission systems (FACTS) tool that has been utilized to overcome this problem is the Unified Power Flow Controller (UPFC). Lastly, the proposed MFO algorithm would include the following parameters in its output: bus voltages, line losses, generated power, total generating expenditures, and generator profits. In this work, the proposed method is tested on the IEEE 57-bus network also shows that it improves upon the OPF problem.


Introduction
Electric service engineering has entered a new era, marked by competition between service-owned and sovereign authorities and long-standing power dynamics [1,2].Some licenses are close to each other.From countryside to countryside, and by growth a brief market where numerous consumers buy least client pricing power.This improved use of market pressures, new dealer support and confidence growing contemporary power model and finance system power deal corporation union has increased electric load organize transmission.The goal is to promote financial competence in the use of electric power organizations.Transmission of financial data from connected electric power facilities.Networks provide a typical discussion starter.Well-organized power markets.Besides description, financial send out maximize low Plant usability affects pay rates.Transmission constraints of LMP is the little price of providing the next electric power surge at a bus considering generating marginal cost and physical transmission system aspects.
Competitiveness among market actors facilitates power trade.It will boost industrial production and lower electricity costs for all consumers [3].Market players like power producers, deregulated energy markets benefit customers and system operators.However, Energy market difficulties include generating loss, line outages, etc. [4,5].The Transmission systems are widely used due to electric market restructuring for electricity trading.To integrate in a deregulated system, needs suitable formulation between regulatory entities like pool operators' system managers.This study emphasizes the latter of these difficulties.We study pool, bilateral, and multilateral dispatch coordination and construct mathematical models.How forward and real-time dispatch works when all three modalities coexist is addressed [6].Producing and distributing companies' agreements cause transmission congestion in deregulated electricity systems globally.Transmission line congestion may be handled in deregulated energy networks for safe and economical operation.In overloaded lines, series connected UPFC devices are installed to ease system congestion [7].Energy power flows must be estimated and improved in an electrical generating system.Locating FACTS devices and improving the power transmission line Available Transfer Capability (ATC) is crucial.It reduces system congestion and boosts power [8].
Calculating the LMP is crucial for evaluating generation unit performance and profit.This relies on transmission line capacity and OPF to minimize generator costs, alleviate transmission line congestion, and lower market electricity prices [9].The RLMP is a novel power market clearing method developed in this study.The risk-based security-constrained economic dispatch model generates the RLMP by modeling system security risk [10].This study introduces two methods for placing series FACTS devices in deregulated energy markets to minimize congestion.Like the sensitivity factor-based strategy, the suggested strategies prioritize and narrow the solution space.The suggested methods use LMP differences and congestion rent, respectively [11].Congestion in transmission lines might make it difficult to dispatch all planned power in a deregulated energy market.An interline power flow controller may enhance system stability and loadability by reducing system loss and power flow in severely laden lines.This study suggests using a Disparity Line Utilization Factor and Gravitational Search method to optimize placement and manage transmission line congestion [12].We present singleobjective and multi-objective optimization methods for optimal choice, location, and size of Static Var Compensators (SVC) and TCS in deregulated power systems to reduce branch loading (congestion), voltage stability, and line losses [13].This research introduces an effective approach for optimizing FACTS device locations for congestion management by modifying device characteristics.Using FACTS devices for congestion control involves a two-step process.
To improve the network, first determine the ideal device placement and then optimize the control parameters [14].After defining irrigation efficiency equations, hierarchical analysis developed goal function coefficients for all irrigation efficiencies in SWDC model.All irrigation efficiency formulae depend on input discharge [15].Many recent research optimized furrow irrigation control settings.These experiments either optimized just complete irrigation status or not all infiltration parameters.This study uses MS visual basic (VB) programming to calculate the optimal soil water distribution curve equation [16].Model training and forecasting utilize 42 and 5 years of monthly discharges from the 47-year period.The RMSE metric was used to compare static and dynamic artificial neural network models.Starting with data from October 1960 to September 2002, the finest static and dynamic neural network topologies are identified [17].In addition, an impedance compensation approach is presented to address the numerical instability or numerical difficulties of Interline Power Flow Controller (IPFC) and a generalized unified power flow controller (GUPFC) models with low coupling transformer impedances or transformer-less controllers [18].Multi transmission lines are controlled by an IPFC in this work.However, IPFC installation in the transmission line is difficult.The suggested technique uses tabu search (TS) algorithm and artificial neural network (ANN) to discover the optimal IPFC installation sites in a multi transmission line system [19].Due to transmission corridor congestion, a deregulated energy market may not be able to dispatch all contractual power transactions.Environmental, right-of-way, and economic issues prevent power transmission network growth, thus power system reorganization must unleash transmission system potentials [20].This work introduces a reliable and efficient meta-heuristic technique for congestion issue solving.This study proposes using the firefly algorithm (FFA) to reduce transmission network congestion in a pool-based energy market by rescheduling producers using active power [21].Reference [22] proposes enhanced harmony search to tackle transmission expansion planning with adequacy-security issues in deregulated power systems.Zhuang and Galiana performed simulated annealing (SA) on unit commitment [23].Jang et al. [24] proposed a computationally simple random search technique (RSM) for optimization issues.
The FFA, a meta-heuristic inspired by fireflies [25], is becoming more popular in practically all fields of science and technology for optimization.Reference [26] solved non-linear design issue using FFA.The FFA was used in reference [27] to improve transmission system control variables for actual power loss and voltage stability limit.Reference [28] designs a Smith predictor controller for integration and unstable delay processes using the modified FFA.Current study proposes FFA for power network rescheduling to reduce congestion.Many optimization and congestion management [29,30] approaches have been suggested to reduce congestion cost and loss in transmission networks, according to a literature review.However, the approach may be improved to reduce transaction curtailment, loss, and rescheduling expenses.This study introduces UPFC with MFO to manage transmission network congestion.
In this paper, generating scaling factor (GSF) was used to prevent congestion in minimum local points and calculate the power flow for each change in control variables.If the algorithm [31] violates line capacity, it exits this optimal point and continues to find the best response.It decreases convergence speed, makes power flow actual, and costs less than previous ways.A 24-hours of power flow on an IEEE 30 and 57-Node network was performed after MFO algorithm [32] introduction.The generator profit was computed by estimating the power price using UMP or LMP and comparing it to economic dispatching (ED) and quadratic programming using Lagrangian coefficients.

