Optimal Placement of Renewable Energy Sources and Fuel Cell in Power System using Line Stability Index

Optimal Placement of Renewable Energy Sources and Fuel Cell in Power System using Line Stability Index

Santosh Kumar Jha (M.TECH Scholar)

Department of Electrical Engineering, RKDF Institute of Science & Technology, Bhopal SRK UNIVERSITY, BHOPAL

Deep Mala

Department of Electrical Engineering, RKDF Institute of Science & Technology, Bhopal SRK UNIVERSITY, BHOPAL

Abstract – The increasing penetration of renewable energy sources (RES) in modern power systems has raised concerns regarding voltage stability and system reliability. Proper placement and sizing of renewable energy sources and fuel cells are essential to enhance system performance while maintaining stability limits. This paper presents an optimal placement strategy for renewable energy sources and a fuel cell in a power system using the Line Stability Index (LSI) as a voltage stability indicator. Initially, load flow analysis is performed to identify weak transmission lines based on their LSI values. Buses associated with high LSI values are considered as candidate locations for the integration of RES and fuel cell units. An optimization problem is formulated with the objective of minimizing the maximum LSI, improving voltage profile, and reducing real power losses, subject to system operational constraints. A suitable optimization technique is employed to determine the optimal locations and capacities of the RES and fuel cell. Simulation studies conducted on a standard IEEE test system demonstrate that the proposed approach significantly enhances voltage stability, reduces power losses, and improves overall system performance. The results confirm the effectiveness of the Line Stability Index as a reliable tool for optimal resource placement in power systems with high renewable penetration. To overcome this limitation, a Fuel Cellcapable of continuously supplying both active and reactive poweris also installed at the same weak bus. A re-analysis shows that Fuel Cells provide greater improvements in voltage stability and L-index reduction compared to PV systems, particularly under varying load scenarios. To further assess system performance, a cost function evaluation is conducted to examine the economic implications of the integration. The algorithms tested include the Frilled Lizard Optimization (FLO), Osprey Optimization Algorithm (OOA), and Coati Optimization Algorithm (COA). Results indicate that FLO and OOA exhibit strong convergence and efficient search capabilities, making them highly effective for emission minimization in power system optimization. In conclusion, the research highlights the critical role of carefully planned renewable energy placement in improving grid stability while reducing environmental impacts. The combined methodology spanning load flow analysis, Lindex evaluation, and optimization

algorithm benchmarking – offers a comprehensive framework for future advantage.

Keywords – Renewable Energy Sources, Fuel Cell, Optimal Placement, Line Stability Index, Voltage Stability, Power System Planning, Distributed Generation, Load Flow Analysis, Power Loss Minimization, Optimization Techniques. Flow Analysis; Reactive Power Support; Optimization Algorithms; Emission Reduction.

1. INTRODUCTION

   The rapid growth in electricity demand and increasing environmental concerns have accelerated the integration of renewable energy sources (RES) into modern power systems. Renewable sources such as solar photovoltaic and wind energy offer clean and sustainable alternatives to conventional fossil- fuel-based generation. However, the intermittent nature of these resources and their improper placement within the power network can lead to operational challenges, including voltage instability, increased power losses, and line congestion.

   Voltage stability has become a critical issue in power system planning and operation, particularly with the rising penetration of distributed generation. Weak transmission lines and heavily loaded buses are more susceptible to voltage collapse, which can compromise system reliability. Therefore, identifying vulnerable locations and reinforcing them with suitable energy sources is essential to maintain stable and secure operation.

   Fuel cells have emerged as a promising complementary energy source due to their high efficiency, fast dynamic response, and ability to supply both active and reactive power. When strategically integrated alongside renewable energy sources, fuel cells can mitigate the adverse effects of renewable intermittency and enhance voltage support in critical areas of the network.

   This paper proposes an optimal placement methodology for renewable energy sources and a fuel cell using the Line Stability Index as the primary stability assessment tool. Load flow analysis is initially performed to determine the base-case operating condition and identify weak lines. An optimization framework is then applied to determine the optimal locations and capacities of the RES and fuel cell with the objectives of improving voltage stability, enhancing voltage profiles, and reducing system power losses. The effectiveness of the

   proposed approach is validated through simulation studies on a standard IEEE test system.

