30 results
Search Results
2. A Collaborative Planning Method for the Source and Grid in a Distribution System That Considers Risk Measurement.
- Author
-
Deng, Jiahao, Lin, Lingxue, Zhang, Yongjie, and Ma, Yuxin
- Subjects
GRIDS (Cartography) ,CORPORATE profits ,GENETIC algorithms ,INCOME distribution ,DISTRIBUTION planning ,SEARCH algorithms - Abstract
The existing distribution system planning methods do not fully consider improving power supply capacity and reliability through the coordination of multiple planning factors, and they are not comprehensive enough in quantifying planning risks. Therefore, this paper proposes a collaborative planning method for sources and networks that considers risk measurement. A multi-layer planning model is first constructed that includes a grid planning layer, a power planning layer, a switch planning layer, and an operation optimization layer. In the model, a risk measurement method combining opportunity constraints and conditional value-at-risk objectives is used to comprehensively assess the risk of the node voltage and branch current exceeding the limit caused by load uncertainty. Then, a solution strategy based on a genetic algorithm and a sparrow search algorithm is proposed to coordinate the contradiction between the solution time and the accuracy of the multi-layer model. Finally, taking a planned area to be expanded as an example, the results show that compared to the existing collaborative planning methods for sources and networks, the proposed method in this paper reduces the planning risks caused by load uncertainty by more than 50% and increases the annual net income of the power distribution company and the DG operators by RMB 1.5 million and RMB 1.1 million, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Behavior-Aware Aggregation of Distributed Energy Resources for Risk-Aware Operational Scheduling of Distribution Systems.
- Author
-
He, Mingyue, Soltani, Zahra, Khorsand, Mojdeh, Dock, Aaron, Malaty, Patrick, and Esmaili, Masoud
- Subjects
POWER resources ,ELECTRICAL load ,SCHEDULING - Abstract
Recently there has been a considerable increase in the penetration level of distributed energy resources (DERs) due to various factors, such as the increasing affordability of these resources, the global movement towards sustainable energy, and the energy democracy movement. However, the uncertainty and variability of DERs introduce new challenges for power system operations. Advanced techniques that account for the characteristics of DERs, i.e., their intermittency and human-in-the-loop factors, are essential to improving distribution system operations. This paper proposes a behavior-aware approach to analyze and aggregate prosumers' participation in demand response (DR) programs. A convexified AC optimal power flow (ACOPF) via a second-order cone programming (SOCP) technique is used for system scheduling with DERs. A chance-constrained framework for the system operation is constructed as an iterative two-stage algorithm that can integrate loads, DERs' uncertainty, and SOCP-based ACOPF into one framework to manage the violation probability of the distribution system's security limits. The benefits of the analyzed prosumers' behaviors are shown in this paper by comparing the optimal system scheduling with socially aware and non-socially aware approaches. The case study illustrates that the socially aware approach within the chance-constrained framework can utilize up to 43% more PV generation and improve the reliability and operation of distribution systems. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
4. On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints.
- Author
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Heitsch, Holger, Henrion, René, Kleinert, Thomas, and Schmidt, Martin
- Subjects
BILEVEL programming ,DECISION making ,PROBLEM solving ,GASES ,NATURAL gas ,THEORY-practice relationship - Abstract
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
5. Tight and Compact Sample Average Approximation for Joint Chance-Constrained Problems with Applications to Optimal Power Flow.
- Author
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Porras, Álvaro, Domínguez, Concepción, Morales, Juan Miguel, and Pineda, Salvador
- Subjects
- *
ELECTRICAL load , *CONSTRAINT algorithms , *REGIONAL development , *COLLEGE teachers , *TEACHER training - Abstract
In this paper, we tackle the resolution of chance-constrained problems reformulated via sample average approximation. The resulting data-driven deterministic reformulation takes the form of a large-scale mixed-integer program (MIP) cursed with Big-Ms. We introduce an exact resolution method for the MIP that combines the addition of a set of valid inequalities to tighten the linear relaxation bound with coefficient strengthening and constraint screening algorithms to improve its Big-Ms and considerably reduce its size. The proposed valid inequalities are based on the notion of k-envelopes and can be computed off-line using polynomial-time algorithms and added to the MIP program all at once. Furthermore, they are equally useful to boost the strengthening of the Big-Ms and the screening rate of superfluous constraints. We apply our procedures to a probabilistically constrained version of the DC optimal power flow problem with uncertain demand. The chance constraint requires that the probability of violating any of the power system's constraints be lower than some positive threshold. In a series of numerical experiments that involve five power systems of different size, we show the efficiency of the proposed methodology and compare it with some of the best performing convex inner approximations currently available in the literature. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported in part by the European Research Council under the EU Horizon 2020 research and innovation program [Grant 755705], in part by the Spanish Ministry of Science and Innovation [Grant AEI/10.13039/501100011033] through project PID2020-115460GB-I00, and in part by the Junta de Andalucía and the European Regional Development Fund through the research project P20_00153. Á. Porras is also financially supported by the Spanish Ministry of Science, Innovation and Universities through the University Teacher Training Program with fellowship number FPU19/03053. Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.0302. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
