Newton-Raphson Power Flow Algorithm Research Articles

Use of Inverter-Based Air Conditioners to Provide Voltage Regulation Services in Unbalanced Distribution Networks

The large-scale integration of photovoltaic generation and electric vehicles results in over-voltage, under-voltage, and voltage unbalance problems in three-phase distribution networks. The power consumption of the air conditioners (ACs) is large among the daily electrical appliances and can be regulated to provide voltage regulation services. To protect occupants' privacy and utilize the existing dispatch strategy of the battery, we propose a thermal battery equivalent model of the inverter-based AC to regulate the active power and provide a voltage regulation service. Moreover, an improved Newton-Raphson power-flow algorithm is developed to reduce the computational burden. The affinity propagation method is applied to cluster ACs according to different operating states. Thus, the ACs' operating frequencies are adjusted to reset the corresponding operating power. The feasibility of the thermal battery equivalent model and voltage regulation algorithm is verified based on case studies utilizing the revised IEEE 33-node three-phase power distribution network.

Part 1: 조류해석에 있어서 무효전력 제어 모선의 동작 알고리즘에 관한 연구

Recently, distributed energy resources (DERs), including not only an active load that controls active power and reactive power but also power electronics-based inverters capable of supplying reactive power, have been introduced into the power generation, transmission, and distribution grids. For example, properly controlled reactive power can reduce voltage variations and losses. Therefore, the objective of this study is to present an algorithm to control reactive power in power-flow studies. For this purpose, this study introduces the Newton-Raphson power-flow analysis algorithm, which is able to examine the effect of reactive power control and management on voltage variations, and combines the proposed algorithm into the Newton-Raphson power-flow algorithm. This study also verifies the proposed algorithm in various test systems, including IEEE 30-bus test system. As a case study, the proposed algorithm can be used for the power-flow analysis studies of reactive power control and management.

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.

Analysis of Line Outage Detection in Nigeria 330kV Transmission Lines using Phasor Measurement Units

In this work, an analysis of line outage detection in Nigeria 330kV transmission lines using Phasor Measurement Units was presented. This requires collection and analysis of the data obtained from Transmission Company of Nigeria with the aid of PSAT 2.10.1 / MATLAB SIMULINK using Newton-Raphson power flow algorithm and also to determine the effectiveness of PMU when introduced in our power system network. 12 buses and 3 Generators system were considered for the studied. This was achieved by collecting relevant transmission parameters for 330kV line and was simulated on PSAT 2.10.1 and MATLAB 2015a using Newton-Raphson power flow algorithm. The work involved an offline and online analysis. For the offline analysis the admittance / impedance matrix for Y-bus and bus voltage for pre-outage was obtained via the power flow analysis and change in impedance for the lines were calculated. These values were further normalised in order to reduce the value to a row echelon form. Then for the online analysis; the change in phase angle from the Phasor Measurement Unit (PMU) online simulation for pre-outage and also post-outage was calculated and a normalised column matrix was gotten. Finally, the effectiveness of the line outage detection was graphically represented using MATLAB software to plot the values of the normalised values of the offline and online analysis; i.e., by comparing the normalised form of the offline and online values. These results clearly show that PMUs gives an accurate monitoring and total observability when introduced in Nigeria power system.

Robust complex-valued Levenberg-Marquardt algorithm as applied to power flow analysis

This paper deals with a robust complex-valued Levenberg-Marquardt algorithm specially developed for solving ill-conditioned power flow problems. Moreover, it can also be a useful tool for voltage instability and voltage collapse studies. Because power flow models are nonlinear, the Wirtinger calculus is applied to develop iterative algorithms based on Taylor series expansions of nonlinear functions of complex variables and their complex conjugates. Our proposal in complex plane is straightforward derived in rectangular coordinates. Consequently, its performance is compared to the well-known optimized multiplier based load flow method. Aiming this purpose, we show that few changes in the codes are required to transform the complex-valued Newton-Raphson power flow algorithm into the complex-valued Levenberg-Marquardt power flow one. Furthermore, we show that the latter lends itself well to modeling new smart grid technologies while exhibiting a bi-quadratic convergence rate and superior performance as compared to the former procedure. The performance of our proposal is demonstrated and analyzed on well-conditioned IEEE-14, −30, −57 and −118 bus systems and the Brazilian Southern-equivalent system termed SIN-1916 bus. Furthermore, its performance is also demonstrated on the ill-conditioned IEEE-11, −43 bus systems besides the SIN-1916 under stressed operating conditions or higher R/X ratios of transmission lines.

