In this letter, we present an alternative mixed-integer non-liner programming formulation of the reactive optimal power flow (ROPF) problem. We utilize a mixed-integer second-order cone programming (MISOCP) based approach to find global optimal solutions of the proposed ROPF problem formulation. We strengthen the MISOCP relaxation via the addition of convex envelopes and cutting planes. Computational experiments on challenging test cases show that the MISOCP-based approach yields promising results compared to a semidefinite programming based approach from the literature.
As the modern transmission control and relay technologies evolve, transmission line switching has become an important option in power system operators' toolkits to reduce operational cost and improve system reliability. Most recent research has relied on the DC approximation of the power flow model in the optimal transmission switching problem. However, it is known that DC approximation may lead to inaccurate flow solutions and also overlook stability issues. In this paper, we focus on the optimal transmission switching problem with the full AC power flow model, abbreviated as AC OTS. We propo…
High penetration of distributed energy resources (DERs) is transforming the paradigm in power system operation. The ability to provide electricity to customers while the main grid is disrupted has introduced the concept of microgrids with many challenges and opportunities. Emergency control of dangerous transients caused by the transition between the grid-connected and island modes in microgrids is one of the main challenges in this context. To address this challenge, this paper proposes a comprehensive optimization and real-time control framework for maintaining frequency stability of multi-m…
Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are …
Integration of plug-in electric vehicles (PEVs) with distributed renewable resources will decrease PEVs' well-to-wheels greenhouse gas emissions, promote renewable power adoption and defer power system investments. This paper proposes a multidisciplinary approach to jointly planning PEV fast-charging stations and distributed photovoltaic (PV) power plants on coupled transportation and power networks. First, we develop models of 1) PEV fast-charging stations; 2) highway transportation networks under PEV driving range constraints; 3) PV power plants with reactive power control. Then, we formulat…
The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The ORPD problem is modelled as a mixed-integer nonlinear optimization problem and its complexity is increased compared to the ACOPF problem, which is highly nonconvex and generally hard to solve. Recently, convex relaxations of the ACOPF problem have attracted a significant interest since they can lead to global optimality. We propose a tight conic relaxation of…
In this paper, we propose a distributed voltage control in power distribution networks through reactive power compensation. The proposed control can (i) operate in a distributed fashion where each bus makes its decision based on local voltage measurements and communication with neighboring buses, (ii) always satisfy the reactive power capacity constraint, (iii) drive the voltage magnitude into an acceptable range, and (iv) minimize an operational cost. We also perform various numerical case studies to demonstrate the effectiveness and robustness of the controller using the nonlinear power flow…
The ever increasing utilization of sensitive loads in the industrial, commercial and residential areas in distribution networks requires enhanced reliability and quality of supply. This can be achieved thanks to self healing features of smart grids that already include the control technologies necessary for the restoration strategy in case of a fault. In this paper, an analytical and global optimization model is proposed for the restoration problem. A novel mathematical formulation is presented for the reconfiguration problem reducing the number of required binary variables while covering more…
A mixed-integer convex (MI-convex) optimization problem is one that becomes convex when all integrality constraints are relaxed. We present a branch-and-bound LP outer approximation algorithm for an MI-convex problem transformed to MI-conic form. The polyhedral relaxations are refined with $\mathcal{K}^*$ cuts derived from conic certificates for continuous primal-dual conic subproblems. Under the assumption that all subproblems are well-posed, the algorithm detects infeasibility or unboundedness or returns an optimal solution in finite time. Using properties of the conic certificates, we show …
High penetration of distributed energy resources presents several challenges and opportunities for voltage regulation in power distribution systems. A local reactive power (VAR) control framework will be developed that can fast respond to voltage mismatch and address the robustness issues of (de-)centralized approaches against communication delays and noises. Using local bus voltage measurements, the proposed gradient-projection based schemes explicitly account for the VAR limit of every bus, and are proven convergent to a surrogate centralized problem with proper parameter choices. This optim…