6. Joint Optimization of Base Station Activation and User Association in Ultra Dense Networks Under Traffic Uncertainty.
- Author
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Teng, Wei, Sheng, Min, Chu, Xiaoli, Guo, Kun, Wen, Juan, and Qiu, Zhiliang
- Subjects
CONSTRAINT programming ,TRAFFIC surveys ,MARKOV processes ,NONLINEAR equations ,INTEGER programming - Abstract
In ultra-dense networks (UDNs), the dense deployment of base stations (BSs) is facing challenges due to the pronounced unbalanced traffic loads, severe inter-cell interference, and uncertain traffic demands. In this paper, we tame traffic uncertainty for the joint optimization of BS activation and user association in UDNs to mitigate interference and balance traffic loads among BSs. Specifically, we address the traffic uncertainty by using chance constraint programming with the known first- and second-order statistics of the uncertain traffic. We formulate the joint BS activation and user association problem as a mixed integer non-linear programming problem, which is then decomposed into a set of user association sub-problems by modeling the BS states (active or idle) as a Markov chain. We solve the user association sub-problem at each BS state by transforming it into a convex problem over the positive orthant. In particular, at each BS state, the candidate serving BSs that lead to the optimal load balancing performance are identified for each user and parts of the user’s traffic are offloaded to the identified BSs. Based on the obtained solutions, we propose a distributed near-optimal BS activation and user association scheme. Numerical results demonstrate that our proposed scheme is more robust to traffic uncertainty and provides better load-balancing performance than the existing schemes. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
7. Distributionally Robust Chance Constrained Geometric Optimization.
- Author
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Liu, Jia, Lisser, Abdel, and Chen, Zhiping
- Subjects
CONSTRAINED optimization ,STRUCTURAL optimization ,RANDOM variables ,RANDOM sets - Abstract
This paper discusses distributionally robust geometric programs with individual or joint chance constraints. Several groups of uncertainty sets are considered: uncertainty sets with first two order moments information; uncertainty sets with known first order or first two order moments information under nonnegative support; uncertainty sets constrained by the Kullback–Leibler divergence with a normal or discrete reference distribution; uncertainty sets constrained by the Wasserstein distance under discrete, full, or nonnegative real-space support; and joint uncertainty sets for the product of random variables. Under each group of uncertainty sets, we find deterministic reformulations of the distributionally robust geometric programs with individual or joint chance constraints. Convexity, solution methods, and relationships of the reformulation programs are discussed. Finally, numerical tests are carried out on a shape optimization problem. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
8. A Collaborative Planning Method for the Source and Grid in a Distribution System That Considers Risk Measurement
- Author
-
Jiahao Deng, Lingxue Lin, Yongjie Zhang, and Yuxin Ma
- Subjects
a collaborative planning for the source and gird ,chance constraints ,conditional value at risk ,genetic algorithm ,sparrow search algorithm ,Technology - Abstract
The existing distribution system planning methods do not fully consider improving power supply capacity and reliability through the coordination of multiple planning factors, and they are not comprehensive enough in quantifying planning risks. Therefore, this paper proposes a collaborative planning method for sources and networks that considers risk measurement. A multi-layer planning model is first constructed that includes a grid planning layer, a power planning layer, a switch planning layer, and an operation optimization layer. In the model, a risk measurement method combining opportunity constraints and conditional value-at-risk objectives is used to comprehensively assess the risk of the node voltage and branch current exceeding the limit caused by load uncertainty. Then, a solution strategy based on a genetic algorithm and a sparrow search algorithm is proposed to coordinate the contradiction between the solution time and the accuracy of the multi-layer model. Finally, taking a planned area to be expanded as an example, the results show that compared to the existing collaborative planning methods for sources and networks, the proposed method in this paper reduces the planning risks caused by load uncertainty by more than 50% and increases the annual net income of the power distribution company and the DG operators by RMB 1.5 million and RMB 1.1 million, respectively.
- Published
- 2023
- Full Text
- View/download PDF
9. A stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs
- Author
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Kannan, Rohit and Luedtke, James R.
