Robust Optimal Power Flow Research Articles

Transferability-Oriented Adversarial Robust Security-Constrained Optimal Power Flow

Transferability-Oriented Adversarial Robust Security-Constrained Optimal Power Flow

Robust optimal power flow considering uncertainty in wind power probability distribution

This paper proposes an optimal power flow model that takes into account the uncertainty in the probability distribution of wind power. The model can schedule controllable generators under any possible distribution of wind power to ensure the safe and economic operation of the system. Firstly, considering the incompleteness of historical wind power data, the paper models the uncertainty of wind power using second-order moments of probability distribution and their fluctuation intervals. Subsequently, a robust optimal power flow model based on probability distribution model and joint chance constraints is established. The Lagrangian duality theorem is then employed to eliminate random variables from the optimization model, transforming the uncertainty model into a deterministic linear matrix inequality problem. Finally, a convex optimization algorithm is used to solve the deterministic problem, and the results are compared with traditional chance-constrained optimal power flow model. The feasibility and effectiveness of the proposed method are validated through case study simulations.

A data-aided robust approach for bottleneck identification in power transmission grids for achieving transportation electrification ambition: a case study in New York state

As the enthusiasm for electric vehicles passes the range anxiety and other tests, large-scale transportation electrification becomes a prominent topic in research and policy discussions. In consequence, the public attention has shifted upstream and holistically towards the integration of large-scale transportation electrification to power systems. This paper proposes a method to identify bottlenecks in power transmission systems to accommodate large-scale and stochastic electric vehicles charging demands. First, a distributionally robust chance-constrained direct current optimal power flow model is developed to quantify the impacts of stochastic electric vehicles charging demands. Subsequently, an agent-based model with the trip-chain method is applied to obtain the spatiotemporal distributions of electric vehicles charging demands for both light-duty electric vehicles and medium and heavy-duty electric vehicles. The first two moments of those distributions are extracted to build an ambiguity set of electric vehicles charging demands. Finally, a 121-bus synthetic transmission network for New York State power systems is used to validate the future transportation electrification in New York State from 2025 to 2035. Results show that the large-scale transportation electrification in New York State will account for approximately 13.33 % to 16.79 % of the total load demand by 2035. The transmission capacity is the major bottleneck in supporting New York State to achieve its transportation electrification. To resolve the bottlenecks, we explore some possible solutions, such as transmission capacity expansion and distributed energy resources investment. Wind power shows an advantage over solar energy in terms of total operational costs due to better peak alignment between wind power and electric vehicles charging demand.

Unifying Chance-Constrained and Robust Optimal Power Flow for Resilient Network Operations

Unifying Chance-Constrained and Robust Optimal Power Flow for Resilient Network Operations

Distributionally Robust Optimal Power Flow via Ellipsoidal Approximation

This paper proposes a distributionally robust joint chance-constrained AC optimal power flow to manage the risk of operational limits violations which are caused by uncertain renewable generation. By determining the dispatch schedule, this approach can help to decrease the risk of renewable curtailment, load shedding, or emergency redispatch in real-time. To model the proposed approach, the renewable uncertainty is first modeled as a distributionally robust ellipsoidal bound based on the Wasserstein metric. This bound is built upon a limited historical renewable forecast errors dataset without any assumption on the probability distribution of uncertainty. Then, this uncertainty bound is adopted within a semidefinite relaxation of the optimal power flow. The system responses to the renewable generation forecast errors are modeled as linear sensitivities, where all conventional generators are responsible for compensating the impacts of renewable forecast errors. Numerical experiments on IEEE 14-bus and 118-bus systems show the validity and scalability of the proposed method. Furthermore, the effectiveness of the proposed approach in terms of meeting probabilistic guarantees, cost-effectiveness and computational time is also demonstrated in the experiments.