In the last decade, the integration of Renewable Energy Sources (RES) in distribution networks has been constantly increasing due to their many technical, economical, and environmental benefits. However, the large-scale penetration of RESs is limited by the grid security constraints, e.g., voltage and current limits. The control of inverter-interfaced RESs can guarantee to comply with those constraints while preserving the RESs performance. However, the installation of additional controllable converter units introduces supplementary investment costs and has therefore to be limited. In this pap…
We show how distributed control of reactive power can serve to regulate voltage and minimize resistive losses in a distribution circuit that includes a significant level of photovoltaic (PV) generation. To demonstrate the technique, we consider a radial distribution circuit with a single branch consisting of sequentially-arranged residential-scale loads that consume both real and reactive power. In parallel, some loads also have PV generation capability. We postulate that the inverters associated with each PV system are also capable of limited reactive power generation or consumption, and we s…
In this paper, we propose an approach to determine the optimal operation strategies for a PV-diesel-battery microgrid covering industrial loads under grid blackouts. A special property of the industrial loads is that they have low power factors. Therefore, the reactive power consumption of the load cannot be neglected. In this study, a novel model of a PV-battery-diesel microgrid is developed considering the active as well reactive power of the microgrid components. Furthermore, an optimization approach is proposed to optimize the active as well reactive power flow in the microgrid for coverin…
We consider the problem of exploiting the microgenerators dispersed in the power distribution network in order to provide distributed reactive power compensation for power losses minimization and voltage regulation. In the proposed strategy, microgenerators are smart agents that can measure their phasorial voltage, share these data with the other agents on a cyber layer, and adjust the amount of reactive power injected into the grid, according to a feedback control law that descends from duality-based methods applied to the optimal reactive power flow problem. Convergence to the configuration …
RTE (Réseau de Transport d’Electricité)（RTE电力传输网（法国输电网络公司））；University of Edinburgh（爱丁堡大学）；Polytechnique Montréal（蒙特利尔理工学院）；Université Sorbonne Paris Nord（巴黎北索邦大学）
The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action on the voltage are modelled in the ROPF problem such as the possible activation of shunts, which implies discrete variables. The ROPF problem belongs to the class of nonconvex MINLPs (Mixed-Integer Nonlinear Problems), which are NP-hard problems. In this paper, we solve three new variants of the ROPF problem by using a semidefinite optimization-based Branch-a…
This paper considers the day-ahead operational planning problem of radial distribution networks hosting Distributed Energy Resources, such as Solar Photovoltaic (PV) and Electric Vehicles (EVs). We present an enhanced AC Optimal Power Flow (OPF) model that estimates dynamic Distribution nodal Location Marginal Costs (DLMCs) encompassing transformer degradation as a short-run network variable cost. We decompose real/reactive power DLMCs into additive marginal cost components representing respectively the costs of real/reactive power transactions at the T\&D interface, real/reactive power margin…
Aiming for the median solution between cyber-intensive optimal power flow (OPF) solutions and subpar local control, this work advocates deciding inverter injection setpoints using deep neural networks (DNNs). Instead of fitting OPF solutions in a black-box manner, inverter DNNs are naturally integrated with the feeder model and trained to minimize a grid-wide objective subject to inverter and network constraints enforced on the average over uncertain grid conditions. Learning occurs in a quasi-stationary fashion and is posed as a stochastic OPF, handled via stochastic primal-dual updates actin…
Decentralized methods for computing optimal real and reactive power setpoints for residential photovoltaic (PV) inverters are developed in this paper. It is known that conventional PV inverter controllers, which are designed to extract maximum power at unity power factor, cannot address secondary performance objectives such as voltage regulation and network loss minimization. Optimal power flow techniques can be utilized to select which inverters will provide ancillary services, and to compute their optimal real and reactive power setpoints. Leveraging advances in semidefinite relaxation techn…
A standard operational requirement in power systems is that the voltage magnitudes lie within prespecified bounds. Conventional engineering wisdom suggests that such a tightly-regulated profile, imposed for system design purposes and good operation of the network, should also guarantee a secure system, operating far from static bifurcation instabilities such as voltage collapse. In general however, these two objectives are distinct and must be separately enforced. We formulate an optimization problem which maximizes the distance to voltage collapse through injections of reactive power, subject…