- Published
- 2021
- Full Text
- View/download PDF
10. Behavior-Aware Aggregation of Distributed Energy Resources for Risk-Aware Operational Scheduling of Distribution Systems
- Author
-
Mingyue He, Zahra Soltani, Mojdeh Khorsand, Aaron Dock, Patrick Malaty, and Masoud Esmaili
- Subjects
AC optimal power flow ,chance constraints ,distributed energy resources ,human-in-the-loop ,risk aware ,socially aware ,Technology - Abstract
Recently there has been a considerable increase in the penetration level of distributed energy resources (DERs) due to various factors, such as the increasing affordability of these resources, the global movement towards sustainable energy, and the energy democracy movement. However, the uncertainty and variability of DERs introduce new challenges for power system operations. Advanced techniques that account for the characteristics of DERs, i.e., their intermittency and human-in-the-loop factors, are essential to improving distribution system operations. This paper proposes a behavior-aware approach to analyze and aggregate prosumers’ participation in demand response (DR) programs. A convexified AC optimal power flow (ACOPF) via a second-order cone programming (SOCP) technique is used for system scheduling with DERs. A chance-constrained framework for the system operation is constructed as an iterative two-stage algorithm that can integrate loads, DERs’ uncertainty, and SOCP-based ACOPF into one framework to manage the violation probability of the distribution system’s security limits. The benefits of the analyzed prosumers’ behaviors are shown in this paper by comparing the optimal system scheduling with socially aware and non-socially aware approaches. The case study illustrates that the socially aware approach within the chance-constrained framework can utilize up to 43% more PV generation and improve the reliability and operation of distribution systems.
- Published
- 2022
- Full Text
- View/download PDF
11. Distributionally Robust Generation Expansion Planning With Unimodality and Risk Constraints.
- Author
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Pourahmadi, Farzaneh and Kazempour, Jalal
- Subjects
WIND forecasting ,NUMERICAL analysis ,DISTRIBUTION (Probability theory) ,OPERATIONAL risk ,STOCHASTIC models - Abstract
As more renewables are integrated into the power system, capacity expansion planners need more advanced long-term decision-making tools to properly model short-term stochastic production uncertainty and to explore its effects on expansion decisions. We develop a distributionally robust generation expansion planning model, accounting for a family of potential probability distributions of wind forecast error uncertainty. Aiming to include more realistic distributions, we construct more informed moment-based ambiguity sets by adding structural information of unimodality. We include operational-stage unit commitment constraints and model the risk of operational limit violations in two distinct forms: chance and conditional value-at-risk (CVaR) constraints. In both forms, the resulting expansion planning model is a mixed-integer second-order cone program. Using a thorough out-of-sample numerical analysis, we conclude: (i) the distributionally robust chance-constrained generation expansion planning model exhibits a better out-of-sample performance only if sufficiently accurate information about the first- and the second-order moments as well as the mode location of potential distributions is available; (ii) conversely, if such accurate information is unavailable, the distributionally robust CVaR-constrained generation expansion planning model outperforms; (iii) these two models have a similar performance when unimodality information is excluded. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
12. Risk-Aware Stochastic MPC for Chance-Constrained Linear Systems
- Author
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Pouria Tooranjipour, Bahare Kiumarsi, and Hamidreza Modares
- Subjects
Chance constraints ,conditional value at risk ,distributionally robust optimization ,risk -aware MPC ,Control engineering systems. Automatic machinery (General) ,TJ212-225 ,Technology - Abstract
This paper presents a fully risk-aware model predictive control (MPC) framework for chance-constrained discrete-time linear control systems with process noise. Conditional value-at-risk (CVaR) as a popular coherent risk measure is incorporated in both the constraints and the cost function of the MPC framework. This allows the system to navigate the entire spectrum of risk assessments, from worst-case to risk-neutral scenarios, ensuring both constraint satisfaction and performance optimization in stochastic environments. The recursive feasibility and risk-aware exponential stability of the resulting risk-aware MPC are demonstrated through rigorous theoretical analysis by considering the disturbance feedback policy parameterization. In the end, two numerical examples are given to elucidate the efficacy of the proposed method.
- Published
- 2024
- Full Text
- View/download PDF
13. Model predictive control of distributed energy resources in residential buildings considering forecast uncertainties.
