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Register a new userSelf-optimal Piecewise Linearization Based Network Power Flow Constraints in Electrical Distribution System Optimization
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As a representative mathematical expression of power flow (PF) constraints in electrical distribution system (EDS), the piecewise linearization (PWL) based PF constraints have been widely used in different EDS optimization scenarios. However, the linearized approximation errors originating from the currently-used PWL approximation function can be very large and thus affect the applicability of the PWL based PF constraints. This letter analyzes the approximation error self-optimal (ESO) condition of the PWL approximation function, refines the PWL function formulas, and proposes the self-optimal (SO)-PWL based PF constraints in EDS optimization which can ensure the minimum approximation errors. Numerical results demonstrate the effectiveness of the proposed method.
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In this paper, a flexible optimization-based framework for intentional islanding is presented. The decision is made of which transmission lines to switch in order to split the network while minimizing disruption, the amount of load shed, or grouping coherent generators. The approach uses a piecewise linear model of AC power flow, which allows the voltage and reactive power to be considered directly when designing the islands. Demonstrations on standard test networks show that solution of the problem provides islands that are balanced in real and reactive power, satisfy AC power flow laws, and have a healthy voltage profile.
The load pick-up (LPP) problem searches the optimal configuration of the electrical distribution system (EDS), aiming to minimize the power loss or provide maximum power to the load ends. The piecewise linearization (PWL) approximation method can be used to tackle the nonlinearity and nonconvexity in network power flow (PF) constraints, and transform the LPP model into a mixed-integer linear programming model (LPP-MILP model).However, for the PWL approximation based PF constraints, big linear approximation errors will affect the accuracy and feasibility of the LPP-MILP models solving results. And the long modeling and solving time of the direct solution procedure of the LPP-MILP model may affect the applicability of the LPP optimization scheme. This paper proposes a multi-step PWL approximation based solution for the LPP problem in the EDS. In the proposed multi-step solution procedure, the variable upper bounds in the PWL approximation functions are dynamically renewed to reduce the approximation errors effectively. And the multi-step solution procedure can significantly decrease the modeling and solving time of the LPP-MILP model, which ensure the applicability of the LPP optimization scheme. For the two main application schemes for the LPP problem (i.e. network optimization reconfiguration and service restoration), the effectiveness of the proposed method is demonstrated via case studies using a real 13-bus EDS and a real 1066-bus EDS.
Despite strong connections through shared application areas, research efforts on power market optimization (e.g., unit commitment) and power network optimization (e.g., optimal power flow) remain largely independent. A notable illustration of this is the treatment of power generation cost functions, where nonlinear network optimization has largely used polynomial representations and market optimization has adopted piecewise linear encodings. This work combines state-of-the-art results from both lines of research to understand the best mathematical formulations of the nonlinear AC optimal power flow problem with piecewise linear generation cost functions. An extensive numerical analysis of non-convex models, linear approximations, and convex relaxations across fifty-four realistic test cases illustrates that nonlinear optimization methods are surprisingly sensitive to the mathematical formulation of piecewise linear functions. The results indicate that a poor formulation choice can slow down algorithm performance by a factor of ten, increasing the runtime from seconds to minutes. These results provide valuable insights into the best formulations of nonlinear optimal power flow problems with piecewise linear cost functions, a important step towards building a new generation of energy markets that incorporate the nonlinear AC power flow model.
We propose a framework for integrating optimal power flow (OPF) with state estimation (SE) in the loop for distribution networks. Our approach combines a primal-dual gradient-based OPF solver with a SE feedback loop based on a limited set of sensors for system monitoring, instead of assuming exact knowledge of all states. The estimation algorithm reduces uncertainty on unmeasured grid states based on a few appropriate online state measurements and noisy pseudo-measurements. We analyze the convergence of the proposed algorithm and quantify the statistical estimation errors based on a weighted least squares (WLS) estimator. The numerical results on a 4521-node network demonstrate that this approach can scale to extremely large networks and provide robustness to both large pseudo measurement variability and inherent sensor measurement noise.
We derive the branch ampacity constraint associated to power losses for the convex optimal power flow (OPF) model based on the branch flow formulation. The branch ampacity constraint derivation is motivated by the physical interpretation of the transmission line {Pi}-model and practical engineering considerations. We rigorously prove and derive: (i) the loop constraint of voltage phase angle, required to make the branch flow model valid for meshed power networks, is a relaxation of the original nonconvex alternating current optimal power flow (o-ACOPF) model; (ii) the necessary conditions to recover a feasible solution of the o-ACOPF model from the optimal solution of the convex second-order cone ACOPF (SOC-ACOPF) model; (iii) the expression of the global optimal solution of the o-ACOPF model providing that the relaxation of the SOC-ACOPF model is tight; (iv) the (parametric) optimal value function of the o-ACOPF or SOC-ACOPF model is monotonic with regarding to the power loads if the objective function is monotonic with regarding to the nodal power generations; (v) tight solutions of the SOC-ACOPF model always exist when the power loads are sufficiently large. Numerical experiments using benchmark power networks to validate our findings and to compare with other convex OPF models, are given and discussed.
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