Reserve requirements in AC power systems with uncertain generation

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.

The existing research on market price-affecting agents, i.e. price makers, neglects or simplifies the nature of AC power flows in the power system as it predominantly relies on DC power flows. This paper proposes a novel bilevel formulation based on the smoothing technique, where any price-affecting strategic player can be modelled in the upper level, while the market clearing problem in the lower level uses convex quadratic transmission AC optimal power flow (AC OPF), with the goal of achieving accuracy close to the one of the exact nonlinear formulations. Achieving convexity in the lower level is the foundation for bilevel modeling since traditional single-level reduction techniques do not hold for nonconvex models. The bilevel market participation problem with the AC OPF formulation in the lower level is transformed into a single-level problem and solved using multiple techniques such as the primal-dual counterpart, the strong duality theorem, the McCormick envelopes, the complementary slackness, the penalty factor, the interaction discretization as well as the proposed smoothing techniques. Due to an extensive amount of information and descriptions, the overall work is presented as a two-part paper. This first part provides a literature overview, positions the work and presents the model and the solution algorithm, while the solution techniques and case studies are provided in the accompanying paper.

This paper proposes a methodology to determine the optimal location and sizing of a battery-based energy storage system in order to minimize generation cost in a power system. The methodology is based on the formulation of optimal power flow and includes the injection of renewable energy as well as the charge or discharge of the battery, according to the requirements of the electrical network, optimizing the costs of its operation. The formulated problem is a nonlinear mixed integer programming and its solution is implemented using the Y ALMIP interface to achieve to an optimal solution. Case studies are presented to show the effectiveness of the implemented methodology when distinct penetration levels of renewable sources are assumed for a period of time of operation of the electrical system.

This paper proposes the comparison results of various optimal power flow algorithms (OPF) to calculate the locational marginal prices (LMP) of the unreduced full scale Korean transmission system. Five different types of optimal power flow models are employed: Full AC OPF, Cubic AC OPF, Quadratic AC OPF, Linear AC OPF and DC OPF. As the results, full AC OPF and cubic AC OPF model provides LMP calculation results very similar to each other while the calculation time of cubic AC OPF model is faster than that of the Full AC OPF. Other simplified OPF models, quadratic AC OPF, linear AC OPF and DC OPF offer erroneous results even though the calculation times are much faster than the Full AC OPF and the Cubic AC OPF. Given the condition that the OPF models sometimes fail to find the optimal solution due to the severe complexity of the Korean transmission power system, the Full AC OPF should be used as the primary OPF model while the Cubic AC OPF can be a promising backup OPF model for the LMP calculations and/or real-time operation.

This paper investigates the effect of thyristor controlled series capacitor (TCSC) on the voltage stability constrained optimal power flow (OPF) formulation where the objective function is to minimize power system load curtailment. Incorporating TCSC affects the topology and hence the power flow distribution. Some numerical cases are presented to discuss the effects of TCSC that is expected when it is incorporated into the load curtailment formulation. The test result reflects the impacts TCSC has in reducing load curtailment during a line congestion situation. The paper also discusses the applicability of the approach in security based reliability studies for systems having control components like TCSC.

Linear power flow formulations and optimal operation of three-phase autonomous droop-controlled Microgrids

This paper presents an alternate iterative method to perform AC/DC optimal power flow (AC/DC OPF) calculation considering wind farm integration. Firstly, an original AC/DC OPF model considering wind farm integration is constructed. Then, according to the decoupling theory in the alternate iterative method, the decoupling optimization model of AC/DC OPF model is derived, where the high voltage direct current (HVDC) transmission power is equivalent to constant load for AC OPF calculation while AC system is equivalent to a constant voltage on the converter AC bus for DC system equations calculation. Besides, AC OPF problem is solved by path following interior point method and DC system equation is solved by an improved levenebrg-marquardt method, respectively. Numerical results show that, the AC/DC OPF problem is solved quickly and effectively by using the alternate iterative method, and the impacts of variational wind speeds and locations of wind farms integration on the AC/DC OPF results are systematically analyzed.