- Author
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Langner, Felix, Wang, Weimin, Frahm, Moritz, and Hagenmeyer, Veit
- Abstract
Forecast uncertainties pose a considerable challenge to the success of model predictive control (MPC) in buildings. Numerous possibilities for considering forecast uncertainties in MPCs are available, but an in-depth comparison is lacking. This paper compares two main approaches to consider uncertainties: robust and stochastic MPC. They are benchmarked against a deterministic MPC and an MPC with perfect forecast. The MPCs utilize a holistic building model to reflect modern smart homes that include photovoltaic power generation and storage, thermally controlled loads, and smart appliances. Real-world data are used to identify the thermal building model. The performance of the various controllers is investigated under three levels of uncertainty for two building models with different envelope performance. For the highly insulated building, the deterministic MPC achieves satisfactory thermal comfort when the forecast error is medium or low, but the thermal comfort is compromised for high forecast errors. In the poorly insulated building, thermal comfort is compromised at medium and high forecast errors. Compared to the deterministic MPC, the robust MPC increases the electricity cost by up to 4.5% and provides complete temperature constraint satisfaction while the stochastic MPC increases the electricity cost by less than 1% and fulfills the thermal comfort requirements. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
14. A risk-averse day-ahead bidding strategy of transactive energy sharing microgrids with data-driven chance constraints.
- Author
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Wang, Yubin, Yang, Qiang, Zhou, Yue, and Zheng, Yanchong
- Subjects
- *
BIDDING strategies , *MICROGRIDS , *DISTRIBUTION (Probability theory) , *ELECTRICITY markets , *ECONOMIC uncertainty - Abstract
The rapid development of microgrids (MGs) with various prosumers promotes the accommodation of renewable distributed generation (RDG) and provides platforms for local energy sharing among prosumers. However, the operational uncertainties pose enormous challenges to the day-ahead bidding of MGs in the wholesale electricity market and there is an urgent need for a local market to facilitate the local energy sharing. Thus, this paper proposes a risk-averse day-ahead bidding strategy for MGs with full consideration of the multiple uncertainties originating from the wholesale electricity market, RDG and loads. Based on the transactive energy (TE) sharing concept, the local market is formulated as a Stackelberg game (SG) to effectively capture the strategic interaction among the MG and prosumers, where a distributed iterative algorithm with a bisection approach that only requires exchanging TE-related information is adopted to achieve the SG equilibrium without compromising privacy concerns. To handle the uncertainties of RDG and loads, the power balances are formulated as chance constraints and a data-driven quantile forecasting method is developed for achieving the computational tractability of chance constraints without any prior knowledge or probability distribution assumptions. Furthermore, a risk criterion of the conditional value-at-risk is incorporated in the day-ahead bidding model of MGs for risk aversion towards uncertainties of the wholesale electricity market. The effectiveness of the proposed solution is extensively demonstrated through numerical simulation. • A risk-averse day-ahead bidding strategy of TE sharing MGs is presented. • A SG-based local TE market with privacy protection is developed. • The wholesale market uncertainties are addressed in a risk-averse manner via CVaR. • The power balance chance constraints are built to handle RDG and load uncertainties. • A data-driven quantile forecasting method is proposed to solve chance constraints. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
15. Data-driven stochastic AC-OPF using Gaussian process regression.
- Author
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Mitrovic, Mile, Lukashevich, Aleksandr, Vorobev, Petr, Terzija, Vladimir, Budennyy, Semen, Maximov, Yury, and Deka, Deepjyoti
- Subjects
- *
KRIGING , *RENEWABLE energy sources , *GREENHOUSE gases , *DISTRIBUTION (Probability theory) , *ELECTRICAL load , *WIND power - Abstract
At present, electricity generation is responsible for more than a quarter of the greenhouse gas emissions in the US. Integrating significant amounts of renewable energy sources into a power grid is probably the most accessible way to reduce carbon emissions from power grids and slow down climate change. Unfortunately, the most accessible renewable power sources, such as wind and solar, are highly intermittent and thus bring a lot of uncertainty to power grid operation and challenge existing optimization and control policies. The chance-constrained (CC) alternating current optimal power flow (AC-OPF) framework finds the minimum cost of generation dispatch, maintaining the power grid operation within security limits with a prescribed probability. Unfortunately, the AC-OPF problem's chance-constrained extension is non-convex, computationally challenging, and requires knowledge of system parameters and also needs additional assumptions to be made about the behavior of renewable generation probability distribution. Known linear and convex approximations to the above problems, though tractable, are too conservative for operational practice and do not consider uncertainty in system parameters. This paper presents an alternative data-driven approach for solving the stochastic AC-OPF problem, based on Gaussian process regression (GPR) to close this gap. The Gaussian process (GP) approach learns a simple yet non-convex data-driven approximation to the AC power flow equations that can incorporate uncertain inputs. The latter is then used to determine the solution of CC-OPF efficiently, by accounting for both input and parameter uncertainty. The practical efficiency of the proposed approach using different approximations for GP-uncertainty propagation is validated and illustrated using a number of standard IEEE test cases. • Chance constrained optimal power flow based on data-driven approach. • Gaussian process regression for solving stochastic optimal power flow. • Gaussian processes for handling uncertainties in power systems. • Machine learning for power system optimization. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
