Multi-objective Optimal Power Flow Model Research Articles

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.

Optimal Power Flow with Stochastic Solar Power Using Clustering-Based Multi-Objective Differential Evolution

Optimal power flow is one of the fundamental optimal operation problems for power systems. With the increasing scale of solar energy integrated into power systems, the uncertainty of solar power brings intractable challenges to the power system operation. The multi-objective optimal power flow (MOOPF) considering the solar energy becomes a hotspot issue. In this study, a MOOPF model considering the uncertainty of solar power is proposed. Both scenarios of overestimation and underestimation of solar power are modeled and penalized in the form of operating cost. In order to solve this multi-objective optimization model effectively, this study proposes a clustering-based multi-objective differential evolution (CMODE) which is based on the main features: (1) extending DE into multi-objective algorithm, (2) introducing the feasible solution priority technique to deal with different constraints, and (3) combining the feasible solution priority technique and the merged hierarchical clustering method to determine the optimal Pareto frontier. The simulation outcomes on two cases based on the IEEE 57-bus system verify the reliability and superiority of CMODE over other peer methods in addressing the MOOPF.

Increment-Exchange-Based Decentralized Multiobjective Optimal Power Flow for Active Distribution Grids

To increase distributed energy resource (DER) utilization while reducing their negative influence, this article proposes an increment-exchange-based decentralized multiobjective optimal power flow (MO-OPF) algorithm for distribution grids with high-DER integration. In the MO-OPF model, the network operator and DER owners pursue their own operational and economic objectives while ensuring that voltages and branch power limits are satisfied throughout the network. The proposed algorithm enables the solution of the MO-OPF problem in a decentralized manner, without exposing any DER's private information to the network operator. Its core idea is to use the quadratic functions of coupling variables' increments to describe the impact of DER owners on the network operator; then the network operator computes variables' increments by solving accumulated quadratic programming problems. The resulting method can provide the same evenly distributed Pareto-optimal solutions as the centralized model, and it has plug-and-play features and scalability properties. Case studies on an IEEE 33-bus and a real 266-bus distribution system are carried out to demonstrate the merits of the proposed algorithm.

A two-stage reactive power optimization in transmission network incorporating reserves from voltage-dependent loads

With the integration of intermittent resources, more reserves are required for uncertainties. Traditionally, reactive power optimization in transmission network focuses on loss minimization problems, regarding loads as voltage-independent injections. In fact, the bus voltage magnitude affects the load active/reactive injection, providing a possibility for system operators to regulate the power of loads through voltage regulation. Inspired by this inherent feature of loads, this paper considers the regulation of voltage-dependent loads (VDLs) for fast reserves through reactive power optimization and voltage control under the coordination of transmission and distribution networks. A two-stage multi-objective optimal power flow model is developed to incorporate reserves from VDLs. The first stage is to optimize the minimization of losses and the maximization of the reserves that the VDLs can provide, which is modeled as an AC optimal power flow problem. In the second stage, it is verified whether the reserves from the first stage can be delivered by voltage regulation to settle down the possible imbalance power in the power system. Case studies show that the proposed method can estimate the amount of reserves from VDLs and optimize the bus voltages accordingly.

Two-stage multi-objective OPF for AC/DC grids with VSC-HVDC: Incorporating decisions analysis into optimization process

A two-stage solution approach for solving the problem of multi-objective optimal power flow (MOPF) is proposed for hybrid AC/DC grids with VSC-HVDC. First, a MOPF model for hybrid AC/DC grids is built to coordinate the economy, voltage deviation and environmental benefits. Then, a two-stage solution approach, incorporating decision analysis into optimization process, is presented to solve the model. The first stage of the approach is consisted of a multi-objective particle swarm optimization algorithm with a hybrid coding scheme employed to find multiple Pareto-optimal solutions. The second stage will have the obtained solutions clustered into different groups using fuzzy c-means (FCM) clustering, and then the ‘best’ compromise solutions are obtained by calculating the priority memberships of the solutions belonging to the same groups via grey relation projection (GRP) method. The novelty of this approach lies primarily in incorporating the FCM-GRP based decisions analysis technique into MOPF studies, thereby assisting decision makers to automatically identify the ‘best’ operation points. The effectiveness of the proposed approach is verified based on the test results of the IEEE 14- and 300- bus systems.

