Efficient Computation of Sensitivity Coefficients of Node Voltages and Line Currents in Unbalanced Radial Electrical Distribution Networks

The problem of optimal control of power distribution systems is becoming increasingly compelling due to the progressive penetration of distributed energy resources in this specific layer of the electrical infrastructure. Distribution systems are, indeed, experiencing significant changes in terms of operation philosophies that are often based on optimal control strategies relying on the computation of linearized dependencies between controlled (e.g. voltages, frequency in case of islanding operation) and control variables (e.g. power injections, transformers tap positions). As the implementation of these strategies in real-time controllers imposes stringent time constraints, the derivation of analytical dependency between controlled and control variables becomes a non-trivial task to be solved. With reference to optimal voltage and power flow controls, this paper aims at providing an analytical derivation of node voltage and line current flows as a function of the nodal power injections and transformers tap-changers positions. Compared to other approaches presented in the literature, the one proposed here is based on the use of the [Y] compound matrix of a generic multi-phase radial unbalanced network. In order to estimate the computational benefits of the proposed approach, the relevant improvements are also quantified versus traditional methods. The validation of the proposed method is carried out by using both IEEE 13 and 34 node test feeders. The paper finally shows the use of the proposed method for the problem of optimal voltage control applied to the IEEE 34 node test feeder.Comment: accepted for publication to IEEE Transactions on Smart Gri

Optimal Voltage Regulation of Unbalanced Distribution Networks with Coordination of OLTC and PV Generation

Photovoltaic (PV) smart inverters can regulate voltage in distribution systems by modulating reactive power of PV systems. In this paper, an optimization framework for optimal coordination of reactive power injection of smart inverters and tap operations of voltage regulators for multi-phase unbalanced distribution systems is proposed. Optimization objectives are minimization of voltage deviations and tap operations. A novel linearization method convexifies the problem and speeds up the solution. The proposed method is validated against conventional rule-based autonomous voltage regulation (AVR) on the highly-unbalanced IEEE 37 bus test system. Simulation results show that the proposed method estimates feeder voltage accurately, voltage deviation reductions are significant, over-voltage problems are mitigated, and voltage imbalance is reduced.Comment: IEEE Power and Energy Society General Meeting 201

Advanced probabilistic load flow methodology for voltage unbalance assessment in PV penetrated distribution grids

The balancing of three-phase node voltages in modern power distribution grids can be significantly deteriorated by the penetration of single-phase PV renewable sources. For a given grid topology and prescribed loads, voltage unbalance critically depends on the nodes where power is injected. Its amount can vary substantially at different observations Buses in the grid. In this paper, we present a methodology that can inform network operators about the critical Buses in the grid and critical injection scenarios. The method is based on a numerically efficient but accurate probabilistic load flow that can handle the case of many PV sources and provides detailed information on the probability distribution of voltage unbalance. The proposed methodology relies on the complex-domain modeling of voltage unbalance sensitivity and on accelerating Monte Carlo simulations via parameter space partitioning

Coordination of OLTC and Smart Inverters for Optimal Voltage Regulation of Unbalanced Distribution Networks

Photovoltaic (PV) smart inverters can improve the voltage profile of distribution networks. A multi-objective optimization framework for coordination of reactive power injection of smart inverters and tap operations of on-load tap changers (OLTCs) for multi-phase unbalanced distribution systems is proposed. The optimization objective is to minimize voltage deviations and the number of tap operations simultaneously. A novel linearization method is proposed to linearize power flow equations and to convexify the problem, which guarantees convergence of the optimization and less computation costs. The optimization is modeled and solved using mixed-integer linear programming (MILP). The proposed method is validated against conventional rule-based autonomous voltage regulation (AVR) on the highly-unbalanced modified IEEE 37 bus test system and a large California utility feeder. Simulation results show that the proposed method accurately estimates feeder voltage, significantly reduces voltage deviations, mitigates over-voltage problems, and reduces voltage unbalance while eliminating unnecessary tap operations. The robustness of the method is validated against various levels of forecast error. The computational efficiency and scalability of the proposed approach are also demonstrated through the simulations on the large utility feeder.Comment: Accepted for Electric Power Systems Research. arXiv admin note: text overlap with arXiv:1901.0950

Generalized Analytical Estimation of Sensitivity Matrices in Unbalanced Distribution Networks

Fast and accurate estimation of sensitivity matrices is significant for the enhancement of distribution system modeling and automation. Analytical estimations have mainly focused on voltage magnitude sensitivity to active/reactive power injections for unbalance networks with Wye-connected loads and neglecting DERs' smart inverter functionality. Hence, this paper enhances the scope of analytical estimation of sensitivity matrices for unbalanced networks with 1-phase, 2-phase, and 3-phase Delta/Wye-connected loads, DERs with smart inverter functionality, and substation/line step-voltage regulators (SVR). A composite bus model comprising of DER, Delta- and Wye-connected load is proposed to represent a generic distribution bus, which can be simplified to load, PV, or voltage-controlled bus as required. The proposed matrix-based analytical method consolidates voltage magnitude and angle sensitivity to active/reactive power injection and tap-position of all SVRs into a single algorithm. Extensive case studies on IEEE networks show the accuracy and wide scope of the proposed algorithm compared to the existing benchmark method.Comment: submitted to IEEE transaction on Power System