16. Balancing Project Schedule, Cost, and Value under Uncertainty: A Reinforcement Learning Approach.
- Author
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Szwarcfiter, Claudio, Herer, Yale T., and Shtub, Avraham
- Subjects
COST overruns ,NET present value ,LEAN management ,MATHEMATICAL programming ,PROJECT management - Abstract
Industrial projects are plagued by uncertainties, often resulting in both time and cost overruns. This research introduces an innovative approach, employing Reinforcement Learning (RL), to address three distinct project management challenges within a setting of uncertain activity durations. The primary objective is to identify stable baseline schedules. The first challenge encompasses the multimode lean project management problem, wherein the goal is to maximize a project's value function while adhering to both due date and budget chance constraints. The second challenge involves the chance-constrained critical chain buffer management problem in a multimode context. Here, the aim is to minimize the project delivery date while considering resource constraints and duration-chance constraints. The third challenge revolves around striking a balance between the project value and its net present value (NPV) within a resource-constrained multimode environment. To tackle these three challenges, we devised mathematical programming models, some of which were solved optimally. Additionally, we developed competitive RL-based algorithms and verified their performance against established benchmarks. Our RL algorithms consistently generated schedules that compared favorably with the benchmarks, leading to higher project values and NPVs and shorter schedules while staying within the stakeholders' risk thresholds. The potential beneficiaries of this research are project managers and decision-makers who can use this approach to generate an efficient frontier of optimal project plans. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
17. Research on distributionally robust optimization method considering the flexibility of power grids along CZ railway
- Author
-
Jiawei Liu, Min Li, Jing Gou, Wenhao Sun, Qiao Zhang, and Zhigang Liu
- Subjects
CZ railway ,Flexibility ,Wasserstein distance ,Chance constraints ,Distributionally robust ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
To avoid the problem of insufficient flexibility of the power grid along the cz railway due to source-load fluctuations, a distributionally robust optimization method considering flexibility is proposed in this paper. Firstly, Wasserstein distance is used to establish the uncertainty set of flexibility demand caused by source-load fluctuation, and a risk-cost model of insufficient flexibility is constructed to couple to the objective function. Combined with the flexibility chance constraint, the flexibility over-limit probability is limited to a certain confidence level in the fuzzy set, and a distributionally robust chance constraint optimization model based on Wasserstein distance is established. Then, the proposed model is transformed into a linear programming problem to be solved by dual theory and inner approximation transformation. Finally, a simulation study of the power grid along the CZ railway is carried out to verify the correctness and effectiveness of the model. The experimental results show that the proposed method can improve the flexibility capacity of the system without sacrificing economy.
- Published
- 2023
- Full Text
- View/download PDF
18. Model Predictive Control of Parabolic PDE Systems under Chance Constraints.
- Author
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Voropai, Ruslan, Geletu, Abebe, and Li, Pu
- Subjects
THERMAL conductivity ,PREDICTION models ,HEAT flux - Abstract
Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described by parabolic partial differential equations (PDEs) with random parameters. Inequality constraints on time- and space-dependent state variables are defined in terms of chance constraints. Using a discretization scheme, the resulting high-dimensional chance constrained optimization problem is solved by our recently developed inner–outer approximation which renders the problem computationally amenable. The proposed MPC scheme automatically generates probability tubes significantly simplifying the derivation of feasible solutions. We demonstrate the viability and versatility of the approach through a case study of tumor hyperthermia cancer treatment control, where the randomness arises from the thermal conductivity coefficient characterizing heat flux in human tissue. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
19. Convergence Analysis of Fixed Point Chance Constrained Optimal Power Flow Problems.
- Author
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Brust, Johannes J. and Anitescu, Mihai
- Subjects
ELECTRICAL load ,LINEAR programming - Abstract
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not necessarily guaranteed. This article analyses the convergence conditions for this fixed point approach, and reports numerical experiments including for large IEEE networks. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
