Two-Stage Robust Sizing and Operation Co-Optimization for Residential PV–Battery Systems Considering the Uncertainty of PV Generation and Load

There are different uncertainties in microgrids’ (MG) operation such as output power of renewable energy sources (RESs), electricity price and load demand. Ignoring these existing uncertainties in the optimization problem imposes high cost to the system and the lack of reliability. This paper presents a general linear framework for microgrid optimization problem using robust optimization method. Adaptive robust optimization (ARO) model is a min-max-min problem in which the first level targets to determine the on/off status of dispatchable units, the second one aims find the worst case of uncertain parameters and eventually in third level the operational costs are minimized. This model is converted to a min-max one by using Karush-Kuhn-Tucker (KKT) conditions and then the ensuing model is linearized. A control parameter named budget of uncertainty is considered to determine the level of robustness and being conservative. The more budget of uncertainty we consider, the more robust model we obtain. An optimum point in which the expected cost is minimal and a compromise between the level of robustness and operational cost is reached. A modified IEEE-33 bus system is considered to evaluate the adequacy of proposed linear ARO model. Simulation results prove that the proposed ARO model is appropriately able to deal with the existing uncertainties and results in lower expected cost compared to deterministic model.

Adaptive robust scheduling of a hydro/photovoltaic/pumped-storage hybrid system in day-ahead electricity and hydrogen markets

This article presents an adaptive robust co-optimization for capacity allocation and bidding strategy of a prosumer equipped with photovoltaic system (PV), wind turbine (WT), and battery energy storage (BES). The uncertainties of load and PV/WT productions are modeled through controllable user-defined polyhedral uncertainty sets. The proposed co-optimization determines the optimal capacity of PV-WT-BES, while maximizing prosumer's benefit by 1) optimal self-scheduling of PV-WT-BES, and 2) effective interactions with grid through optimal buying/selling bids under uncertainties. In previous min-max-min robust models, it was not possible to characterize bidding strategy binary variables as recourse decisions which was due to the use of duality theory in solving the inner max-min problem (duality theory is weak and nontractable in the presence of binary variables). In this study, block coordinate descent (BCD) method is used to solve the inner max-min problem by means of Taylor series instead of transforming it into a single-level max problem by duality theory. As a result, prosumer's bidding status (indicated by binary variables) can be successfully modeled as recourse decisions, which make the obtained solutions more realistic and robust. Linearization of the dualized inner problem is also avoided as Lagrange multipliers are eliminated. A post-event analysis is developed to avoid over/under conservative solutions and to determine the optimal robust settings of the model. A comprehensive case study is conducted for an industrial prosumer. To illustrate the effectiveness of the proposed BCD robust model, its long-term performance is compared with conventional dual-based models in the literature. Results show 10% long-term cost reductions when using the proposed model under uncertainties.

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

This article presents a new robust incentive-based integrated demand response (IDR) model for energy hub systems (EHSs). The considered incentive-based demand response (IBDR) schemes are interruptible/curtailable service and capacity market program. The proposed IDR model integrates the arbitrage ability of EHS storages as well as energy conversion into the IDR model. The objective of the IDR optimization problem is to maximize/minimize the allocated incentives/penalties in targeted time periods by IBDR schemes while supplying must-run processes with no interruption. Uncertainties of load and energy prices are considered through user-defined polyhedral uncertainty sets. A trilevel robust optimization (RO) is developed, which includes a trilevel min–max–min problem. To solve the trilevel adaptive robust model, the column-and-constraint generation technique is employed by means of a decomposition methodology recasting the trilevel model into a single-level min problem and a bilevel max–min problem. Unlike previous RO models that solve the inner max–min problem by duality theory, a block-coordinate-descent (BCD) methodology is used to solve the max–min problem by means of the first-order Taylor series in this study. The use of the BCD technique instead of duality theory enables a recourse-based characterization of integer variables, such as EHS storage status, which was not applicable in previous models (due to the use of duality theory). Moreover, Lagrange multipliers are eliminated as no duality is conducted. A postevent analysis is conducted to justify the long-term performance of the robust solutions and determine the optimal settings of the BCD robust approach. Results indicate that the IDR model significantly reduces the EHS input electricity in targeted time periods (four hours per day) by IBDR schemes and covers the required electricity with must-run processes by combined heat and power unit, using natural gas. This implies a 2.13% reduction in the operation cost as incentives are obtained through IBDR schemes.

Adjustable robust optimization approach for two-stage operation of energy hub-based microgrids

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.