Robust optimization model of flexible distribution network considering source-load uncertainty

The increase in renewable energy permeability and the electrical load uncertainty aggravates the fluctuation of power flow and bus voltage magnitudes of the distribution network (DN). Then, the fluctuation threatens system security and makes increasing difficulties in DN regulation. However, the widespread utilities of power electronic technology promote rapid developments in flexible distribution networks, thereby providing certain opportunities to treat the open question. Therefore, this study proposes a robust optimization model of flexible distribution network allowing for system security and economy. Firstly, a optimal power flow (OPF) model of flexible distribution network with various active management strategies is derived and constructed by taking the minimum loss and voltage offset as the objective function. The model is linearized and relaxed to convex problem by a second-order cone. Then, the robust OPF model of flexible distribution network is established considering the uncertainty of load and renewable energy. Finally, a relaxation-based co-evolution algorithm is proposed to solve the model. The modified IEEE 33 bus system and PG&E 69 bus system are involved for case studies, in which the calculation results under various scenarios are compared. Consequently, the effectiveness and practicability of proposed model to locate and cope with the worst situation is demonstrated.

A sequential deep learning algorithm for sampled mixed-integer optimisation problems

Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each iteration step of both algorithms, we first test the feasibility of a given test solution for each and every constraint associated with the sampled optimisation at hand, while also identifying those constraints that are violated. Subsequently, an optimisation problem is constructed with a constraint set consisting of the current basis—namely, the smallest set of constraints that fully specifies the current test solution—as well as constraints related to a limited number of the identified violating samples. We show that both algorithms exhibit finite-time convergence towards the optimal solution. Algorithm 2 features a neural network classifier that notably improves the computational performance compared to Algorithm 1. We quantitatively establish these algorithms' efficacy through three numerical tests: robust optimal power flow, robust unit commitment, and robust random mixed-integer linear program.

Distributionally robust optimal power flow with contextual information

In this paper, we develop a distributionally robust chance-constrained formulation of the Optimal Power Flow problem (OPF) whereby the system operator can leverage contextual information. For this purpose, we exploit an ambiguity set based on probability trimmings and optimal transport through which the dispatch solution is protected against the incomplete knowledge of the relationship between the OPF uncertainties and the context that is conveyed by a sample of their joint probability distribution. We provide a tractable reformulation of the proposed distributionally robust chance-constrained OPF problem under the popular conditional-value-at-risk approximation. By way of numerical experiments run on a modified IEEE-118 bus network with wind uncertainty, we show how the power system can substantially benefit from taking into account the well-known statistical dependence between the point forecast of wind power outputs and its associated prediction error. Furthermore, the experiments conducted also reveal that the distributional robustness conferred on the OPF solution by our probability-trimmings-based approach is superior to that bestowed by alternative approaches in terms of expected cost and system reliability.

An optimization under uncertainty in system equations and applications to robust AC optimal power flow

AbstractThis paper presents a formulation of an optimization of uncertain systems and the solution technique. The optimization under uncertainties is formulated as an optimization problem which includes unknown variables in equality constraints called system equations as well as in an objective function and inequality constraints. As countermeasures against the uncertainties, a min‐max criterion is applied to the objective function and robustness criteria are introduced to the inequality constraints. By differentiating state variables satisfying the equality constraints from the decision variables, we reformulate the optimization problem based on the worst‐case scenario of the state variables corresponding to the uncertain variables and we propose a “constraints‐relaxation procedure” based method considering the equality constraints to solve the reformulated problem. In this method, a constraints‐relaxed problem is solved corresponding to a finite number of samples of uncertain variables. Furthermore, a new sample of uncertain variables is sequentially generated corresponding to the inequality constraint which the solution violates most, together with state variables satisfying the system equations at the new worst‐case scenario. Finally, the effectiveness of the proposed method is illustrated by numerical examples including robust AC optimal power flow considering distributed energy resources.