20. Data-driven assisted chance-constrained energy and reserve scheduling with wind curtailment.
- Author
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Lei, Xingyu, Yang, Zhifang, Zhao, Junbo, and Yu, Juan
- Subjects
- *
CONVEX programming , *LINEAR programming , *WIND power , *SCHEDULING , *ERROR correction (Information theory) - Abstract
• A novel data-driven surrogate is developed for chance constraint reformulation. • Wind curtailment dispatch is explicitly modeled in chance constraints. • A correction strategy is proposed to ensure modeling accuracy. • The proposed approach is effective under arbitrary distribution assumptions. Chance-constrained optimization (CCO) has been widely used for uncertainty management in power system operation. With the prevalence of wind energy, it becomes necessary to consider wind curtailment as a dispatch variable in CCO. However, the wind curtailment will cause an impulse for the uncertainty distribution, yielding challenges for explicit modeling of chance constraint. In this paper, a novel data-driven framework is developed to handle this issue. By modeling the wind curtailment as a cap enforced on the wind power output, the proposed framework constructs a data-driven surrogate to describe the relationship between wind curtailment and the tightening boundary of chance constraints. This allows us to reformulate the CCO with wind curtailment as a mixed-integer second-order cone programming (MI-SOCP) problem. An error correction strategy is developed by solving a convex linear programming (LP) to improve the modeling accuracy. The notable characteristic of the proposed method is that the chance constraints with wind curtailment can be explicitly and accurately handled without any distribution assumptions, which provides great convenience for the power dispatch under a high percentage of renewables. Case studies performed on the PJM 5-bus and IEEE 118-bus systems demonstrate that the proposed method is capable of accurately accounting the influence of wind curtailment dispatch in CCO. It shows that the proposed method outperforms existing methods by producing more economic and secure solutions for the chance-constrained energy and reserve scheduling problem under uncertainties. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
21. Chance constrained dynamic optimization approach for single machine scheduling involving flexible maintenance, production, and uncertainty.
- Author
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Wu, Xiang and Zhang, Kanjian
- Subjects
- *
CONSTRAINED optimization , *SEARCH algorithms , *PRODUCTION scheduling , *MANUFACTURING processes , *SCHEDULING , *SMOOTHNESS of functions - Abstract
Chance constraints are suitable for industrial process modeling under uncertain conditions, where constraints cannot be strictly satisfied or do not need to be fully satisfied. In this paper, a single machine scheduling problem involving flexible maintenance, production, and uncertainty is modeled as a chance constrained dynamic optimization problem (CCDOP). A novel method is proposed for transforming the CCDOP into an equivalent deterministic dynamic optimization problem (DOP) with fixed state jump times. Furthermore, by using the idea of l 1 penalty function and a smooth approximation technique, the resulting deterministic DOP becomes a smoothing penalty problem, which is a non-convex nonlinear parameter optimization problem (NNPOP) with simple bounds on the variables. To solve the NNPOP, a gradient-based stochastic search algorithm (GSSA) is developed based on a gradient-based adaptive search algorithm (GASA) and a novel stochastic search algorithm (NSSA). The convergence analysis result shows that the GSSA is a globally convergent algorithm. Finally, two numerical examples are used to illustrate the effectiveness of the proposed method. Numerical results show that the GSSA has excellent convergence behavior with robust computation feature, providing better results compared with the other typical methods. • A CCDOA is developed for the single machine scheduling problem. • Propose a novel technique to transform the CCDOP into an equivalent CDPOP. • Design a GASA, which is effective for ill-conditioned problems. • Design a NSSA, in which no parameters tuning is required. • Propose a GSSA for the NNPOP and comparison results imply its superiority. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
22. Multi-Area Reserve Dimensioning Using Chance-Constrained Optimization.
- Author
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Papavasiliou, Anthony, Bouso, Alberte, Apelfrojd, Senad, Wik, Ellika, Gueuning, Thomas, and Langer, Yves
- Subjects
HEURISTIC algorithms ,POWER transmission ,PROBLEM solving ,SENSITIVITY analysis ,RELIABILITY in engineering - Abstract
We propose a chance-constrained formulation for the problem of dimensioning frequency restoration reserves on a power transmission network. We cast our problem as a two-stage stochastic mixed integer linear program, and propose a heuristic algorithm for solving the problem. Our model accounts for the simultaneous sizing of both upward and downward reserves, and uncertainty driven by imbalances, contingencies and available transmission capacity. Our core methodology is further adapted in order to minimize inter-zonal flows and in order to split reserve requirements between automatic and manual frequency restoration reserves. We apply our methodology to the problem of sizing reserves in the four load frequency control areas of the Swedish power system. We demonstrate the benefits of our method in terms of decreasing reserve requirements in the absence of reserve sharing, we analyze the spatial allocation of reserves, and we perform various sensitivity analyses. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
