Calculation of Voltage Stability Margins and Certification of Power Flow Insolvability Using Second-Order Cone Programming

Molzahn, Daniel K.; Hiskens, Ian A.; Lesieutre, Bernard C.

doi:10.1109/hicss.2016.289

Cited by 12 publications

(7 citation statements)

References 32 publications

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“…The best critical global integration of RES into the distribution network is provided by a robust methodology-based Political Optimizer and Objective Function Approach [12]. A second-order cone programming (SOCP) formulation has been studied that directly gives upper limits on voltage stability margin without the need to specify a configuration [13]. For cases like the 59-bus in Cairo and the 83-bus in Taiwan, a probabilistic bilevel multi-objective nonlinear programming optimization problem is formulated to maximize the penetration of RES via distribution network reconfiguration without taking into account its intermittent nature [14].…”

Section: Related Workmentioning

confidence: 99%

Modified Analytical Technique for Multi-Objective Optimal Placement of High-Level Renewable Energy Penetration Connected to Egyptian Power System

et al. 2023

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The 2022 United Nations Climate Change Conference (COP27) recommended that Egypt be converted to green energy, in addition to increasing the demand for annual energy consumption, which will lead to an increase in the use of renewable energy sources (RES) in Egypt. The Egyptian Ministry of Energy and Electricity plans to build RES (photovoltaic systems and wind farms) connected to the Egyptian power system (EPS). It is a defect to choose the position and size of the RES based on only power calculations because the RES is an intermittent source. This paper presents a modified analytical energy technique for locating RES in IEEE 33-bus and 69-bus distribution networks and a realistic 25-bus 500 kV EPS. An analytical multi-objective function has been developed to determine the optimal locations of DGs or RESs based on power losses and annual energy loss calculations of the system depending on weather conditions. The efficiency and feasibility of the proposed algorithm based on the IEEE 33-bus and 69-bus distribution networks and the realistic 25-bus 500 kV EPS have been tested and compared with PSO and GA. The impact of RESs on the performance of the 25-bus 500 kV EPS has been investigated based on annual energy losses and operation stability depending on weather conditions. The results showed that the proposed technique used these effective values to obtain optimal weather-adjusted locations. The optimal locations of PV systems or wind systems based on energy calculation improved the voltage profile better than power calculation by about 2%, and the annual energy losses decreased by about 7%. The performance of the 25-bus 500 kV EPS, due to the addition of RES, resulted in a decrease in the annual energy losses of 47% and an improvement in the voltage profile and system stability.

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Section: Related Workmentioning

confidence: 99%

Modified Analytical Technique for Multi-Objective Optimal Placement of High-Level Renewable Energy Penetration Connected to Egyptian Power System

et al. 2023

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“…The OPF problem determines a minimum cost operating point for an electric power system subject to both network constraints (i.e., the power flow equations) and engineering limits (e.g., bounds on voltage magnitudes, active and reactive power injections, and line flows). This section presents the MSOS relaxations in terms of the OPF problem; however, note that the MSOS formulations could be applied to a variety of other power system optimization problems (e.g., transmission expansion planning [65], [66], voltage regulation [67], state estimation [68], and calculating voltage stability margins [12]- [14]). Further, when applied to an optimization problem with a feasible space defined by polynomial equality constraints and a constant objective function, MSOS relaxations with sufficiently high relaxation order can find all solutions to the polynomials [41].…”

Section: Moment/sum-of-squares Relaxations Of the Power Flow Equationsmentioning

confidence: 99%

“…After identifying such a region, any solution contained within can be quickly calculated. Convex relaxation techniques can also calculate power flow solutions [11] and certify infeasibility [12]- [14]. Additionally, progress has been made using "decoupling" approximations that facilitate separate analysis of the active and reactive power flow equations [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Recent advances in computational methods for the power flow equations

Mehta

Molzahn

Turitsyn

2016

2016 American Control Conference (ACC)

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The power flow equations are at the core of most of the computations for designing and operating electric power systems. The power flow equations are a system of multivariate nonlinear equations which relate the power injections and voltages in a power system. A plethora of methods have been devised to solve these equations, starting from Newton-based methods to homotopy continuation and other optimization-based methods. While many of these methods often efficiently find a high-voltage, stable solution due to its large basin of attraction, most of the methods struggle to find low-voltage solutions which play significant role in certain stability-related computations. While we do not claim to have exhausted the existing literature on all related methods, this tutorial paper introduces some of the recent advances in methods for solving power flow equations to the wider power systems community as well as bringing attention from the computational mathematics and optimization communities to the power systems problems. After briefly reviewing some of the traditional computational methods used to solve the power flow equations, we focus on three emerging methods: the numerical polynomial homotopy continuation method, Gröbner basis techniques, and moment/sum-of-squares relaxations using semidefinite programming. In passing, we also emphasize the importance of an upper bound on the number of solutions of the power flow equations and review the current status of research in this direction.

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“…Although continuation methods [4], [5] are mature technology for solving ML, they are not directly applicable to MLD and rely on proper initialization [6], [7]. The optimization methods, however, offer higher modeling flexibility at a higher computational cost [1], [7].…”

Section: Introductionmentioning

confidence: 99%

Sequential Second-Order Cone Programming for AC Load Maximization Problems

Akbari

Sansavini

2022

2022 IEEE 7th International Energy Conference (ENERGYCON)

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AC load maximization problems are challenging to solve in their nonconvex form. Second-order cone programming relaxations facilitate an efficient solution but often result in infeasible solutions especially for meshed networks. This paper proposes a sequential convex programming procedure to recover feasibility by augmenting the relaxed problem with linearized branch and voltage angle constraints. Systematic experiments on radial and meshed networks are designed to identify the effective formulations of constraints. The quantitative results certify the efficacy of the proposed procedure in retrieving nearglobal solutions for a wide range of test cases. Comparison with established nonlinear solvers reveals the computational superiority of the proposed procedure, which is especially important in making timely maximal load delivery decisions.

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Calculation of Voltage Stability Margins and Certification of Power Flow Insolvability Using Second-Order Cone Programming

Cited by 12 publications

References 32 publications

Modified Analytical Technique for Multi-Objective Optimal Placement of High-Level Renewable Energy Penetration Connected to Egyptian Power System

Modified Analytical Technique for Multi-Objective Optimal Placement of High-Level Renewable Energy Penetration Connected to Egyptian Power System

Recent advances in computational methods for the power flow equations

Sequential Second-Order Cone Programming for AC Load Maximization Problems

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