Integrating unimodality into distributionally robust optimal power flow

Integrating unimodality into distributionally robust optimal power flow

Robust Optimal Power Flow under Renewable Uncertainty with Pairwise Convex Hull and Non-Affine AGC Redispatch Strategy

To accommodate the intermittent and uncertain renewable energy resources (RESs) in the power system, a novel robust optimal power flow (ROPF) method under RES uncertainty is proposed in this paper. A novel convex set, the pairwise convex hull, is applied to characterize the RES uncertainty. Then, an adjustable ROPF model is built to integrate RESs, where non-affine re-dispatch constraints are designed to cope with the situation when the automatic generation control (AGC) units’ power outputs hit their lower or upper bound during the re-dispatch process. The resulting ROPF problem is then solved with an adversarial approach (constraint generation) in which the potential binding constraints are identified to speed up the calculation. By solving the proposed ROPF model, the base point can be obtained to not only serve the forecasted load, but also ensure a feasible solution for all realizations of RES outputs within the pre-defined uncertainty set. Numerical studies on the 39-bus and 500-bus systems show that the proposed pairwise convex hull can capture the complicated distribution of RES outputs and is computationally very efficient. The binding constraint identification scheme can further dramatically speed up the computation. In addition, the non-affine AGC power re-dispatch scheme can achieve a lower objective value, for example, the proposed non-affine AGC re-dispatch-based ROPF method saves 0.389% and 0.1665% of the total costs for the 39-bus and 500-bus systems.

Distributionally Robust Multi-Energy Dynamic Optimal Power Flow Considering Water Spillage with Wasserstein Metric

This paper proposes a distributed robust multi-energy dynamic optimal power flow (DR-DOPF) model to overcome the uncertainty of new energy outputs and to reduce water spillage in hydropower plants. The proposed model uses an ambiguity set based on the Wasserstein metric to address the uncertainty of wind and solar power forecasting errors, rendering the model data-driven. With increasing sample size, the conservativeness of the ambiguity set was found to decrease. By deducing the worst-case expectation in the objective function and the distributed robust chance constraints, the exact equivalent form of the worst-case expectation and approximate equivalent form of the distributed robust chance constraints were obtained. The test results of the IEEE-118 and IEEE-300 node systems indicate that the proposed model could reduce water spillage by more than 85% and comprehensive operation cost by approximately 12%. With an increasing number of samples, the model could reduce conservativeness on the premise of satisfying the reliability of safety constraints.

An Optimization under Uncertainty in System Equations and Applications to Robust AC Optimal Power Flow

An Optimization under Uncertainty in System Equations and Applications to Robust AC Optimal Power Flow

Distributed adjustable robust optimal power-gas flow considering wind power uncertainty

The rapid uptake of natural gas-fired units in energy systems poses significant challenges in coordinating the electricity and gas systems. Besides, the uncertainty caused by integrated renewable energy such as wind power raises more requirements on the robustness of the operation for integrated electricity and natural gas system (IEGS). To address these challenges, this paper investigates the distributed adjustable robust optimal power and gas flow (OPGF) model for IEGS. Using linear decision rules (LDRs), we first propose an improved adjustable robust model combining with the automatic generation control systems to fully exploit its potential in dealing with renewable energy uncertainty while utilizing the controllable polyhedral uncertainty set to reduce solution conservatism. This improved LDRs based adjustable robust approach can reduce the computational burden caused by the existing decomposition based robust approach when applied to distributed optimization. Then, to preserve the information privacy and decision-making independence of subsystems, two tailored alternating direction method of multipliers (ADMM) based distributed optimization frameworks for IEGS with and without a central coordinator are presented, respectively. Effectiveness is illustrated through benchmark case studies.

Distributionally Robust Stochastic Optimal Power Flow Considering N-1 Security Constraints with renewable

This paper proposes a data-driven stochastic optimal power flow model considering the uncertainties of renewable energy sources. The proposed model also focuses on the constraints of reactive voltage, aiming at improving the safety of voltage amplitude and reactive power output at each bus. Using data-driven linearization techniques, we simplified the calculation of system. In addition, Wasserstein ambiguity set was used to describe the uncertainties of renewable energy prediction error distribution, and a robust stochastic optimal power flow model considering N-1 security constraints is established. The simulation results on IEEE-39 system showed the accuracy and effectiveness of the distributionally robust optimization model and the reactive voltage constraint model provided a more stable operation schedule.