2. LINE STABILITY INDEX
   1. IEEE 39-bus system)

      The Line Stability Index (L-index) is employed to assess voltage stability by evaluating the power transfer capability of transmission lines. It is derived from the power flow equations of a two-bus system and depends on parameters such as line reactance, reactive power demand, sending-end voltage magnitude, and power angle. The IEEE 39-bus system, a widely used benchmark in power system studies, has been analyzed using load flow analysis to evaluate the steady-state operational conditions of electrical grids. Through the usage of this analysis, it helps to determine voltage magnitudes, power flows, and stability across the network. Recent studies, including voltage stability analysis, have also highlighted the application of line stability indices to assess the system’s robustness under varying load conditions. Specifically, the Line Stability Index (Lmn) has been utilized to monitor the stability of transmission lines within the IEEE 39-bus systems L-index value close to zero indicates a stable operating condition, while a value approaching unity signifies proximity to voltage collapse. In this study, L-index values are calculated for all transmission lines in the IEEE 39-bus system. The bus associated with the maximum L-index value is identified as the weakest bus and selected for renewable energy integration.

   2. System Modeling (IEEE 39-Bus Test System)

   The IEEE 39-bus (New England) test system is used to validate the proposed methodology. The system consists of 39 buses, 10 generators, 19 load buses, and multiple transmission lines and transformers. It is widely accepted as a standard benchmark for voltage stability and optimization studies. Results show that the system, under typical operating conditions, exhibits stable performance with most transmission lines classified as stable, indicating that the power network can withstand minor disturbances without significant risk of instability. The integration of these stability indices enhances the understanding of the systems resilience, confirming its adequacy in both normal and stressed operational scenarios. In addition to that, Optimization algorithms have also been introduced to the system and the outcome of each algorithm has been compared to highlight their problem soving capability.

   Solar PV Modeling

   The Solar PV system is modeled as a distributed generation unit connected to the identified weak bus. The PV unit injects active power into the system and provides limited reactive power support through inverter control. While PV integration improves voltage profile, its output varies with solar irradiance, affecting system reliability

   Fuel Cell Modeling

   The Fuel Cell system is modeled to supply continuous active and reactive power. Unlike Solar PV, the Fuel Cell provides stable output regardless of environmental

   conditions, making it suitable for enhancing voltage stability under varying load scenarios

3. OPTIMIZATION ALGORITHMS

   Frilled Lizard Optimization (FLO)

   FLO is inspired by the hunting and defensive behavior of frilled lizards. It effectively balances exploration and exploitation by dynamically updating candidate solutions, resulting in fast convergence and improved global search capability. The Frilled Lizard Optimization (FLO) algorithm is a bio-inspired metaheuristic method modelled after the natural behaviours of the frilled lizard, particularly its sit-and-wait hunting strategy and its tendency to retreat to treetops after feeding. The algorithm emulates these behaviours by incorporating an exploration phase, which mimics the lizard’s sudden attack on prey, leading to significant positional changes in the population to enhance global search capabilities. Conversely, the exploitation phase replicates the lizard’s retreat to a treetop, focusing on refining solutions in promising regions to improve convergence toward optimal solutions. Key parameters governing FLO’s performance include population size, maximum number of iterations, exploration rate, and exploitation rate, which collectively balance the algorithm’s search dynamics between broad exploration and localized refinement. This biologically inspired approach ensures an adaptive and efficient optimization process suitable for complex problem-solving. The mathematical model of FLO is as follows.

