Power Flow Model Research Articles

Optimal power flow calculation method for regional integrated energy system based on double-layer optimization

In this paper, a two-layer optimization calculation method is proposed to improve the practical application efficiency of the integrated energy system and to improve the different problems of power flow calculation. Firstly, the power flow model is constructed and the optimization function is established based on indicators such as economy and environmental protection. The two-layer optimization method is proposed by combining the quadratic programming method and the particle swarm algorithm. Then, the obtained operating conditions of each energy equipment are used as the input of the power flow. The processing of each device and the energy flow of the power flow network are calculated and the effectiveness of the algorithm is verified by MATLAB power analysis.

Optimal dispatching of wind turbine-photovoltaic-pumped storage new energies and thermal generators combined distribution network

This paper mainly investigates the optimal dispatching problem of the combined distribution network consisting of wind turbine generators (WTGs), photovoltaic generators (PVGs), pumped storage generators (PSGs) and thermal generators (TGs). According to the load demand in the distribution network and the output conditions of different renewable energy generators, PSGs and TGs, a joint optimal dispatching model based on the operation cost of the distribution network is set up. Based on the power flow model of second-order cone relaxation (SOCR) technology, the nonlinear constraints on voltage and current in the distribution network are linearized, so as to solve the cost optimization scheduling problem more efficiently. Finally, an improved IEEE33-node distribution network is used as the basic grid model for simulation analysis, so as to verify the effectiveness of the proposed model.

Optimal power flow research of AC–DC hybrid grid with multiple energy routers

AC/DC hybrid grids are the future development trends of grids, and energy routers (ERs) can play key roles in controlling power flow, realizing the regulation of electric energy and improving power quality in the grids. At present, there have been many studies on the structure and control strategy of ERs, but only a few studies are on the power flow distribution and optimization of AC/DC hybrid grids with ERs. To enhance the efficacy of ERs in system-wide regulation and operational optimization, a multi-objective optimal power flow model is formulated for AC–DC hybrid systems with multiple ERs. In order to make ERs play a better role in overall regulation and operation optimization, the multi-objective optimal power flow model of AC–DC hybrid system with multi-ERS is established based on Newton–Raphson method (NR) and alternating iteration method with power consumption and voltage deviation as optimization objectives. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) is used to optimize the model, and a smoother Pareto solution set is obtained compared with multi-objective particle swarm optimization (MOPSO). Then, fuzzy membership method is used to make compromise decision on the Pareto solution set to obtain the optimal compromise solution. Simulation and analysis on an enhanced IEEE 69 bus system verifies the validity of the model. In addition, the results obtained from the compromise solution are compared with the optimization results of MOPF obtained by MOPSO and that of single-objective power flow (SOPF) obtained by Particle Swarm Algorithm (PSO) in the same system. It is proved that the optimization model established can achieve the optimization objectives of reducing voltage deviation and power loss simultaneously to improve the overall performance of the system and optimize the operation state of the system.

Digital twin modeling and intelligent optimization for rail operation safety assessment

Currently, the use of fixed empirical parameters combined with traditional algorithms to construct train parameter prediction models for estimating train energy consumption is often used. However, due to changes in train related parameters, there is a significant error between the estimated results of this method and the actual values, which cannot reflect the true state of train operation. It affects the subsequent maintenance and repair of trains, thereby affecting the safety of the entire subway operation system. To address the above issues, a train traction power flow model based on digital twin technology is proposed. The swarm intelligence optimization algorithm is not used to correct model parameters. By correcting the deviation of train passenger load, accurate prediction of train energy consumption can be achieved. The experimental results show that the power flow model constructed by the research institute can reduce the power error of single interval trains by over 11.91%. The average DC voltage error of the train power flow model after parameter correction is 0.19%. The average DC current error is 12.07%. The root mean square error range of passenger capacity for similar day neural network models is [0.0521,0.0811]. The experimental results indicate that the model constructed by the research institute can accurately predict train energy consumption and ensure the safety of the subway operation system.

Efficient Constraint Learning for Data-Driven Active Distribution Network Operation

Scheduling flexible sources to promote the integration of renewable generation is one fundamental problem for operating active distribution networks (ADNs). However, existing works are usually based on power flow models, which require network parameters (e.g., topology and line impedance) that may be unavailable in practice. To address this issue, we propose an efficient constraint learning method to operate ADNs. This method first trains multilayer perceptrons (MLPs) based on historical data to learn the mappings from decisions to constraint violations and power loss. Then, power flow constraints can be replicated by these MLPs without network parameters. We further prove that MLPs learn constraints by formulating a union of disjoint polytopes to approximate the corresponding feasible region. Thus, the proposed method can be interpreted as a piecewise linearization method, which also explains its desirable ability to replicate complex constraints. Finally, a novel pruning method is developed to remove the useless binary variable solutions in advance, which can enhance the solution's reliability and reduce the computational complexity. Numerical experiments based on the IEEE 33- and 123-bus test systems validate that the proposed method can achieve desirable optimality, feasibility, and computational efficiency simultaneously.