Robust Stochastic Dynamic Optimal Power Flow Model of Electricity-Gas Integrated Energy System considering Wind Power Uncertainty

The application of gas turbines and power to gas equipment deepens the coupling relationship between power systems and natural gas systems and provides a new way to absorb the uncertain wind power as well. The traditional stochastic optimization and robust optimization algorithms have some limitations and deficiencies in dealing with the uncertainty of wind power output. Therefore, we propose a robust stochastic optimization (RSO) model to solve the dynamic optimal power flow model for electricity-gas integrated energy systems (IES) considering wind power uncertainty, where the ambiguity set of wind power output is constructed based on Wasserstein distance. Then, the Wasserstein ambiguity set is affined to the eventwise ambiguity set, and the proposed RSO model is transformed into a mixed-integer programming model, which can be solved rapidly and accurately using commercial solvers. Numerical results for EG-4 and EG-118 systems verify the rationality and effectiveness of the proposed model.

Stochastic multi-period optimal dispatch of energy storage in unbalanced distribution feeders

This paper presents a convex, multi-period, AC-feasible Optimal Power Flow (OPF) framework that robustly dispatches flexible demand-side resources in unbalanced distribution feeders against uncertainty in very-short timescale solar Photo-Voltaic (PV) forecasts. This is valuable for power systems with significant behind-the-meter solar PV generation as their operation is affected by uncertainty from forecasts of demand and solar PV generation. The aim of this work is then to ensure the feasibility and reliability of distribution system operation under high solar PV penetration. We develop and present a novel, robust OPF formulation that accounts for both the nonlinear power flow constraints and the uncertainty in forecasts. This is achieved by linearizing an optimal trajectory and using first-order methods to systematically tighten voltage bounds. Case studies on a realistic distribution feeder shows the effectiveness of a receding-horizon implementation.

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

Distributionally Robust Optimal Power Flow in Multi-Microgrids With Decomposition and Guaranteed Convergence

Multi-microgrids (MMGs) are emerging as a cost-effective solution to provide ancillary services. To reconcile external reserve provision and internal risk hedging for MMGs, a novel comprehensive multi-area dynamic optimal power flow (MADOPF) model is established, where energy-reserve co-optimization, three-phase unbalanced network intrinsics and dual control time-scales are all addressed. To better hedge the uncertainties of distributed generation and loads, distributionally robust model predictive control (MPC) is applied to the MADOPF problem. To preserve operational independence and information privacy for each microgrid, decomposition of the nonconvex model is devised with guaranteed convergence. Numerical tests on a two-area system and a real large-scale 16-area system derived from Shandong Power Grid validate the effectiveness of the proposed method. The advantages are demonstrated by the comparison with the conventional MPC, stochastic and robust methods.

On-Line Control of DERs to Enhance the Dynamic Thermal Rating of Transmission Lines

The increasing penetration of variable distributed generation causes the transmission lines to operate closer to their design thermal limits. In this context, Dynamic Thermal Rating is a very promising technique, since it permits a better exploitation of the real capability margins of the infrastructures and eliminate network congestions. In this vein, the article proposes a novel control strategy that allows maintaining the conductor temperature of a given line within its thermal limit through the real-time curtailment of distributed energy resources in the network. The impact of weather volatility and measurement uncertainty on the dynamic response of the controller is evaluated. A comprehensive case study, based on a real-world Italian sub-transmission system and measurement data serve to illustrate the dynamic behavior of the proposed controller. The effect of measurement noise and delays is also discussed. Finally, the performance of the proposed control strategy is compared with a conventional robust optimal power flow approach.