   Osprey Optimization Algorithm (OOA)

   OOA is based on the hunting strategy of ospreys, combining wide-area exploration through aerial surveillance and precise local exploitation through targeted dives. This dual behavior enhances convergence speed and solution accuracy. The Coati Optimization Algorithm (COA) is a bio-inspired metaheuristic technique that emulates the behaviour of coatis, social mammals closely related to raccoons. This algorithm replicates the collective hunting tactics and movement dynamics of coatis as they explore their environment for food, transforming these natural processes into an effective optimization method. COA operates through two key stages: an exploration phase, where simulated coatis disperse widely to discover potential food locations (analogous to global search), and an exploitation phase, where they focus on rich areas to maximize resource utilization (similar to local search). In the exploration stage, individual agents (representing coatis) navigate randomly or follow probabilistic cues to ensure comprehensive search space coverage. During exploitation, information sharing within the group drives coordinated movements toward high-quality solutions, enhancing precision.

   Coati Optimization Algorithm (COA)

   COA mimics the cooperative hunting behavior of coatis. It utilizes social interaction and group coordination to explore the search space and avoid local minima

   C . Cost Function and Emission Modeling

   The economic performance of the system is evaluated using a cost function that considers generation cost and operational constraints. Emission modeling is carried out for a system comprising ten generators over a 24-hour operating period. The objective is to minimize total emissions while satisfying power balance and generator constraint.

   D.Units

   • V Volt
   • kV Kilovolt
   • A Ampere
   • MW Megawatt (Active Power)
   • MVAr MegavoltAmpere Reactive
   • Ohm
   • Hz Hertz
   • p.u. Per Unit System

   E.Equations

   Power Flow Equations

   The active and reactive power at bus i are expressed as

   Pi=j=1NViVj (Gijcosij+Bijsinij) Qi=j=1NViVj(GijsinijBijcosij)

   where

   Vj,Vj are bus voltages,

   Gij,Bij are elements of the bus admittance matrix,

   ij is the voltage angle difference.

   Line Stability Index (L-index)

   he L-index for a transmission line connecting sending bus s

   and receiving bus r is given by:

   L= 4XQr / Vs2sin2()

   Where

   X is the line reactance.

   Qr is the reactive power at the receiving end. Vs is the sending-end voltage magnitude.

   is the power angle difference.

   Cost Function

   The total generation cost is expressed as:

   C=i=1Ng(aiPi2+biPi+ci)

   Where

   ai,bi,ci are cost coefficients of generator i

   Pi is the active power output, Ng is the number of generators Fuel Cell Power Output PFC=VFC×IFC

   Where

   VFC is fuel cell voltage IFC is fuel cell current. Solar PV Output Power PPV=ag

   PPV=AG

   Where,

   is PV efficiency,

   A is panel area

   G is solar irradiance

4. MODELLING OF STANDARD IEEE 39-BUS TEST SYSTEM

A typical bus system in power systems serves as a node in a power grid allowing for power distribution between elements in the system. Buses are commonly divided into three types:

1. PQ Bus: Also known as load bus. This type of bus has both real and reactive power specified and based on these power values, the voltage is determined.
2. PV Bus: Both active power and voltage is mentioned in this type of bus. The reactive power is adjusted to maintain the voltage. Hence it also known as Generator bus.
3. Swing Bus: This bus type is usually used as a reference point for the system where both voltage and real power are adjusted to balance out the system.

39-Bus system

The IEEE 39-bus system is a power network in the New England area of the V.S. It consists of 10 generators, 39 busbars, 12 transformers, loads, capacitors banks and transmission lines. IEEE bus systems are used by researchers to implement new ideas and concept. These bus systems consist of load, capacitor banks, transmission lines and generators. With the help of these bus systems, certain theoretical analysis can be performed on software such as Authors and Affiliations. MATLAB (SIMULINK), etc to chart out the possible characteristics and behaviour of a system without physically involving

1. Maximum Power Point Tracking (MPPT)

   MPPT technology is aimed at the maximum optimization of energy generation from the solar panel by continuously adjusting the parameters of the process so that it lies on the variable MPP. This is more critical since, when the PV system does not lie on the MPP, the environmental conditions, in the course of a day, change and lead to losses in power. Operating points that are conventionally set will not tend to these changes resulting in suboptimal energy capture. In solar power systems, MPPT can help eradicate the need for extra panels or storages to be installed to compensate for the frequently required energy.

