Dynamic Optimal Power Flow with Storage Restrictions Using Augmented Lagrangian Algorithm

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

With the increasing levels of wind generator penetration in modern power systems, one of major challenges in the present and coming years is the optimization control, such as optimal power flow including wind farms. The power flow model for a fixed speed wind generator(FSWG) system and a variable speed wind generator(VSWG) system is discussed respectively. The expectation model of wind generators' active power outputs is adopted. Dynamic optimal power flow (DOPF) is a typical complex multi-constrained non-convex non-linear programming problem in wind power integrated system when considering the valve-point effect of conventional generators. Moreover, it is mixed integer when considering the discreteness of FSWG reactive compensation devices. DOPF model is established in this paper, and then a novel shuffled frog leaping algorithm (SFLA)is proposed for solving the established DOPF model. According to the principle of the nearest reactive power compensation, the required reactive power of FSWG doesn't absorb from the system as much as possible, but mainly from its reactive compensation devices. Improved IEEE 30-bus system is used to illustrate the effectiveness of the proposed method compared with those obtained from particle swarm optimization (PSO) algorithm. The test results show that the proposed method is effective and has a certain practicality.

SUMMARY This paper proposes a hybrid particle swarm optimization and simulated annealing (PSO-SA) method to solve the dynamic optimal power flow (DOPF) problem while the prohibited zones, valve-point effects, and ramp rate constraints are taken into account. In the conventional optimal power flow, the total load is constant and the problem is solved for just one period, but in the proposed approach, the multiperiod OPF is considered. Also, the operating region of the units having prohibited zones is broken into isolated feasible sub-regions, which results in multiple decision spaces for the discontinuous OPF problem. Also, nonlinear characteristics of the alternative current (AC) power flow as well as technical constraints, for example, valve-point effect and transmission constraints, are all considered for the realistic operation, and they further complicate the proposed problem. These features make the DOPF as a complicated nonlinear and non-convex optimization problem. This paper proposes a hybrid PSO-SA algorithm to solve the DOPF problem. The hybrid PSO-SA algorithm can efficiently search and explore solution space while it profits from privileges of both PSO and SA algorithms. The IEEE 30-bus test system is implemented to illustrate the application of the proposed modeling framework. Copyright © 2012 John Wiley & Sons, Ltd.

The traditional concepts and practices of power systems are superimposed by economic market management. So OPF has become complex, and classical optimization methods were used to solve OPF effectively. But, in recent years, Artificial Intelligence methods (GA, etc.) have emerged that can solve highly complex OPF problems. In this work two algorithms, were used for the solution of dynamic optimal power flow (OPF) problem taking the transmission losses and the cost of generation as the main constraints. Both algorithms were tested on a 14-bus IEEE test system. The contingency analysis was considered in the application of the algorithms. Additionally, a comparison was made between the two algorithms. The obtained results showed the effectiveness of the GA algorithm over the traditional algorithm

To implement privacy protection and high‐efficiency distributed computing of the large‐scale dynamic optimal power flow (DOPF) of the multi‐area interconnected power system, the regularised term (RT) and primal–dual interior‐point method (PDIPM), denoted by R‐PDIPM, is proposed to distribute and parallel such DOPF solutions. First, the DOPF is transformed into a prime block‐angular problem through the replication of the coupling node variables, and the multi‐area decoupling of the power grid is realised. However, it is easier to develop a singular (ill‐conditioned) block matrix of Newton's system under the distributed computing of PDIPM. Second, though introducing the RT into the Lagrangian function of PDIPM based on regular technology, the matrix of Newton's system becomes quasi‐definite and strongly factorisable. The robustness of distributed computing of PDIPM is enhanced, and the convergence speed is also improved. Case studies on the 3012 and 3074 node systems over 2–4 time intervals are presented. The results show that the R‐PDIPM is more robust in efficiently solving the problem than PDIPM in distributed computing, which is suited for distributed calculation of DOPF in a large‐scale multi‐area power system.

