Qifeng Li - Academia.edu (original) (raw)

Papers by Qifeng Li

arXiv (Cornell University), Sep 12, 2019

Though the convex optimization has been widely used in power systems, it still cannot guarantee t... more Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for AC power flow equations that differs from the existing convex relaxations. The proposed approach is based on quadratic power flow equations in rectangular coordinates and it can be used in both balanced and unbalanced three-phase power networks. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flows, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional SDP relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails.

arXiv (Cornell University), May 19, 2018

This paper investigates the water network's potential ability to provide demand response services... more This paper investigates the water network's potential ability to provide demand response services to the power grid under the framework of a distribution-level water-energy nexus (micro-WEN). In particular, the hidden controllability of water loads, such as irrigation systems, was closely studied to improve the flexibility of electrical grids. A optimization model is developed for the demand-side management (DSM) of micro-WEN, and the simulation results assert that grid flexibility indeed benefits from controllable water loads. Although the proposed optimal DSM model is an intractable mixed-integer nonlinear programming (MINLP) problem, quasi-convex hull techniques were developed to relax the MINLP into a mixed-integer convex programming (MICP) problem. The numerical study shows that the quasi-convex hull relaxation is tight and that the resulting MICP problem is computationally efficient.

Energies, 2019

The secure operation of 110-kV networks should be considered in the optimal generation dispatch o... more The secure operation of 110-kV networks should be considered in the optimal generation dispatch of regional power grids in large central cities. However, since 110-kV lines do not satisfy the premise of R << X in the direct current power flow (DCPF) model, the DCPF, which is mostly applied in the security-constrained unit commitment (SCUC) problem of high-voltage power grids, is no longer suitable for describing the active power flow of regional power grids in large central cities. Hence, the quadratic active power flow (QAPF) model considering the resistance of lines is proposed to describe the network security constraints, and an SCUC model for power system with 110-kV network and pumped-storage hydro (PSH) units is established. The analytical expressions of the spinning reserve (SR) capacity of PSH units are given considering different operational modes, and the SR capacity of PSH units is included in the constraint of the SR capacity requirement of the system. The QAPF is ...

arXiv (Cornell University), Mar 2, 2021

This paper defines a security injection region (SIR) to guarantee reliable operation of water dis... more This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.

IEEE Access

This paper introduces a data-driven optimization (DDO) method based on novel strategic sampling (... more This paper introduces a data-driven optimization (DDO) method based on novel strategic sampling (SS) considering data correlations for multiperiod optimal power flow (OPF) considering energy storage devices under uncertainty (OPF-ESDUU) of uncertain renewable energy and power loads (UREPL). This DDO method depends only on the uncertainty samples to yield an optimal solution that satisfies a specific confidence level, which is effective because of two resounding learning algorithms: Bayesian hierarchical modeling (BHM) and determinantal point process (DPP). Considering both the local bus information and spatial correlations over all buses, BHM learns the convex approximation of AC power flow (CAACPF) more accurately than the existing learning methods, converting the originally non-convex OPF-ESDUU to a convex optimization problem. DPP considers the correlations between samples to find a small set of significant samples by measuring the relative weight of each sample using the random matrix theory, significantly decreasing the data samples required by the existing SS. The experimental analysis in IEEE test cases shows that after considering data correlations, 1) BHM learns CAACPF better with 13-90% accuracy improvement, compared with the existing learning methods, and 2) the proposed DDO performs more efficiently than the existing DDO as DPP-based SS boosts the sampling efficiency by 50% at least. INDEX TERMS Bayesian hierarchical modeling, determinantal point process, power flow, strategic sampling.