A Second-Order Cone Programming (SOCP) Based Optimal Power Flow (OPF) Model With Cyclic Constraints for Power Transmission Systems

For meshed power networks, even though the conic relaxation is shown to be exact, the relaxation of angles may not be exact using the existing Second-Order Cone Programming (SOCP) based optimal power flow (OPF) models. Power transmission networks generally have meshed orientation, and the cyclic angle constraints are not satisfied with the existing SOCP-OPF models. This work proposes a SOCP-OPF model for power transmission networks that satisfies the cyclic angle constraints for any mesh in the network. The novelty of the proposed OPF model is that it defines a convex envelope to represent the relative bus voltage angles that satisfy the cyclic constraint criteria for a meshed network. The proposed SOCP-OPF model is tested on the IEEE 14-bus, 57-bus, 118-bus, 500-bus, and 2736-bus networks. The case studies demonstrate that the proposed model is computationally efficient and scalable for large transmission networks compared to the Nonlinear Programming (NLP) and semi-definite programming (SDP) counterparts.

A SOCP-Based ACOPF for Operational Scheduling of Three-Phase Unbalanced Distribution Systems and Coordination of PV Smart Inverters

The proliferation of distributed energy resources (DERs) imposes new challenges to distribution system operation, e.g., power quality issues. To overcome these challenges and enhance system operation, it is critical to effectively utilize all available resources and accurately characterize unbalanced distribution networks in operational tools. This paper proposes a convex second-order-cone programming (SOCP)-based AC optimal power flow (ACOPF) model for three-phase unbalanced distribution networks, including smart inverters and Volt-VAr controller (VVC) devices. Reactive power-voltage (Q-V) characteristics of smart inverters of solar photovoltaic (PV) units are also modeled. Moreover, the settings of Q-V characteristics of VVC are co-optimized within the proposed ACOPF, considering the allowable range of the IEEE 1547-2018 standard. Furthermore, dynamic analyses are conducted to verify the stability of optimal settings of VVC. The proposed models are tested on an actual 1747-node primary distribution feeder in Arizona. The results illustrate the effectiveness of the proposed ACOPF for unbalanced systems in providing an optimal solution while capturing the non-linearity and non-convexity of ACOPF. By co-optimizing settings, system operation is improved due to the flexibility of adjusting reactive power output from PV units with VVC. The time-domain simulations show that the optimal settings cause no stability issue for the distribution system.

Power Flow Model for Medium-voltage Distribution Systems Considering Measurement and Structure Characteristics

Power Flow Model for Medium-voltage Distribution Systems Considering Measurement and Structure Characteristics

AC Network-Constrained Unit Commitment Based on Adaptive Linear Power Flow Model

AC Network-Constrained Unit Commitment Based on Adaptive Linear Power Flow Model

Voltage Stability Constrained Operation Optimization: An Ensemble Sparse Oblique Regression Tree Method

Voltage stability remains a main challenge for high renewable penetrated power systems. In future power systems, the dispatch needs to consider the voltage stability margin. However, considering static and transient voltage stability is challenging because a complex relationship exists between voltage stability and operation state variables. This paper proposes an ensemble sparse oblique regression tree method for voltage stability constrained operation optimization. First, we train multiple oblique regression trees on voltage stability simulation datasets. The trained trees are then grouped into ensemble using a boosting method to extract accurate and understandable voltage stability rules. Finally, the rules are embedded as mixed-integer linear programming constraints in a linear optimal power flow model. Validation on the IEEE-14 case shows the interpretability and efficiency of the proposed algorithm. Case studies on the Qinghai power grid and IEEE-118 further show that the proposed strategy can effectively improve the voltage stability margin of optimized operation states.

Robust and Chance-Constrained Dispatch Policies for Linear Power Systems

Several methods have recently been proposed to determine optimal feedback control policies for generator dispatch under uncertain grid in-feeds. This work presents and explains two such approaches based on a constrained linear power flow model in a unified notation, a robust method based on linear programming and a chance-constrained one based on polynomial chaos expansions and second order cone programming. This work compares both methods on the same small test example and discusses consequences for long-term grid expansion planning. While the robust method is easier to implement, it is also not more restrictive. For the chance-constrained method, we highlight a serious drawback in reformulations common in the literature. As an aside, we extend the existing formulation to cases where not all disturbances can be measured, and combine it with a robust pre-processing scheme.