Steady State Control Enhancement and Power Flow Analysis of Longitudinal Power Systems Incorporating Interline Power Flow Controller

Transmission lines operating in steady state are prone to several challenges such as; poor steady-state power flow control, active and reactive power loss and voltage limit violations. These challenges can be solved either by the use of Flexible Alternating Current Transmission System (FACTS) controllers such as Interline Power Flow Controller (IPFC) and Generalized Unified Power Flow Controller (GUPFC) or other non-economical means such as building additional generation and transmission facilities. Previous works have incorporated IPFC to solve the challenges in meshed transmission system but has not been applied to solve the inherent challenges of the longitudinal Nigerian transmission system operating in steady state. This work performs power flow analysis with the incorporation of IPFC into the Nigerian 330-kV, 28-bus transmission system to solve its steady state challenges. Steady state power system component model produces a set of algebraic equations while the steady state IPFC model in rectangular form produces another set of algebraic equations for power flow analysis. The sets of equations were solved simultaneously using Newton-Raphson numerical iteration method, due to its fast quadratic convergence and high efficiency. Newton-Raphson power flow algorithm was implemented using MATLAB 8.1.0.604 (version R2013b) and the analysis was performed without and with the incorporation of IPFC data into the Institute of Electrical and Electronic Engineers (IEEE) 14-bus and the Transmission Company of Nigeria (TCN) 330-kV, 28-bus system. The performance evaluation of IPFC was investigated using active and reactive power as performance variables. The incorporation of IPFC rectangular model into the Nigerian 330-kV, 28-Bus TCN and IEEE 14-bus system demonstrated the capability of IPFC to control active and reactive power flow. IPFC typifies effective enhancement and the maximum use of Nigerian 330-kV, 28-Bus TCN and IEEE 14-bus transmission infrastructure for better delivery of electrical power to the end users.

Neuro-Fuzzy Based Interline Power Flow Controller for Real Time Power Flow Control in Multiline Power System

This article investigates the power quality enhancement in power system using one of the most famous series converter based FACTS controller like IPFC (Interline Power Flow Controller) in Power Injection Model (PIM). The parameters of PIM are derived with help of the Newton-Raphson power flow algorithm. In general, a sample test power system without FACTs devices has generated more reactive power, decreased real power, more harmonics, small power factor and poor dynamic performance under line and load variations. In order to improve the real power, compensating the reactive power, proficient power factor and excellent load voltage regulation in the sample test power system, an IPFC is designed. The D-Q technique is utilized here to derive the reference current of the converter and its D.C link capacitor voltage is regulated. Also, the reference voltage of the inverter is arrived by park transformation technique and its load voltage is controlled. Here, a sample 230 KV test power system is taken for study. Further as the conventional PI controllers are designed at one nominal operating point they are not competent to respond satisfactorily in dynamic operating conditions. This can be circumvented by a Fuzzy and Neural network based IPFC and its detailed Simulink model is developed using MATLAB and the overall performance analysis is carried out under different operating state of affairs.

Three Phase Power Flow Incorporating Static Var Compensator

Application of Flexible AC Transmission Systems (FACTS) devices in a power system is a promising and more efficient way for the transfer and control of bulk amount of power. One of the problems encountered in power-systems operation is the generation of unbalanced voltages and currents in the presence of long transmission lines with few or no transpositions. This includes possible unbalances arising in source and load conditions, or indeed any items of plant such as shunt and series reactors. To improve or investigate these unbalance effects in any detail, a 3-phase load-flow solution that allows representation of all possible unbalances as they exist in the power-systems network without making any assumptions is essential. This paper deals with the three phase power flow incorporating Static Var Compensator (SVC). Here SVC is modeled using variable reactance modeling technique and incorporated into the single phase and three phase load flow. Newton Raphson power flow algorithm is adopted here. The performance of SVC to control the power flow and regulating voltage in the network is discussed. The performance analysis is carried out for 4 case studies namely single phase power flow, single phase power flow with SVC, three phase power flow and three phase power flow with SVC. The change in power flow and losses due to the unbalanced load condition in the three phases in illustrated. The studies are carried out in a standard 5 bus test system. Keywords: Three Phase Power flow, Static Var Compensator, Unbalanced system, Negative sequence components, Zero sequence components.

