Optimal Power Flow Constraints Research Articles

Optimize globally, control locally: Coordinated optimal local voltage control in hybrid AC/DC microgrid

The increasing penetration of photovoltaic (PV) generation leads to voltage violations in hybrid AC/DC microgrids. Due to the uncertainty and volatility of PV outputs, fast-responding voltage control devices are obliged to coordinate with each other and regulate nodal voltages in real time. This paper follows the concept of optimizing globally and controlling locally to propose a combined central and local voltage control strategy based on a two-stage voltage control framework. In the first stage, minutely optimal power flow based on predicted PV outputs within one hour is performed in microgrid central controller (MGCC) to calculate voltage and optimal power settings for each controllable device. The uncertainty of PV is considered using chance constraint optimal power flow (CCOPF) method. In the second stage, according to minutely voltage and power settings, local controller (LC) generates improved voltage control curves based on curve fitting method. With minutely measurements of nodal voltages, power outputs of PVs, smart loads (SLs) energy storage systems (ESSs) and VSC are cooperated based on improved local control curves to minimize power losses without communication requirements. In order to coordinate the active and reactive power of SLs ESSs, and VSC, a combined P(V) and Q(V) curve is proposed. The piecewise linear curve fitting method is used to generate optimal voltage control curves due to its higher fitting accuracy compared with other fitting methods. Simulations are performed to verify the effectiveness of the proposed voltage control strategy in mitigating voltage rise problems and reducing power losses.

Loss Minimization With Optimal Power Dispatch in Multi-Frequency HVac Power Systems

Low-frequency high-voltage ac transmission scheme has recently been proposed as an alternative approach for bulk power transmission. This paper proposes a multi-period optimal power flow (OPF) for a multi-frequency HVac transmission system that interconnects both conventional 50/60-Hz and low-frequency grids using back-to-back converters with a centralized control scheme. The OPF objective is to minimize system losses by determining the optimal dispatch for generators, shunt capacitors, and converters. The OPF constraints include the operational constraints of all HVac grid and converter stations. The resulting mixed-integer nonlinear programing problem is solved using a proposed framework based on the predictor-corrector primal-dual interior-point method. The proposed OPF formulation and solution approach are verified using a multi-frequency HVac transmission system that is modified from the IEEE 57-bus system. The results with the optimal dispatch from the proposed method during a simulated day show a significant loss reduction and an improved voltage regulation compared to those when an arbitrary dispatch is chosen.

Solving Multiperiod OPF Problems Using an AC-QP Algorithm Initialized With an SOCP Relaxation

Renewable generation and energy storage are playing an ever increasing role in power systems. Hence, there is a growing need for integrating these resources into the optimal power flow (OPF) problem. While storage devices are important for mitigating renewable variability, they introduce temporal coupling in the OPF constraints, resulting in a multiperiod OPF formulation. This paper explores a solution method for multiperiod AC OPF that combines a successive quadratic programming approach (AC-QP) with a second-order cone programming (SOCP) relaxation of the OPF problem. The SOCP relaxation's solution is used to initialize the AC-QP OPF algorithm. Additionally, the lower bound on the objective value obtained from the SOCP relaxation provides a measure of solution quality. This combined method is demonstrated on several test cases with up to 4259 nodes and a time horizon of eight time steps. A comparison of initialization schemes indicates that the SOCP-based approach offers improved convergence rate, execution time, and solution quality.

Solving the Optimal Power Flow Quadratic Cost Functions using Vortex Search Algorithm

This study proposes solving the constraint optimal power flow problem (OPF) by using vortex search algorithm (VSA). VSA is inspired by natural vortexes. Piecewise quadratic fuel cost and quadratic cost curve with valve point loadings test cases are solved on IEEE-30 bus test system by taking into consideration the system constraints such as generation limits, voltages at nodes, tap settings. The obtained test results show that VSA gives better results than any other algorithms which are used to solve the OPF problem.

A novel approach to solve transient stability constrained optimal power flow problems

This paper proposes an approach to solve the transient stability constraint optimal power flow (TSC-OPF) problem. The transient stability constraints are expressed as the critical clearing time (CCT) of different contingencies, and are approximated using artificial neural networks (ANNs). The ANNs provide a nonlinear, differentiable mapping between the load flow variables and the CCT. As a result, the TSC-OPF with multiple transient stability constraints can be solved very efficiently with little additional computational burden. The effectiveness of the proposed method is demonstrated with the IEEE 39 bus and the IEEE 300 bus systems.

