Current Injection Equations Research Articles

Alternative Current Injection Newton and Fast Decoupled Power Flow

This article presents an alternative Newton-Raphson power flow method version. This method has been developed based on current injection equations formulated in polar coordinates. Likewise, the fast decoupled power flow, elaborated using current injection (BX version), is presented. These methods are tested considering electrical power systems composed of 57-, 118-, and 300-bus, as well as a realistic system of 787-bus. For the robustness analysis, simulations were performed considering different loading conditions and R/X ratios of the transmission line. Based on the simulations that were realized, there is evidence that the performance of the proposed current injection methods is similar to the power injection methods.

Optimal Power Quality Compensation of Energy Storage System in Distribution Networks Based on Unified Multi-Phase OPF Model

Energy Storage System (ESS) is a promising solution to suppress the peak-valley difference of residential distribution networks (RDN) with high penetration of distributed photovoltaic generations. Meanwhile, it can also provide certain power quality compensations to RDN due to the flexible adjusting ability of its converter interface. To make full use of this feature, this paper investigates the optimal power quality compensation of the ESS. This is achieved by formulating and solving an optimal power flow (OPF) problem, the objectives of which are to minimize the power loss, harmonic distortion, and voltage unbalance of the network. Noticeably, the established model includes the neutral line and inter-phase loads; thus, it is unified and can be easily extended to networks with different structures. However, the coupling between different phases and the inclusion of harmonic variables significantly increase the complexity of the OPF problem. To address this issue, the optimization model is further transformed into a convex quadratic constrained quadratic program (QCQP) by replacing power flow equations with current injection equations. As a result, the problem can be solved by the primal-dual interior-point method (PDIPM) with guaranteed convergence and computational efficiency. An iterative solution method is further proposed to improve the accuracy of the solution. Finally, the proposed method is verified using a three-phase three-wire 25-node distribution network and a three-phase four-wire 162-node distribution network in North America.

A Linear AC Power Flow Model for Unbalanced Multi-Phase Distribution Networks Based on Current Injection Equations

A realistic and practicable modeling of unbalanced distribution networks (DNs) is the missing link in most studies undertaken in these networks, e.g., optimal power flow (OPF), energy markets, etc. To address the issue, this letter proposes an unbalanced linear three-phase four-wire power flow (PF) model based on current injection equations at nodes. Also, the ZIP representation is considered for loads. The model can be easily generalized for unbalanced three-wire networks with minor changes and assumptions. Hence, the scope of the proposed method can be extended to cover both low-voltage and medium-voltage DNs. The performance of the proposed model is verified through simulations on two IEEE test feeders.

Improving security and economy of interconnected power network through explicit feasible region of tie-line power transfer

With the increasing power demand and renewables, the efficient utilization of power resources in each regional network relies on the tie-line power exchanges in interconnected power networks. Consequently, an accurate characterization of the feasible region of tie-line power transfer is crucial for scheduling tie-line power to achieve a secure and efficient utilization of power resources. This paper proposes a characterization method to explicitly capture a feasible region of tie-line power transfer considering steady-state constraints with reactive power and voltage limits and transient constraints. The steady-state and transient constraints are explicitly derived: 1) a power transfer distribution factor matrix with reactive power and voltage magnitude is derived to equivalently reflect the steady-state operational region with fewer variables and constraints; 2) the transient constraints of the tie-line power are derived based on the swing and current injection equations and a constraint transcription technology is adopted to convert transient constraints from continuous-time domain to a vector space, which makes it possible to identify the feasible region of tie-line power transfer. The steady-state and transient constraints are explicitly projected to the tie-line power space via a vertex search method. Finally, this paper utilizes the feasible region of tie-line power transfer to perform the tie-line scheduling via the proposed linear programming model. The proposed tie-line scheduling model can promote the optimal utilization of generation dispatches, which guarantees security and improve economics in the interconnected power network. The numerical results based on the IEEE 9-bus and IEEE 118-bus test systems verify the effectiveness of the proposed methods.

A new unbalanced three-phase governor power flow formulation based on the current injections method

This paper presents a new unbalanced three-phase governor power flow formulation using the three-phase current injection equations (TCIM) expressed as a function of voltages expressed in rectangular coordinates. The proposed technique considers the representation of the primary frequency regulation for synchronous generators, as well as, voltage and frequency regulation in a droop-based control for distributed generation units (DGs). The static response of the generation governor, droop control equations and an equation to define the network reference angle for a given value are incorporated into the modeling. As the system is unbalanced, an internal additional bus, having balanced voltages, was created for each synchronous generator. As a consequence, two additional equations were included to keep internal voltages balanced. The inclusion of new equations results in an augmented formulation which is then linearized and solved using the Newton–Raphson method, in which the original structure of the Jacobian matrix from the current injections method is preserved. The proposed formulation allows the distribution of the active losses among the generating units as well as the determination of the frequency deviation due to variations, either in the total amount of generation or in the total system load. Any bus (load or generation bus) of the system can be chosen as the system reference bus. The results obtained using the unbalanced three-phase 6-bus test system were validated using the well known RTDS (real time digital simulator). The 25-bus islanded test system was also used in the simulations with the inclusion of synchronous generation (SG) units to demonstrate the effectiveness of the proposed methodology.

