Reactive Power Limits Research Articles

Coordinated voltage control for large-scale wind farms with ESS and SVG based on MPC considering wake effect

The wake effect reduces the wind speed at downstream wind turbines (WTs), making it necessary for the central controller to collect wind power generation data from each WT. However, wind farms (WFs) face a more complex problem in maintaining the voltage stability at the WT terminal while following the transmission system operator (TSO) instructions due to the information collection as well as the possible data loss during transmission. Therefore, this study proposes a coordinated control method for WTs and multiple power sources based on model predictive control under wake disturbance conditions, aiming to reduce the average voltage deviation in WT terminals and go close to the rated voltage and ensure effective compliance with TSO commands in large-scale WFs. Accordingly, the Jensen wake model was utilized to accurately calculate the available active and reactive power limits for each WT. Energy storage systems and static Var generators were modeled to coordinate and maintain the voltage in all WT terminals within the feasible range, providing peak shaving and valley filling support to reduce wind energy waste and shortfall, thereby enhancing the economic and operational reliability of WF. Further, the effectiveness of the proposed method was validated in MATLAB/Simulink.

Can we compute the worst voltage case under power flows uncertainty at TSO-DSO interfaces?

This paper proposes the new problem of calculating the worst-voltage-case (WVC) under power flows uncertainty, particularly at interfaces between transmission and distribution grid operators. The goal of the calculation is to verify if the realization of the worst uncertainty scenario leads to abnormal voltages, or assure where the voltage instability is not a risk, and inform the transmission system operator. The problem is formulated as a tailored non-convex, nonlinear optimal power flow (OPF) with complementarity or equilibrium constraints (ECs). The latter model the generator switch between under voltage control and under reactive power limit. The problem is converted into a mathematically equivalent nonlinear programming OPF problem in which ECs are handled as penalty terms in the objective function. The paper has conducted a series of experiments on the 60-bus Nordic system, which have pointed out the challenges associated to such computations to obtain meaningful results and unveiled new insights. The findings and scalability are confirmed using a real-world 1203-bus system.

Static voltage stability considering reactive power limit of salient synchronous generator and active power loss of exciter

With increasing load, it is difficult to maintain power system static voltage stability (SVS). The existing SVS analysis based on the reactive power limit (RPL) of the non-salient synchronous generator (SG) and ignoring the exciter’s loss is inaccurate. This paper proposes an SVS model with exact description to the SG. The novelties are: (1) Seeing that the SVS is deteriorated when the SG reaches the RPL, a solution to the RPL of the salient SG with different reactances along the direct and quadrature axis is newly proposed. (2) The active power loss of the exciter of the SG is newly included in the power flow and the SVS analysis. (3) By deriving the sensitivity of the L index with respect to the load, an index is newly defined to quantify the dependency of the SVS on the RPL. The simulation results show that the RPL of the salient SG considering the stator resistance is narrower. The active power loss of the exciter has more obvious impact on the power flow under heavier loading conditions. When the proposed index is positive, the RPL instead of the L index is more critical to maintain the SVS.

Distributed Voltage Reactive Power Control of Distribution Network Considering the Coordination Between DPV and SVC

With the increasing permeability rate of DPV in the distribution network, the safe and economic operation of the distribution network is faced with many challenges, among which the problem of voltage exceeding the limit must be solved urgently. A method for distributed voltage reactive power control, which involves coordinating DPV and SVC, is suggested to enhance the voltage regulation capacity in high-permeability distribution networks. Firstly, considering the limited reactive power regulation capacity of DPV, a coordinated control strategy is proposed to enable SVC when the reactive power capacity of DPV is insufficient. Secondly, a voltage-reactive power control model for distribution networks is established, with a focus on minimizing node voltage deviations and network losses. An adaptive penalty factor adjustment strategy, based on the alternating direction multiplier method, is introduced to achieve a comprehensive solution for this model. Finally, the enhanced IEEE 33-node system is utilized for verification and analysis. The outcomes demonstrate that the suggested coordination strategy involving DPV and SVC, alongside the distributed optimization control method, offers economic advantages and effectively achieves the safe and cost-effective operation of the distribution network.

