Stochastic Optimal Power Flow Research Articles

Stochastic optimal power flow framework with incorporation of wind turbines and solar PVs using improved liver cancer algorithm

AbstractThe present study introduces a nature inspired improved liver cancer algorithm (ILCA) for solving the non‐convex engineering optimization issues. The traditional LCA (t‐LCA) inspires from the conduct of liver tumours and integrates biological ethics during the optimization procedure. However, t‐LCA facing stagnation issues and may trap into local optima. To avoid such issues and provide the optimal solution, there are some modifications are implemented into the internal structure of t‐LCA based on Weibull flight operator, mutation‐based approach, quasi‐opposite‐based learning and gorilla troops exploitation‐based mechanisms to enhance the overall strength of the algorithm to obtain the global solution. For validation of ILCA, the non‐parametric and the statistical analysis are performed using benchmark standard functions. Moreover, ILCA is applied to resolve the stochastic renewable‐based (wind turbines + PVs) optimal power flow problem using a modified RER‐based IEEE 57‐bus. The objective of this work is to obtain the minimum predicted power losses and enhance the predicted voltage stability. By incorporation of renewable resources into the modified IEEE57‐bus network can help the system to reduce the power losses from 5.6622 to 3.8142 MW, while the voltage stability is enhanced from 0.1700 to 0.1164 p.u.

Stochastic dual dynamic programming for optimal power flow problems under uncertainty

Planning in the power sector has to take into account the physical laws of alternating current (AC) power flows as well as uncertainty in the data of the problems, both of which greatly complicate optimal decision making. We propose a computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in AC power systems. Our approach uses recent results on dual convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the stochastic dual dynamic programming (SDDP) algorithm for problems with a Markovian structure. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal policy of the stochastic AC-OPF problem as long as the SDP relaxations are tight. To test the practical viability of our approach, we set up a case study of a storage siting, sizing, and operations problem. We show that the convex SDP relaxation of the stochastic problem is usually tight and discuss ways to obtain near-optimal physically feasible solutions when this is not the case. The algorithm finds a physically feasible policy with an optimality gap of 3% and yields a significant added value of 27% over a rolling deterministic policy, which leads to overly optimistic policies and underinvestment in flexibility. This suggests that the common industry practice of assuming direct current and deterministic problems should be reevaluated by considering models that incorporate realistic AC flows and stochastic elements in the data as potentially more realistic alternatives.

Day-ahead dynamic operating envelopes using stochastic unbalanced optimal power flow

Driven by the energy transition, distribution networks are dealing with increasing uptake of distributed energy resources, including solar photovoltaic generation. Residential rooftop solar allows customers to minimize exposure to price increases in the market, which has led to high penetration of PV in regions with high amounts of solar hours such as Australia. Eventually, this leads to congestion in the network, either due to voltage rise, or due to overcurrent in lines or transformers. Distribution utilities are now moving on from static export limits for customers in congested networks, to dynamic limits that are based on the state of the network. It is considered thoughtful to give customers advance warning, e.g. day-ahead, of the moments and degrees of export limitation, despite uncertainty surrounding the future state of the network. Therefore, in this paper, we consider the application of general polynomial chaos expansion based stochastic unbalanced optimal power flow to the day-ahead determination of dynamic export limits. We perform a numerical study on a European style low voltage feeder and illustrate the impact of fairness principles on chance-constrained stochastic nonlinear optimization without the need of sampling, linearizing the power flow equations, or applying relaxations. Case studies show the necessity of considering unbalanced study of distribution system. It was observed that equality measures reduce the overall output of the system in an attempt to achieve equal relative injection, while alpha fairness with a higher value of alpha is a compromise between the efficiency and fairness in DOEs.