2022 IEEE Power & Energy Society General Meeting (PESGM)

Water and power systems are increasingly interdependent due to the growing number of electricity-... more Water and power systems are increasingly interdependent due to the growing number of electricity-driven water facilities. The security of one system can be affected by a contingency in the other system. This paper investigates a securityconstrained operation problem of the energy-water nexus (EWN), which is a computationally challenging optimization problem due to the nonlinearity, nonconvexity, and size. We propose a two-step iterative contingency filtering method based on the feasibility and rating of the contingencies to decrease the size of the problem. The optimal power and water flow are obtained in a normal situation by considering the set of contingencies that can not be controlled with corrective actions. The feasibility check of the contingencies is performed in the second step, followed by a rating of the uncontrollable contingencies. Finally, the critical contingencies are obtained and added to the first step for the next iteration. We also employ convex technologies to reduce the computation burden. The proposed method is validated via two case studies. Results indicate that this approach can efficiently attain optimal values. Index Terms-contingency filtering, energy water nexus, optimal power and water flow, security constrained.

AHFE International

In this paper, we propose a novel gait recognition method based on a bag-of-words feature represe... more In this paper, we propose a novel gait recognition method based on a bag-of-words feature representation method. The algorithm is trained, tested and evaluated on a unique human gait data consisting of 93 individuals who walked with comfortable pace between two end-points during two different sessions. To evaluate the effectiveness of the proposed model, the results are compared with the outputs of the classification using extracted features. As it is presented, the proposed method results in significant improvement accuracy compared to using common statistical features, in all the used classifiers.

2020 IEEE Power & Energy Society General Meeting (PESGM)

This paper develops an ensemble learning-based linearization approach for power flow, which diffe... more This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as a basic learner to capture the linear relationships between the bus voltage as the independent variable and the active or reactive power as the dependent variable in rectangular coordinates. Then, gradient boosting (GB) and bagging as ensemble learning methods are introduced to combine all basic learners to boost the model performance. The fitted linear power flow model is also relaxed to compute the optimal power flow (OPF). The simulating results of standard IEEE cases indicate that (1) ensemble learning methods outperform PR and GB works better than bagging; (2) as for solving OPF, the data-driven model excels the DC model and the SDP relaxation in the computational accuracy, and works faster than ACOPF and SDPOPF.

arXiv (Cornell University), Sep 17, 2015

An optimization problem considering AC power flow constraints and integer decision variables can ... more An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear equalities are applied to strengthen the semidefinite program (SDP) relaxation of the MIQCQP problem without significantly increasing the problem dimension so that an enhanced mixed-integer SDP (MISDP) relaxation, which is a mixed-integer convex problem, is obtained. Then, the enhanced MISDP relaxation is reformulated as a disjunctive programming (DP) problem which is tighter than the former one, since the disjunctions are designed to capture the disjunctive nature of the terms in the rank-1 constraint about the integral variables. The DP relaxation is then equivalently converted back into a MISDP problem the feasible set of whose continuous relaxation is the convex hull of feasible region of the DP problem. Finally, globally optimal solution of the DP problem which is the tightest relaxation for the MIQCQP proposed in the paper is obtained by solving the resulting MISDP problem using a branch-and-bound (B&B) algorithm. Computational efficiency of the B&B algorithm is expected to be high since feasible set of the continuous relaxation of a MISDP sub-problem is the convex hull of that of the corresponding DP sub-problem. To further reduce the dimension of the resulting MISDP problem, a compact formulation of this problem is proposed considering the sparsity. An optimal placement problem of smart PV inverter in distribution systems integrated with high penetration of PV, which is an MIQCQP problem, is studied as an example. The proposed approach is tested on an IEEE distribution system. The results show that it can effectively improve the tightness and feasibility of the SDP relaxation.

This paper proposes an ensemble learning based approach for convexifying AC power flow equations,... more This paper proposes an ensemble learning based approach for convexifying AC power flow equations, which differs from the existing relaxation-based convexification techniques. The proposed approach is based on the quadratic power flow equations in rectangular coordinates. To develop this data-driven convex model of power flow, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms, i.e. gradient boosting (GB) and bagging, are introduced to combine learners to boost model performance. Based on the learned convex models of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases illustrate that, 1) GB outperforms PR and bagging on the prediction accuracy, 2) in context of solving OPF, the proposed data-driven convex model outperforms the conventional SDP relaxation in both accuracy...