The robust curve-fitting based method for coordinated voltage regulation with distributed generator and OLTC in distribution network

The voltage violation in distribution networks may occur frequently due to the rising integration of flexible demands and supplies. In this paper, the reactive power of the inverter-based distributed generator (DG) and OLTC tap position are adjusted for voltage regulation in coordinated manner. Firstly, the reactive power adjustment for the voltage regulation has been carried out by use of the DG reactive power capacity. Afterwards, the tap position of the OLTC has been changed to regulate the bus voltage that has a voltage violation problem in the case of insufficient reactive power capacity of the DG inverter. The value of the distributed generator reactive power output that regulates the voltage on the bus that has a voltage violation is found with proposed curve-fitting method and tested with the Grid Search, Artificial Bee Colony methods. The proposed method derives mathematical expressions between DG reactive power output and bus voltages as quadratic equations by curve-fitting technique. Moreover, addition to inherent upper and lower reactive power limits of the DG inverter, they are determined by the proposed curve-fitting based technique while considering voltage constraints on all buses. Proposed method is much faster than other two methods because of its plain structure and gives adequate accurate results.

Benders‐Decomposition‐Based Voltage‐Stability‐Constrained Unit‐Commitment Taking Reactive Power Limit into Account

To determine economic‐efficient and secure generation schedules, unit commitment (UC) with network and stability constraints will play an important role in the electricity market. We define a voltage‐stability‐constrained unit commitment problem taking reactive power limit into account (VSCUC‐QLIM) since the decreasing of synchronous generators may threat the voltage stability of electricity systems. This VSCUC‐QLIM problem is modeled as a mixed‐integer nonlinear programming with equilibrium constraints, which is too complex to be solved directly. Therefore, we apply Benders decomposition to solve this complex problem: the master problem consists of the UC problem to determine the commitment states for generators, and the subproblem consists of the voltage‐stability‐constrained optimal power flow with complementarity constraints problem. However, the subproblem calculation may not converge depending on the commitment states due to the following reasons: (i) any power‐flow solution cannot be obtained or (ii) the voltage stability requirement cannot be satisfied on the commitment state given by the master problem. To deal with these difficulties, two partial problems of the subproblem are added as a pre‐subproblem and post‐subproblem in the proposed method. The combination of these subproblems generate different types of Benders cut depending on the condition. The proposed method was implemented on MATPOWER, and evaluated for daily scheduling on an IEEE six‐bus test system and IEEJ standard WEST10 system. The evaluation results validated the effectiveness of the proposed method from the perspective of economic efficiency and voltage stability. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A Mathematical Modeling Approach for Power Flow and State Estimation Analysis in Electric Power Systems through AMPL

This paper presents a mathematical modeling approach by which to solve the power flow and state estimation problems in electric power systems through a mathematical programming language (AMPL). The main purpose of this work is to show the advantages of representing these problems through mathematical optimization models in AMPL, which is a modeling language extensively used in a wide range of research applications. The proposed mathematical optimization models allow for dealing with particular issues in that they are not usually considered in the classical approach for power flow and state estimation, such as solving the power flow problem considering reactive power limits in generation buses, as well as the treatment of errors in state estimation analysis. Furthermore, the linearized mathematical optimization models for both problems at hand are also presented and discussed. Several tests were carried out to validate the proposed optimization models, evidencing the applicability of the proposed approach.

Power Loss Minimization and Voltage Profile Improvement by System Reconfiguration, DG Sizing, and Placement

A number of algorithms that aim to reduce power system losses and improve voltage profiles by optimizing distributed generator (DG) location and size have already been proposed, but they are still subject to several limitations. Hence, new algorithms can be developed or existing ones can be improved so that this important issue can be addressed more appropriately and effectively. This study proposes a reconfiguration methodology based on a hybrid optimization algorithm, consisting of a combination of the genetic algorithm (GA) and the improved particle swam optimization (IPSO) algorithm for minimizing active power loss and maintaining the voltage magnitude at about 1 p.u. The buses at which DGs should be injected were identified based on optimal real power loss and reactive power limit. When applying the proposed optimization algorithm for DGs allocation in power system, the search space or number of iterations was reduced, increasing its convergence rate. The proposed reconfiguration methodology was test in an IEEE-30 bus electrical network system with DGs allocations and the simulations were conducted using MATLAB software compared to other optimization algorithms, such as GA, PSO, and IPSO, the combination of GA and IPSO or Hybrid GA & IPSO (HGAIPSO) method has a smaller number of iterations and is more effective in optimization problems. The effectiveness of the proposed HGAIPSO has been tested on IEEE-30 bus network system with DGs allocations, and the obtained test results have been compared to those from other methods (i.e., GA, PSO, and IPSO). The simulation results show that the proposed HGAIPSO can be an efficient and promising optimization algorithm for distribution network reconfiguration problems. The IEEE-30 bus test system with DGs integrated at various location revealed reductions in overall real power loss of 40.7040%, 36.2403%, and 42.9406% for type 1, type 2, and type 3 DGs allocation, respectively. The highest bus voltage profile goes to 1.01 pu in the IEEE-30 bus.