The Unit Commitment Problem With AC Optimal Power Flow Constraints

We propose a mathematical programming-based approach to optimize the unit commitment problem with alternating current optimal power flow (ACOPF) network constraints. This problem is a nonconvex mixed-integer nonlinear program (MINLP) that we solve through a solution technique based on the outer approximation method. Our solution technique cooptimizes real and reactive power scheduling and dispatch subject to both unit commitment constraints and ACOPF constraints. The proposed approach is a local solution method that leverages powerful linear and mixed-integer commercial solvers. We demonstrate the relative economic and operational impact of more accurate ACOPF constraint modeling on the unit commitment problem, when compared with copperplate and DCOPF constraint modeling approaches; we use a six-bus, the IEEE RTS-79, and the IEEE-118 test systems for this analysis. Our approach can be extended to solve larger scale power systems as well as include security constraints or uncertainty through decomposition techniques.

A Numerical Study of the Fixed-Threshold Criterion for Expressing Transient Stability Constraints in Optimal Power Flow

A numerical study of the widely used fixed-threshold criterion for expressing transient stability constraints in optimal power flow (TSCOPF) is conducted. Based on a stability-region framework, a more accurate expression of transient stability constraint in TSCOPF is presented. A method for computing system exact threshold values is proposed and employed for the study of threshold values under different conditions. It is shown via numerical results on the WSCC9 and IEEE145 systems that the exact threshold value for each system and contingency is in fact not a constant, and can vary greatly depending on several factors such as types of contingency, loading conditions, and network topology.

Improving the transient stability-constrained optimal power flow with Thyristor Controlled Series Compensators

Due to the rapid increase of electricity demand and the deregulation of electricity markets, power systems tend to operate closer to stability boundaries. The scheme of preventive control should bring in a tradeoff between economics and security, which are often the two major inconsistent requirements for the daily operation of many power systems in the world. Optimal power flow (OPF) is a powerful tool to weaken the conflict between economy and security, but the main obstacle faced is that, the complexity involved for OPF with transient stability constraints is several orders of magnitude higher than that of conventional OPF with merely static constraints. Therefore, consideration of Transient Stability Constraints in Optimal Power Flow (OPF) problems is becoming more and more imperative. FACTS devices such as Thyristor Controlled Series Compensator (TCSC) can be very effective to power system security in case of a contingency. In this paper, we concentrate on the improving transient stability-constrained optimal power flow to against single contingencies via the use of TCSC. Study results on IEEE 30-bus system have proved the effectiveness of using TCSC to improve transient stability-constrained optimal power flow (TSCOPF).

Preventive control approach for voltage stability improvement using voltage stability constrained optimal power flow based on static line voltage stability indices

Voltage stability improvement is a challenging issue in planning and security assessment of power systems. As modern systems are being operated under heavily stressed conditions with reduced stability margins, incorporation of voltage stability criteria in the operation of power systems began receiving great attention. This study presents a novel voltage stability constrained optimal power flow (VSC-OPF) approach based on static line voltage stability indices to simultaneously improve voltage stability and minimise power system losses under stressed and contingency conditions. The proposed methodology uses a voltage collapse proximity indicator (VCPI) to provide important information about the proximity of the system to voltage instability. The VCPI index is incorporated into the optimal power flow (OPF) formulation in two ways; first it can be added as a new voltage stability constraint in the OPF constraints, or used as a voltage stability objective function. The proposed approach has been evaluated on the standard IEEE 30-bus and 57-bus test systems under different cases and compared with two well proved VSC-OPF approaches based on the bus voltage indicator L - index and the minimum singular value. The simulation results are promising and demonstrate the effectiveness of the proposed VSC-OPF based on the line voltage stability index.

Extended Sequential Truncation Technique for Adaptive Dynamic Programming Based Security-Constrained Unit Commitment with Optimal Power Flow Constraints

Considering the economics and securities for the operation of a power system, this paper presents a new adaptive dynamic programming approach for security-constrained unit commitment (SCUC) problems. In response to the “curse of dimension” problem of dynamic programming, the approach solves the Bellman’s equation of SCUC approximately by solving a sequence of simplified single stage optimization problems. An extended sequential truncation technique is proposed to explore the state space of the approach, which is superior to traditional sequential truncation in daily cost for unit commitment. Different test cases from 30 to 300 buses over a 24 h horizon are analyzed. Extensive numerical comparisons show that the proposed approach is capable of obtaining the optimal unit commitment schedules without any network and bus voltage violations, and minimizing the operation cost as well.

