Robust Optimal Allocation Research Articles

Two-Stage Distributed Robust Optimal Allocation of Integrated Energy Systems under Carbon Trading Mechanism

The development of renewable energy and the construction of a comprehensive energy system with multiple complementary energy sources have gradually become the main direction of China’s energy development. As the penetration rate of renewable energy increases, the intermittent and fluctuating output of wind and solar power has a more significant impact on the system. This article conducts research on the optimization configuration of integrated energy system (IES) considering photovoltaic output uncertainty under a ladder carbon trading mechanism. Firstly, a two-stage distributed robust optimization (DRO) configuration model for integrated energy system is established. In detail, a deterministic model aimed at minimizing investment costs is given in the first stage and an uncertainty model aimed at minimizing operating costs in the probability distribution of the worst scenario is built in the second stage. Then, a data-driven distributed robust optimization method is adopted to deal with the uncertainty of photovoltaic output using MATLAB software (R2020A). Finally, the column and constraint generation (C&CG) algorithm is used to solve the problem, and the optimal investment capacity and cost results of the integrated energy system considering demand response under a ladder carbon trading mechanism are obtained. Through analysis, the proposed method achieves a 5.54% reduction in carbon emission costs while maintaining nearly unchanged investment costs, thus balancing economic and environmental benefits. Additionally, the CCG algorithm can effectively improve computational efficiency and guarantee the optimality of the solution.

Distributed robust optimal configuration of multi-microgrid interconnected systems based on multi-objective bee colony algorithm

The distributed robust optimal allocation method for multi-microgrid interconnected systems usually involves a large number of variables and constraints, and the computational complexity is high in practical applications, which makes it difficult to solve the problem. Therefore, a distributed robust optimal allocation method for multi-microgrid interconnection systems based on multi-objective swarm algorithm is proposed. A distributed robust optimization configuration constraint index model for multi-microgrid interconnection system is established. Considering the influence of energy storage technology operation characteristics on its service life, a micro-grid hybrid energy storage capacity optimization configuration model with the minimum annual comprehensive energy storage cost as the objective function is established with charge and discharge power and residual power as the constraint conditions. The multi-objective swarm algorithm is used to realize the optimization model of distributed robust configuration microgrid interconnection system. By determining the power capacity configuration of the optimal energy storage system and the corresponding frequency dividing points, the power capacity configuration of the optimal energy storage system and the corresponding frequency dividing points are determined. The hybrid energy storage configuration model of multi-microgrid interconnection system is established with the minimum alternative operating cost as the objective function, so as to realize the distributed robust optimal configuration of multi-microgrid interconnection system. The simulation results show that the distributed configuration of multi-microgrid interconnection system with the proposed method has good robustness and strong optimization control ability.

Coordinated Distributionally Robust Optimal Allocation of Energy Storage System for HV-MV Distribution Network Resilience Enhancement

Coordinated Distributionally Robust Optimal Allocation of Energy Storage System for HV-MV Distribution Network Resilience Enhancement

Robust optimal allocation of multi-energy storage in a power-heating system based on operational risk

In this study, a configuration model that accounts for operational risks is proposed for the combined power-heating system with energy storage. First, the thermal network storage is taken into account to create a model of the thermal network’s quasi-dynamic operation, and then the combined optimization with the power grid is taken into account to improve the collaborative electric-thermal modeling. Then, the value-at-risk parameter is introduced to make the difficult-to-determine uncertainty interval of new energy self-adaptive, thereby balancing economy and robustness. Finally, the Nested-C&CG algorithm is used to solve the two-stage robust problem with 0 - 1 integer variables in the lower layer. The case study’s findings demonstrate the value of the model and algorithm suggested in this research.

Distributionally Robust Optimal Allocation with Costly Verification

Distributionally Robust Optimal Allocation with Costly Verification

A Two-stage Robust Optimal Allocation Model of Distributed Generation Considering Capacity Curve and Real-time Price Based Demand Response

Demand response, the reactive power output of distributed generation (DG), and network reconfiguration have significant impacts on a DG allocation strategy. In this context, a novel real-time price-based demand response formulation is integrated into the allocation model of DG. The tariff is regulated by the difference between the load and active power of renewable energy. Meanwhile, network reconfiguration and the capacity curve describing the active and reactive power limits of DG are included in the optimization model for promoting the allocation of DG. With these measures, the optimal allocation model of DG is established with the goal of maximizing the net annual profit while guaranteeing the efficient utilization of renewable energy. In addition, the uncertainties of renewable energy are considered on the basis of a two-stage robust optimization method. Finally, the entire optimization model is solved by the column and constraint generation algorithm in the IEEE 33-bus distribution system and a practical 99-bus distribution system. Numerical simulations show that the proposed model is effective in terms of improving both the usage of renewable energy and net annual profit.