Static Voltage Stability Assessment Using a Random UnderSampling Bagging BP Method

The increase in demand and generator reaching reactive power limits may operate the power system in stressed conditions leading to voltage instability. Thus, the voltage stability assessment is essential for estimating the loadability margin of the power system. The grid operators urgently need a voltage stability assessment (VSA) method with high accuracy, fast response speed, and good scalability. The static VSA problem is defined as a regression problem. Moreover, an artificial neural network is constructed for online assessment of the regression problem. Firstly, the training sample set is obtained through scene simulation, power flow calculation, and local voltage stability index calculation; then, the class imbalance problem of the training samples is solved by the random under-sampling bagging (RUSBagging) method. Then, the mapping relationship between each feature and voltage stability is obtained by an artificial neural network. Finally, taking the modified IEEE39 node system as an example, by setting up four groups of methods for comparison, it is verified that the proposed method has a relatively ideal modeling speed and high accuracy, and can meet the requirements of power system voltage stability assessment.

A Hierarchical Voltage Control Scheme for Wind Power Plants Through Enhanced Reactive Power Support

To maximize reactive power support from a wind power plant (WPP) and maintain power factor at the point of interconnection (POI) within acceptable limits, a novel hierarchical voltage control scheme consisting of a central WPP controller and a local wind turbine generator (WTG) controller is proposed in this article, and both controllers are operated in voltage control mode. When a voltage deviation is detected, if it is within the normal range, the central WPP controller turns on the integrated power factor controller to regulate the power factor at the POI. If the voltage deviation exceeds the normal range, the local WTG controller relies on the adaptive droop coefficient and the adaptive proportional setpoint weight-based rotor side converter controller to push the WTG toward its maximum reactive power limit to provide reactive power compensation during contingencies. For accurate estimation of the maximum reactive power capability of a WTG, a comprehensive model with various limiting factors is used. The proposed controllers are equipped with a memory, which ensures continuous operation during a communication failure. The proposed control scheme is validated by case and sensitivity studies using a practical WPP currently in operation in Newfoundland, Canada. It shows excellent performance when compared with the two existing methods.

Distributed Three-Phase Power Flow for AC/DC Hybrid Networked Microgrids Considering Converter Limiting Constraints

In three-phase AC/DC hybrid networked microgrids (NMGs), the operational limits of AC/DC interconnected converters and distributed generator (DG) interface inverters increase the non-convexity of the power flow model, and conventional distributed power flow (DPF) algorithms based on heuristic rule may encounter convergence problems when processing limit. This paper proposed a fully DPF calculation method that can robustly handle the non-smooth reactive power limits of converters and non-smooth voltage regulation of step voltage regulators, also reducing the model dependence on the initial values. In this algorithm, the non-smooth constraints were converted into smooth functions, and based on a bi-level augmented Lagrangian alternating direction inexact Newton (ALADIN) method with the second-order convergence rate the original DPF problem was transformed into the problem of distributed step increment optimization. Accurate power flow results can be obtained by exchanging boundary information between microgrids, and the proposed algorithm can converge rapidly with step increment optimization at the second level. Numerical experiments demonstrated the accuracy, convergence, and efficiency of the proposed method.

Reactive power limits of Cascaded H-Bridge STATCOMs in star and delta configuration under negative-sequence current withstanding

Flexible AC Transmission System devices (FATCS) and in particular Static Synchronous Compensators (STATCOM) play a key role in the evolution of the modern power grids to the future smart grids. The STATCOM is used in an increasingly wider variety of scenarios in which the operation under unbalanced conditions stands out. This paper analyzes and compares the reactive power limits of Cascaded H-Bridge (CHB) STATCOMs in star (YCHB) and delta (DCHB) configuration to withstand negative-sequence current. Zero-sequence voltage for the YCHB and zero-sequence current for the DCHB are injected in order to correct the intercluster uneven active power distribution and thus to preserve the dc-link voltage balancing. Both solutions will have an impact on the power rating of the converter. This work clearly quantifies the reactive power limits of each CHB STATCOM configuration depending on the current unbalance at converter terminals, by means of a systematic procedure. Improved explicit expressions of the zero-sequence current in the DCHB are also provided. Experimental results obtained from a real-scale set-up in a MV laboratory validate the theoretical analysis.

