Linearized Load Flow Model Research Articles

Observability Analysis and Restoration for Distribution Grids: A Robust Greedy Numerical Algorithm

This paper presents a robust and efficient algorithm for analyzing and restoring the observability of distribution grids. A linearized load flow model is used to characterize three-and multi-phase distribution grids under balanced and unbalanced conditions. Assuming that metering devices are installed to measure nodal magnitudes at some buses, the rank of the matrix associated with the non-metered magnitudes is determined by using a greedy strategy combined with a Gram-Schmidt orthonormalization procedure. Unlike other numerical-based techniques, the proposed algorithm avoids common errors caused by denominators close to zero. As an additional salient feature, a mathematically sound stopping criterion is provided to guarantee the robustness of the proposed algorithm. Furthermore, for unobservable grids, the algorithm identifies the linearly dependent rows in the aforementioned matrix, which correspond to the buses that should be metered to restore grid observability. The effective performance of the proposed algorithm is illustrated using several medium-and low-voltage benchmarks with up to 906 buses.

Stochastic security-constrained optimal power flow for a microgrid considering tie-line switching

With the rapid development of microgrid, its tie-line switching from grid-connected to islanded mode is a topic worth discussing for considering both main grid resilience and microgrid security. In this paper, a stochastic security-constrained optimal power flow (OPF) method is proposed to deal with these conditions under high uncertainties. Firstly, a linear load flow model and a backward forward sweep algorithm are applied to present microgrid power flow with reduced computing burdens. Secondly, with consideration of tie-line switching from grid-connected to islanded operation mode, a security-constrained OPF problem for a microgrid is proposed to minimize operating cost and by optimizing microturbine setpoints and load shedding coefficient. To promise stable islanded operation after disconnection from the main grid, a Benders decomposition method is developed to decouple the OPF problem into a grid-connected master problem and an islanded sub-problem and then solve them iteratively with Benders cuts to guarantee microgrid security after tie-line switching. Last, a stochastic optimization method with probabilistic modelling is adopted to address the uncertainty issue caused by renewable energy sources and loads. The proposed stochastic security-constrained OPF method has been verified with high computing efficiency and robust security via comprehensive numerical simulations.

Analysis of Energy Transition Impact on the Low-Voltage Network Using Stochastic Load and Generation Models

The energy transition poses a challenge for the electricity distribution network design as new energy technologies cause increasing and uncertain network loads. Traditional static load models cannot cope with the stochastic nature of this new technology adoption. Furthermore, traditional nonlinear power methods have difficulty evaluating very large networks with millions of cables, because they are computationally expensive. This paper proposes a method which uses copulas for modeling the uncertainty of technology adoption and load profiles, and combines it with a fast linear load flow model. The copulas are able to accurately model the stochastic behavior of solar irradiance, load measurements, and mobility data, converting them into electricity load profiles. The linear load flow model has better scalability and stability compared to traditional load flow models. The models are applied to a case study which uses a real-world dataset consisting of a realistic technology adoption scenario and a low-voltage network with millions of cables, which considers both voltage and current problems. Results show that risk profiles can be generated for all cables in the network, resulting in a valuable map for the district network operator as to where to focus their efforts.

Characterizing the Reserve Provision Capability Area of Active Distribution Networks: A Linear Robust Optimization Method

Distributed energy resources (DERs) installed in active distribution networks (ADNs) can be exploited to provide both active and reactive power reserves to the upper-layer grid (i.e., sub-transmission and transmission systems) at their connection point. This paper introduces a method to determine the capability area of an ADN for the provision of both active and reactive power reserves while considering the forecast errors of loads and stochastic generation, as well as the operational constraints of the grid and DERs. The method leverages a linearized load flow model and introduces a set of linear scenario-based robust optimization problems to estimate the reserve provision capability (RPC) area of the ADN. It is proved that, under certain assumptions, the RPC area is convex. The performance of the proposed method is tested on a modified version of the IEEE 33-bus distribution test system.

Evaluation of the effect of high penetration of renewable energy sources (RES) on system frequency regulation using stochastic risk assessment technique (an approach based on improved cumulant)

Abstract The great proliferation of renewable energy generation worldwide has brought about severe challenges to system planning and operation, i.e. the increase of operating risks. Due to the volatility and uncertainty of wind/or photovoltaic (PV) power, a switch to probabilistic methods which could handle uncertain variables has been advocated. In this paper, Authors propose a stochastic risk assessment approach to give a comprehensive evaluation of system security considering frequency regulation under high penetration of wind/PV generation. Authors present a new way of evaluating the security for RES-integrated power systems with the consideration of primary frequency regulation. The assessment relies on an improved cumulant-based PLF method using the multi-linearized model. For fast identification of operating limit violations, authors develop a cumulant-based procedure to get the overall power flow information. In addition, multi-linear processing is employed to reduce the truncated error caused by linearized load flow model for accuracy enhancement. The proposed risk model fully considers the likelihood and consequences of limit violation events by quantifying associated risk indices. Authors demonstrate the salient feature of the proposed method on a modified IEEE 57-bus system and its prospect for on-line application.