23. Two-Stage Cooperative Intelligent Home Energy Management System for Optimal Scheduling.
- Author
-
Wei, Xuan, Amin, M. Asim, Xu, Yinliang, Jing, Tao, Yi, Zhongkai, Wang, Xiaoming, Xie, Yuguang, Li, Duanchao, Wang, Shenghe, and Zhai, Yue
- Subjects
ENERGY management ,ENERGY demand management ,WIND power ,SCHEDULING ,HOUSEHOLD appliances - Abstract
Intelligent home energy management system (IHEMS) manages various home appliances depending on user preferences in order to save energy cost and assure user satisfaction. To realize cooperation between the distribution system operator (DSO) and end-user, a two-stage scheduling optimization model is developed based on the flexibility quantification, with the user privacy in demand-side management in a specific cluster taken into account. It also aids to reduce the network operation cost, and the distribution system's uncertainty caused by wind power is represented using chance constraints. The user uploads the IHEMS-calculated offered flexibility to DSO via cluster; DSO optimizes the optimal flexibility to minimize the operation cost; then, clusters distribute the flexibility requirement based on the flexibility index; finally, the user updates the optimal schedule. The numerical results using MATLAB are provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
24. COBALT: COnstrained Bayesian optimizAtion of computationaLly expensive grey-box models exploiting derivaTive information.
- Author
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Paulson, Joel A. and Lu, Congwen
- Subjects
- *
CONSTRAINED optimization , *GAUSSIAN processes , *EXPECTED utility , *UTILITY functions , *NONLINEAR programming - Abstract
• Novel constrained grey-box optimization framework using Gaussian process models. • New almost everywhere differentiable acquisition function for composite functions. • Efficient moment-based approximation of chance constraints. • Tailored algorithm for enrichment sub-problem that exploits model structure. • Performance comparison with Bayesian optimization on diverse set of test problems. [Display omitted] Many engineering problems involve the optimization of computationally expensive models for which derivative information is not readily available. The Bayesian optimization (BO) framework is a particularly promising approach for solving these problems, which uses Gaussian process (GP) models and an expected utility function to systematically tradeoff between exploitation and exploration of the design space. BO, however, is fundamentally limited by the black-box model assumption that does not take into account any underlying problem structure. In this paper, we propose a new algorithm, COBALT, for constrained grey-box optimization problems that combines multivariate GP models with a novel constrained expected utility function whose structure can be exploited by state-of-the-art nonlinear programming solvers. COBALT is compared to traditional BO on seven test problems including the calibration of a genome-scale bioreactor model to experimental data. Overall, COBALT shows very promising performance on both unconstrained and constrained test problems. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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25. On the stochastic vehicle routing problem with time windows, correlated travel times, and time dependency.
- Author
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Bomboi, Federica, Buchheim, Christoph, and Pruente, Jonas
- Abstract
Most state-of-the-art algorithms for the Vehicle Routing Problem, such as Branch-and-Price algorithms or meta heuristics, rely on a fast feasibility test for a given route. We devise the first approach to approximately check feasibility in the Stochastic Vehicle Routing Problem with time windows, where travel times are correlated and depend on the time of the day. Assuming jointly normally distributed travel times, we use a chance constraint approach to model feasibility, where two different application scenarios are considered, depending on whether missing a customer makes the rest of the route infeasible or not. The former case may arise, e.g., in drayage applications or in the pickup-and-delivery VRP. In addition, we present an adaptive sampling algorithm that is tailored for our setting and is much faster than standard sampling techniques. We use a case study for both scenarios, based on instances with realistic travel times, to illustrate that taking correlations and time dependencies into account significantly improves the quality of the solutions, i.e., the precision of the feasibility decision. In particular, the nonconsideration of correlations often leads to solutions containing infeasible routes. [ABSTRACT FROM AUTHOR]
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- 2022
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26. Optimality conditions in control problems with random state constraints in probabilistic or almost-sure form
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Geiersbach, Caroline and Henrion, René
- Subjects
Optimality conditions ,chance constraints ,stochastic optimization ,almost sure constraints ,90C15 ,PDE-constrained optimization under uncertainty ,Optimization and Control (math.OC) ,35Q93 ,FOS: Mathematics ,robust constraints ,49K20, 49K45, 35Q93, 49J52, 90C15 ,49K45 ,49J52 ,Mathematics - Optimization and Control ,49K20 - Abstract
In this paper, we discuss optimality conditions for optimization problems subject to random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation (PDE) with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them to a model based on robust constraints with respect to the (compact) support of the given distribution.
- Published
- 2023
27. On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints
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Holger Heitsch, René Henrion, Thomas Kleinert, and Martin Schmidt
- Subjects
Control and Optimization ,Applied Mathematics ,Bilevel optimization ,chance constraints ,European gas market ,Management Science and Operations Research ,90C46 ,cutting planes ,90B15 ,Computer Science Applications ,90C90 ,black-box constraints ,Business, Management and Accounting (miscellaneous) - Abstract
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.