A Game-Theoretic Approach for Electric Vehicle Aggregators Participating in Phase Balancing Considering Network Topology

With the increasing popularity of electric vehicles (EVs), uncontrolled charging of single-phase plug-in EVs will result in severe three-phase unbalance problem in distribution networks. To solve the problem, a phase balancing (PB) scheme performed by EV aggregators (EVAs) based on the linear multiphase power flow model is proposed in this paper. In the scheme, the PB compensations are provided to encourage EVAs to help the distribution system operator reduce the phase unbalance of the entire grid. Considering all EVAs are selfish and rational, the PB scheme is formulated as a game problem, in which each EVA competes with other EVAs to determine its charging strategy to minimize the charging cost minus the PB compensation. The consideration of coupling voltage constraints leads this game model to a challenging generalized Nash equilibrium problem (GNEP). By employing the theory of variational inequality, the properties of solutions for the GNEP are investigated. Furthermore, a two-level distributed algorithm is designed to find the unique variational solution, a fair and stable solution. Finally, comprehensive case studies are conducted on the IEEE-13 and IEEE-123 test systems to corroborate that the proposed PB game model can effectively mitigate voltage unbalance and cut EV users’ costs.

Semi-Definite Programming Based Scalable and Accurate Optimal Power Flow Models for Radial Distribution Networks

Semi-Definite Programming Based Scalable and Accurate Optimal Power Flow Models for Radial Distribution Networks

Modular Linear Power Flow Model Against Large Fluctuations

The linear power flow model based on an empirical operating point is generally employed in power generation dispatch. However, with the increasing penetration of renewable energy sources (RESs) and frequent topology changes, the expansion of the operating region causes considerable modeling errors in the static linear power flow model. In this paper, the sources of linearization error are thoroughly analyzed, and a modular linear power flow modeling framework is proposed. It is found that the key features that affect the accuracy of linearization are the truncation error and its first derivative. This motivates us to cluster historical scenarios based on selected features. The key approach is to individually select a linear power flow model for power system operating conditions with similar linearization error features. This allows us to derive a refined linear power flow model for each cluster to avoid excessive linearization errors using a uniform linear power flow model. Numerical results for several IEEE and Polish test systems show that the linearization error of the proposed method is reduced up to 52.98% compared to current methods. The results demonstrate that the proposed method can use a small number of linearization segments to deal with topology changes.

Sensitivity-Based Expression of the Voltage-Power Characteristic (VPC) of the Wind Farm From the VPCs of the DFIGs and the Collector

Considering the power loss of the collector and the doubly-fed induction generators (DFIGs), power outputs of wind farms are related to the voltage at the point of common coupling and the reactive power outputs of the DFIGs. This voltage-power characteristic (VPC) influences the power flows of the wind farm and the main system, and is newly expressed with the sensitivity model in this paper. The originalities lie in, 1) the master-slave splitting method is newly applied to solve the collector and the DFIGs alternatively to reduce the problem size. 2) The VPC of the wind farm is newly derived from the VPCs of the collector and the DFIGs. 3) The optimal power flow model of the main system with the VPC of wind farm is proposed. The sensitivity-based VPC model of the wind farm is verified by comparing with the parameter perturbation method to verify the accuracy of the VPC model and its impact on the wind farm and the main system.

Conditions for Estimation of Sensitivities of Voltage Magnitudes to Complex Power Injections

Voltage phase angle measurements are often unavailable from sensors in distribution networks and transmission network boundaries. Therefore, this paper addresses the conditions for estimating sensitivities of voltage magnitudes with respect to complex (active and reactive) electric power injections based on sensor measurements. These sensitivities represent submatrices of the inverse power flow Jacobian. We extend previous results to show that the sensitivities of a bus voltage magnitude with respect to active power injections are unique and different from those with respect to reactive power. The classical Newton-Raphson power flow model is used to derive a novel representation of bus voltage magnitudes as an underdetermined linear operator of the active and reactive power injections—parameterized by the bus power factors. Two conditions that ensure the existence of unique complex power injections given voltage magnitudes are established for this underdetermined linear system, thereby compressing the solution space. The first is a sufficient condition based on the bus power factors. The second is a necessary and sufficient condition based on the system eigenvalues. We use matrix completion theory to develop estimation methods for recovering sensitivity matrices with varying levels of sensor availability. Simulations verify the results and demonstrate engineering use of the proposed methods.