   Block diagram of MPPT algorithm

   The energy produced by the MPPT controller can now be fed directly into DC loads or stored in a battery for later use. The stored DC energy can be used to feed the loads that work on AC, after converting it via an inverter, thus making this setup work in accordance with standard electrical appliances. Therefore, different load types can have energy converted and stored efficiently The energy produce by the MPPT controller can now be fed directly into DC loads or stored in battery for later use. The stored DC energy can be used to feed the loads that work on AC, after converting it via an inverter, thus making this setup work in accordance with standard electrical appliances. Therefore, different load types can have energy converted and stored efficiently.The perturb and observe algorithm is one of the popular techniques for MPPT in PV systems, working by periodically perturbing the PV system operating voltage and observing the result of the perturbation on the power output. In case the power output increases after a perturbation, the system adjusts in the same direction; in case the power decreases, the adjustment direction is reversed. This forms an iterative process through which the system converges to the Maximum Power Point (MPP) to provide maximum possible power that the PV system can offer under given environmental conditions.

   FLOW CHART MPPT IN PV

2. BATTERY STORAGE SYSTEM

   A battery storage system has also been implemented for an optimal usage of the PV array energy source. The PV array model supplies the input energy through the transmission lines and a DC-DC converter has been implemented in the system to convert the receiving energy suitable for the battery to store. Given below isa small glimpse of the Battery system implemented

   the battery system implemented Specifications of IEEE 39 bus system The standard IEEE 39 bus system adopted in this work consists of 10 generators where 19 buses are considered as PQ load buses where loads are connected. The general specifications of IEEE 39 bus system are given below [19].Types of element and their quantity

   E. Specifications of IEEE 39 bus system

   The standard IEEE 39 bus system adopted in this work consists of 10 generators where 19 buses are considered as PQ load buses where loads are connected. The general specifications of IEEE 39 bus system are given below

   . Types of elements and their quantity

   TABLE I. TABLE STYLES

   ELEMENTS NAME	NO. OF ELEMENTS
   GENETORTS	10
   LOAD	19
   BUSBARS	39

   TAB LE-1I Load data of IEEE 39-bus system

   BUS	P(pu)	Q(pu)
   3	3.220	0.024
   4	5.000	1.840
   7	2.338	0.840
   8	5.220	0.840

   a.

   Bus	P(pu)	Q(pu)
   12	5.220	0.880
   15	0.075	1.530
   16	3.200	0.323
   18	3.294	0.300
   20	1.580	1.030
   21	6.800	1.150
   23	2.740	0.846
   24	2.475	-0.922
   25	3.086	0.472
   26	2.240	0.170
   27	1.390	0.755
   28	2.810	0.276
   29	2.060	0.269
   30	2.835	0.046
   31	0.092	0.086
   39	11.04	2.500

   Table III. Transmission line characteristics of IEEE 39-bus system

   From Bus	To Bus	R (pu/m)	X (pu/m)	B (pu/m)
   1	2	0.0035	0.0411	0.6987
   1	39	0.0010	0.0250	0.7500
   2	3	0.0013	0.0151	0.2572
   2	25	0.0070	0.0086	0.1460
   3	4	0.0013	0.0213	0.2214
   3	18	0.0011	0.0133	0.2138
   4	5	0.0008	0.0128	0.1342
   4	14	0.0008	0.0129	0.1382
   5	6	0.0002	0.0026	0.0434
   5	8	0.0008	0.0112	0.1476
   6	7	0.0006		0.0092	0.1130
   6	11	0.0007		0.0082	0.1389
   7	8	0.0004		0.0046	0.0780
   8	9	0.0023		0.0363	0.3804
   9	39	0.0010		0.0250	1.2000
   10	11	0.0004		0.0043	0.0729
   10	13	0.0004		0.0043	0.0729
   13	14	0.0009		0.0101	0.1723
   14	15	0.0018		0.0217	0.3660
   15	16	0.0009		0.0094	0.1710
   16	17	0.0007		0.0089	0.1342
   16	19	0.0016		0.0195	0.3040
   16	21	0.0008		0.0135	0.2548
   16	24	0.0003		0.0059	0.0680
   17	18	0.0007		0.0082	0.1319
   17	27	0.0013		0.0173	0.3216
   22	23	0.0006		0.0096	0.1846

