Iterative Decomposition of Joint Chance Constraints in OPF

Jia, Mengshuo; Hug, Gabriela; Shen, Chen

doi:10.1109/tpwrs.2021.3072541

Cited by 16 publications

(13 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Each of these methods consists of two critical steps, namely (i) the approximation step and (ii) the conversion step. The approximation step transforms the AC power flow model into a linear one [4]- [11]. This step seems to be unavoidable, as a linear model can not only convert the OPF into a convex problem, but also yield an explicit mapping relationship between power flows and power injections, which is the foundation for the following conversion step.…”

Section: Introductionmentioning

confidence: 99%

“…This step seems to be unavoidable, as a linear model can not only convert the OPF into a convex problem, but also yield an explicit mapping relationship between power flows and power injections, which is the foundation for the following conversion step. Among all the approximation techniques used, the DC power flow is the most commonly-used approach [4]- [6], [11].…”

Section: Introductionmentioning

confidence: 99%

“…The conversion step converts chance constraints into their deterministic versions. According to the chance constraint type, the conversion step can be further divided into two categories, namely converting single chance constraints (SCCs) [4]- [8], and converting joint chance constraints (JCCs) [9]- [11]. The SCC restricts the violation probability of a single system state (e.g., a line flow) whereas a JCC restricts the combined violation probability of multiple system states simultaneously.…”

Section: Introductionmentioning

confidence: 99%

“…The SCC restricts the violation probability of a single system state (e.g., a line flow) whereas a JCC restricts the combined violation probability of multiple system states simultaneously. While JCCs provide a stronger guarantee of the overall system security compared to SCCs [12], a number of existing methods [9]- [11] are capable to decompose JCCs into SCCs. Therefore, converting SCCs into deterministic constraints is the more fundamental step.…”

Section: Introductionmentioning

confidence: 99%

“…However, the hypothesis of following a normal distribution is not suitable for non-Gaussian wind power uncertainty [13]. To address this problem, a Gaussian mixture model (GMM), which is flexible enough to capture different distribution characteristics (including bias, heavy tail, and multi-peak) [14], is adopted by many existing works to formulate the probability distribution of wind power uncertainty [11], [13], [15]. Conveniently, the quantile-based conversion strategy is still applicable to GMMs and therefore, any distribution model can be considered.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Chance-constrained OPF: A Distributed Method with Confidentiality Preservation

Jia¹,

Hug²,

Su³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chance-constrained OPF: A Distributed Method with Confidentiality Preservation

Jia¹,

Hug²,

Su³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

et al. 2022

View full text Add to dashboard Cite

We present a robust approximation of joint chance constrained DC optimal power flow in combination with a model-based prediction of uncertain power supply via R-vine copulas. It is applied to optimize the discrete curtailment of solar feed-in in an electrical distribution network and guarantees network stability under fluctuating feed-in. This is modeled by a two-stage mixed-integer stochastic optimization problem proposed by Aigner et al. (Eur J Oper Res (2022) https://doi.org/10.1016/j.ejor.2021.10.051). The solution approach is based on the approximation of chance constraints via robust constraints using suitable uncertainty sets. The resulting robust optimization problem has a known equivalent tractable reformulation. To compute uncertainty sets that lead to an inner approximation of the stochastic problem, an R-vine copula model is fitted to the distribution of the multi-dimensional power forecast error, i.e., the difference between the forecasted solar power and the measured feed-in at several network nodes. The uncertainty sets are determined by encompassing a sufficient number of samples drawn from the R-vine copula model. Furthermore, an enhanced algorithm is proposed to fit R-vine copulas which can be used to draw conditional samples for given solar radiation forecasts. The experimental results obtained for real-world weather and network data demonstrate the effectiveness of the combination of stochastic programming and model-based prediction of uncertainty via copulas. We improve the outcomes of previous work by showing that the resulting uncertainty sets are much smaller and lead to less conservative solutions while maintaining the same probabilistic guarantees.

show abstract

Data-driven tuning for chance constrained optimization: analysis and extensions

Hou

Roald

2022

TOP

View full text Add to dashboard Cite

Iterative Decomposition of Joint Chance Constraints in OPF

Cited by 16 publications

References 12 publications

Chance-constrained OPF: A Distributed Method with Confidentiality Preservation

Chance-constrained OPF: A Distributed Method with Confidentiality Preservation

Robust DC optimal power flow with modeling of solar power supply uncertainty via R-vine copulas

Data-driven tuning for chance constrained optimization: analysis and extensions

Contact Info

Product

Resources

About