Generally, the main focus of the grid-linked photovoltaic systems is to scale up the photovoltaic penetration level to ensure full electricity consumption coverage. However, due to the stochasticity and nondispatchable nature of its generation, significant adverse impacts such as power overloading, voltage, harmonics, current, and frequency instabilities on the utility grid arise. These impacts vary in severity as a function of the degree of penetration level of the photovoltaic system. Thus, the design problem involves optimizing the two conflicting objectives in the presence of uncertainty without violating the grid’s operational limitations. Nevertheless, existing studies avoid the technical impact and scalarize the conflicting stochastic objectives into a single stochastic objective to lessen the degree of complexity of the problem. This study proposes a stochastic multiobjective methodology to decide on the optimum allowable photovoltaic penetration level for an electricity grid system at an optimum cost without violating the system’s operational constraints. Five cutting-edge multiobjective optimization algorithms were implemented and compared using hypervolume metric, execution time, and nonparametric statistical analysis to obtain a quality solution. The results indicated that a Hybrid NSGAII-MOPSO had better convergence, diversity, and execution time capacity to handle the complex problem. The analysis of the obtained optimal solution shows that a practical design methodology could accurately decide the maximum allowable photovoltaic penetration level to match up the energy demand of any grid-linked system at a minimum cost without collapsing the grid’s operational limitations even under fluctuating weather conditions. Comparatively, the stochastic approach enables the development of a more sustainable and affordable grid-connected system.

In terms of energy production, combining conventional and renewable energy sources prove to be more sustainable and cost-effective. Nevertheless, efficient planning and designing of such systems are extremely complex due to the intermittency of renewable sources. Many existing studies fail to capture the stochasticity and/or avoid detailed reliability analysis. This research proposes a practical stochastic multi-objective optimization tool for optimally laying out and sizing the components of a grid-linked system to optimize system power at a low cost. A comparative analysis of four state-of-the-art algorithms using the hypervolume measure, execution time, and nonparametric statistical analysis revealed that the nondominated sorting genetic algorithm III (NSGA-III) was more promising, despite its significantly longer execution time. According to the NSGA-III calculations, given solar irradiance and energy profiles, the household would need to install a 5.5 (kWh) solar panel tilted at 26.3° and orientated at 0.52° to produce 65.6 (kWh) of power. The best battery size needed to store enough excess power to improve reliability was 2.3 (kWh). The cost for the design was $73520. In comparison, the stochastic technique allows for the construction of a grid-linked system that is far more cost-effective and reliable.

Renewable Energy Resources have been identified among the most promising sources of harnessing power for industrial and household consumption but their power generations highly uctuate so building renewable power systems without critical reliability analysis might result in frequent blackouts in the power system. Therefore, in this paper, a robust, effective and ecient design approach is proposed to handle the reliability issues. The study involves a Mathematical modelling strategy of the PV system to estimate the total PV power produced and the Bottom-Up approach for predicting the household load demand. The reliability is defined in terms of Loss of Load Probability. The design methodology was validated with a University Household. The data used for the analysis consists of daily average global solar irradiance and load profiles. The results revealed that throughout the year, November-February is where the system seems to be more reliable. Also, the results indicated that without buck-up systems, the system would experience an average annual power loss of 17.8753% and thus, it is recommended that either solar batteries or the grid are used as backup system to achieve a complete level of reliability.

Integrating a high Penetration level of Solar Photovoltaic (SPV) power in the electricity grid could enhance the system’s sustainability, reliability, and affordability. Nevertheless, at higher Penetrations, the intermittency, non-dispatchable nature of the SPV generation, and the extensive utilization of inverter-based interfaces generate excessive harmonic distortions that damage power system devices and interrupt the smooth operation of the power system. Thus, the severity of the harmonic distortion impacts varies as a function of the degree of the SPV Penetration level in the grid-connected system. Though the problem is highly nonlinear stochastic programming with multiple conflicting power quality criteria, no existing study holistically captures the randomness, the contradictory nature of the objectives, and the grid’s technical limitations simultaneously. This study proposes a novel Monte-Carlo-based Hybrid multi-objective methodology to scale up the Photovoltaic Penetration level with a minimum Total Harmonic Distortion (THD) for multilevel SPV inverters in grid-connected systems without violating the system’s standard operational limitations. Six state-of-the-art Multi-Objective Evolutionary algorithms were implemented and compared using hypervolume indica- tor, execution time, and parametric statistical analysis to obtain a quality solution. The results showed that the Hybrid NSGAII-MOPSO outflanked the rest in terms of convergence, diversity, and execution time. It could be inferred that even under variable weather conditions, this harmonic suppression design approach could accurately optimize the SPV Penetration level and mitigate the THD without degrading the grid’s standard operational constraints. In comparison, the stochastic design technique creates a far more reliable SPV grid-connected system than the deterministic approach.

Determining optimal consumption and bequest policies is complex but essential aspect of retirement planning. It can balance the immediate need for consumption with the desire to leave a legacy, managing risks and economic activities more sustainably and efficiently. One of the key challenges for such optimal retirement planning is the stochasticity in the retiree’s income, which can include uncertain pension payments, fluctuating investment returns, or unexpected windfalls or losses. This paper proposes a robust Monte Carlo-based-dynamic programming technique to approximate the deterministic equivalent of the intractable stochastic utility bequest-consumption problem. The utility function is modelled using constant relative risk aversion (CRRA), and a weighting function modulates the bequest utility. This stochastic approach allows for a more realistic representation of the uncertainties faced by retirees. The dynamic programming approach involves recursive value functions that consider the maximum expected utility from the current period to the end of the planning horizon, given the state variables of wealth and income. This paper contributes to retirement planning by offering a sophisticated tool for optimizing consumption and bequest strategies in uncertain future income and survival probabilities.