Optimal power dispatch in hybrid power system for medium- and large-scale practical power systems using self-adaptive bonobo optimizer algorithm

Incorporating renewable energy sources (RESs) introduces a notable amount of uncertainty in the optimal planning and operation of electrical power grids. Under these circumstances, this paper proposes the application of a recently introduced metaheuristic optimization technique to solve the stochastic optimal power flow (OPF) problem involving wind and solar power sources. The self-adaptive bonobo optimizer (SaBO) is used to minimize three distinct objective functions: (i) Total generation cost (TGC) minimization, including both thermal and wind/solar generation costs, (ii) Power loss minimization, (iii) Combined generation cost and emissions effect minimization. The costs associated with the stochastic generation of wind and solar power included direct costs, reserves and penalty costs from the overestimation and underestimation of available wind and solar power, respectively. The performance of the proposed algorithm is evaluated on two power systems: the modified IEEE 30-bus and the Algerian DZA 114-bus test systems. To demonstrate the efficacy of the SaBO, the obtained results have been compared with those obtained from the Kepler optimization algorithm (KOA) and other recently published optimizers under the same case studies and constraints. The comparative results clearly show the superiority of the SaBO algorithm over all other well-known optimization algorithms provided in the literature for solving the OPF problem. This is evidenced by minimizing total generation costs of 781.2363 $/h for the modified IEEE 30-bus and 16,706.1630 $/h for the Algerian DZA-114-bus system. Furthermore, the integration of RES led to a notable 2.33% and 11.67% reduction in total generation cost for the IEEE 30-bus and Algerian DZA 114-bus systems, respectively, compared to their initial configurations without RESs. The promising findings highlight the powerful of the optimizer to solve non-linear and complex optimization problems in power systems.

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

ABSTRACT We investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

A solution to multi Objective Stochastic Optimal Power Flow problem using mutualism and elite strategy based Pelican Optimization Algorithm

Wind Energy is rapidly growing into one of the most popular energy options for power generation. However, the unpredictability of wind necessitates the employment of a distribution function when describing the wind environment. In the depiction of wind speeds, the two significant parameters of the Weibull distribution, such as the scale parameter and the shape parameter are often utilized. Therefore, it is essential to choose the most appropriate approach for estimating these parameters. Furthermore, the uncertainty in delegated power from variable wind speeds makes system management challenging. In this paper, the Weibull distribution parameters were determined using the Pelican Optimization Algorithm (POA). POA has gained extensive popularity among the research community and is currently used to address a wide range of optimization problems. However, the exploration and exploitation are not properly balanced in this algorithm. To overcome this problem a novel hybrid algorithm namely Mutualism phase based POA (MPOA) is proposed with the help of mutualism phase of Symbiotic Organisms Search (SOS) algorithm. To demonstrate the efficacy and robustness MPOA is applied on multi-objective Optimal Power Flow (MO-OPF) problems. For this study IEEE 30 bus standard system and modified IEEE 30 bus system consisting of two wind farms are taken. The purpose of this work is to examine the impact of changing the Weibull parameters, reverse and penalty cost coefficients on the overall generation cost while considering all the security aspects.

Optimal power flow of thermal-wind-solar power system using enhanced Kepler optimization algorithm: Case study of a large-scale practical power system

In the current century, electrical networks have witnessed great developments and continuous increases in the demand for fossil fuels based energy, leading to an excessive rise in the total production cost (TPC), as well as the pollutant (toxic) gases emitted by thermal plants. Under this circumstances, energy supply from different resources became necessary, such as renewable energy sources (RES) as an alternative solution. This latter, however, characterized with uncertainty nature in its operation principle, especially when operator system wants to define the optimal contribution of each resource in an effort to ensure economic and enhanced reliability of grid. This paper presents an Enhanced version of Kepler optimization algorithm (EKOA) to solve the problem of stochastic optimal power flow (SOPF) in a most efficient way incorporating wind power generators and solar photovoltaic with different objective functions, the stochastic nature of wind speed and solar is modeled using Weibull and lognormal probability density functions respectively. To prove the effectiveness of the proposed EKOA, various case studies were carried out on two test systems IEEE 30-bus system and Algerian power system 114-bus, obtained results were evaluated in comparison with those obtained using the original KOA and other methods published in the literatures. Thus, shows the effectiveness and superiority of the efficient EKOA over other optimizers to solve complex problem. The incorporation of RES resulted in a significant 2.39% decrease in production cost, showcasing EKOA’s efficiency with a $780/h, compared to KOA’s $781/h, for IEEE 30-bus system. For the DZA 114-bus system revealed even more substantial reductions, with EKOA achieving an impressive 12.6% reduction, and KOA following closely with a 12.4% decrease in production cost.