Single Iteration Conditional Based DSE Considering Spatial and Temporal Correlation

The increasing complexity of distribution network calls for advancement in distribution system state estimation (DSSE) to monitor the operating conditions more accurately. Sufficient number of measurements is imperative for a reliable and accurate state estimation. The limitation on the measurement devices is generally tackled with using the so-called pseudo measured data. However, the errors in pseudo data by cur-rent techniques are quite high leading to a poor DSSE. As customer loads in distribution networks show high cross-correlation in various locations and over successive time steps, it is plausible that deploying the spatial-temporal dependencies can improve the pseudo data accuracy and estimation. Although, the role of spatial dependency in DSSE has been addressed in the literature, one can hardly find an efficient DSSE framework capable of incorporating temporal dependencies present in customer loads. Consequently, to obtain a more efficient and accurate state estimation, we propose a new non-iterative DSSE framework to involve spatial-temporal dependencies together. The spatial-temporal dependencies are modeled by conditional multivariate complex Gaussian distributions and are studied for both static and real-time state estimations, where information at preceding time steps are employed to increase the accuracy of DSSE. The efficiency of the proposed approach is verified based on quality and accuracy indices, standard deviation and computational time. Two balanced medium voltage (MV) and one unbalanced low voltage (LV) distribution case studies are used for evaluations

Ordinal optimization technique for three phase distribution network state estimation including discrete variables

This paper has discussed transformer tap pos ition estimation with continuous and discrete variables in the context of three phase distribution state estimation (SE). Ordinal optimization (OO) technique has been applied to estimate the transformer tap position for the first time in unbalanced three p hase distribution network model. The results on 129 bus system model have demonstrated that OO method can generate a reliable estimate for transformer exact tap position with discrete variables in distribution system state estimation (DSSE) and also in sho rt period of time. In this paper the node voltages and power losses are calculated for 129 bus network. It is also demonstrated that OO is much faster than other accurate methods such HPSO. The losses obtained with OO are much accurate. In view of this OO performs better than WLS as it provides higher accuracy of the loss calculation. In a distribution network where about 5 - 6% of electricity generated is lost, accurate estimation of this loss has significant technical and commercial value. The authors belie ve the technique proposed will help realize those benefits

Real-Time Optimal Controls for Active Distribution Networks:From Concepts to Applications

Decentralized generation, distributed energy storage systems and active participation of end-users in the lower level of the electrical infrastructure, intelligently managed to provide grid support, define the notion of Active Distribution Networks (ADNs). The presence of distributed generation in ADNs incurs severe impacts on planning and operational procedures and calls for intelligent control techniques. This thesis focuses on the compelling problem of optimal operation and control of ADNs, with particular reference to the design of real-time voltage control and lines congestion management algorithms. In the first part of the thesis, we adopt a centralized architecture for voltage control and lines congestion management in ADNs. The goal of the proposed controller is to schedule the active and reactive power injections of a set of controllable resources, in coordination with traditional resources, in order to achieve an optimal grid operation. The controller relies on a linearized approach that links control variables and controlled quantities using sensitivity coefficients. Once the proposed algorithm is validated, as a further step, we relax the assumption that the DNO has an accurate knowledge of the system model, i.e., a correct admittance matrix and we adapt the proposed control architecture to such a scenario. When the controllable resources are heterogeneous and numerous, control schemes that rely on two-way communication between the controllable entity and the DNO cannot scale in the number of network buses and controllable resources. In this direction, in the second part of this thesis, we propose the use of broadcast-based control schemes that rely on state estimation for the feedback channel. We propose a low-overhead broadcast-based control mechanism, called Grid Explicit Congestion Notification (GECN), intended for provision of grid ancillary services by a seamless control of large populations of distributed, heterogeneous energy resources. Two promising candidates in terms of controllable resources are energy storage systems and elastic loads. Therefore, we choose to validate GECN in the case of aggregations of thermostatically controlled loads, as well as of distributed electrochemical-based storage systems. In the last part of the thesis, we formulate the control problem of interest as a non-approximated AC optimal power flow problem (OPF). The AC-OPF problem is non-convex, thus difficult to solve efficiently. A recent approach that focuses on the branch-flow convexification of the problem is claimed to be exact for radial networks under specific assumptions. We show that this claim, does not hold, as it leads to an incorrect system model. Therefore, there is a need to develop algorithms for the solution of the non-approximated, inherently non-convex OPF problem. We propose an algorithm for the AC-OPF problem in radial networks that uses an augmented Lagrangian approach, relies on the method of multipliers and does not require convexity. We design a centralized algorithm that converges to a local minimum of the original problem. When controlling multiple dispersed energy resources, it is of interest to define also a distributed method. We investigate the alternating direction method of multipliers (ADMM) for the distributed solution of the OPF problem and we show cases for which it fails to converge. As a solution we present a distributed version of the proposed OPF algorithm that is based on a primal decomposition