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

This paper presents the semismooth Newton-type algorithms for solving optimal power flow (OPF) problems. Considering that there exist plentiful bounded constraints in OPF, the paper treats general inequality constraints and bounded constraints separately. By introducing a diagonal matrix and the nonlinear complementarity function, the Karush-Kuhn-Tucker (KKT) system of the OPF is transformed equivalently to a system of nonsmooth bounded constrained equations. Comparing with the classical OPF methods and the nonlinear complementarity problem (NCP) method, this treatment has two remarkable advantages. First, it has a strong ability to handle the inequality constraints in OPF problems. Second, it reduces the number of dual variables in the KKT system. Based on the reformulated equations, the paper designs a projected semismooth Newton algorithm which has nice global and local convergence property. Furthermore, according to the weak-coupling property in power systems, the paper presents a decoupled semismooth Newton-type algorithm. The decoupled method solves the system of equations via solving two lower dimension problems. Therefore the method saves the computing cost in theory. Some standard IEEE systems are used to test the two algorithms, and numerical results show that the proposed algorithms are promising for solving OPF problems

The transient stability constrained optimal power flow (TSC‐OPF) is a big challenge in the field of power systems because of its high complexity and extensive computation effort involved in its solution. This study presents a new approach to compute the transient stability constraint formulated by the critical clearing time (CCT) in TSC‐OPF. CCT has been determined by dual‐kriging, a space interpolation method which has primarily been used in natural resources evaluation. Given the huge dimensionality of the problem, Pareto analysis is firstly used to reduce the number of input variables in an initial database to those which are significant to compute CCT. With the reduced variables, a new database has been constructed using a design of experiment to obtain a reduced number of observed points. As a result of this approach, the sets of dynamic and transient stability constraints to be considered in the optimisation process are reduced to one single stability constraint with only a few variables. Ultimately, the size of the resulting optimisation problem is almost similar to that of a conventional optimal power flow. The effectiveness of the proposed method is tested on the New England 10‐machine 39‐bus system and the larger 50‐machine 145‐bus power system.

A new transient stability‐constrained optimal power flow (TSCOPF) model for power system optimal operations is presented in this study. The proposed model is a non‐linear, non‐convex, discrete, and non‐differentiable optimisation problem, and very difficult to be solved by classic programming algorithms. In this study, an effective optimisation framework is developed to address the TSCOPF problem. The self‐adaptive differential evolution (SaDE) algorithm is employed in the framework, which can effectively eliminate the needs for the strategy selection process and at the same time improve the robustness of the DE search process. The benchmark New England 10‐generator, 39‐bus system is used to verify the efficacy of this algorithm. The simulation result obtained using SaDE is compared with both conventional mathematical method and the recently published heuristic methods for OPF problems. The simulation results reveal that the SaDE optimisation technique outperforms other algorithms in both terms of robustness and solution quality.

A novel approach based on both single machine equivalent (SIME) and trajectory sensitivity methods is proposed to formulate a transient stability-constrained optimal power flow (TSC-OPF) in the Euclidian space, where only one single stability constraint is necessary in the optimization problem to represent all dynamic and transient stability constraints of the multi-machine system, resulting in a tractable approach to the preventive control of transient stability in realistic power systems. A unified framework of time domain analysis is proposed, where the transient stability, trajectory sensitivity and SIME analyses are all combined to assess the system's stability and to compute the sensitivity coefficients of the proposed transient stability constraint. Based on these sensitivity coefficients, a non-heuristic selection criterion is proposed to perform the preventive control by rescheduling only a selected number of generators, which is the commonly accepted practice followed by the system's operators. The validity and the effectiveness of the proposed method is numerically demonstrated in the Mexican 46-machine, 190-bus system.

Transient stability constrained optimal power flow considering fourth-order synchronous generator model and controls

Objective: In this paper, an improved hybrid differential evolution (IHDE) algorithm based on differential evolution (DE) algorithm and particle swarm optimization (PSO) has been proposed to solve the optimal power flow (OPF) problem of power system which is a multi-constrained, large-scale and nonlinear optimization problem. Method: In IHDE algorithm, the DE is employed as the main optimizer; and the three factors of PSO, which are inertia, cognition, and society, are used to improve the mutation of DE. Then the learning mechanism and the adaptive control of the parameters are added to the crossover, and the greedy selection considering the value of penalty function is proposed. Furthermore, the replacement mechanism is added to the IHDE for reducing the probability of falling into the local optimum. The performance of this method is tested on the IEEE30-bus and IEEE57-bus systems, and the generator quadratic cost and the transmission real power losses are considered as objective functions. Results: The simulation results demonstrate that IHDE algorithm can solve the OPF problem successfully and obtain the better solution compared with other methods reported in the recent literatures.