Constrained Reinforcement Learning for Predictive Control in Real-Time Stochastic Dynamic Optimal Power Flow

Constrained Reinforcement Learning for Predictive Control in Real-Time Stochastic Dynamic Optimal Power Flow

Two-Stage Stochastic Optimal Power Flow for Microgrids With Uncertain Wildfire Effects

Two-Stage Stochastic Optimal Power Flow for Microgrids With Uncertain Wildfire Effects

Stochastic Optimal Power Flow Integrating With Renewable Energy Resources and V2G Uncertainty Considering Time-Varying Demand: Hybrid GTO-MRFO Algorithm

Stochastic Optimal Power Flow Integrating With Renewable Energy Resources and V2G Uncertainty Considering Time-Varying Demand: Hybrid GTO-MRFO Algorithm

Optimal site and size of FACTS devices with the integration of uncertain wind generation on a solution of stochastic multi-objective optimal power flow problem

To reduce the Carbon footprint and reduce emissions from the globe, the world has kicked-off to leave reliance of fossil fuels and generate electrical energy from renewable energy sources. The MOOPF problem is becoming more complex, and the number of decision variables is increasing, with the introduction of power electronics-based Flexible AC Transmission Systems (FACTS) devices. These power system components can all be used to increase controllability, effectiveness, stability, and sustainability. The added uncertainty and variability that FACTS devices and wind generation provide to the power system makes it challenging to find the right solution to MOOPF issues. In order to determine the best combination of control and state variables for the MOOPF problem, this paper develops three cases of competing objective functions. These cases include minimizing the total cost of power produced as well as over- and underestimating the cost of wind generation, emission rate, and the cost of power loss caused by transmission lines. In the case studies, power system optimization is done while dealing with both fixed and variable load scenarios. The proposed algorithm was tested on three different cases with different objective functions. The algorithm achieved an expected cost of $833.014/h and an emission rate of conventional thermal generators of 0.665 t/h in the case 1. In Case 2, the algorithm obtained a minimum cost of $731.419/h for active power generation and a cost of power loss is 124.498 $/h for energy loss. In Case 3, three objective functions were minimized simultaneously, leading to costs of $806.6/h for emissions, 0.647 t/h, and $214.9/h for power loss.

Integrating renewable energy and V2G uncertainty into optimal power flow: A gradient bald eagle search optimization algorithm with local escaping operator

AbstractHere, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

A Tractable Linearization-Based Approximated Solution Methodology to Stochastic Multi-Period AC Security-Constrained Optimal Power Flow

The growing presence of renewable energy sources (RES), energy storage systems (ESSs) and flexible loads (FLs) in power systems necessitates a new approach to N-1 security in day-ahead operation planning considering stochasticity and time coupling. To this end, a comprehensive approach based on stochastic multi-period AC security-constrained optimal power flow (S-MP-AC-SCOPF) was proposed recently in a form of a large-scale non-linear programming problem, which is not scalable. This paper proposes the first-time new tractable solution methodology for the most complete AC-SCOPF problem to date: S-MP-AC-SCOPF. As other main novelty, the proposed methodology achieves tractability by solving sequentially a limited number of different linear approximations of the full S-MP-AC-SCOPF problem. These linear approximations differ in terms of: state dependency regarding losses approximation, carefully reduced sets of constraints or tightening of critical constraints. The performance of the methodology is demonstrated in power system models of Sweden and Portugal. Extensive numerical experiments have shown that the methodology is able to reduce progressively until complete removal the number of violated thermal or voltage constraints. It leads to reasonably accurate solution with small optimality gap within few iterations and is at least 85% faster than the competitor IPOPT solver.