Accurate conversion loss models are the keys to guarantee the more efficient operation of networked hybrid ac/dc microgrids (N-ac/dc-MGs). A two-stage stochastic unit commitment (UC) problem is proposed to improve the operational efficiency of N-ac/dc-MGs under uncertain renewable energy generation output and loads. The nonlinear power losses of ac/dc converters and dc/dc converters under different operating modes are formulated as novel multivariate nonlinear functions of both power and voltage. These functions are approximated by linear surrogate models and adopted by the dynamic optimal power flow (OPF), where the voltage and power of the converters can be optimized considering the physical laws among voltages of converters. Embedding the dynamic OPF problem as mixed-integer recourse, a two-stage stochastic programming problem is formulated for the day-ahead operation of N-ac/dc-MGs. To reduce the computational cost, a finite iteration convergent Benders decomposition algorithm is proposed to solve the UC problem. Case studies are performed on hybrid ac/dc MGs and N-ac/dc-MGs. Simulation results reveal that using more accurate conversion loss models, the output commands, especially the dc bus voltage, from the energy management systems will lead to more efficient system operation, and thus, save energy.

This article describes an approach for the dynamic optimal power flow problem using interior point method (IPM) and Benders decomposition considering both active and reactive constraints. An efficient predictor-corrector primal-dual interior-point algorithm is used to solve the linearized dynamic OPF problem. The inclusion of active and reactive security constraints will assure a subsequent feasible solution for the dynamic OPF problem. The dynamic OPF problem is decomposed into a master problem and subproblems for checking the feasibility of the active and reactive constraints. The master problem is formulated and solved without active and reactive constraints to avoid complexity. The obtained dynamic OPF schedule from the master problem is applied to the active and reactive subproblems to minimize the violations. In case the current mix of scheduled units cannot remove the violations, additional constraints will be introduced in the master problem for rescheduling dynamic OPF. The proposed approach has been evaluated on an IEEE 118-bus test system. The results obtained with the proposed approach are presented and compared favorably with results of other stochastic techniques.

In developing countries, gas infrastructures are not well established yet. Consequently, insufficient gas supply for gas turbine generator unit may occur during peak load hours. Dual firing unit can overcome such limitation by switching the fuel to High Speed Diesel Oil. However, it will significantly increase the operation cost since High Speed Diesel fuel is much more expensive than natural gas. Recently, a compressed natural gas system has been widely used to solve inadequacy of gas supply during peak load hours. This system compresses the remaining natural gas supply from gas provider during off-peak load hours and stores it into gas tubes. The compressed gas is then released to top up gas supply to gas turbine during peak load hours. Thus, the unit can fully operate on gas at both peak and off-peak load hours. As a result, the operation cost will be lower. This paper proposes an approach in optimizing system operation cost of large system, which has gas turbine generator unit with compressed natural gas system. Furthermore, load curtailment and implementation of take or pay energy contract is also included. The problem is formulated as dynamic optimal power flow and solved using quadratic programming. The proposed approach is tested using IEEE 30 bus and Jawa Bali 500 kV. The results show the effectiveness of the approach in optimizing daily gas usage as well as satisfying take or pay energy contract.

For a high penetration of intermittent renewable energy sources, the transmission capacity constraints become more important for secure and economic operation of power systems because of the high variability in the transmission line current. In this study, the fundamental characteristics of the dynamic optimal power flow are analyzed with the line-temperature constraints in transmission networks. Numerical simulations show that the load reduction induced by the current variation can be reduced by the line-temperature constraints rather than the current constraints.

Day-ahead multi-period scheduling can provide reasonable operation plans for various power sources and energy storage systems in distribution networks, so as to reduce costs and improve energy utilization. In this paper, the dynamic power flow optimization model of radial distribution network with wind/PV/energy storage is established firstly. The model takes the output of various power sources and the charge-discharge power of energy storage systems as decision variables, which belongs to nonconvex nonlinear programming problems. Then the second-order cone relaxation is applied to the power flow equation, and the problem is transformed into a second-order cone programming model which can be solved strictly and efficiently. Finally, the extended IEEE 30-node system is simulated, and the software Gurobi is used to obtain the optimal scheduling scheme, which verifies the effectiveness of this method. Test results show that the operating cost is reduced by adding wind/PV/energy storage into networks, and the consumption of renewable energy is increased by considering the punishment for wind and PV abandonment.