Problem formulation
The optimum power dispatch model in the deregulated energy market aims to minimize deviation from contract power transactions for market utilities.Simultaneously, operational equality and inequality requirements must be met for uninterrupted transactions.

Objective function
OPF aims to reduce active power generation expenses.The active power-based cost function of each producing unit is shown by this quadratic curve.Add each generator's cost function to get the system's goal function.

Equality constraints
Production should minimize cost while meeting power demand and transmission losses.So, power flow equations are equivalent limitations and which are given in (2) and (3).

Inequality constraints
OPF limits vary according on power system equipment and dependability.Uneven constraints in buses connecting to power and producing units are usually high and low voltage.Generation restrictions include generator active power, transmission line capacity, TCUL tap adjustment, and phase shift.Limitations of unequal issue variables: Generatorpowered buses have high and low active power.The voltage, Watt and wattles power and UPFC limits are given from equations ( 4) to (7) respectively.

V min
Gi ≤ V Gi ≤ V max Gi (4)

Electricity market price calculation
After calculating OPF and line power flow, we may compute electricity market price using two approaches.The first technique (UMP) uses power flow data without congestion, calculating electricity prices from the overall cost of functioning generators.Each node will have the equal power tariff.The nextprocess (LMP) is used when one or more transmission lines are at capacity and the power cost for each node will vary based on generator output.

UMP price
Consider the IEEE 30-BUS network's generation units to determine the generators' ultimate cost for the minimal producing power: Power price (π) will be determined by the cost of the more expensive generator, since employing the cheaper generator would result in losses and be unfeasible.Electricity costs are based on generators' lowest power to keep prices low.