Genetic Algorithm Based Optimal Placement of T csc and Upfc in the Nigeria 330KV Integrated Transmission Line Network at Different Reactive Power Loadings

The Nigeria 330KV integrated power network consisting of 52 buses, 64 transmission lines and sixteen generating stations was studied. The network was subjected to different reactive power loadings ranging from 25%, 50%, 75%, 100%, 125% and 150% respectively with and without UPFC and TCSC FACTS devices using Newton-Raphson power flow algorithm and Genetic Algorithm (GA) for optimally locating these devices on the network. The heavily loaded active power lines were identified. The heavily loaded active power lines are thirteen (13). These include: Katampe- Shiroro, Akangba-Ikejawest, Aiyede-Oshogbo, Alaoji-Onitsha, Egbin-ikejawest, Jebba-Oshogbo, Jebba-Shiroro, Jos- Makurdi, Kaduna-Shiroro, Kaduna-Kano, Ajaokuta-Benin, Benin-Ikejawest, and Benin-Onitsha. The ten(10) heavily loaded reactive power lines include: B-Kebbi-Kainji, Benin-Oshogbo, Benin-Egbin, Benin-Sapele, Damaturu-Gombe, Damaturu-Maiduguri, Gombe-Yola, Jalingo-Yola, Ikeja West-Oshogbo and Jos-New Haven. Weak buses were New- Haven(0.9201pu),Damaturu (0.9283pu), Gombe (0.9405pu), Maiduguri(0.9425pu), Makurdi (0.9260pu), Jalingo (0.9354pu),Erunkan(0.9314pu) and Jos (0.9461pu).Ten(10) heavily loaded reactive power lines include:B-Kebbi-Kainji, Benin-Oshogbo, Benin-Egbin, Benin-Sapele, Damaturu-Gombe, Damaturu-Maiduguri, Gombe-Yola, Jalingo-Yola, Ikeja West-Oshogbo and Jos-New Haven. Using GA for optimal location of these devices, eight (8) of the thirteen (13) lines were installed with UPFC. These are Akangba-Ikejawest, Alaoji-Onitsha, Jebba-Oshogbo, Jos-Makurdi, Kaduna-Kano, Ajaokuta-Benin, Benin-Ikeja west, and Benin-Onitsha . Also of the eight (8) weak buses six (6) had UPFC and the improved bus voltage values are Damaturu (0.9983pu), Gombe (0.9751 pu), Maiduguri (0.9815 pu), Makurdi (0.9804 pu), Jalingo (0.9541 pu) and Jos (0.9646 pu). Six (6) TCSC devices were incorporated on the ten (10) heavily loaded lines, which include Ikeja West-Oshogbo, Damaturu-Maiduguri, Gombe-Yola, Jos-New Haven, Benin-Oshogbo and B- Kebbi-Kainji. Comparison was made between the power losses with and without FACTS devices at the various percentage loadings. Real and active power losses.

Improved Power Flow Initialization of Dynamic Studies with Non-linear Composite Load Model

A power flow solution using a static constant MVA load model is a straightforward approach to initialize power system dynamic simulations. Using this model to represent induction motor load, however, may not be suitable due to a natural mismatch between initial bus scheduled powers and actual input powers that are computed afterward using their converged bus voltages. To avoid this mismatch occurrence, the Newton–Raphson power flow algorithm has been newly extended to incorporate non-linear characteristics of a composite load model in order to get an exact operating point of each individual induction motor and static load. The power flow solution of the applied 13-bus industrial power system reveals that the extended algorithm is capable of giving an exact active and reactive power input of the motors in correlation with their converged slips, internal bus voltages, and mechanical load torque characteristics and of voltage-dependent loads in relation to their exponent indices. Moreover, the computational efficiencies of the algorithm have been investigated using IEEE 14-bus and 57-bus networks. The results show that embedding induction motor and static exponent load models directly into the power flow mismatch function and Jacobian can improve computational efficiency since the power flow solution is well converged in a satisfactory quadratic manner.

INFLUENCE OF TCSC FACTS DEVICE ON STEADY STATE VOLTAGE STABILITY

The influence of series Flexible AC Transmission Systems (FACTS) device namely, Thyristor-Controlled Series Capacitors (TCSC) on the steady state voltage stability is the main objective of this paper. The Line stability Index LSI under excepted lines outage contingencies is used to identify the critical line which is considered as the best location for TCSC. A modal analysis is used to define the weakest bus of the studied system. The FACTS device is implemented and included into the Newton-Raphson power flow algorithm, and the control function is formulated to achieve the voltage stability enhancement goal. The analysis is preformed on standard IEEE 30 bus system. The proposed scheme are tested under different loading conditions and different nonlinear voltage dependent loads. The simulation results demonstrate the feasibility and effectiveness of the device and the proposed algorithm.