A machine learning approach to two-stage adaptive robust optimization

Deciphering Latent Uncertainty Sources with Principal Component Analysis for Adaptive Robust Optimization

Considering the increasing penetration of renewable energy sources (RESs) into power grids, adopting efficient energy management strategies is vital to mitigate the uncertainty issues resulting from the intermittent nature of their output power. This paper aims to resolve the energy management problem by presenting an adaptive robust optimization (ARO) model in which uncertainties associated with solar and wind powers, consumer demand, and electricity prices are considered. The proposed model comprises three stages, one master and two subproblems, using both linearized and convexified power flow equations. Meanwhile, a new optimization-based bound tightening (OBBT) method is also presented to strengthen the relaxation. The proposed solution method solves the microgrid (MG) operation management problem with high accuracy due to considering the convexification method in a reasonable computational time and reducing operational costs compared to conventional models. The numerical results indicate the benefits of the proposed ARO and solution approach over traditional methods.

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.

In this paper, we consider two types of problems that have some similarity in their structure, namely, min-min problems and min-max saddle-point problems. Our approach is based on considering the outer minimization problem as a minimization problem with inexact oracle. This inexact oracle is calculated via inexact solution of the inner problem, which is either minimization or a maximization problem. Our main assumptions are that the problem is smooth and the available oracle is mixed: it is only possible to evaluate the gradient w.r.t. the outer block of variables which corresponds to the outer minimization problem, whereas for the inner problem only zeroth-order oracle is available. To solve the inner problem we use accelerated gradient-free method with zeroth-order oracle. To solve the outer problem we use either inexact variant of Vaydya's cutting-plane method or a variant of accelerated gradient method. As a result, we propose a framework that leads to non-asymptotic complexity bounds for both min-min and min-max problems. Moreover, we estimate separately the number of first- and zeroth-order oracle calls which are sufficient to reach any desired accuracy.

Chemical Lithium battery energy storage (BES) systems are considered as critical assets in providing flexibility and reliability for today's power and energy systems. However, BES degradation, which is due to the electrolyte reaction in lithium batteries, introduces some challenges to smart grid operators in terms of optimal charging/discharging management strategies. Although, considering degradation in BES operation can lead to long-term benefits, the associated uncertainties of renewable generations, load, and energy prices can pose a noticeable effect on BES operation optimality and accordingly affect the associated long-term benefits, if ignored. In fact, disregarding uncertainties in BES operation can lead to nonoptimal or even infeasible charging/discharging solutions, resulting in extra costs and even higher BES degradation rates. This paper presents an adaptive robust optimization approach to optimally characterize degradation in charging/discharging management of BES at the presence of uncertainties. The model is developed for a multi-energy system with electricity and natural gas as operating energy types. A Lithium Nickel Cobalt Aluminum Oxide (LiNiCoAlO2) battery is considered as the BES in the multi-energy system. Uncertainties of load, renewable generation, and energy prices are characterized with bounded interval through polyhedral uncertainty sets. The proposed model is solved through a column-and-constraint generation approach. A post-event analysis is conducted to evaluate the long-term performance of the proposed model. According to the obtained results, the proposed adaptive robust energy management model shows 18% growth in long-term benefit recovery and 15% reduction in loss of load, compare to deterministic model, considering battery degradation effects.

Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty

Of significance in wireless multimedia sensor networks (WMSN) is the maintenance of media quality and the extension of route lifetime since media stream is more sensitive in quality requirement than data flow. In this paper, the problem of how to balance the needs on constraining end-to-end (e2e) quality and prolonging lifetime in an established route can be interpreted as a nonlinear optimization paradigm, which is then shown to be a max—min composite formulation when an e2e frame-error probability is given. To solve this max—min problem, we propose two novel methods: route-associated power management (RAPM) and link-associated power management (LAPM). For computation-restricted sensor nodes, the RAPM scheme with adding a simplification condition on power management can effectively reduce the power cost at computation and also rapidly determine optimum lifetime from numerous candidate routes. On the other hand, if computing power is not the major concern in a sink node, rather than using a heuristic method, we employ the LAPM algorithm to solve the lifetime maximization problem in a more accurate fashion. Solid theoretical analysis and simulation results are presented to validate our proposed schemes. Both analytical and simulation results demonstrate that the LAPM scheme is very comparable to the heuristic approach. Copyright © 2009 John Wiley & Sons, Ltd. In this paper, the problem of how to balance the needs on constraining end-to-end quality and prolonging lifetime in an established route can be interpreted as a non-linear optimization paradigm, which is shown to be a max-min composite formulation when an end-to-end frame-error probability is given. Two novel methods are proposed to solve this max-min problem: route-associated power management (RAPM) and link-associated power management (LAPM). Solid theoretical analysis and simulation results are presented to validate our proposed schemes.