The performance of a power system can be measured and evaluated by its power flow analysis. Along with the penetration of renewable energies such as wind and solar, the power flow problem has become a complex optimization problem. In addition to this, constraint handling is another challenging task of this problem. The main critical problem of this dynamic power system having such variable energy sources is the intermittency of these VESs and complexity of constraint handling for a real-time optimal power flow (RT-OPF) problem. Therefore, optimal scheduling of generation sources with constraint satisfaction is the main goal of this study. Hence, a renewable energy forecasting–based, day-ahead dynamic optimal power flow (DA-DOPF) is presented in this paper with the forecasting of solar and wind patterns by using artificial neural networks. Moreover, contribution factors are calculated using triangular fuzzy membership function (T-FMF) in the sub-interval time slots. Furthermore, the superiority of feasible (SF) solution constraint handling approach is used to avoid the constraint violation of inequality constraints of optimal power flow. The IEEE 30-bus transmission network has been amended to integrate a solar photovoltaic and wind farm in different buses. In this approach, the computing program is based on MATPOWER which is a tool of MATLAB for load flow analysis which uses the Newton–Raphson technique because of its rapid convergence. Meteorological information has been gathered during the time frame January 1, 2015, to December 31, 2017, from Danyore Weather Station (DWS) at Hunza, Pakistan. A Levenberg–Marquardt calculation–based artificial neural network model is utilized to foresee the breeze speed and sunlight-based irradiance in light of its versatile nature. Finally, the results are discussed analytically to select the best generation schedule and control variable values.

The solution of nonlinear optimal power flow (OPF) problems by interior-point (IP) and noninterior-point (NIP) methods for nonlinear programming (NLP) is described. The mathematical development of both algorithms is based on a standard form NLP problem. A distinctive feature of the NIP method is that, in contrast to IP methods, it can start from arbitrary points. Test results are reported.

Dynamic Optimal Power Flow in FSWGs Integrated Power System

The incorporation of renewable energy sources (RES) such as wind and solar power plants into traditional power systems offers numerous technical and environmental benefits. However, improper operation of power grids with RES may lead to high operating costs and higher system losses, as well as voltage fluctuations. To solve these problems, in this paper a formulation of the dynamic optimal power flow (DOPF) problem has been proposed with the integration of RES in the grid. The maximum allowable number of switching operations in a day for on-load tap-changer (OLTC) of transformers is taken into consideration as practical constraint. For 24 hours, the objective functions were to minimize the total operating cost (including fuel cost and cost of power loss), minimize power loss and the daily number of tap operations for transformer's OLTC. The minimization of the daily number of operations for transformers was taken as the goal to preserve the service life of transformers, reduce maintenance and depreciation. The objectives were minimized by coordination between control variables such as the output power of generators, the voltage of generators, transformer tap changer, and shunt capacitor. The improved practical swarm optimization (PSO) algorithm has been employed successfully to solve DOPF with discrete and continuous decision variables in the electric power system.

Optimal power flow (OPF) is a crucial aspect of distribution network planning and operation. Conventional heuristic algorithms fail to meet the system requirements for speed and accuracy, while linearized OPF approaches are inadequate for distribution networks with high R/X ratios. To address these issues and cater to multi-period scenarios, this study proposes a dynamic linearized second-order cone programming-based (SOCP) OPF model. The model is built by first establishing a dynamic OPF model based on linearized second-order conic relaxation (LSOCR-DOPF). The components of the active distribution network, such as renewable energy power generation units, energy storage units, on-load-tap-changers, static var compensators, and capacitor banks, are then separately modeled. The model is implemented in MATLAB and solved by YALMIP and GUROBI. Finally, three representative scenarios are used to evaluate the model accuracy and effectiveness. The results show that the proposed LSOCR-DOPF model can ensure calculation time within 3 min, voltage stability, and error control within 10−6 for all three applications. This method has strong practical value in the fields of active distribution network day-ahead dispatch, accurate modeling of ZIP load, and real-time operation.