arXiv: Optimization and Control, 2017

For many nonlinear control systems, the chosen equilibrium determines both the steady-state effic... more For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation criteria for a Lur'e-type system and such an equilibrium can also guarantee a sufficiently large stability region in the dynamic domain such that the system can tolerate some given disturbance. For this purpose, a set of computationally tractable algebraic constraints, which can properly represent the stability certificate under the optimization framework, are proposed. The existing methods formulate the dynamic performance under the optimization framework by discretizing the differential-algebraic equations, which are computationally intractable for large-scale Lur'e systems like power grids. Dissimilarly, the introduced approach first constructs the stability region based on quadratic Lyapunov functions. Then, a novel method is proposed t...

2021 American Control Conference (ACC), 2021

This paper defines a security injection region (SIR) to guarantee reliable operation of water dis... more This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.

Energies, 2021

The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both ... more The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both islanded and grid-connected modes require coordinated control strategies. DERs are interfaced with voltage source inverters (VSIs) enabling interconnection. This paper proposes a load demand sharing scheme for the parallel operation of VSIs in an islanded voltage source inverter-based microgrid (VSI-MG). The ride-through capability of a heavily loaded VSI-MG, where some of the VSIs are fully loaded due to the occurrence of an event is investigated. In developing analytical equations to model the VSI, the concept of virtual synchronous machines (VSM) is applied to enable the VSI mimic the inertia effect of synchronous machines. A power frame transformation (PFT) that takes the line ratios of the MG network into account is also incorporated to yield satisfactory transient responses of both network frequency and bus voltages in the MG network. A Jacobian-based method is then developed to ta...

IEEE Transactions on Power Systems, 2021

This paper presents a novel optimization framework of modeling three-phase optimal power flow tha... more This paper presents a novel optimization framework of modeling three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework that is less complex than the existing frameworks with uncertainty, and 2) convex such that it admits polynomial-time algorithms and mature distributed optimization methods. To construct the UaO framework, a methodology of learning-based uncertainty-aware modeling with prediction errors of stochastic variables as the measurement of uncertainty and a theory of data-driven convexification are proposed. Theoretically, the UaO framework is applicable for modeling general optimization problems under uncertainty.

2019 North American Power Symposium (NAPS), 2019

Energy storage has been proven to yield positive effects on planning, operation and control of el... more Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categorieslinear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed-integer linear and convex nonlinear sub-categories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

IEEE Transactions on Power Systems, 2017

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial... more Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic (PV) resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow (OPF) problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter SDP relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP (ESDP) relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder.

arXiv (Cornell University), Oct 10, 2018

This paper presents a novel scalable framework to solve the optimization of a nonlinear system wi... more This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to certain disturbances. Existing solution approaches to analogous DAEconstrained problems are based on discretization of DAE system into a large set of nonlinear algebraic equations representing the time-marching schemes. These approaches are not scalable to large size models. The proposed framework, based on LaSalle's invariance principle, uses convex Lyapunov functions to develop a novel stability certificate which consists of a limited number of algebraic constraints. We develop specific algorithms for two major types of nonlinearities, namely Lur'e, and quasi-polynomial systems. Quadratic and convex-sum-of-square Lyapunov functions are constructed for the Lur'e-type and quasi-polynomial systems respectively. A numerical experiment is performed on a 3-generator power network to obtain a solution for transientstability-constrained optimal power flow.

IEEE Transactions on Power Systems, 2017

A branch flow model (BFM) is used to formulate the AC power flow in general networks. For each br... more A branch flow model (BFM) is used to formulate the AC power flow in general networks. For each branch/line, the BFM contains a non-convex quadratic equality. A mathematical formulation of its convex hull is proposed, which is the tightest convex relaxation of this quadratic equation. The convex hull formulation consists of a second order cone inequality and a linear inequality within the physical bounds of power flows. The convex hull formulation is analytically proved and geometrically validated. An optimal scheduling problem of distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is investigated in this paper. To capture the performance of both the battery and converter, a second-order DES model is proposed. Following the convex hull of the quadratic branch flow equation, the convex hull formulation of the nonconvex constraint in the DES model is also derived. The proposed convex hull models are used to generate a tight convex relaxation of the DES optimal scheduling (DESOS) problem. The proposed approach is tested on several radial systems. A discussion on the extension to meshed networks is provided.