3. SIMULATION AND RESULTS

The IEEE 39-bus system, also known as the New England power system, is a well-established benchmark for power system analysis. It represents a simplified model derived from a section of the New England electric grid and is designed to

study power flow, stability, and dynamic performance under various operating scenarios. This system comprises 39 buses,

10 generators, 46 transmission lines, 19 loads, and 12 transformers, offering a practical yet simplified representation of a real-world power network, making it highly valuable for both academic research and industrial applications [20].

System is the inclusion of an infinite bus at Bus 39, which serves as a strong and stable voltage source. This systems interconnection with a larger grid. The system’s is distributed across various buses, mirroring real-world consumption patterns. Transmission lines and transformers are modelled parameters, such as resistance (R), reactance (X), and susceptance (B), making the system suitable for a wide range of analyses, including power flow studies, fault simulations, and dynamic stability tests.

This is widely used for stability studies, encompassing both small-signal and transient stability analyses. It enables researchers to investigate network behaviour under disturbances such as generator outages, line faults, or sudden load variations. Additionally, it serves as a standard test case for optimization problems like economic dispatch, unit commitment, and optimal power flow (OPF).

Diagram for base system of 39-bus

F. Load Flow Results

The first stage of the test was done with the completion of acquiring the Load Flow Analysis data (Table 4). The data collected works as a reference point from which the later analysis operations are done. Given below are the data taken

from the Load Flow analysis done performed through MATLAB Simulink.

Table IV Active and Reactive power values of IEEE 39 bus system without PV integration

After load flow analysis, this data will be take for reference Line Stability Index calculation

The Line Stability Index (LSI) is a critical parameter for evaluating the stability and security of power transmission lines. LSI calculation becomes important when integrating

The line stability index for the IEEE 39 bus system was primarily carried out on standard system without adding any renewable energy sources with the help of load flow studies in MATLAB Simulink software. The L index values show that with the introduction of renewable energy sources, the stability of the system, although not

drastically but improvements are visible

. L index values for the lines connected in IEEE 39 bus system with different cases

Cost Function Analysis for the system

Table V Cost Function comparisons for the algorithms

COA, OOA, and FLO, relative to the baseline system without optimization. The findings revealed substantial cost savings: COA reduced expenses by 29.25%, OOA by 32.67%, and FLO outperformed both with a 39.3% reduction. FLOs exceptional results suggest its superior capability in lowering generation costs, attributed to its balanced approach between global search and local refinement

The emission study monitored output from 10 generators across a full day, comparing standard operations against COA, OOA, and FLO implementations. While all three optimization methods successfully curbed pollution levels, FLO emerged as the most effective, consistently producing the cleanest results

CONCLUSION AND FUTURE WORK

Conclusion

This research examined the incorporation of solar photovoltaic arrays and fuel cell technology within the IEEE 39-bus electrical network to improve operational stability and performance. Through comprehensive power flow studies and stability index evaluations, critical system vulnerabilities were pinpointed, enabling strategic deployment of renewable energy resources. While solar installations enhanced voltage regulation, their variable output necessitated supplemental solutions, with fuel cells proving more effective by delivering reliable power and substantially improving stability metrics.

An assessment of nature-inspired optimization methods – including Frilled Lizard, Osprey, and Coati algorithms – revealed significant potential for economic and environmental optimization. The Frilled Lizard approach showed particular promise, delivering nearly 40% cost savings and superior emission control capabilities in daily operations. These results emphasize the value of integrating computational optimization with traditional power system analysis.

The study recommends adopting combined renewable energy configurations with energy storage to address generation variability. Potential extensions of this work include adaptive control strategies, AI-driven power quality management, and expanded renewable integration scenarios. These findings contribute meaningful guidance for energy sector stakeholders pursuing sustainable infrastructure development

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