Reliability Assessment of Power System based on Load Flow Analysis of the IEEE 57 Bus used in Micro Grid Applications

The complex power system consists of more interconnections; therefore, modelling such a type of network is a very difficult task in the commercialization area cycle. MATPOWER has all steady-state power system models, which are extensively used in academic research for power flow (PF) modeling. The PF architecture designed in this is extensible; it is easy to add or modify variables and constraints in the standard case structure. This paper presents the details of the mathematically scaled loads in IEEE 57 bus power system network modelling by using the standard test case data. Internally, all the bus voltages are expressed in p.u., and phase angles are expressed in radians, but the generators and loads are expressed in terms of power ratings. The scaling of these is defined based on the scaled voltage of the corresponding bus voltage. The scaling load procedure used in this paper is very useful for designing a low-voltage power system network for practical analysis purposes. Two simulations are performed in this paper for the analysis of the actual load flow (ALF) and scaled load flow (SLF) power system models. The voltage, phase angle, and power flow through the lines are compared to analyze the accuracy of both simulations. When compared with ALF, it has shown good accuracy, computational efficiency, and convergence properties.

Quantifying Sustainable Urban Energy Solutions: Statistical Analysis of Renewable Adoption, Economic Viability, and Technological Innovations

In the context of quantifying sustainable and reliable urban microgrid energy solutions economic feasibility, and technological innovation, this study investigates the potential advantages of hybrid AC-DC microgrids (HMGs) over traditional AC microgrids by eliminating the need for voltage inverters and mitigating energy losses associated with AC-DC converters. We propose a probabilistic strategy for economic feasibility and optimizing the unit commitment of HMGs while considering the integration of renewable energy sources and batteries. To account for uncertainties stemming from load demand fluctuations, energy market price variations, and renewable energy source output power variability, we introduce a stochastic power flow model based on the 2 m point estimation method for economic feasibility and technological innovation of HMGs. Furthermore, we present a novel and robust hybrid optimization approach that combines the harmony search optimization method and genetic algorithm to explore the problem space and identify optimal solutions. This hybrid optimization method incorporates a unique two-stage modification technique, enhancing its search capabilities while preventing convergence to local optima. To assess the performance of our proposed method, we apply it to the IEEE test system. The results demonstrate the effectiveness of our approach in achieving optimal management of the microgrid system, emphasizing its relevance to the quantification of sustainable and reliable urban microgrid energy solutions.

A linear Distflow model considering line shunts for fast calculation and voltage control of power distribution systems

The line shunts are usually ignored by various linear power flow (PF) models in power distribution system analysis, planning and optimization. However, “charging effects” from line shunts of underground/submarine power cables would cause non-negligible model errors for these commonly used PF models. In this paper, we propose a modified Linear Distflow model (LinDist) with line shunts, i.e., LinDistS. We also further propose its extensions considering the ZIP load, weakly-meshed topology and unbalanced three-phase systems. Moreover, the linearization error of voltage component is theoretically analyzed. Case studies show that compared with other models, the proposed LinDistS achieves the descent calculation accuracy and efficiency. We also show the application scope of LinDistS by a Volt/VAr control (VVC) framework with distributed generators, mainly photovoltaic (PV), and the non-negligible “charging effect”. Simulation exhibits that with LinDistS, the VVC can optimally dispatch the shunt capacitors and also optimize the real-time reactive power output of PV. Moreover, with LinDistS, the VVC shows better solutions’ consistency and higher computing efficiency compared to traditional VVC methods.

A novel state estimation method for distribution networks with low observability based on linear AC optimal power flow model

The state estimation (SE) problem is one of the key functions in real-time control and management of modern electrical distribution networks. However, due to the complex network configuration and the limited number of measuring devices in these networks, the SE problem faces many challenges. In this manuscript, a new state estimation methodology is proposed based on the AC optimal power flow (ACOPF) model for distribution networks with a small number of real-time measurements. The proposed method is formulated in the form of a mixed integer linear programming problem (MILP), where the estimated states are regarded as the decision variables in the optimization problem. The load consumption values are also assumed as the decision variables where the estimation limits of these variables are determined by pseudo-measurements taken from the historical data. The main objective function is to maximize the state estimation accuracy, while the power flow equations are defined as the problem constraints. The efficiency of the proposed methodology is evaluated by implementing on the test networks and comparing the estimation results accuracy with the conventional weighted least squares (WLS) method. The obtained numerical results show the superior performance of OPF-based SE model to WLS method. Moreover, linearizing the formulation demonstrates an acceptable precision while ensuring convergence and optimum solution in low observability conditions.