A New Current Injection Based Power Flow Formulation

This paper presents a novel current injection-based Newton-Raphson power flow algorithm with new PV bus representation for improving the convergence characteristics. In this proposed algorithm, rectangular coordinates are used to represent all non-linear current injection equations. Test results are produced to discuss the reasons behind the non-convergence of different PV bus representation schemes, also their performance comparison was done on the unbalanced 3-phase radial (18-Bus, 28-Bus, 84- Bus and 140-Bus) and meshed (6-Bus, 14-Bus, 24-Bus, 30-Bus, 57-Bus, 118-Bus and 300-bus, and 1354-Bus) test systems. Experimental results show that the proposed power flow method provides better convergence property for distribution system with a large number of PV buses. Also, the modification leads to a smaller Jacobian matrix and therefore reduces computational time.

New Developments in the Interval Current Injection Power Flow Formulation

Power flow analysis uses a given set of generation and loads to determine steady state operating conditions of electric power systems. As the input data are imprecise, this paper employs the affine arithmetic to incorporate the effect of load data uncertainties on this analysis. The power flow model is expressed in terms of current injection equations, with the bus voltages represented in rectangular coordinates. Therefore, this paper addresses new developments in the interval current injection power flow. At each iteration, the resulting interval nonlinear system of equations is solved using Krawczyk method. The proposed developments are implemented in the Matlab environment using the Intlab toolbox. The IEEE 57-bus is used as test system. Results are later compared with the Monte Carlo Simulation and interval arithmetic.

New representation of PV buses in the current injection Newton power flow

This paper presents a comparative analysis of the influence of PV bus representation on the convergence characteristics of the Newton-Raphson Current Injection method. The methods used for solving the power flow problem are based on current injection equations written in polar coordinates. Several tests are presented to clarify the reasons of non-convergence and to provide a broad and fair comparison and evaluation of the performance of the PV bus representation schemes. Performance analyzes were conducted for 57-, 118- and 300-bus IEEE test systems and for two realistic Brazilian systems of 638 and 787 buses, corresponding to parts of the South-Southeast Brazilian system. Several R/X transmission line ratios and loading conditions were considered. The simulation results show that the proposed PV bus representation improves the convergence characteristics of the method.

Three-Phase Power Flow Based on Four-Conductor Current Injection Method for Unbalanced Distribution Networks

This work presents a new formulation for the power flow problem, with explicit representation of the neutral conductor and grounding. This methodology has been named the four-conductor current injection method (FCIM). The Newton-Raphson method is applied to solve the set of nonlinear current injection equations that are derived using phase coordinates, and the complex variables are written in rectangular form. The proposed algorithm can be used to analyze both balanced and unbalanced systems, meshed or radial, with controls and distributed generation, and is shown to be very efficient and robust for large scale systems.

05/02529 A second order power flow based on current injection equations

05/02529 A second order power flow based on current injection equations

A second order power flow based on current injection equations

This paper presents a new second order power flow methodology by using current injection equations expressed in voltage rectangular coordinates instead of using traditional rectangular power flow equations. The results presented show that the proposed method leads to a substantially faster second order power flow solution, when compared to the conventional method expressed in terms of power mismatches and written in rectangular coordinates. In order to evaluate the performance of the proposed methodology, different heavily loaded and overloaded systems, as well as ill-conditioned distribution systems have been tested. These results show the feasibility of employing this new methodology as an additional tool for power flow studies.

Novos desenvolvimentos numa formulação de injeção de corrente para solução do fluxo de potência

Este artigo apresenta uma metodologia genérica de representação de dispositivos de controle no problema de fluxo de potência, utilizando-se uma formulação Newton Raphson esparsa expressa em termos de equações de injeção de corrente em coordenadas retangulares. Tal formulação possui a mesma trajetória de convergência da formulação convencional em coordenadas polares. Os resultados obtidos validam a metodologia proposta.

An augmented Newton–Raphson power flow formulation based on current injections

This paper presents a new procedure for the solution of power flow problem, by using the current injection equations written in rectangular coordinates. From this formulation, it is possible to obtain the same convergence characteristics of the conventional power flow expressed in terms of power mismatches and written in polar coordinates. By using this methodology, a highly sparse augmented formulation suited to the incorporation of FACTS devices and control of any kind is also obtained. The results presented validate the proposed method.

Three-phase power flow calculations using the current injection method

This paper presents a new sparse formulation for the solution of unbalanced three-phase power systems using the Newton-Raphson method. The three-phase current injection equations are written in rectangular coordinates resulting in an order 6n system of equations. The Jacobian matrix is composed of 6/spl times/6 block matrices and retains the same structure as the nodal admittance matrix. Practical distribution systems were used to test the method and to compare its robustness with that of the backward/forward sweep method.

Developments in the Newton Raphson power flow formulation based on current injections

This paper describes a sparse Newton Raphson formulation for the solution of the power flow problem, comprising 2n current injection equations written in rectangular coordinates. The Jacobian matrix has the same structure as the (2n/spl times/2n) nodal admittance matrix, in which each network branch is represented by a (2/spl times/2) block. Except for PV buses, the off-diagonal (2/spl times/2) blocks of the proposed Jacobian equations are equal to those of the nodal admittance matrix. The results presented show that the proposed method leads to a substantially faster power flow solution, when compared to the conventional Newton Raphson formulation, expressed in terms of power mismatches and written in polar coordinates.