arXiv (Cornell University), Sep 12, 2019

Though the convex optimization has been widely used in power systems, it still cannot guarantee t... more Though the convex optimization has been widely used in power systems, it still cannot guarantee to yield a tight (accurate) solution to some problems. To mitigate this issue, this paper proposes an ensemble learning based convex approximation for AC power flow equations that differs from the existing convex relaxations. The proposed approach is based on quadratic power flow equations in rectangular coordinates and it can be used in both balanced and unbalanced three-phase power networks. To develop this data-driven convex approximation of power flows, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms such as gradient boosting (GB) and bagging are introduced to combine learners to boost model performance. Based on the learned convex approximation of power flows, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases show that, in the context of solving OPF, the proposed data-driven convex approximation outperforms the conventional SDP relaxation in both accuracy and computational efficiency, especially in the cases that the conventional SDP relaxation fails.

arXiv (Cornell University), May 19, 2018

This paper investigates the water network's potential ability to provide demand response services... more This paper investigates the water network's potential ability to provide demand response services to the power grid under the framework of a distribution-level water-energy nexus (micro-WEN). In particular, the hidden controllability of water loads, such as irrigation systems, was closely studied to improve the flexibility of electrical grids. A optimization model is developed for the demand-side management (DSM) of micro-WEN, and the simulation results assert that grid flexibility indeed benefits from controllable water loads. Although the proposed optimal DSM model is an intractable mixed-integer nonlinear programming (MINLP) problem, quasi-convex hull techniques were developed to relax the MINLP into a mixed-integer convex programming (MICP) problem. The numerical study shows that the quasi-convex hull relaxation is tight and that the resulting MICP problem is computationally efficient.

Energies, 2019

The secure operation of 110-kV networks should be considered in the optimal generation dispatch o... more The secure operation of 110-kV networks should be considered in the optimal generation dispatch of regional power grids in large central cities. However, since 110-kV lines do not satisfy the premise of R << X in the direct current power flow (DCPF) model, the DCPF, which is mostly applied in the security-constrained unit commitment (SCUC) problem of high-voltage power grids, is no longer suitable for describing the active power flow of regional power grids in large central cities. Hence, the quadratic active power flow (QAPF) model considering the resistance of lines is proposed to describe the network security constraints, and an SCUC model for power system with 110-kV network and pumped-storage hydro (PSH) units is established. The analytical expressions of the spinning reserve (SR) capacity of PSH units are given considering different operational modes, and the SR capacity of PSH units is included in the constraint of the SR capacity requirement of the system. The QAPF is ...

arXiv (Cornell University), Mar 2, 2021

This paper defines a security injection region (SIR) to guarantee reliable operation of water dis... more This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.

IEEE Access

This paper introduces a data-driven optimization (DDO) method based on novel strategic sampling (... more This paper introduces a data-driven optimization (DDO) method based on novel strategic sampling (SS) considering data correlations for multiperiod optimal power flow (OPF) considering energy storage devices under uncertainty (OPF-ESDUU) of uncertain renewable energy and power loads (UREPL). This DDO method depends only on the uncertainty samples to yield an optimal solution that satisfies a specific confidence level, which is effective because of two resounding learning algorithms: Bayesian hierarchical modeling (BHM) and determinantal point process (DPP). Considering both the local bus information and spatial correlations over all buses, BHM learns the convex approximation of AC power flow (CAACPF) more accurately than the existing learning methods, converting the originally non-convex OPF-ESDUU to a convex optimization problem. DPP considers the correlations between samples to find a small set of significant samples by measuring the relative weight of each sample using the random matrix theory, significantly decreasing the data samples required by the existing SS. The experimental analysis in IEEE test cases shows that after considering data correlations, 1) BHM learns CAACPF better with 13-90% accuracy improvement, compared with the existing learning methods, and 2) the proposed DDO performs more efficiently than the existing DDO as DPP-based SS boosts the sampling efficiency by 50% at least. INDEX TERMS Bayesian hierarchical modeling, determinantal point process, power flow, strategic sampling.