Development of a new power injection model with embedded multi-control functions for static synchronous series compensator

A novel power injection model with multi-control functions of the static synchronous series compensator (SSSC) is presented. In this model, no simplification is performed and the complex impedance of the series coupling transformer and the charging susceptance as well as the complex impedance of the line are all taken into consideration. The proposed model is developed while the original admittance and the Jacobian matrix are kept unchanged. The new Jacobian corresponding to the SSSC device is integrated with the original Jacobian. Furthermore, the proposed model is general since it takes into account any possible bus type at the end of the line where SSSC is installed. In addition, two new control modes of SSSC namely the active and the reactive power losses control are proposed. The model is validated on IEEE 6-bus, IEEE 30-bus and realistic Algerian 114-bus. The simulation results demonstrate the effectiveness of the proposed SSSC model with the newly proposed control functions. It is also observed that the proposed Newton–Raphson power flow algorithm applied to a large and realistic power system is computationally inexpensive and the proposed model has satisfactory performance for steady state analysis and optimisation of the power system with SSSC device.

Newton-Raphson Power-Flow Analysis Including Induction Motor Loads

This paper presents an extended method of Newton-Raphson power flow algorithm to incorporate nonlinear model of induction motor loads. The proposed method is used for finding correct power system operating conditions, which can be employed for solving the problem of initializing the dynamic models of induction motor for stability studies. The power flow solution with a group of induction motor loads is demonstrated through 14buses industrial power system. Moreover, the computational efficiency of the extended algorithm has been investigated using IEEE-30buses network. The results show that this algorithm gives an exact solution of motor’s active and reactive powers that are related with converged slips, terminal voltages, and mechanical torque profiles. Furthermore, the extended algorithm shows a good convergent characteristic in quadratic manner.

Power flow initialisation of dynamic studies with induction motor loads

The initialisation of most power system stability studies is carried out with the outcome of a power flow solution using a constant power representation of the load that may contain voltage dependency. However, such an approach may not be suitable when an important component of the system load is made up of induction motors because of a natural mismatch between the power flow scheduled power and the actual induction motor power, which is computed using the final converged value of the motor terminal bus voltage. To solve this problem, a method for incorporating the non-linear model of induction motors in Newton–Raphson power flow algorithm is put forward in this study. The prowess of the improved power flow algorithm is demonstrated using the Ward–Hale, the IEEE 30-bus and the New-England test systems in connection with industrial motor subsystems. The results show that the extended power flow algorithm provides the correct steady-state initialisation and still preserves the basic Newton–Raphson's quadratic convergence characteristics.

Comparison of Practical Unit Commitment Problem Solutions

In this article, a comparative study has been done for the unit commitment problem (UCP) with operational, power flow, and environmental constraints along with contingencies to plan a secure and economical hourly generation schedule based on the solutions obtained. The UCP solutions obtained without considering power-flow constraints are not practical due to secure operation of the power network. The UCP with power-flow constraints obtains the minimum system-operating cost, satisfying both unit and network constraints using hybrid Lagrangian multiplier and Newton–Raphson power-flow algorithms. Considering various environmental aspects, there is a need to include environment constraints to get a realistic unit commitment (UC) schedule. The UC solution for the environmentally constrained problem has been formulated as a multi-objective problem by considering both economic load dispatch and economic emission dispatch simultaneously. The combined economic emission dispatch bi-objective problem is converted to a single objective function by adding a modified price penalty factor. The UC schedule must withstand, even if there are any contingencies that have occurred in any line of the network, which can be incorporated by performing contingency analysis by removing one line from the system and performing optimal power flow (OPF) until all of the lines are removed once for each possible state. The state that converges for OPF for every line removal is selected, and OPF is performed again without any contingencies. In this article, the UC solutions obtained with operational, power flow, and environmental constraints, along with contingencies in the network, are compared for the IEEE 30-bus and the Indian utility practical systems scheduled for 24 hr. The algorithm and simulation are carried through a Matlab environment, and the results obtained are quite encouraging.

