Adaptive Robust Optimization Research Articles

Optimal placement and sizing of the virtual power plant constrained to flexible-renewable energy proving in the smart distribution network

Increasing integration of distributed energy resources (DERs) within distribution feeders provides unprecedented flexibility at the distribution-transmission interconnection. To exploit this flexibility and to use the capacity potential of aggregate DERs, feasible substation power injection trajectories need to be efficiently characterized. This letter provides an ellipsoidal inner approximation of the set of feasible power injection trajectories at the substation such that for any point in the set, there exists a feasible disaggregation strategy of DERs for any load uncertainty realization. The problem is formulated as one of finding the robust maximum volume ellipsoid inside the flexibility region under uncertainty. Though the problem is NP-hard even in the deterministic case, this letter derives novel approximations of the resulting adaptive robust optimization problem based on optimal second-stage policies. The proposed approach yields less conservative flexibility characterization than existing flexibility region approximation formulations. The efficacy of the proposed method is demonstrated on a realistic distribution feeder.

Abstract Power distribution systems have become more complex in recent years due to the integration of new technologies. Motivated by these challenges, this paper describes a model to solve the multi‐period expansion planning problem of active distribution systems, considering uncertainty, reliability, distributed generation, self‐healing, reactive power support, switches, and energy storage devices. The objective is to determine the best installation times and locations of new components, minimizing the total cost, and ensuring desired reliability levels. The approach consists of a three‐level decomposition. The first level identifies expansion proposals, the second level finds the worst‐case scenario using adaptive robust optimization, and the third level performs a Monte Carlo Simulation to compute reliability indexes. The main contributions are the introduction of a novel reliability sensitivity matrix to improve computational performance and the representation of the hours of the day inside the expansion planning formulation. The proposed method is illustrated using the IEEE 123‐bus test system. The analyses show high computational efficiency as compared with similar works. The impacts on the number of expansion components placed in the system and on the total cost are presented and discussed using cases varying the uncertainty budget and not considering some of these components.

Adaptive robust optimization (ARO) is a well-known technique to deal with the parameter uncertainty in optimization problems. While the ARO framework can actually be borrowed to solve some special problems without uncertain parameters, such as the power flexibility aggregation problem studied in this paper. To effectively harness the significant flexibility from massive distributed energy resources (DERs), power flexibility aggregation is performed for a distribution system to compute the feasible region of the exchanged power at the substation over time. Based on two-stage ARO, this paper proposes a novel method to aggregate system-level multi-period power flexibility, considering heterogeneous DER facilities, network operational constraints, and an unbalanced power flow model. This method is applicable to aggregate only the active (or reactive) power, and the joint active-reactive power domain. Accordingly, two power aggregation models with two-stage optimization are developed: one focuses on aggregating active power and computes its optimal feasible intervals over multiple periods, and the other solves the optimal elliptical feasible regions for the aggregate active-reactive power. By leveraging the ARO technique, the disaggregation feasibility of the obtained feasible regions is guaranteed with optimality. Numerical simulations on a real-world distribution feeder with 126 multi-phase nodes demonstrate the effectiveness of the proposed method.

Abstract This article proposes a novel Nash game‐theoretical optimal adaptive robust control design approach to address the constraint‐following control problem for the uncertain underactuated mechanical systems with fuzzy evidence theory. First, the uncertainty is considered bounded and the bound is unknown but lies in a specified fuzzy evidence number. Second, a deterministic adaptive robust control scheme is proposed based on the servo constraint following control method, which renders the uncertain underactuated mechanical system to follow the specified constraints accurately with deterministic performance (guarantee uniform boundedness and uniform ultimate boundedness). It is shown that the designed self‐adjusting leakage‐type adaptive law can compensate for the uncertainty and avoid overcompensation. Third, based on the performance analysis and the fuzzy evidence description of uncertainty, the Nash game theory is introduced into the multi‐parameter optimization design for the two tunable control gains selected as two players. The cost functions for two players are relevant to the system constraint‐following performance and control cost. Then we can obtain the optimal control gains by seeking the Nash equilibrium which is always proved to exist. Ultimately, the simulation results on the two‐wheeled self‐balancing robot demonstrate the availability of the proposed control scheme and the optimal design approach for the underactuated mechanical systems with uncertainties.

Adaptive robust vulnerability analysis of power systems under uncertainty: A multilevel OPF-based optimization approach

The micro-energy network is a subset of the electricity, gas, and heat energy grid. Due to its limited capacity, the energy and spare capacity of micro-energy network should be shared through interconnection. It can not only reduce the operating cost of the micro-energy network caused by power interchange deviation but also increase the consumption rate of intermittent distributed generation (IDG). On account of this assumption, a control structure and a double-layer dispatch model of the interconnected micro-energy network system are proposed in this paper. An economic dispatch model based on adaptive robust optimization is proposed to deal with the uncertainty produced by IDG and minimize the operation cost. Then, a cooperative game model of an interconnected system is built to allocate the profits obtained. Simulation results demonstrate that the proposed scheduling method can significantly reduce the cost of a single micro-energy network and interconnected system. In addition, compared to the noninteractive model and traditional deterministic method, it is proved that the proposed method has a strong capability to deal with uncertain risks, improve the consumption rate of IDG, and realize the coordinated economic optimal operation of multiple micro-energy networks.