Background: The energy router based on power electronic technology is the core equipment of energy internet. Energy router can control the voltage of the port and regulate the power injected into the network flexibly. It is of great significance to study how the capability of the energy router can be used to improve characteristics of the power system. Methods: Based on the analysis of energy router, we construct a unified AC-DC power flow model for energy router considering its different control modes. Then, we establish an optimal power flow formulation for the energy router incorporated AC-DC network and propose the multi-objective function to optimize the comprehensive performance of the network. Several cases are observed and analyzed on a modified IEEE-57 system. Results: The result verifies that the optimal power flow formulation can optimize the control values of ports of the energy router and improve the operating state of the power system. The optimal target presented in this paper can improve the characteristics of the grid better than a single optimal target. Conclusion: Energy router will play a vital role in the energy internet based on the power system. The characters of the power system can be improved and the operating costs can be reduced by utilizing the functionality of energy router in regulating power flow.

Chapter 4 - Data-driven robust stochastic optimization for power systems operations

Transformer models are important components of power systems. Under certain configurations, incorporating transformer models with the nodal admittance matrix of the power flow (PF) formulation makes it singular, rendering the resultant PF algorithm unfeasible. This paper addresses these issues by modelling special transformer configurations (center-tap, three winding, voltage regulators) into a unique Augmented Jacobian based multiphase PF formulation. In this formulation, power system components can be modelled with PF constraints independently and accurately resolving associated singularities in classical nodal admittance matrix. The proposed method is evaluated on two IEEE feeders (modified IEEE-9 bus and IEEE-8500 node). Results are validated with benchmark published results and IPSA software. Numerical examples confirm the effectiveness of the proposed models and algorithm in successfully resolving matrix singularity.

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in dc networks such that stability and operational constraint satisfaction are of concern. Most existing dc network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. In contrast, this article studies a DN-OPF formulation, which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this article’s robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the feasible region using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator setpoints are obtained by optimizing over the proposed convex stability set. The validity and value of the proposed algorithm are demonstrated through various dc networks adapted from IEEE test cases.

In this paper, a new technique based on particle swarm optimization (PSO) is proposed to incorporate voltage stability limits into traditional optimal power flow (OPF) formulations. Two objective functions such as fuel cost and voltage stability margin (loadability) are considered to be optimized. In proposed method systempsilas maximum loading margin (loadability) is calculated by continuation power flow (CPF). Particle swarm optimization (PSO) is employed to solve the proposed multi-objective OPF problem. The proposed method allows system operators in order to control the desired level of system security via adjusting the weighting factors of the different objective functions directly. Simulation results for the IEEE 30-bus test system demonstrate the effectiveness of the PSO in solving multi-objective OPF problems.

Linear active-power-only power flow approximations are pervasive in the planning and control of power systems. However, AC power systems are governed by a system of nonlinear nonconvex power flow equations. Existing linear approximations fail to capture key power flow variables, including reactive power and voltage magnitudes, both of which are necessary in many applications that require voltage management and AC power flow feasibility. This paper proposes novel linear-programming models (the LPAC models) that incorporate reactive power and voltage magnitudes in a linear power flow approximation. The LPAC models are built on a polyhedral relaxation of the cosine terms in the AC equations as well as Taylor approximations of the remaining nonlinear terms. Experimental comparisons with AC solutions on a variety of standard IEEE and Matpower benchmarks show that the LPAC models produce accurate values for active and reactive power, phase angles, and voltage magnitudes. The potential benefits of the LPAC models are illustrated on two “proof-of-concept” studies in power restoration and capacitor placement.

This paper presents the inclusion of a pulse width modulated (PWM) AC link unified power flow controller into a power flow program; such device controls the magnitude and angular position of the injected series voltage to control the active and reactive power flow on the transmission line. Similarly, a PWM series compensator is embedded into a power system in order to regulate the active power flow on the corresponding transmission line; the main advantage of these FACTS controllers is that it does not require a DC link. The inclusion of these devices into a Newton-Raphson power flow algorithm is presented. Simulation results are exhibited on a 9-buses power system

The paper reviews the formulation of optimal power flow (OPF) and its role in dispatch. It then outlines possible uses of OPF market structures and describe the major drawbacks. The use of OPF for market players with a portfolio of generating units, however, is an appropriate and useful application of OPF in competitive markets. The OPF in such cases is a useful tool to determine the most cost-effective approach to discharge certain contracted market obligations since there is a centrally controlled single ownership situation. The application of OPF in such cases is reviewed. The paper emphasizes the limitations and capabilities of applying the OPF tool in market structures.