Convex Reformulation for Two-sided Distributionally Robust Chance Constraints with Inexact Moment Information

Constraints on each node and line in power systems generally have upper and lower bounds,denoted as twosided constraints.Most existing power system optimization methods with the distributionally robust(DR)chance-constrained program treat the two-sided DR chance constraint separately,which is an inexact approximation.This letter derives an equivalent reformulation for the generic two-sided DR chance constraint under the interval moment based ambiguity set,which does not require the exact moment information.The derived reformulation is a second-order cone program(SOCP)formulation and is then applied to the optimal power flow(OPF)problem under uncertainty.Numerical results on several IEEE systems demonstrate the effectiveness of the proposed SOCP formulation and show the differences with other DR chance-constrained OPF approaches.

A dynamical neural network approach for distributionally robust chance-constrained Markov decision process

In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.

Centralized-local PV voltage control considering opportunity constraint of short-term fluctuation

This study proposes a two-stage photovoltaic(PV)voltage control strategy for centralized control that ignores short-term load fluctuations.In the first stage,a deterministic power flow model optimizes the 15-minute active cycle of the inverter and reactive outputs to reduce network loss and light rejection.In the second stage,the local control stabilizes the fluctuations and tracks the system state of the first stage.The uncertain interval model establishes a chance constraint model for the inverter voltage-reactive power local control.Second-order cone optimization and sensitivity theories were employed to solve the models.The effectiveness of the model was confirmed using a modified IEEE 33 bus example.The intraday control outcome for distributed power generation considering the effects of fluctuation uncertainty,PV penetration rate,and inverter capacity is analyzed.

A Multi-objective Chance-constrained Information-gap Decision Model for Active Management to Accommodate Multiple Uncertainties in Distribution Networks

The load demand and distributed generation(DG)integration capacity in distribution networks(DNs)increase constantly,and it means that the violation of security constraints may occur in the future.This can be further worsened by short-term power fluctuations.In this paper,a scheduling method based on a multi-objective chance-constrained information-gap decision(IGD)model is proposed to obtain the active management schemes for distribution system operators(DSOs)to address these problems.The maximum robust adaptability of multiple uncertainties,including the deviations of growth prediction and their relevant power fluctuations,can be obtained based on the limited budget of active management.The systematic solution of the proposed model is developed.The max term constraint in the IGD model is converted into a group of normal constraints corresponding to extreme points of the max term.Considering the stochastic characteristics and correlations of power fluctuations,the original model is equivalently reformulated by using the properties of multivariate Gaussian distribution.The effectiveness of the proposed model is verified by a modified IEEE 33-bus distribution network.The simulation result delineates a robust accommodation space to represent the adaptability of multiple uncertainties,which corresponds to an optional active management strategy set for future selection.

A predictive chance constraint rebalancing approach to mobility-on-demand services

This paper considers the problem of supply-demand imbalances in Mobility-on-Demand(MoD)services.These imbalances occur due to uneven stochastic travel demand and can be mitigated by proactively rebalancing empty vehicles to areas where the demand is high.To achieve this,we propose a method that takes into account uncertainties of predicted travel demand while minimizing pick-up time and rebalance mileage for autonomous MoD ride-hailing.More precisely,first travel demand is predicted using Gaussian Process Regression(GPR)which provides uncertainty bounds on the prediction.We then formulate a stochastic model predictive control(MPC)for the autonomous ride-hailing service and integrate the demand predictions with uncertainty bounds.In order to guarantee constraint satisfaction in the optimization under estimated stochastic demand prediction,we employ a probabilistic constraining method with user-defined confidence interval,using Chance Constrained MPC(CCMPC).The benefits of the proposed method are twofold.First,travel demand uncertainty prediction from data can naturally be embedded into the MoD optimization framework,allowing us to keep the imbalance at each station below a certain threshold with a user-defined probability.Second,CCMPC can be relaxed into a Mixed-Integer-Linear-Program(MILP)and the MILP can be solved as a corresponding Linear-Program,which always admits an integral solution.Our transportation simulations show that by tuning the confidence bound on the chance constraint,close to optimal oracle performance can be achieved,with a median customer wait time reduction of 4%compared to using only the mean prediction of the GPR.