Bypass Inductor Type LCL Filter Parameter Optimization for Three-Level Grid-Connected Converter

In the application of the three-level grid-connected system, passive damping is the most common method to keep the LCL filter working stably. However, in the case of high power density, the low switching frequency of the grid-connected converter results in the complexity of filter parameter design, and the increase in passive components leads to lower equipment utilization efficiency. To solve the above problems, based on the optimization of resonant frequency and system loss, this study proposes a set of LCL filter parameter design processes of a three-level neutral point clamped (NPC) converter, which can switch components freely and is easy to achieve. This study explores the theoretical evidence and application value of the proposed design, considering the influence of the current ripple and the reactive power limit. The design adopts the improved passive damping method to select the appropriate inductance ratio and impedance ratio to make the resonance frequency of the whole system and the extra loss of the system smaller. The simulation and experiments show that compared with the conventional method, the improved design method reduces the current THD of the grid side by 1.5% and the damping resistance loss by 0.17%.

Examining Impact of Distribution System Characteristics on Transmission Security Assessment of Future Power Systems

The nature and characteristics of distribution systems are changing continuously with the increased penetration of distributed energy resources. With this, the need for examining the transmission and distribution (T&D) interaction while assessing the voltage security has become significant. In much of the analysis and practices reported so far, voltage security assessment studies are performed separately for T&D systems. Thus, a transmission system operator (TSO) is oblivious to the operations and controls taking place at the distribution system (DS) level. Some of the recent studies examine the impact of an active DS on the voltage security assessment of future power systems. However, the effect of various factors like voltage dependency of loads, reactive power capability of renewable energy sources (RES), location of distributed generation units, and network losses on the voltage stability margin (VSM) of transmission system has not been reported comprehensively so far. This paper first theoretically examines the impact of these factors on VSM. Then, to get the more realistic results for VSM, continuation power flow (CPF) is performed in a coordinated fashion including both T&D systems. The simulations show that considering losses, load characteristics dependency on voltage and reactive power limits of RES in a DS for transmission voltage security assessment studies lead to a more rational outcome than when neglected.

A Novel FFHE-Inspired Method for Large Power System Static Stability Computation

This article proposes a novel method termed HEAP for fast and reliably computing nose points, tracing the entire PV curve, and assessing static stability limits. Here, the prefix “HE” in HEAP refers to (fast and flexible) <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</u> olomorphic <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</u> mbedding, and “AP” is short for <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</u> rc-length <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</u> arametrization. This novel method uses an arc-length parametrization and piecewise approximants that enable it to have the favorable feature of Continuation Power Flow that can pass through the nose point without numerical difficulties. Another outstanding feature of the proposed method HEAP is its computational efficiency by enabling the accurate approximation over a long interval of the parameter (i.e., a large step size). This is because of the large convergence region of HEAP. The existing methods for similar tasks usually suffer from several issues such as empirical criteria for detecting nose points, small convergence regions of correctors, numerous intermediate points, and large memory space consumption. These issues are well addressed by HEAP. To examine its numerical performance, HEAP is tested on various power system models with as many as 70,000 buses, and numerical results substantiate the outstanding features of HEAP. Depending on intended applications (e.g., only locating the nose point or fully tracking the curve), two tailored approaches are devised to effectively derive numerical solutions. In comparison with the continuation-based power flow method, HEAP attains speedups of 3x to 300x and notably attains speedups of at least 19x for all large test cases with 10,000 or more buses. The continuation-based power flow method fails in several large test cases, however, all of which are successfully solved by HEAP. After enforcing the generator reactive power limit, HEAP also produces the same accurate results as the continuation-based power flow method.

Multi-Objective Optimization for Optimal Allocation and Coordination of Wind and Solar DGs, BESSs and Capacitors in Presence of Demand Response

The renewable energy sources (RES) based distributed generations (DGs) have been proven to be of great technical and economic benefits if optimally allocated in distribution networks. Their proper deployment is usually made in conjunction with demand response (DR) programs and renewables curtailment to match the demand load with the available generated power. Battery energy storage systems (BESSs) and capacitor banks (CBs) are two other tools that can compensate for the shortcomings of the RES. BESSs could complement the renewables generation intermittency and improve the reliability of the system while CBs could indemnify the limited reactive power support of the RES and improve the power quality of the system. Thus, the simultaneous integration of RES-based DGs, DR, BESSs, CBs, and curtailment could have great benefits if optimally planned and coordinated. In this paper, a multi-objective optimization planning model is formulated to determine the optimal locations and capacities of different RES-based DGs, BESSs, and CBs in presence of DR and renewables curtailment to maximize the economic index and the average voltage stability factor, and to minimize the average power losses in distribution networks. The modelling of RES-generated power is considered. The proposed model is implemented and tested on standard IEEE 33-bus radial distribution system, the model is formulated and solved in GAMS environment. Different renewable configurations and test cases are investigated. The obtained results validate the effectiveness of the simultaneous integration of the used tools in optimizing the techno-economic benefits.