Multi-objective optimal power flow for active distribution network considering the stochastic characteristic of photovoltaic

To mitigate the impact on the distribution networks caused by the stochastic characteristic and high penetration of photovoltaic, a multi-objective optimal power flow model is proposed in this paper. The regulation capability of capacitor, inverter of photovoltaic and energy storage system embedded in active distribution network are considered to minimize the expected value of active power the T loss and probability of voltage violation in this model. Firstly, a probabilistic power flow based on cumulant method is introduced to calculate the value of the objectives. Secondly, NSGA-II algorithm is adopted for optimization to obtain the Pareto optimal solutions. Finally, the best compromise solution can be achieved through fuzzy membership degree method. By the multi-objective optimization calculation of IEEE34-node distribution network, the results show that the model can effectively improve the voltage security and economy of the distribution network on different levels of photovoltaic penetration.

An Improved Artificial Bee Colony Algorithm and Its Application to Multi-Objective Optimal Power Flow

Optimal power flow (OPF) objective functions involve minimization of the total fuel costs of generating units, minimization of atmospheric pollutant emissions, minimization of active power losses and minimization of voltage deviations. In this paper, a fuzzy multi-objective OPF model is established by the fuzzy membership functions and the fuzzy satisfaction-maximizing method. The improved artificial bee colony (IABC) algorithm is applied to solve the model. In the IABC algorithm, the mutation and crossover operations of a differential evolution algorithm are utilized to generate new solutions to improve exploitation capacity; tent chaos mapping is utilized to generate initial swarms, reference mutation solutions and the reference dimensions of crossover operations to improve swarm diversity. The proposed method is applied to multi-objective OPF problems in IEEE 30-bus, IEEE 57-bus and IEEE 300-bus test systems. The results are compared with those obtained by other algorithms, which demonstrates the effectiveness and superiority of the IABC algorithm, and how the optimal scheme obtained by the proposed model can make systems more economical and stable.

Comprehensive optimal photovoltaic inverter control strategy in unbalanced three‐phase four‐wire low voltage distribution networks

The continuous expansion of consumer-driven installations of residential rooftop photovoltaic (PV) systems causes serious power quality, notable voltage variations and unbalance, which limit the number and capacity of the further connections. The latent reactive power capability of PV inverters can increase the network PV hosting capability. This study proposes both reactive power control and real power curtailment as a comprehensive inverter control strategy to improve the operating performance of unbalanced three-phase four-wire low voltage distribution networks with high penetrations of residential PV systems. A multi-objective optimal power flow (OPF) problem that can simultaneously improve voltage magnitude and balance profiles while minimising network loss and generation costs is defined. The solution is found using the global solver based on Sequential Quadratic Programming algorithm with multiple starting points in Matlab. Detailed simulations are performed and analysed for typical operating scenarios over 24-h period on a real three-phase four-wire unbalanced distribution network in Perth Solar City trial, Australia. Smart meter readings are used to justify the accuracy and validation of the network model and the proposed multi-objective OPF model.

Chance-Constrained Optimization-Based Unbalanced Optimal Power Flow for Radial Distribution Networks

Optimal power flow (OPF) is an important tool for active management of distribution networks with renewable energy generation (REG). It is better to treat REG as stochastic variables in the distribution network OPF. In addition, distribution networks are unbalanced in nature. Thus, in this paper, a chance constrained optimization-based multiobjective OPF model is formulated to consider the forecast errors of REG in the short-term operation of radial unbalanced distribution networks. In the model, expected total active power losses of distribution lines, expected overload risk and voltage violation risk with respect to N-1 contingencies are minimized, and inequality constraints in the normal state are satisfied with a predefined probability level. Thus, the profitability and security can be balanced in the presence of stochastic REG. The proposed multiobjective OPF problem is solved by the multiobjective group search optimization and the two-point estimate method. Simulation results show that distribution network economy and postcontingency performance deteriorate with increased penetration level of REG, and the penetration level has a greater impact than the forecast errors of REG.