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- 2022
28. Chance-constrained model predictive control-based operation management of more-electric aircraft using energy storage systems under uncertainty
- Author
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Xin Wang, Najmeh Bazmohammadi, Jason Atkin, Serhiy Bozhko, and Josep M. Guerrero
- Subjects
Multi-failure ,Operation management ,Renewable Energy, Sustainability and the Environment ,Online Monte-Carlo simulation ,Energy Engineering and Power Technology ,Model predictive control ,Electrical and Electronic Engineering ,More-electric aircraft ,Chance constraints ,Multi-uncertainty - Abstract
On more electric aircraft (MEA), reducing fuel consumption and guaranteeing flight safety are pursued by efficient operational management of the electrical power system (EPS). Considering the growing number of onboard electric loads and the increasing complexity of EPS architecture due to the integration of multiple power converters and energy storage systems (ESSs), system-level operation control is required to manage power distribution, load scheduling, and ESSs. In this paper, a chance-constrained stochastic model predictive control (CC-SMPC) method is proposed to improve both the system operation in terms of the system's cost and reconfiguration activities as well as the ability to cope with uncertainties due to fluctuating load demands. Both normal and faulty operating conditions are investigated with multi-failure cases, resulting in different uncertainty propagation paths. The system's operational and technical requirements are formulated as a set of deterministic and probabilistic constraints in the CC-SMPC model. To verify the effectiveness of the proposed strategy, a comprehensive comparison study is conducted. Two uncertainty/failure cases are taken into account and simulations are performed for both offline and online control strategies while the Monte-Carlo algorithm is used for scenario generation. The results are evaluated using the proposed evaluation framework, showing that the CC-SMPC achieves better performance compared to deterministic MPC (DMPC) in both cases. In an offline testing framework, comparing the performance of DMPC and CC-SMPC strategies shows that CC-SMPC reduces the power constraint violations for batteries and generators in all cases following the selected confidence level. In addition, in an online testing framework with 1 % violation probability, the following results are observed in the two cases: In the EPS normal condition, CC-SMPC reduces the total cost by 31.4 % and the overall constraint violation cost by 93 %; while in the EPS faulty condition, CC-SMPC reduces the total cost by 4.37 %, and the overall constraint violation cost by 96 %.
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- 2022
29. A Branch-and-Cut Algorithm for Chance-Constrained Multi-Area Reserve Sizing
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Cho, Jehum, Papavasiliou, Anthony, and UCL - SSH/LIDAM/CORE - Center for operations research and econometrics
- Subjects
Multi-area reserve sizing ,mixed-integer programming ,chance constraints ,probabilistic constraints - Abstract
We implement an exact mixed-integer programming algorithm for the chance-constrained multi-area reserve sizing problem in the presence of transmission network constraints. The problem can be cast as a two-stage stochastic mixed integer linear program using sample approximation. Due to the complicated structure of the problem, existing methods attempt to find a feasible solution based on heuristics. However, a recent development of integer programming techniques allow us to reformulate the problem into a form where we can solve it to optimality. In this paper, we apply this integer programming approach to solve our problem to optimality and compare the results with that of the existing heuristics.
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- 2022
30. Chance-constrained OPF: A Distributed Method with Confidentiality Preservation
- Author
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Jia, Mengshuo, Hug, Gabriela, Su, Yifan, and Shen, Chen
- Subjects
OPF ,Confidentiality preservation ,wind power ,Chance constraints ,Distributed computing - Abstract
Given the increased percentage of wind power in power systems, chance-constrained optimal power flow (CC-OPF) calculation, as a means to take wind power uncertainty into account with a guaranteed security level, is being promoted. Compared to the local CC-OPF within a regional grid, the global CC-OPF of a multi-regional interconnected grid is able to coordinate across different regions and therefore improve the economic efficiency when integrating high percentage of wind power generation. In this global problem, however, multiple regional independent system operators (ISOs) participate in the decision-making process, raising the need for distributed but coordinated approaches. Most notably, due to regulation restrictions, commercial interest, and data security, regional ISOs may refuse to share confidential information with others, including generation cost, load data, system topologies, and line parameters. But this information is needed to build and solve the global CC-OPF spanning multiple areas. To tackle these issues, this paper proposes a distributed CC-OPF method with confidentiality preservation, which enables regional ISOs to determine the optimal dispatchable generations within their regions without disclosing confidential data. This method does not require parameter tunings and will not suffer from convergence challenges. Results from IEEE test cases show that this method is highly accurate.
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- 2022
- Full Text
- View/download PDF
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