Impact of Wind Farm Location on Voltage Stability

Recently, the use of wind farm in power systems is increasing rapidly it is having a more noticeable impact on the manner in which these power systems operate. When large wind farms are connected to a power system network, voltage stability is a concern as it affects system operation. This paper investigates the impact of wind farm location on voltage stability in power system network when the reactive power limitation of wind generators is taken into consideration and a system reaches its maximum loading. An IEEE-14 bus test system was modified by connecting wind farms to the system at different buses, with different connection scenarios at different wind penetration levels, and the wind farm consists of several variable speed doubly fed induction generator (DFIG) wind turbines. In addition, a voltage collapse proximity indicator (VCPI), based on network loadability, is employed to investigate the contribution of wind generator location to voltage stability. The results of this paper show that system voltage stability is affected positively or negatively depending on the location of wind farm.

Dynamic reactive power optimization of distribution network with distributed generation based on fuzzy time clustering

In order to solve the coordinated optimization problem of distributed generation (DG), on-load tap changer (OLTC) and capacitor banks, a dynamic reactive power optimization (DRPO) method based on fuzzy time clustering is proposed. In the method, fuzzy time clustering algorithm is used to cluster the static optimal switching sequence of OLTC and capacitor banks. The time decoupling of control variables is realized and it meets the constraints of the maximum switching times. Next, the influencing factors of DG reactive power limit are analysed. Considering the control ability of OLTC, capacitor banks and DG in voltage and reactive power optimization, a coordinated optimization method is proposed. Since the adjustment of OLTC tap position directly affects the voltage and reactive power distribution of the whole line, the switching time and tap position of OLTC are determined based on the static optimization results of each time and fuzzy time clustering algorithm. Then, the switching time of capacitor banks is determined by fuzzy time clustering algorithm. At last, the switching capacity of capacitor banks and DG reactive power are jointly optimized to get the final control scheme. The proposed method demonstrated good performance in the modified IEEE33 node system and two actual power grid examples.

An Active Voltage Coordinate Control Strategy of DFIG-Based Wind Farm with Hybrid Energy Storage System

In a power system with wind farms, the point of common coupling (PCC) usually suffers from voltage instability under large wind speed variations and the load impact. Using the internal converter of a doubly fed induction generator (DFIG)-based wind turbine to provide voltage support auxiliary service is an effective scheme to suppress the voltage fluctuation at PCC. To satisfy the reactive power demand of the connected grid, an active voltage coordinate control strategy with the hybrid energy storage system of the wind farm is proposed. The dynamic reactive power balance model is established to show the interaction between the reactive power limitation of the wind farm and the reactive power compensation demand of the grid. This indicates the initial conditions of the active voltage coordinate control strategy. According to the critical operating point and the operation state of the DFIG, the active and reactive power coordinate control strategy composed of active ω-β coordinate control and active β control is proposed to enhance the reactive power support capability and stabilize the grid voltage. To compensate the active power shortage, an auxiliary control strategy based on the hybrid energy storage system is introduced. The simulation results show that the proposed strategy can suppress the voltage fluctuation effectively and make full use of primary energy.

Power flow analysis of integrated energy microgrid considering non‐smooth characteristics

With the development of electric energy substitution technologies such as electric auxiliary heating, the relationship between electric energy and thermal energy is getting closer, and it is of great significance to in-depth study of integrated energy micro-grids containing electricity and heat. However, the integrated energy microgrid power flow (PF) model has non-smooth characteristics such as distributed generations (DGs) limits, converter stations limits and the unknown direction of pipeline mass flow, which can easily lead to the failure of PF convergence. This paper establishes an integrated energy microgrid model including three-phase unbalanced AC/DC hybrid microgrid and heating system. Firstly, the correctness of the converter station model is verified by electromagnetic transient simulation, and then the non-smooth constraint models considering DG and converter station's reactive power limits and pipeline mass flow direction unknown are established based on complementary constraints, and the non-smooth constraints are smoothed by Fischer-Burmeister (FB) function. Finally, the integrated energy microgrid is used for PF analysis, and the results verify the rationality of the model and the effectiveness of the proposed non-smooth characteristics treatment method.