Transient stability constrained optimal power flow (TSCOPF) is a non-linear optimisation problem used to perform economic dispatches while ensuring TS. This study proposes a multi-contingency TSCOPF model that retains the dynamics of all generators and includes a transient synchronous generator fourth-order dq-axis model. A program is developed that automatically reads the system data from standard files, builds the multiple-contingency TSCOPF model on a high-level modelling system and solves it using a non-heuristic interior point algorithm. This approach facilitates the application of the model to a variety of systems and scenarios. A TSC based on the speed deviation instead of the rotor angle is proposed. Results obtained on several standard systems are shown. The proposed method is applied to the northwest Spanish transmission system to obtain an optimised dispatch that ensures TS after any of a number of faults, and to assess the economic impact of fault-clearing times at different substations.

Transient stability constrained optimal power flow (TSCOPF) is one the most computational-intensive applications in power systems. Research efforts were made to utilize high performance computing (HPC) technology to parallelize and accelerate TSCOPF solving process, but challenges still exist in performance analysis to identify bottlenecks and improve efficiency on practical HPC platforms such as Beowulf clusters. Based on first two authors' previous work [8, 12] - two-level parallel TSCOPF with reduced-space interior point method (RIPM), a systematic performance analysis approach is demonstrated in this paper. Comprehensive performance analysis procedures - wall time analysis, MPI/OpenMP profiling and tracing - is employed in order to discover performance bottlenecks. State-of-the-art performance analysis software are employed to generate and visualize performance data, providing guidelines for parallel performance enhancement. Numerical results on a 2746-bus system show effectiveness of the proposed approach and relative low overhead in solving large-scale multi-contingency TSCOPF on a Beowulf cluster.

In general, power system expansion planning can be classified into three types such as generation expansion planning (GEP), transmission expansion planning (TEP) and distribution system expansion planning (DEP). Several researches have been performed in GEP and TEP. But, a huge research gap is still available in the topic of DEP. DEP can be classified into two optimization problems, namely substation expansion planning (SEP) and optimal feeder routing. This study attempts to solve real-time SEP problem for the power sector of Tamil Nadu, a state in India. Due to several design variables, the grouping of discrete and continuous variables frames the SEP problem as complicated. Hence, a promising optimization algorithm is essential to solve this complicated problem. The application of differential evolution (DE) algorithm has been presented to obtain the results with the sizes and sites of both the existing and proposed substations (SS) by satisfying the subjected constraints.KeywordsSubstation expansion planningDifferential evolutionTamil NaduLeast cost

There are many voltage‐dependent loads (VDLs) in power systems. When the unit reserve supply is low, the transmission network adjusts the voltage of grid‐connected nodes to provide additional resources. Many reactive power devices with different regulatory performance levels and timescales must be coordinated to employ flexible VDLs to the maximum extent, and consequently, a transient stability‐constrained optimal power flow (TSCOPF) problem with mixed integers and multiperiod coupling must be solved. A multitimescale scheduling ‘day‐ahead‐intraday‐real‐time’ framework is designed for the optimal economic scheduling of VDLs. In the day‐ahead stage, the optimal scheduling period of the discrete reactive power control devices is determined. In the intraday stage, a rolling optimization model based on model predictive control is established, and the specific action times of the discrete reactive power devices are determined. In the real‐time stage, the optimal regulation strategy of the continuous reactive power control device is optimized by rolling. Then, to consider the speed and accuracy of the solution at the same time, a continuous sensitivity correction method is adopted to simplify and solve the original model. Finally, with a modified IEEE‐39 system and a modified IEEE‐118 system as examples, it is verified that the multitimescale scheduling framework maximizes the exploitation of the flexible resources of VDLs to ensure voltage security and stability and improve the economy of system operation under different scenarios.