Set-Based Group Search Optimizer for Stochastic Many-Objective Optimal Power Flow

The conventional optimal power flow (OPF) is confronted with challenges in tackling more than three objectives and the stochastic characteristics due to the uncertainty and intermittence of the RESs. However, there are few methods available that simultaneously address high-dimensional objective optimization and uncertainty handling. This paper proposes a set-based group search optimizer (SetGSO) to tackle the stochastic many-objective optimal power flow (MaOPF) of power systems penetrated with renewable energy sources. The proposed SetGSO depicts the original stochastic variables by set-based individuals under the evolutionary strategy of the basic GSO, without using repeated sampling or probabilistic information. Consequently, two metrics, hyper-volume and average imprecision, are introduced to transform the stochastic MaOPF into a deterministic bi-objective OPF, guaranteeing a much superior Pareto-optimal front. Finally, our method was evaluated on three modified bus systems containing renewable energy sources, and compared with the basic GSO using Monte Carlo sampling (GSO-MC) and a set-based genetic algorithm (SetGA) in solving the stochastic MaOPF. The numerical results demonstrate a saving of 90% of the computation time in the proposed SetGSO method compared to sampling-based approaches and it achieves improvements in both the hyper-volume and average imprecision indicators, with a maximum enhancement of approximately 30% and 7% compared to SetGA.

Convex Stochastic Approaches for the Optimal Allocation of Distributed Energy Resources in AC Distribution Networks with Measurements Fitted to a Continuous Probability Distribution Function

This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.

Stochastic optimal power flow analysis of power system with renewable energy sources using Adaptive Lightning Attachment Procedure Optimizer

The integration of several renewable energy sources (RESs), such as photovoltaic generation (PVG) and wind turbine generation (WTG), introduces a significant amount of uncertainty for the optimal planning of the electrical power systems. The optimal power flow (OPF) problem became more difficult to solve when RESs uncertainties were taken into account. In this research, the stochastic OPF problem is solved using an Adaptive Lightning Attachment Procedure Optimizer (ALAPO) with the integration of RESs. The ALAPO is proposed in this study to improve both the exploration and exploitation process of the conventional Lightning Attachment Procedure Optimizer (LAPO). In order to create a number of scenarios that account for the uncertainties associated with load demand, wind speed, and solar irradiation, the scenario based reduction method is utilized. Further, to determine the optimal setting of active power of generators, tap setting of the transformers, reactive power of the capacitor banks, and the voltage profile at the generator buses for each scenario of RESs the objective function considered in this study is to minimize the power loss, voltage deviation, and voltage stability index of the power system. The effectiveness of the proposed algorithm is tested on IEEE 57-bus system. The results in this study show that the proposed ALAPO is superior for solving the OPF with the integration of RESs compared to the conventional methods like LAPO, Particle Swarm Optimization (PSO), Sand Cat Swarm Optimizer (SCSO), Gray Wolf Optimizer (GOW), Whale Optimization Algorithm (WOA), Black Widow Optimization Algorithm (BWO), and Capuchin Search Algorithm (CapSA).

Stochastic optimal power flow analysis of power systems with wind/PV/ TCSC using a developed Runge Kutta optimizer

Recently, renewable energy resources such as wind turbines (WTs) and photovoltaic (PV) systems are wildly installed in electrical systems. However, the main challenge that related to these resources is the optimal planning and operation of the power system due to their stochastic natural and intermittency. However, OPF solution in case of considering the uncertainties of RERs and optimal integration of FACTS device became more complex and not easy task. Consequently, this paper proposes a modified version of the RUNge Kutta optimizer (MRUN) for solving the stochastic OPF problem with optimal integration of the WTs and PV systems along with Thyristor controlled series compensator (TCSC). The Modified RUNge Kutta optimizer (MRUN) is based on Cauchy mutation and the quasi-oppositional based learning techniques to render the RUN optimization technique to be more robust and powerful. The objective functions of the current optimization problem are the total expected power losses (TEPL), the total expected voltage deviations (TEVD) and the total expected voltage stability (TEVS). The proposed algorithm is tested on IEEE 57-bus system. After the RERs and TCSCs integration under uncertainty state, the reduction in the TEPL and TEVD are 24.75 %, and 14.74 % while the TEVS is enhanced by 18.33 % compared to based case (without RERs and TCSCs). In addition to that the proposed MRUN is superior for solving the OPF and assigning the optimal sites and sizes of the RERs and the TCSCs compared to the conventional RUN.