Monotonicity Properties of Physical Network Flows and Application to Robust Optimal Allocation

We derive conditions for monotonicity properties that characterize general flows of a commodity over a network, where the flow is described by potential and flow dynamics on the edges, as well as potential continuity and the Kirchhoff–Neumann mass balance requirements at nodes. The transported commodity may be injected or withdrawn at any of the network nodes, and its movement throughout the network is controlled by nodal actuators. For a class of dissipative nonlinear parabolic partial differential equation (PDE) systems on networks, we derive conditions for monotonicity properties in steady-state flow, as well as for propagation of monotone ordering of states with respect to time-varying boundary condition parameters. In the latter case, initial conditions and time-varying parameters in the coupling conditions at vertices provide an initial boundary value problem (IBVP). We prove that ordering properties of the solution to the IBVP are preserved when the initial conditions and the parameters of the time-varying coupling law are appropriately ordered. Then, we prove that when monotone ordering is not preserved, the first crossing of solutions occurs at a network node. We consider the implications for robust optimization and optimal control formulations and real-time monitoring of uncertain dynamic flows on networks and discuss the application to subsonic compressible fluid flow with energy dissipation on physical networks. The main result and monitoring policy are demonstrated for gas pipeline test networks and a case study using data corresponding to a real working system. We propose applications of this general result to the control and monitoring of natural gas transmission networks.

Data-Driven Robust Optimal Allocation of Shared Parking Spaces Strategy Considering Uncertainty of Public Users’ and Owners’ Arrival and Departure: An Agent-Based Approach

To alleviate the problem between parking demand and supply, as well as improving urban traffic environment, shared parking has attracted great interest among researchers, policymakers, and entrepreneurs. Naturally, it is a prerequisite of sharing private parking spaces with public users (P-users) that all of the owners (O-users) providing parking spaces have space to park whenever they come back, with a unified management of all parking resources. However, it remains a challenge both in theory and practice. To solve this problem, firstly, we introduced a management framework of shared parking resource in terms of time and spatial dimension. Under this framework, to control the access to parking spaces of P-users, four phases (preparatory phase, open phase, releasing phase, and reconstructive phase) are divided in time dimension, and two types of parking spaces (the prestored parking spaces, and the shared parking spaces) are classified in spatial dimension. Then, based on the proposed management framework, an intelligent parking management system (IPMS) was developed to simulate the operation of shared parking considering the uncertainties of P-users’ and O-users’ arrival and departure. Furthermore, detailed sensitivity analysis, based on real-world data and simulations, evaluated the proposed framework and the developed IPMS in a case study concerning parking lots in Beijing, China. The results show that the IPMS can not only realize that there will always be enough available parking spaces satisfying O-users’ parking demand, but also bring about vast improvements in both utilization and turnover rate of parking spaces, comparing with the non-shared management strategy.

Robust Optimal Allocation of Decentralized Reactive Power Compensation in Three-Phase Four-Wire Low-Voltage Distribution Networks Considering the Uncertainty of Photovoltaic Generation

Due to the unbalanced three-phase loads, the single-phase distributed photovoltaic (PV) integration, the long feeders, and the heavy loads in a three-phase four-wire low voltage distribution network (LVDN), the voltage unbalance factor (VUF), the network loss and the voltage deviation are relatively high. Considering the uncertain fluctuation of the PV output and the load power, a robust optimal allocation of decentralized reactive power compensation (RPC) devices model for a three-phase four-wire LVDN is proposed. In this model, the uncertain variables are described as box uncertain sets, the three-phase simultaneous switching capacity and single-phase independent switching capacity of the RPC devices are taken as decision variables, and the objective is to minimize the total power loss of the LVDN under the extreme scenarios of uncertain variables. The bi-level optimization method is used to transform the robust optimization model with uncertain variables into bi-level deterministic optimization models, which could be solved alternately. The nonlinear programming solver IPOPT in the mature commercial software GAMS is adopted to solve the upper and lower deterministic optimization models to obtain a robust optimal allocation scheme of decentralized RPC devices. Finally, the simulation results for an actual LVDN show that the obtained decentralized RPC scheme can ensure that the voltage deviation and the VUF of each bus satisfied the secure operation requirement no matter how the PV output and load power changed within their own uncertain sets, and the network loss could be effectively reduced.

Quantile-Based Risk Sharing

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. To study risk sharing in a competitive market, an Arrow-Debreu equilibrium is established for some simple, yet natural settings. Further, we investigate the problem of model uncertainty in risk sharing, and show that, generally, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed, and several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.

Quantile-Based Risk Sharing

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. The family of RVaR includes the Value-at-Risk (VaR) and the Expected Shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the risk sharing problem is solved through explicit construction. Three relevant issues on optimal allocation are investigated: extra sources of randomness, comonotonicty, and model uncertainty. We show that, in general, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed. In particular, in the context of the calculation of regulatory capital, we provide some general guidelines on how a regulatory risk measure can lead to certain desirable or undesirable properties of risk sharing among firms. Several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.

Quantile-Based Risk Sharing

We address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called range-value-at-risk (RVaR), as their preferences. The family of RVaR includes the value-at-risk (VaR) and the expected shortfall (ES), the two popular and competing regulatory risk measures, as special cases. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the Pareto-optimal risk sharing problem is solved through explicit construction. To study risk sharing in a competitive market, an Arrow–Debreu equilibrium is established for some simple yet natural settings. Furthermore, we investigate the problem of model uncertainty in risk sharing and show that, in general, a robust optimal allocation exists if and only if none of the underlying risk measures is a VaR. Practical implications of our main results for risk management and policy makers are discussed, and several novel advantages of ES over VaR from the perspective of a regulator are thereby revealed.The e-companion is available at https://doi.org/10.1287/opre.2017.1716 .

Study on Vehicle Stability Control by Using Model Predictive Controller and Tire-road Force Robust Optimal Allocation

Study on Vehicle Stability Control by Using Model Predictive Controller and Tire-road Force Robust Optimal Allocation