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WIREs Energy Environ.
Impact Factor: 2.922

Applications of optimization models for electricity distribution networks

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Abstract Increased penetration of low‐carbon technologies, such as residential photovoltaic systems, electric vehicles, and batteries, can potentially cause voltage quality issues in distribution networks. Active distribution networks adopt control schemes where these assets are actively managed to prevent potential issues, increasing the network utilization. Mathematical optimization is a key technology in enabling such applications, either directly as the underlying solution, or for benchmarking effectiveness. As networks are operated closer to their engineering limits, models representing distribution network physics become increasingly important. This article reviews how distribution networks are modeled with varying degrees of detail in the context of optimization problems. It goes on to catalog the applications that use such models, and ends with an overview of toolchains to implement them, to enable the transition from the passive to active management of the distribution system. This article is categorized under: Energy Systems Analysis > Systems and Infrastructure
This illustration gives an overview of how the main sections of this text are connected. The abbreviations S2–S5 refer to Sections 2–5. The introduction (S1) is left out
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Toolboxes such as JuMP, Pyomo, GAMS, and YALMIP come with an algebraic modeling language, and provide interfaces between this language and various solvers. Distribution modeling tools can build on top of this by translating high‐level problems to the underlying algebraic modeling language. MATPOWER does not support unbalanced (O)PF but is added because it is well‐known
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A series impedance Zl relates the series current to the voltage drop Ui − Uj across the line; we neglect the shunts in the π‐model of the line for simplicity. The series current is only included as a variable in the BFM model
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A unit injects current/power at bus i, and a line connects bus i to j
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A convex relaxation extends the non‐convex feasible set to the convex set . Take for example the minimization problem with objective function f = x2 + y2, that is, finding the point closest to the origin. Part figure (b) shows that the relaxation is inexact, that is, the optimal solution over , b*, is not in . However, the inexact solution does give a lower bound for the optimal solution over the original feasible set , that is, f(b*) ≤ f(a*). Part figure (c) shows the solution to the maximization problem, for which the relaxation is exact
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The voltage magnitudes, parameterized by active consumption of a load in phase a, as calculated by the four‐wire original data, the Kron‐reduced equivalent, and the positive‐sequence approximation. Data: R/X ratio is 1, Zself = 10 · Zmutual, load power factor (PF) of 1, voltage source at 1 pu, all load in phase a, that is, fully unbalanced (Sb = Sc = 0)
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Distribution networks as part of the power system
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This figure illustrates various network models, ordered by decreasing level of modeling detail. The sample system consists of a voltage source at bus i, a multiphase Wye‐connected load at bus j, and a four‐wire line connecting both
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