This two-part paper considers the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs), such as Solar Photovoltaic (PV) and Electric Vehicles (EVs). In Part I, we develop a novel AC Optimal Power Flow (OPF) model that estimates dynamic Distribution nodal Location Marginal Costs (DLMCs) of real and reactive power including transformer degradation. These all-inclusive DLMCs are key in the co-optimization of the distribution network and DER schedules. Part II discusses the implication of using DLMCs to represent the benefit of shiftin…
In this paper, a novel Gaussian bare-bones bat algorithm (GBBBA) and its modified version named as dynamic exploitation Gaussian bare-bones bat algorithm (DeGBBBA) are proposed for solving optimal reactive power dispatch (ORPD) problem. The optimal reactive power dispatch (ORPD) plays a fundamental role in ensuring stable, secure, reliable as well as economical operation of the power system. The ORPD problem is formulated as a complex and nonlinear optimization problem of mixed integers including both discrete and continuous control variables. Bat algorithm (BA) is one of the most popular meta…
For the purpose of addressing the multi-objective optimal reactive power dispatch (MORPD) problem, a two-step approach is proposed in this paper. First of all, to ensure the economy and security of the power system, the MORPD model aiming to minimize active power loss and voltage deviation is formulated. And then the two-step approach integrating decision-making into optimization is proposed to solve the model. Specifically speaking, the first step aims to seek the Pareto optimal solutions (POSs) with good distribution by using a multi-objective optimization (MOO) algorithm named classificatio…
Smart inverters have been advocated as a fast-responding mechanism for voltage regulation in distribution grids. Nevertheless, optimal inverter coordination can be computationally demanding, and preset local control rules are known to be subpar. Leveraging tools from machine learning, the design of customized inverter control rules is posed here as a multi-task learning problem. Each inverter control rule is modeled as a possibly nonlinear function of local and/or remote control inputs. Given the electric coupling, the function outputs interact to yield the feeder voltage profile. Using an app…
This two-part paper considers the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs) including Solar Photovoltaic (PV) and storage-like loads such as Electric Vehicles (EVs). We estimate dynamic Distribution nodal Location Marginal Costs (DLMCs) of real and reactive power and employ them to co-optimize distribution network and DER schedules. In Part I, we develop a novel AC Optimal Power Flow (OPF) model encompassing transformer degradation as a short-run network variable cost, and we decompose real/reactive power DLMCs into addi…
Shunt FACTS devices, such as, a Static Var Compensator (SVC), are capable of providing local reactive power compensation. They are widely used in the network to reduce the real power loss and improve the voltage profile. This paper proposes a planning model based on mixed integer conic programming (MICP) to optimally allocate SVCs in the transmission network considering load uncertainty. The load uncertainties are represented by a number of scenarios. Reformulation and linearization techniques are utilized to transform the original non-convex model into a convex second order cone programming (…
The increasing penetration of renewables in distribution networks calls for faster and more advanced voltage regulation strategies. A promising approach is to formulate the problem as an optimization problem, where the optimal reactive power injection from inverters are calculated to maintain the voltages while satisfying power network constraints. However, existing optimization algorithms require the exact topology and line parameters of underlying distribution system, which are not known for most cases and are difficult to infer. In this paper, we propose to use specifically designed neural …
Optimal power flow (OPF) problem is a class of large-scale and non-convex optimization problem. Various algorithms are proposed to solve the challenging OPF problem. Recent studies show that semidefinite programming (SDP) can either provide an exact or near global optima for many existing OPF problems. However, SDP-based approaches usually have the complexity growing exponentially with respect to the network size, which may not be suitable for large-scale OPF problem. In this paper, we rewrite the OPF problem as a combination of several non-convex subproblems. We then consider SDP convex relax…
Frequent metering of electricity consumption is crucial for demand side management in smart grids. However, metered data can be processed fairly easily by employing well-established nonintrusive appliance load monitoring techniques to infer appliance usage, which reveals information about consumers' private lives. Existing load shaping techniques for privacy primarily focus only on altering metered real power, whereas smart meters collect reactive power consumption data as well for various purposes. This study addresses consumer privacy preservation via load shaping in a demand response scheme…