Adaptive robust optimization for the energy management of the grid-connected energy hubs based on hybrid meta-heuristic algorithm

Robust multi-objective optimal design of islanded hybrid system with renewable and diesel sources/stationary and mobile energy storage systems

Adaptive robust co-optimization of wind energy generation, electric vehicle batteries and flexible AC transmission system devices

Abstract Power system decarbonization is critical for combating climate change, and handling systems uncertainties is essential for designing robust renewable transition pathways. In this study, a bottom-up data-driven multistage adaptive robust optimization (MARO) framework is proposed to address the power systems’ renewable transition under uncertainty. To illustrate the applicability of the proposed framework, a case study for New York State is presented. Machine learning techniques, including a variational algorithm for Dirichlet process mixture model, principal component analysis, and kernel density estimation, are applied for constructing data-driven uncertainty sets, which are integrated into the proposed MARO framework to systematically handle uncertainty. The results show that the total renewable electricity transition costs under uncertainty are 21%-42% higher than deterministic planning, and the costs under the data-driven uncertainty sets are 2%-17% lower than the conventional uncertainty sets. By 2035, on-land wind and offshore wind would be the major power source for the deterministic planning case and robust optimization cases, respectively.

A two-stage model for asynchronously scheduling offshore wind farm maintenance tasks and power productions

Adaptive robust operation of the active distribution network including renewable and flexible sources

This paper investigates the distributed adaptive optimization problem for nonlinear multiagent systems with external disturbances. The main goal is to optimize a global objective function by utilizing local and neighboring information while rejecting the external disturbance signals. Different from the existing results, the weight-balanced directed graph is considered and, by introducing the adaptive technique, the local objective functions are allowed only to be differentiable with locally Lipschitz gradients. Moreover, without requiring the system nonlinear functions to be globally Lipschitz, the global asymptotic convergence is obtained if the global objective function is strongly convex. Finally, simulation results are provided to verify the validity of the proposed algorithm.

Multi-objective two-stage adaptive robust planning method for an integrated energy system considering load uncertainty

This paper addresses the planning problem of residential micro combined heat and power (micro-CHP) systems (including micro-generation units, auxiliary boilers, and thermal storage tanks) considering the associated technical and economic factors. Since the accurate values of the thermal and electrical loads of this system cannot be exactly predicted for the planning horizon, the thermal and electrical load uncertainties are modeled using a two-stage adaptive robust optimization method based on a polyhedral uncertainty set. A solution method, which is composed of column-and-constraint generation (C&CG) algorithm and block coordinate descent (BCD) method, is proposed to efficiently solve this adaptive robust optimization model. Numerical results from a practical case study show the effective performance of the proposed adaptive robust model for residential micro-CHP planning and its solution method.

Robust Conic Satisficing

An AC security constrained unit commitment (AC-SCUC) in the presence of the renewable energy sources (RESs) and shunt flexible AC transmission system (FACTS) devices is conventionally modeled as a deterministic optimization problem to minimize the operation cost of conventional generation units (CGUs) subject to AC optimal power flow (AC-OPF) equations, operation constraints of RESs, shunt FACTS devices, and CGUs. To cope with the uncertainties of load and RES generation, robust and stochastic optimization and linearized formulation have been used to achieve a sub-optimal solution. To arrive at a more optimal solution, an evolutionary algorithm-based adaptive robust optimization (EA-ARO) approach to solve the non-linear and non-convex optimization problem was proposed. A hybrid solver of grey wolf optimization (GWO) and teaching learning-based optimization (TLBO) was proposed to solve the AC-SCUC problem in the worst-case scenario to obtain robust and reliable optimal solution. Finally, the proposed method was simulated on standard IEEE test systems to demonstrate its capabilities, and the results showed the proposed hybrid solver obtained robust optimal solutions with reduced computation time and standard deviation. Moreover, the numerical results proved the proposed strategy’s capabilities of improving the economics of generation units, such as lower operational cost, and enhancing the performance of the transmission networks, such as improved voltage profile and reduced energy losses.

An incentive-compatible distributed integrated energy market mechanism design with adaptive robust approach

Distribution system operators aim to improve hosting capacity (HC) of distribution networks (DNs) to accommodate more distributed rooftop photovoltaics (PVs). Although PV power generation delivers numerous benefits, power unbalance and voltage rise are two major obstacles that limit the network HC. To mitigate these issues, battery energy storage systems (BESSs) can be applied. Thus, this paper proposes a robustly optimal allocation method for BESSs, which aims to reduce the power unbalance and alleviate the voltage rise, and thus improve the HC of the unbalanced three-phase DNs. Considering that locations and capacities of distributed rooftop PVs are determined by customers, future PV installations are regarded as uncertainties. In addition, to deal with the uncertainties, the proposed BESS allocation problem is formulated as an adaptive robust optimization (ARO) model with integer recourse variables. Accordingly, a solution algorithm which integrates an alternating optimization procedure into a column-and-constraint generation algorithm is developed to efficiently solve the ARO model. With the proposed BESS allocation method, a new perspective on HC improvement is provided, which not only considers the worst power unbalance situation but also satisfies the allowed maximum PV capacity. The simulation results verify high efficiency and solution robustness of the proposed allocation method.