For operating electrical power networks, the Optimal Power Flow (OPF) problem plays a central role. The problem is nonconvex and NP hard. Therefore, designing efficient solution algorithms is crucial, though their global optimality is not guaranteed. Existing semi-definite programming relaxation based approaches are restricted to OPF problems for which zero duality holds, whereas for non-convex problems there is a lack of solution methods of provable performance. In this paper, an efficient novel method to address the general nonconvex OPF problem is investigated. The proposed method is based on alternating direction method of multipliers combined with sequential convex approximations. The global OPF problem is decomposed into smaller problems associated to each bus of the network, the solutions of which are coordinated via a light communication protocol. Therefore, the proposed method is highly scalable. The convergence properties of the proposed algorithm are mathematically and numerically substantiated.

Machine learning is playing an increasingly important role in transient stability assessment. One of the key challenges of machine learning-based transient stability assessment in the case of dealing with large-scale and high-dimensional data samples of AC-DC power systems is to eliminate redundant variables to improve the training speed and quickly determine the optimal parameters of the adopted algorithms. Aiming at this problem, this paper proposes a Bayesian optimization-based XGBoost (B-XGBoost) method for transient stability assessment of power systems. The method uses serial integration of multiple regression trees to calculate the importance ranking of transient stability features. Combined with correlation analysis, the relationship between input data and transient stability can be explored more intuitively, and redundant variables can be eliminated; Bayesian optimization is used in training to quickly determine the best parameters of the model. Simulations are performed in a 39-node AC-DC system, and the results show that the B-XGBoost transient stability evaluation method has higher accuracy and a significant advantage in speed compared with other machine learning-based methods such as GBDT, DBN, RF, SVM.

Online transient stability assessment and preventive control are important measures to prevent power system blackouts. Based on the deep cross network (DCN), an online assessment and preventive control method for power system transient stability is proposed. The deep cross network is developed to estimate the critical clearing time (CCT) of the credible fault contingencies. Based on the deep cross network model, the sensitivity of the active power of the generator set to the fault critical clearing time is calculated and then the DCN model-embedded transient stability constrained optimal power flow (TSCOPF) model is proposed to compute the preventive generation re-dispatch strategy. This TSCOPF model is computed by successive linear programming assisted by the DCN. The simulation results of the IEEE 39-bus test system show that this method can give early warning to the operation mode with instability risk and generate preventive control strategies, which can effectively improve the safety level of power grid operation.

Graphics processing unit (GPU) has significantly increased the computing capacity of state-of-the-art high performance computing systems. This paper presents a novel GPU acceleration approach for transient stability-constrained optimal power flow (TSCOPF), which is one of the most computational challenging tasks in large-scale power system applications. Enabled by the revealed two-level decomposition parallelism in reduced-space interior point method, GPUs serve as plug-and-play coprocessors for time-consuming linear algebra operations in TSCOPF solving. Enhanced by multi-GPU processing and mixed-precision iterative refinement technique, the efficiency of solving TSCOPF is greatly improved without redesigning and reimplementing the existing algorithm framework. Numerical studies based on a series of test cases with up to 12 951 buses indicate the effectiveness of the proposed GPU-based approach for large-scale TSCOPF problems.

The impact of numerous distributed generators (DGs) coupled with the implementation of virtual inertia on the transient stability of power systems has been studied extensively. Time-domain simulation is the most accurate and reliable approach to evaluate the dynamic behavior of power systems. However, the computational efficiency is restricted by their multi-time-scale property due to the combination of various DGs and synchronous generators. This paper presents a novel projective integration method (PIM) for the efficient transient stability simulation of power systems with high DG penetration. One procedure of the proposed PIM is decomposed into two stages, which adopt mixed explicit-implicit integration methods to achieve both efficiency and numerical stability. Moreover, the stability of the PIM is not affected by its parameter, which is related to the step size. Based on this property, an adaptive parameter scheme is developed based on error estimation to fit the time constants of the system dynamics and further increase the simulation speed. The presented approach is several times faster than the conventional integration methods with a similar level of accuracy. The proposed method is demonstrated using test systems with DGs and virtual synchronous generators, and the performance is verified against MATLAB/Simulink and DIgSILENT PowerFactory.