Multi-objective Chance-constrained Optimal Day-ahead Scheduling Considering BESS Degradation

As battery technology matures,the battery energy storage system(BESS)becomes a promising candidate for addressing renewable energy uncertainties.BESS degradation is one of key factors in BESS operations,which is usually considered in the planning stage.However,BESS degradations are directly affected by the depth of discharge(DoD),which is closely related to the BESS daily schedule.Specifically,the BESS life losses may be different when providing the same amount of energy under a distinct DoD.Therefore,it is necessary to develop a model to consider the effect of daily discharge on BESS degradation.In this paper,a model quantifying the nonlinear impact of DoD on BESS life loss is proposed.By adopting the chance-constrained goal programming,the degradation in day-ahead unit commitment is formulated as a multi-objective optimization problem.To facilitate an efficient solution,the model is converted into a mixed integer linear programming problem.The effectiveness of the proposed method is verified in a modified IEEE 39-bus system.

Day-ahead Chance-constrained Energy Management of Energy Hubs:A Distributionally Robust Approach

The day-ahead management schedules of hybrid energy hubs are intricate and usually exposed to various uncertainties with the penetration of renewable sources and different demands.Furthermore,it is difficult to access to precise probability distribution functions and exact moment information of uncertain variables.To cope with these issues,an energy management scheme based on the distributionally robust optimization approach is developed for the energy hub.It makes no assumptions of certain probability distributions and can be implemented with limited empirical data and partial information of underlying uncertainties.The operational strategy can provide decision makers with a preliminary and robust optimal solution in the day-ahead market.Numerical results illustrate the economical benefit of the energy model,and the effectiveness of the proposed approach in chance-constrained energy management is demonstrated by comparing with other cases.Index Terms-Chance constraint,distributionally robust optimization,energy hub,energy management.

Learning Reactive Power Control Polices in Distribution Networks Using Conditional Value-at-Risk and Artificial Neural Networks

Scalable coordination of photovoltaic(PV)inverters,considering the uncertainty in PV and load in distribution networks(DNs),is challenging due to the lack of real-time communications.Decentralized PV inverter setpoints can be achieved to address this issue by capitalizing on the abundance of data from smart utility meters and the scalable architecture of artificial neural networks(ANNs).To this end,we first use an offline,centralized data-driven conservative convex approximation of chance-constrained optimal power flow(CVaR-OPF)in which conditional value-at-risk(CVaR)is used to compute reactive power setpoints of PV inverter,taking into account PV and load uncertainties in DNs.Following that,an artificial neural network(ANN)controller is trained for each PV inverter to emulate the optimal behavior of the centralized control setpoints of PV inverter in a decentralized fashion.Additionally,the voltage regulation performance of the developed ANN controllers is compared with other decentralized designs(local controllers)developed using model-based learning(regressionbased controller),optimization(affine feedback controller),and case-based learning(mapping)approaches.Numerical tests using real-world feeders corroborate the effectiveness of ANN controllers in voltage regulation and loss minimization.

Distributionally Robust Co-optimization of Transmission Network Expansion Planning and Penetration Level of Renewable Generation

Transmission network expansion can significantly improve the penetration level of renewable generation.However,existing studies have not explicitly revealed and quantified the trade-off between the investment cost and penetration level of renewable generation.This paper proposes a distributionally robust optimization model to minimize the cost of transmission network expansion under uncertainty and maximize the penetration level of renewable generation.The proposed model includes distributionally robust joint chance constraints,which maximize the minimum expectation of the renewable utilization probability among a set of certain probability distributions within an ambiguity set.The proposed formulation yields a twostage robust optimization model with variable bounds of the uncertain sets,which is hard to solve.By applying the affine decision rule,second-order conic reformulation,and duality,we reformulate it into a single-stage standard robust optimization model and solve it efficiently via commercial solvers.Case studies are carried on the Garver 6-bus and IEEE 118-bus systems to illustrate the validity of the proposed method.

Distributionally Robust Optimal Reactive Power Dispatch with Wasserstein Distance in Active Distribution Network

The uncertainties from renewable energy sources(RESs)will not only introduce significant influences to active power dispatch,but also bring great challenges to the analysis of optimal reactive power dispatch(ORPD).To address the influence of high penetration of RES integrated into active distribution networks,a distributionally robust chance constraint(DRCC)-based ORPD model considering discrete reactive power compensators is proposed in this paper.The proposed ORPD model combines a second-order cone programming(SOCP)-based model at the nominal operation mode and a linear power flow(LPF)model to reflect the system response under certainties.Then,a distributionally robust optimization(WDRO)method with Wasserstein distance is utilized to solve the proposed DRCC-based ORPD model.The WDRO method is data-driven due to the reason that the ambiguity set is constructed by the available historical data without any assumption on the specific probability distribution of the uncertainties.And the more data is available,the smaller the ambiguity would be.Numerical results on IEEE 30-bus and 123-bus systems and comparisons with the other three-benchmark approaches demonstrate the accuracy and effectiveness of the proposed model and method.