LMP price
The power price at network locations will be different if transmission line capacity hits its limit, since producers cannot employ their full generation capacity.This is termed locational marginal pricing.LMP implies adding a 1-MW excess load using the cheapest generators that can generate without exceeding transmission line limits.Therefore, LMP may be calculated by considering generators that are not at their limitations.Final generators are ones with some capacity left.Thus, LMP in buses with final generators equals their ultimate cost.LMP of nodesdevoid of generators or whose generators have surpassed their maximum will also rely on buses with a final generator.Final-generator buses

Contemporary Mathematics
Final generator buses are indicated by i.Finally, Figure 1 displays the flowchart of all stated steps with green blocks representing algorithm outputs.lights.The multi-objective function's solution is assumed to be represented by the moths.One of the parameters of the issue is the spatial distribution of the moths.The following is a summary of the mathematical models of moth behavior: In light of these constraints, we describe the logarithmic spiral used by the MFO method flow diagram shown in Figure 2, as where S is the spiral function, M i is the i −th moth, and F j stands for the j −th flame.
D i is the distance between the i th moth and the j th flame, b is a constant used to define the shape of the logarithmic spiral, and t is a random number in the interval [-1, 1].
where M i is the i th moth for the j th flame and D i is the distance between them.

Contemporary Mathematics
Figure 3 depicts an IEEE 30 node network with 41 lines of transmission, 5 PV nodes, one slack bus, and the remaining load nodes.Currently, UPFCs are only being installed on load buses.Solar and wind power replace the final two remaining thermal generators at bus 23 and bus 27.
There is research being done on the generator reallocation for the IEEE-30 node network.The OPF is carried out for functions with a single goal, and then the multi-objective function optimization is carried out thereafter.The outcomes of both optimizations have been compared.The variable LMP stands for the locational marginal price, the variable UMP stands for the uniform marginal price, and the variable GSF stands for the generation scaling factor.MFO is an abbreviation for the algorithm for moth flame optimization.Table 1 indicates the OPF in 24 h using MFO.Table 2 shows the Calculations for profits of generators in MFO technique.
Figure 4 indicates the network's power demand, generation production and transmission losses and cost convergence in MFO approach shown in Figures 5 and 6.Generation cost profit between with and without UPFC describes in Figure7. Figure 8 indicates the generation loss cost between with and without UPFC.Generation losses between with and without UPFC shown in Figure 9. Voltage convergence with and without UPFC indicates in Figure 10.

IEEE-57 bus system
Figure 11 depicts an IEEE-57 node network with 80 lines of transmission, six PV nodes, one slack bus, and the remaining load nodes.Currently, UPFCs are only being installed on load buses.Solar and wind power replace the final two remaining thermal generators at bus 9 and bus 12.There is research being done on the generator reallocation for the IEEE-57 node network.The OPF is carried out for functions with a single goal, and then the multi-objective function optimization is carried out thereafter.The outcomes of both optimizations have been compared.The variable LMP stands for the locational marginal price, the variable UMP stands for the uniform marginal price, and the variable GSF stands for the generation scaling factor.MFO is an abbreviation for the algorithm for moth flame optimization.Table 3 indicates the OPF in 24 h using MFO.Table 4 shows the Calculations for profits of generators in MFO technique.For 57 bus system, Figure 12 indicates the network's power demand, generation production and transmission losses and cost convergence in MFO approach shown in Figures 13 and 14.Generation cost profit between with and without UPFC describes in Figure15.Figure 16 indicates the generation loss cost between with and without UPFC.Generation losses between with and without UPFC shown in Figure 17.Voltage convergence with and without UPFC indicates in Figure 18.

Conclusion
Through the use of the metaheuristic algorithm MFO, the OPF problem as well as the locational marginal price (LMP) are resolved and calculated in this paper.In the event that the minimum point that is attained does not satisfy the prerequisites for the generation of flow power in the network, the process will be repeated until the prescribed circumstances are satisfied.The power of generating units, network losses, bus voltage, generation cost, and power moving via lines are the outputs of the recommended method.We could also calculate the market price of electricity and the profit of generators by studying the capacity of lines.In addition, we could compute the profit of generators.The results of the simulation illustrate the effectiveness of the MFO algorithm, which has resulted in reduced losses, reduced processing time, reduced producing costs, and an OPF that is better in accordance with the actual situation.In Future, the proposed optimization can be studied for generating systems with different renewable energy sources and the cost and loss estimation for different load and source systems can be studied.

Figure 13 .Figure 14 .Figure 15 .
Figure 13.Generation production and transmission losses in the MFO approach

Table 1 .
MFO outcome from OPF in one day

Table 2 .
Estimates of generator earnings using the MFO technique

Table 3 .
MFO outcome from OPF in one day

Table 4 .
Estimates of generator earnings using the MFO technique