2022 IEEE Power & Energy Society General Meeting (PESGM)

Water and power systems are increasingly interdependent due to the growing number of electricity-... more Water and power systems are increasingly interdependent due to the growing number of electricity-driven water facilities. The security of one system can be affected by a contingency in the other system. This paper investigates a securityconstrained operation problem of the energy-water nexus (EWN), which is a computationally challenging optimization problem due to the nonlinearity, nonconvexity, and size. We propose a two-step iterative contingency filtering method based on the feasibility and rating of the contingencies to decrease the size of the problem. The optimal power and water flow are obtained in a normal situation by considering the set of contingencies that can not be controlled with corrective actions. The feasibility check of the contingencies is performed in the second step, followed by a rating of the uncontrollable contingencies. Finally, the critical contingencies are obtained and added to the first step for the next iteration. We also employ convex technologies to reduce the computation burden. The proposed method is validated via two case studies. Results indicate that this approach can efficiently attain optimal values. Index Terms-contingency filtering, energy water nexus, optimal power and water flow, security constrained.

AHFE International

In this paper, we propose a novel gait recognition method based on a bag-of-words feature represe... more In this paper, we propose a novel gait recognition method based on a bag-of-words feature representation method. The algorithm is trained, tested and evaluated on a unique human gait data consisting of 93 individuals who walked with comfortable pace between two end-points during two different sessions. To evaluate the effectiveness of the proposed model, the results are compared with the outputs of the classification using extracted features. As it is presented, the proposed method results in significant improvement accuracy compared to using common statistical features, in all the used classifiers.

2020 IEEE Power & Energy Society General Meeting (PESGM)

This paper develops an ensemble learning-based linearization approach for power flow, which diffe... more This paper develops an ensemble learning-based linearization approach for power flow, which differs from the network-parameter based direct current (DC) power flow or other extended versions of linearization. As a novel data-driven linearization through data mining, it firstly applies the polynomial regression (PR) as a basic learner to capture the linear relationships between the bus voltage as the independent variable and the active or reactive power as the dependent variable in rectangular coordinates. Then, gradient boosting (GB) and bagging as ensemble learning methods are introduced to combine all basic learners to boost the model performance. The fitted linear power flow model is also relaxed to compute the optimal power flow (OPF). The simulating results of standard IEEE cases indicate that (1) ensemble learning methods outperform PR and GB works better than bagging; (2) as for solving OPF, the data-driven model excels the DC model and the SDP relaxation in the computational accuracy, and works faster than ACOPF and SDPOPF.

arXiv (Cornell University), Sep 17, 2015

An optimization problem considering AC power flow constraints and integer decision variables can ... more An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear equalities are applied to strengthen the semidefinite program (SDP) relaxation of the MIQCQP problem without significantly increasing the problem dimension so that an enhanced mixed-integer SDP (MISDP) relaxation, which is a mixed-integer convex problem, is obtained. Then, the enhanced MISDP relaxation is reformulated as a disjunctive programming (DP) problem which is tighter than the former one, since the disjunctions are designed to capture the disjunctive nature of the terms in the rank-1 constraint about the integral variables. The DP relaxation is then equivalently converted back into a MISDP problem the feasible set of whose continuous relaxation is the convex hull of feasible region of the DP problem. Finally, globally optimal solution of the DP problem which is the tightest relaxation for the MIQCQP proposed in the paper is obtained by solving the resulting MISDP problem using a branch-and-bound (B&B) algorithm. Computational efficiency of the B&B algorithm is expected to be high since feasible set of the continuous relaxation of a MISDP sub-problem is the convex hull of that of the corresponding DP sub-problem. To further reduce the dimension of the resulting MISDP problem, a compact formulation of this problem is proposed considering the sparsity. An optimal placement problem of smart PV inverter in distribution systems integrated with high penetration of PV, which is an MIQCQP problem, is studied as an example. The proposed approach is tested on an IEEE distribution system. The results show that it can effectively improve the tightness and feasibility of the SDP relaxation.