Emission Constraint Optimal Power Flow using Differential Evolution

Objective of the power systems firm is to achieve the maximum profit and customer goodwill by providing reliable and quality power supply. This power system operation problem is solved by Optimal Power Flow (OPF). It gives requirement of operating states which satisfy the objective of the firm. Thermal power plants are the main source of power generation. Fuel cost of these power plants has to minimize for better profit at the same time it should satisfy system load demand, real, reactive power limit, voltage limit, power transmission limit and other limitations. For generation cost minimization Economic Load Dispatch (ELD) and Optimal Power Flow (OPF) was developed. When cost is the single objective, the power generation may pollute the environment. Thermal electric power could not be generated without pollution but this pollution can be reduced for the sake of good and healthy atmospheric condition. Differential Evolution (DE) algorithm is used in this paper to solve Emission Constraint Optimal Power Flow problem. Standard IEEE 30 bus, power system having 6 thermal power plants, is considered to validate the simulation.

An Optimal Power Flow Algorithm to Achieve Robust Operation Considering Load and Renewable Generation Uncertainties

Consideration of uncertain injections in optimal power flow (OPF) calculation is increasingly important because more renewable generators, whose outputs are variable and intermittent, are connected into modern power systems. Since it is often difficult to predict the variations of both load and renewable generator output accurately, this paper proposes an OPF algorithm to make optimized results not only have a high probability to achieve minimized generation cost, but also robust to the uncertain operating states. In this paper, the objective of the OPF is to minimize the generation cost of the scenario which has the largest probability to appear in the future. In order to make the OPF result be able to accommodate other possible scenarios, the OPF constraints are modified. Considering the probabilistic distributions of both load and renewable energy output, the modified constraints are derived from Taguchi's orthogonal array testing and probabilistic power flow calculation. The effectiveness of the proposed OPF method is demonstrated by the cases up to the system with 2736 buses.

New approach for optimal UPFC placement using hybrid immune algorithm in electric power systems

The unified power flow controller (UPFC) is one of the most promising flexible AC transmission systems (FACTS) devices for the load flow control. Simultaneous optimization of location and parameters for UPFCs is an important issue when a given number of UPFCs is applied to the power system with the purpose of increasing system loadability. This paper presents the application of hybrid immune algorithm (HIA) such as immune genetic algorithm (IGA) and immune particle swarm algorithm (IPSO) to find optimal location of UPFC to achieve optimal power flow (OPF). The overall cost function, the objective function in the OPF, includes the total active and reactive production cost function of the generators and installation cost of UPFCs and hence, should be minimized. The OPF constraints are generators, transmission lines and UPFCs limits. In power system, it may not always be possible to dispatch the contracted power transactions completely due to congestion of the corresponding transmission corridors. In this study simulations were performed on IEEE 14-bus and IEEE 30-bus test systems for different methods. Under all equality and inequality constraints, the HIA proposed approach minimized the objective function better than other methods such as GA, PSO, and IA; and as far as HIA methods were concerned, the IPSO algorithm gave better minimum cost than IGA method. Results of simulations are encouraging and could efficiently be employed for power system operations.

Optimal placement of UPFC in power systems using immune algorithm

This paper presents the application of immune algorithm (IA) to find optimal location of unified power flow controller (UPFC) to achieve optimal power flow (OPF) and congestion management. Objective function in the OPF, that is to be minimized, is the overall cost functions, which includes the total active and reactive production cost function of the generators and installation cost of UPFCs. The OPF constraints are generators, transmission lines and UPFCs limits. In power system, it may not always be possible to dispatch all of the contracted power transactions due to congestion of the transmission corridors. We propose IA method to minimize the objective function under all equality and inequality constraints. Simulations are performed on 4-bus, IEEE 14-bus and IEEE 30-bus test systems for optimal location of UPFC and the results obtained are encouraging and will be useful in electrical restructuring.