C0MPREHENSIVE NEWTON-RAPHSON MODEL FOR INCORPORATING UNIFIED POWER FLOW CONTROLLER IN LOAD FLOW STUDIES

Flexible AC Transmission Systems FACTS include unified power flow controllers (UPFC). Incorporation of a UPFC by a comprehensive Newton-Raphson power flow model into an existing MATLAB NewtonRaphson power flow algorithm is the subject of this paper. Unlike existing UPFC models available in open literature, this UPFC power flow model is modified to set control of active and reactive powers and voltage magnitude in any combination or to not control all of them. A set of analytical equations has been derived to provide better UPFC initial conditions. Their solution algorithm exhibits quadratic or near quadratic convergence characteristics. Based on this model, it is possible to estimate the UPFC control variables and the UPFC converters ratings. Also the effects of the UPFC coupling transformers impedances on the UPFC control variables and converters ratings are clarified and highlighted.

Power flow control and solutions with multiple and multi-type FACTS devices

In this paper, a new generalized current injection model of the modified power system using Newton–Raphson power flow algorithm has been proposed for desired power transfer with Flexible AC Transmission Systems (FACTS) devices. So that the FACTS devices can be incorporated in the proposed algorithm and, therefore, whole system with these devices can be easily converted to power injection models without change of original admittance and the Jacobian matrices. Power flow algorithm has been modeled in such a way that it can easily be extended to multiple and multi-type FACTS devices by adding a new Jacobian corresponding to that new device only. Power flow algorithm with the presence of Thyristor Controlled Series Compensators (TCSC), Unified Power Flow Controller (UPFC), and Generalized Unified Power Flow Controller (GUPFC) has been formulated and solved. To demonstrate the performance of the proposed algorithm for multiple and multi-type FACTS devices, different case studies of IEEE 30-bus system has been considered and the results are tabulated. The proposed algorithm is independent of the size of the system and initial starting conditions of the FACTS devices.

Inclusion of a high voltage DC-voltage source converter model in a Newton–Raphson power flow algorithm

Models for high voltage DC-voltage source converter (HVDC-VSC) controllers suitable for direct incorporation into Newton-Raphson power flow algorithms are presented. The models are developed from first principles, starting with a simple VSC model and progressing to encompass the full HVDC-VSC link model. The applied modelling approach is modular in nature and in addition to the shunt-connected voltage source model, which may be used to represent a STATCOM, a series-connected voltage source model is also developed. This enables significant modelling flexibility since by suitably combining shunt and/or series voltage sources several VSC-based flexible AC transmission system (FACTS) controller models are realised quite straightforwardly, namely the back-to-back HVDC-VSC, the full HVDC-VSC link and the unified power flow controller. Attention is focused on the HVDC-VSC models. The models are implemented into an existing OOP power flow computer program written in C++ that incorporates a wide portfolio of FACTS models. The models are tested for reliability towards the convergence and accuracy of results using several power systems with varying degrees of operational complexity and power flow control requirements.

Combining local and optimised power flow remedial measures in bulk reliability assessment

In traditional Newton-Raphson power flow algorithms, the terminal and remote bus voltages are obtained using a local control logic, i.e. reactive power and LTC taps are adjusted to meet pre-specified voltage settings. On the other hand, most of the optimal power flows (OPF) utilised in available reliability programs adopt an optimised logic for voltage control, i.e. the voltage level is optimised inside the pre-specified bounds, meaning that new settings can be calculated in order to avoid or minimise load shedding. However, in several practical situations this is not a feasible approach, due to operational constraints. Local voltage control logic is introduced into the non-linear interior point (IP) optimal power flow of a bulk power system reliability evaluation program in order to represent actual operational practices with increased accuracy. The impact of these two voltage control logics on the reliability indices is then analysed using the new IEEE Reliability Test System (RTS-96) and a 89-bus network derived from the North/Northeastern Brazilian System (NNBS).

Discussion of "A comprehensive Newton-Raphson UPFC model for the quadratic power flow solution of practical power networks"

The authors discuss the paper A comprehensive Newton-Raphson UPFC model for the quadratic power flow solution of practical power networks (see ibid., vol.15, no.1, p.102-9, 2000), arguing that the concept of determining the settings for the state variables of an UPFC by incorporation of a UPFC model into the Newton-Raphson power flow algorithm provides a welcome contribution to the application of FACTS devices in electric power systems. The original authors' responses to the discussion are also included.