This paper derives a set of sufficient conditions guaranteeing that the load-flow problem in unbalanced three-phase distribution networks with wye and delta ZIP loads has a unique solution over a region that can be explicitly calculated from the network parameters. It is also proved that the well-known Z-Bus iterative method is a contraction over the defined region, and hence converges to the unique solution.
In this paper we present new (stochastic) passivity properties for Direct Current (DC) power networks, where the unknown and unpredictable load demand is modelled by a stochastic process. More precisely, the considered power network consists of distributed generation units supplying ZIP loads, i.e., nonlinear loads comprised of impedance (Z), current (I) and power (P) components. Differently from the majority of the results in the literature, where each of these components is assumed to be constant, we consider time-varying loads whose dynamics are described by a class of stochastic differenti…
In smart grid, the demand side management (DSM) techniques need to be designed to process a large number of controllable loads of several types. In this paper, we proposed a framework to study the demand side management in smart grid which contains a variety of loads in two service areas, one with multiple residential households, and one bus with commercial customers. Specifically, each household may have renewable generation as well as interruptible and uninterruptible appliances to make individual scheduling to optimize the electric energy cost by making the best time of the electricity usag…
The 2028 LA Olympics is approaching, and the mass transportation network requires to be expanded. The green electric bus transportation system is gaining increasing attention as an essential step to mitigate emission concerns. However, the introduction of a large electric bus fleet will increase the peak load demand, which will adversely affect the grid. This research addresses the issue of an increase in the peak load demand due to the introduction of the electric bus fleet. Therefore, the potential implementation of stationary battery energy storage systems is investigated to shave the peak …
The Holomorphic Embedding Load Flow Method (HELM) has been suggested as an alternative approach to solve load flow problems. However, the current literature does not provide any HELM models that can accurately handle general power networks containing PV and PQ buses of realistic sizes. The original HELM paper dealt only with PQ buses, while a second paper showed how to include PV buses but suffered from serious accuracy problems. This paper fills this gap by providing several models capable of solving general networks, with computational results for the standard IEEE test cases provided for co…
The transmission grid is often comprised of several control areas that are connected by multiple tie lines in a mesh structure for reliability. It is also well-known that line failures can propagate non-locally and redundancy can exacerbate cascading. In this paper, we propose an integrated approach to grid reliability that (i) judiciously switches off a small number of tie lines so that the control areas are connected in a tree structure; and (ii) leverages a unified frequency control paradigm to provide congestion management in real time. Even though the proposed topology reduces redundancy,…
This paper investigates the potential of wind turbine generators (WTGs) and load aggregators (LAs) to provide supplementary damping control services for low frequency inter-area oscillations (LFOs) through the additional distributed damping control units (DCUs) proposed in their controllers. In order to provide a scalable methodology for the increasing number of WTGs and LAs, a novel distributed control framework is proposed to coordinate damping controllers. Firstly, a distributed algorithm is designed to reconstruct the system Jacobian matrix for each damping bus (buses with damping controll…
This paper presents a method to handle renewable source and load uncertainties in Dynamic Day-ahead Optimal Power Flow (DA-OPF) using post-optimal analysis of linear programming problem. The method does not require the uncertainty distribution information to handle it. A new Participation Factor (PF) to distribute changes caused by uncertainty has been developed based on the current optimal basis. The proposed PF takes care of all the constraints and ensures optimality with uncertain renewable generation and load using Sensitivity Analysis (SA) and Individual Tolerance Ranges (ITR) for individ…
Conventional state estimation routines of electrical grids are mainly reliant on dynamic models of fossil fuel-based resources. These models commonly contain differential equations describing synchronous generator models and algebraic equations modeling power flow/balance equations. Fuel-free power systems that are driven by inertia-less renewable energy resources will hence require new models and upgraded estimation routines. To that end, in this paper we propose a robust estimator for an interconnected model of power networks comprised of a comprehensive ninth order synchronous generator mod…
To implement controllable loads for frequency regulation in transmission networks in a practical way, the control scheme needs to be granulated down at least to subtransmission networks since loads in transmission networks are usually the aggregation of lower voltage networks. However, not only frequency but also bus voltage will be affected by active power changes in subtransmission networks due to a higher R/X ratio of transmission lines. Further, the costs for loads participating in frequency and voltage regulation should also be considered. In this paper, a control scheme is proposed for e…
Distribution grids currently lack comprehensive real-time metering. Nevertheless, grid operators require precise knowledge of loads and renewable generation to accomplish any feeder optimization task. At the same time, new grid technologies, such as solar photovoltaics and energy storage units are interfaced via inverters with advanced sensing and actuation capabilities. In this context, this two-part work puts forth the idea of engaging power electronics to probe an electric grid and record its voltage response at actuated and metered buses, to infer non-metered loads. Probing can be accompli…
This paper presents a novel modified Viterbi algorithm to identify the optimal distribution system restoration plan for improving the grid resiliency. In the proposed algorithm, the switching operations performed for system restoration are the states with the minimum bus voltage being seen as the cost metric for each state and the extent of load recovery as the observed event. When full load recovery is spotted, the dynamic programming algorithm stops, thereby giving the least number of switching pairs necessary for system restoration. Moreover, an improved flexible switching pair operation is…
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 model's solving results.…
We propose an optimization framework for stochastic optimal power flow with uncertain loads and renewable generator capacity. Our model follows previous work in assuming that generator outputs respond to load imbalances according to an affine control policy, but introduces a model of saturation of generator reserves by assuming that when a generator's target level hits its limit, it abandons the affine policy and produces at that limit. This is a particularly interesting feature in models where wind power plants, which have uncertain upper generation limits, are scheduled to provide reserves t…
With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This work puts forth three approaches with complementary strengths towards coping with the PF task in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. The first approach relies on a monotone mapping. In the absence of constant-power generation, the …
We consider the worst-case load-shedding problem in electric power networks where a number of transmission lines are to be taken out of service. The objective is to identify a pre-specified number of line outage that leads to the maximum interruption of power generation and load at the transmission level, subject to the AC power flow model, the load and generation capacity of the buses, and the phase angle limit across the transmission lines. For this nonlinear model with binary constraints, we show that all decision variables are separable except for the nonlinear power flow equations. We dev…