Static planning of the expansion of electrical energy transmission systems using particle swarm optimization

Static planning of the expansion of electrical energy transmission systems consists of determining, among a pre-defined set of candidate expansion circuits, which ones must be built to minimize the operational costs (deficit) and investment in the electrical system, supplying the predicted demand for a planning horizon. Considering this problem, the proposed methodology uses a Constructive Heuristic Algorithm (CHA) to identify the most relevant route from a set of candidate expansion routes to reduce the search space and, consequently, increase the efficiency of the bio-inspired particle swarm search process. Therefore, the proposed methodology is divided into two stages: (i) obtaining the reduced set of candidate expansion routes using the CHA to decrease the search space without losing relevant expansion paths; (ii) using particle swarm optimization and heuristic information from the first stage to find the minimum expansion cost of the transmission system. In both stages, the transmission system is represented by the linearized load flow model, where the expansion decisions are incorporated into the problem using the original equations of the DC model. The proposed methodology was applied to the Garver system and to two real equivalent systems for the South and Southeast of Brazil, where the efficiency of the proposed system can be verified.

Distribution system reconfiguration to reduce resistive losses

Abstract This paper presents an efficient algorithm to solve the reconfiguration problem by a switching operation to reduce the power loss of distribution systems. By utilizing the proposed heuristic rules and performance index PI which represent the loss reduction capability of the switching operation, a better network configuration is obtained. the PI ranking algorithm based on the linearized load flow model is applied to evaluate the PI reduction for each feasible switching operation and the PI ranking algorithm is then used to find the switching operation to be executed to reach the minimum system loss. A two-stage searching approach to the switching operation is proposed in this paper. The evaluation function of each tie switch is estimated and a depth-first search is used to find all possible switching operations. A performance index is then used to evaluate the loss-reduction capability of each feasible switching candidate. Two practical distribution systems of Taiwan Power Company (Taipower) have been selected for computer simulation to demonstrate the effectiveness of the proposed method.

Linear power system equations and security assessment

A linear model of the load flow equations is developed. From this linear model a load flow linear solution is obtained and a linear method for load flow calculation is also deduced. The performance of the new load flow linear model is tested on standard test power systems. A linear method for power system security assessment is also obtained from the linear load flow model. Its performance is tested on a standard test power system.

Mathematical formulation of the economic dispatch problem of a power system by using a linear load flow model

In this paper, the economic dispatch problem of a power system is formulated mathematically by using a linear load flow model. The generation cost is considered as a quadratic function of the generated active power of the generating nodes of the power system. Thus, the optimum allocation of active power generation, among the generating nodes, can be calculated for minimum generation cost.

Optimum HVAC-transmission expansion planning

A new, flexible, mixed-integer formulation is presented for solving the single-stage AC-transmission expansion planning problem. This new formulation handles the discrete nature of equipment additions without resorting to linearized incremental approaches, but still uses integer linear programming. Even the interconnection of an initially disjoint system is handled directly without resorting to an arbitrary initially connected system. The optimal configuration at the end of the planning step under consideration minimizes an annually amortized cost function including the investment cost for equipment additions and the operating cost in terms of real-power transmission losses. Using a new, efficient, linear load-flow model, the formulation developed here is characterized by a complete decoupling between real and reactive equations. Examples have been incorporated to illustrate the potentials of this new optimum planning formulation. A major contribution of this paper is in showing how the power system transmission expansion planning problem can fit into the standard, mixed-integer, linear programming format in both a conventional sensitivity formulation and also with our new implicit enumeration formulation.

Optimum Hvac-Transmission Expansion Planning - A New Formulation

A new flexible mixed-integer formulation is presented in this paper for solving the single-stage ac-transmission expansion planning problem. This new formulation handles exactly the discrete nature of equipment additions without resorting to linearized incremental approaches, but still uses integer linear programming. The interconnection of a disconnected system is handled directly without resorting to an initial connected system. The optimal configuration at the end of the planning step under consideration minimizes an annually amortized cost function including the investment cost for equipment additions and the operating cost in terms of real-power transmission losses. Using a new efficient linear load-flow model, this new formulation is characterized by a complete decoupling between real and reactive equations. Examples have been incorporated to illustrate the potentials of this new optimum planning formulation.

A stochastic model in simultaneous interchange capacity calculations

Recently, a new algorithm for calculating simultaneous power interchange capacity for a power system has appeared in the literature [1]: the method exploits a linearized load flow model appealing to linear programming to maximize the simultaneous power interchange. Realistic constraints in such a calculation must include limitations on available generation via interchanges. The latter is non-deterministic, and it is desirable to use a stochastic model in representing generation margin constraints for interchange studies. In this paper, the linearized load flow model is written in compact matrix notation and generation constraints are considered to be multivariate normal. Under these conditions, the simultaneous interchange capacity becomes a random variable. The statistics of the simultaneous interchange capacity are obtained using information from the Simplex tableau used in the linear programming solution. In a wide variety of cases, virtually no additional calculation is required over the deterministic model in order to obtain these statistics.