Neural-Network Security-Boundary Constrained Optimal Power Flow

This paper proposes a new approach to model stability and security constraints in optimal power flow (OPF) problems based on a neural network (NN) representation of the system security boundary (SB). The novelty of this proposal is that a closed form, differentiable function derived from the system's SB is used to represent security constraints in an OPF model. The procedure involves two main steps: First, an NN representation of the SB is obtained based on back-propagation neural network (BPNN) training. Second, a differentiable mapping function extracted from the BPNN is used to directly incorporate this function as a constraint in the OPF model. This approach ensures that the operating points resulting from the OPF solution process are within a feasible and secure region, whose limits are better represented using the proposed technique compared to typical security-constrained OPF models. The effectiveness and feasibility of the proposed approach is demonstrated through the implementation, as well as testing and comparison using the IEEE two-area and 118-bus benchmark systems, of an optimal dispatch technique that guarantees system security in the context of competitive electricity markets.

OPF with Environmental Constraints with Multi Shunt Dynamic Controllers using Decomposed Parallel GA: Application to the Algerian Network

Due to the rapid increase of electricity demand, consideration of environmental constraints in optimal power flow (OPF) problems is increasingly important. In Algeria, up to 90% of electricity is produced by thermal generators (vapor, gas). In order to keep the emission of gaseous pollutants like sulfur dioxide (SO2) and Nitrogen (NO2) under the admissible ecological limits, many conventional and global optimization methods have been proposed to study the trade-off relation between fuel cost and emissions. This paper presents an efficient decomposed Parallel GA to solve the multi-objective environmental/economic dispatch problem. At the decomposed stage the length of the original chromosome is reduced successively and adapted to the topology of the new partition. Two subproblems are proposed: the first subproblem is related to the active power planning to minimize the total fuel cost, and the second subproblem is a reactive power planning design based in practical rules to make fine corrections to the voltage deviation and reactive power violation using a specified number of shunt dynamic compensators named Static Var Compensators (SVC). To validate the robustness of the proposed approach, the algorithm proposed was tested on the Algerian 59-bus network test and compared with conventional methods and with global optimization methods (GA, FGA, and ACO). The results show that the approach proposed can converge to the near solution and obtain a competitive solution at a critical situation and within a reasonable time.

Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints

Considering the economics and securities for the operation of a power system, a semi-definite programming (SDP) model for the security-constrained unit commitment (SCUC) problem is described here, which is directly solved by the interior-point method for SDP within the polynomial times. The proposed method is promising for the SCUC problems because of its excellent convergence and the ability of handling the non-covex integer variables. No model decomposition and initial relaxation are needed when applying the SDP-based method. When the solution contains minor mismatches in the integer variables, a simple rounding strategy is used to correct the non-integer into integer efficiently. Different test cases from 6 to 118 buses over a 24 h horizon are presented. Extensive numerical simulations have shown that the proposed method is capable of obtaining the optimal UC schedules without any network and bus voltage violations, and minimising the operation cost as well.

Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.

Direct Incorporation of Fault Level Constraints in Optimal Power Flow as a Tool for Network Capacity Analysis

The aim of this paper is to present a method for the direct incorporation of fault level constraints (FLCs) in the optimal power flow (OPF) as a tool for network capacity analysis, i.e., optimal generation expansion planning within an existing network. A mathematical methodology to convert constraints imposed by fault levels to simple nonlinear inequality constraints is developed. No new variables are introduced in the OPF formulation to describe the additional constraints. Most common OPF-solving engines already have the computational capacity to handle numerous nonlinear constraints, such as the ones described by the power balance equations on buses. Therefore, once FLCs are converted to nonlinear constraints described by OPF variables, they can be directly introduced to any optimization process performing the OPF. A 12-bus/15-line test case demonstrates the advantages of the new method in comparison with a previously proposed iterative method that converted them to restrictions on new capacity. It also proves that when FLCs are ignored, the capacity of the network to absorb new generation is overestimated.

A practical algorithm for unit commitment based on unit decommitment ranking

AbstractThis paper presents a practical algorithm for solving Unit Commitment (UC) problems with network constraints represented in Optimal Power Flow (OPF). The proposed algorithm is based on Successive Approximation Dynamic Programming (SADP) according to a Unit Decommitment Ranking (UDR) which is a priority list for unit decommitment procedure. The UDR can be determined by Dynamic Programming (DP) according to the information of OPF consisting of a set of Lagrange multipliers (dual variables). Since the set of Lagrange multipliers represents the relationship between the optimal value of objective function and OPF constraints, the proposed algorithm can determine power system resource scheduling in consideration of network constraints, such as line flow and voltage constraints. The feasibility and effectiveness of the proposed algorithm are demonstrated on a modified IEEE Reliability Test System. © 2001 Scripta Technica, Electr Eng Jpn, 138(2): 1–13, 2002