This paper proposes an ensemble learning based approach for convexifying AC power flow equations,... more This paper proposes an ensemble learning based approach for convexifying AC power flow equations, which differs from the existing relaxation-based convexification techniques. The proposed approach is based on the quadratic power flow equations in rectangular coordinates. To develop this data-driven convex model of power flow, the polynomial regression (PR) is first deployed as a basic learner to fit convex relationships between the independent and dependent variables. Then, ensemble learning algorithms, i.e. gradient boosting (GB) and bagging, are introduced to combine learners to boost model performance. Based on the learned convex models of power flow, optimal power flow (OPF) is formulated as a convex quadratic programming problem. The simulation results on IEEE standard cases illustrate that, 1) GB outperforms PR and bagging on the prediction accuracy, 2) in context of solving OPF, the proposed data-driven convex model outperforms the conventional SDP relaxation in both accuracy...

arXiv: Optimization and Control, 2017

For many nonlinear control systems, the chosen equilibrium determines both the steady-state effic... more For many nonlinear control systems, the chosen equilibrium determines both the steady-state efficiency and the dynamic performance. This paper addresses the issue of obtaining an optimal equilibrium in terms of some steady-state operation criteria for a Lur'e-type system and such an equilibrium can also guarantee a sufficiently large stability region in the dynamic domain such that the system can tolerate some given disturbance. For this purpose, a set of computationally tractable algebraic constraints, which can properly represent the stability certificate under the optimization framework, are proposed. The existing methods formulate the dynamic performance under the optimization framework by discretizing the differential-algebraic equations, which are computationally intractable for large-scale Lur'e systems like power grids. Dissimilarly, the introduced approach first constructs the stability region based on quadratic Lyapunov functions. Then, a novel method is proposed t...

2021 American Control Conference (ACC), 2021

This paper defines a security injection region (SIR) to guarantee reliable operation of water dis... more This paper defines a security injection region (SIR) to guarantee reliable operation of water distribution systems (WDS) under extreme conditions. The model of WDSs is highly nonlinear and nonconvex. Understanding the accurate SIRs of WDSs involves the analysis of nonlinear constraints, which is computationally expensive. To reduce the computational burden, this paper first investigates the convexity of the SIR of WDSs under certain conditions. Then, an algorithm based on a monotone inner polytope sequence is proposed to effectively and accurately determine these SIRs. The proposed algorithm estimates a sequence of inner polytopes that converge to the whole convex region. Each polytope adds a new area to the SIR. The algorithm is validated on two different WDSs, and the conclusion is drawn. The computational study shows this method is applicable and fast for both systems.

Energies, 2021

The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both ... more The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both islanded and grid-connected modes require coordinated control strategies. DERs are interfaced with voltage source inverters (VSIs) enabling interconnection. This paper proposes a load demand sharing scheme for the parallel operation of VSIs in an islanded voltage source inverter-based microgrid (VSI-MG). The ride-through capability of a heavily loaded VSI-MG, where some of the VSIs are fully loaded due to the occurrence of an event is investigated. In developing analytical equations to model the VSI, the concept of virtual synchronous machines (VSM) is applied to enable the VSI mimic the inertia effect of synchronous machines. A power frame transformation (PFT) that takes the line ratios of the MG network into account is also incorporated to yield satisfactory transient responses of both network frequency and bus voltages in the MG network. A Jacobian-based method is then developed to ta...

IEEE Transactions on Power Systems, 2021

This paper presents a novel optimization framework of modeling three-phase optimal power flow tha... more This paper presents a novel optimization framework of modeling three-phase optimal power flow that involves uncertainty. The proposed uncertainty-aware optimization (UaO) framework is: 1) a deterministic framework that is less complex than the existing frameworks with uncertainty, and 2) convex such that it admits polynomial-time algorithms and mature distributed optimization methods. To construct the UaO framework, a methodology of learning-based uncertainty-aware modeling with prediction errors of stochastic variables as the measurement of uncertainty and a theory of data-driven convexification are proposed. Theoretically, the UaO framework is applicable for modeling general optimization problems under uncertainty.