Analytical uncertainty propagation for multi-period stochastic optimal power flow

The increase in renewable energy sources (RESs), like wind or solar power, results in growinguncertainty also in transmission grids. This affects grid stability through fluctuating energy supplyand an increased probability of overloaded lines. One key strategy to cope with this uncertainty isthe use of distributed energy storage systems (ESSs). In order to securely operate power systemscontaining renewables and use storage, optimization models are needed that both handle uncertaintyand apply ESSs. This paper introduces a compact dynamic stochastic chance-constrained DC optimalpower flow (CC-OPF) model, that minimizes generation costs and includes distributed ESSs. AssumingGaussian uncertainty, we use affine policies to obtain a tractable, analytically exact reformulation asa second-order cone problem (SOCP). We test the new model on five different IEEE networks withvarying sizes of 5, 39, 57, 118 and 300 nodes and include complexity analysis. The results showthat the model is computationally efficient and robust with respect to constraint violation risk. Thedistributed energy storage system leads to more stable operation with flattened generation profiles.Storage absorbed RES uncertainty, and reduced generation cost.

Three Solution Approaches to Stochastic Multi-Period AC Optimal Power Flow in Active Distribution Systems

This paper proposes three novel solution approaches (A1, A2, A3) to solve stochastic multi-period AC optimal power flow (S-MP-OPF) for day-ahead flexibility procurement from distributed energy resources (DER) in active distribution systems (ADSs). The S-MP-OPF is a mixed-integer nonlinear programming (MINLP) problem due to the binary variables modeling the operation of storage devices and flexible loads. The proposed three approaches have a shared common first step, which resorts to a new mixed-integer linear programming (MILP) model approximation of the S-MP-OPF problem. The MILP model employs second-order Taylor series expansion of trigonometric terms and formulates the linear approximations relying on variables such as square of voltage magnitude and voltage angle difference. This first step serves also the purpose of fixing the binary variables to the values computed by the MILP problem. Then, the approach A1 only checks the AC feasibility of MILP solution while approaches A2 and A3 further optimize continuous variables. Specifically, the sophisticated heuristic approach A2 employs sequential linear programming and AC power flow while the approach A3 models and solves directly the remaining nonlinear programming (NLP) problem. The performances of these approaches, a benchmark MINLP solver, and a state-of-the-art method are thoroughly compared in three radial or weakly meshed ADSs of 34, 31, and 191 nodes, respectively. The numerical results indicate that, albeit the approach A2 performs best overall, these approaches present distinct accuracy vs speed trade-offs, which make them suitable to problems of different sizes and diverse accuracy or speed requirements.

A new hybrid evolutionary algorithm for multi-objective optimal power flow in an integrated WE, PV, and PEV power system

• A novel hybrid multi-objective evolutionary algorithm (MOEA) was developed based on the decomposition and invasive weed optimization (IWO) techniques for solving the MOOPF problem. • The conventional MOOPF problem was modified by taking stochastic WE, PV, and PEV powers into consideration. • Modeling the stochastic nature of WE, PV, and PEV sources was done using probability distribution functions (PDFs) and calculating its uncertainty cost was done with Monte Carlo simulations. • Using an effective constraint handling method (CHM) known as the superiority of feasible solution (SF) was done to address difficult constraints. • The one-way analysis of variance (ANOVA) test was deployed to give a certain level of confidence to our study. This study proposes a novel hybrid multi-objective evolutionary algorithm (MOEA) based on decomposition and invasive weed optimization (IWO) algorithm for the optimal power flow (OPF) problem in transmission networks. The conventional OPF is modified as a stochastic OPF with the integration of WE, PV, and PEV systems uncertainty. This paper proposes a new constraint-handling method (CHM) that adds the penalty adaptively and avoids parameter reliance on penalty computation. The selection features in the IWO method are deployed to improve the diversity of the proposed method. The OPF problem is represented as a multi-objective optimization (MOO) problem using four objectives: generation cost, emission, power loss, and voltage variation. The generation costs of WE, PV, and PEV sources are evaluated using Monte Carlo simulations to mitigate the whole cost and the influence of intermittency of these systems is investigated in terms of affordability and feasibility. Weibull, lognormal, and normal probability distribution functions (PDFs) are employed to define the uncertainty of WE, PV, and PEV sources respectively. The suggested method's viability is evaluated on IEEE 57 and IEEE 118- bus systems under all conceivable scenarios. In addition, one-way ANOVA test, a statistical approach, is used to evaluate the superiority of the suggested algorithm.