In this paper, we consider the day-ahead operational planning problem of a radial distribution network hosting Distributed Energy Resources (DERs) including rooftop solar and storage-like loads, such as electric vehicles. We present a novel decomposition method that is based on a centralized AC Optimal Power Flow (AC OPF) problem interacting iteratively with self-dispatching DER problems adapting to real and reactive power Distribution Locational Marginal Costs. We illustrate the applicability and tractability of the proposed method on an actual distribution feeder, while modeling the full com…
In this article, we focus on a periodic resource allocation problem applied to a dynamical system which comes from a biological system. More precisely, we consider a system with $N$ resources and $N$ activities, each activity use the allocated resource to evolve up to a given time $T > 0$ where a control (represented by a given permutation) will be applied on the system to reallocate the resources. The goal is to find the optimal control strategies which optimize the cost or the benefit of the system. This problem can be illustrated by an industrial biological application, namely, the optimiza…
Low-voltage distribution feeders were designed to sustain unidirectional power flows to residential neighborhoods. The increased penetration of roof-top photovoltaic (PV) systems has highlighted pressing needs to address power quality and reliability concerns, especially when PV generation exceeds the household demand. A systematic method for determining the active- and reactive-power set points for PV inverters in residential systems is proposed in this paper, with the objective of optimizing the operation of the distribution feeder and ensuring voltage regulation. Binary PV-inverter selectio…
Rare Event Analysis via Stochastic Optimal Control
Microsoft Research New England（微软研究院新英格兰分部）；Cornell University（康奈尔大学）；University of Cambridge（剑桥大学）；Courant Institute of Mathematical Sciences, NYU（纽约大学Courant数学科学研究所）
The rapidly increasing penetration of inverter-based resources into a power transmission network requires more sophisticated voltage control strategies considering their inherent output variabilities. In addition, faults and load variations affect the voltage profile over the power network. This paper proposes a Primal Dual Gradient Dynamics based optimal distributed voltage control approach that optimizes outputs of distributed reactive power sources to maintain an acceptable voltage profile while preserving operational limits. Case studies of this new approach on IEEE test systems have verif…
This paper presents a framework to solve the strategic bidding problem of participants in an electricity market cleared by employing the full AC Optimal Power Flow (ACOPF) problem formulation. Traditionally, the independent system operators (ISOs) leveraged DC Optimal Power Flow (DCOPF) problem formulation to settle the electricity market. The main quest of this work is to find what would be the challenges and opportunities if ISOs leverage the full ACOPF as the market-clearing Problem (MCP)? This paper presents tractable mathematical programming with equilibrium constraints for the convexifie…
Optimized Hierarchical Power Oscillations Control for Distributed Generation Under Unbalanced Conditions
State Grid Customer Service Center（国家电网客户服务中心）；School of Electrical Engineering, Northeast Dianli University（东北电力大学电气工程学院）；Institute of Energy Technology, Aalborg University（奥尔堡大学能源技术研究所）
This paper provides an enhanced modeling of the contingency response that collectively reflects high-fidelity physical and operational characteristics of power grids. Integrating active and reactive power contingency responses into the security-constrained optimal power flow (SCOPF) problem is challenging, due to the nonsmoothness and nonconvexity of feasible sets in consequence of piece-wise curves representing generator characteristics. We introduce a continuously-differentiable model using functions that closely resemble PV/PQ switching and the generator contingency response. These models e…
Convex relaxations of the AC Optimal Power Flow (OPF) problem are essential not only for identifying the globally optimal solution but also for enabling the use of OPF formulations in Bilevel Programming and Mathematical Programs with Equilibrium Constraints (MPEC), which are required for solving problems such as the coordination between transmission and distribution system operator (TSO/DSO) or optimal network investment. Focusing on active distribution grids and radial networks, this paper introduces a framework that collects and compares, for the first time to our knowledge, the performance…
This paper addresses the problem of voltage regulation in a power distribution grid using the reactive power injections of grid-connected power inverters. We first discuss how purely local voltage control schemes cannot regulate the voltages within a desired range under all circumstances and may even yield detrimental control decisions. Communication and, through that, coordination are therefore needed. On the other hand, short-range peer-to-peer communication and knowledge of electric distances between neighbouring controllers are sufficient for this task. We implement such a peer-to-peer con…