2019 North American Power Symposium (NAPS), 2019

Energy storage has been proven to yield positive effects on planning, operation and control of el... more Energy storage has been proven to yield positive effects on planning, operation and control of electric grids. It has become a crucial task to properly model the energy storage systems (ESS) under the framework of grid optimization on transmission and distribution networks including microgrids. This paper presents a review on mathematical models and test cases of ESSs used for grid optimization studies, where the network constraints of power systems are included. The existing ESS models are mainly classified into two categorieslinear and nonlinear models. The two main categories are further divided into several subcategories respectively; such as mixed-integer linear and convex nonlinear sub-categories. Based on the review and discussions, this paper aims at providing suggestions for choosing proper ESS models for specific grid optimization studies considering the chosen power network model.

IEEE Transactions on Power Systems, 2017

Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial... more Convexification of an optimal scheduling algorithm for distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic (PV) resources is studied. The AC power flow equalities are taken into account as constraints in the optimization model. Different from the typical optimal power flow (OPF) problem, the objective function of a DES optimal scheduling (DESOS) problem varies with changing operational requirements. In this paper, three frequently-used objective functions are considered for the DESOS problem. Two of them are monotonic over the feasible set while the third is not. An illustrative example elucidates that the descent direction of a chosen objective function significantly impacts the efficiency of the second order cone programming (SOCP) relaxation for the DESOS problem. To obtain tighter SDP relaxations for the DESOS cases where the SOCP relaxation is not exact, this paper looks for computationally efficient convex constraints that can approximate the rank-1 constraint in the non-iterative framework. The designed non-iterative enhanced SDP (ESDP) relaxations are compared in terms of tightness of convexification for the DESOS problems considering the three objective functions independently. The comparison is performed on several radial IEEE test systems and a real world distribution feeder.

arXiv (Cornell University), Oct 10, 2018

This paper presents a novel scalable framework to solve the optimization of a nonlinear system wi... more This paper presents a novel scalable framework to solve the optimization of a nonlinear system with differential algebraic equation (DAE) constraints that enforce the asymptotic stability of the underlying dynamic model with respect to certain disturbances. Existing solution approaches to analogous DAEconstrained problems are based on discretization of DAE system into a large set of nonlinear algebraic equations representing the time-marching schemes. These approaches are not scalable to large size models. The proposed framework, based on LaSalle's invariance principle, uses convex Lyapunov functions to develop a novel stability certificate which consists of a limited number of algebraic constraints. We develop specific algorithms for two major types of nonlinearities, namely Lur'e, and quasi-polynomial systems. Quadratic and convex-sum-of-square Lyapunov functions are constructed for the Lur'e-type and quasi-polynomial systems respectively. A numerical experiment is performed on a 3-generator power network to obtain a solution for transientstability-constrained optimal power flow.

IEEE Transactions on Power Systems, 2017

A branch flow model (BFM) is used to formulate the AC power flow in general networks. For each br... more A branch flow model (BFM) is used to formulate the AC power flow in general networks. For each branch/line, the BFM contains a non-convex quadratic equality. A mathematical formulation of its convex hull is proposed, which is the tightest convex relaxation of this quadratic equation. The convex hull formulation consists of a second order cone inequality and a linear inequality within the physical bounds of power flows. The convex hull formulation is analytically proved and geometrically validated. An optimal scheduling problem of distributed energy storage (DES) in radial distribution systems with high penetration of photovoltaic resources is investigated in this paper. To capture the performance of both the battery and converter, a second-order DES model is proposed. Following the convex hull of the quadratic branch flow equation, the convex hull formulation of the nonconvex constraint in the DES model is also derived. The proposed convex hull models are used to generate a tight convex relaxation of the DES optimal scheduling (DESOS) problem. The proposed approach is tested on several radial systems. A discussion on the extension to meshed networks is provided.