Search

In this paper, we propose a parallel dual dynamic programming (PDDP)-based decentralized algorithm for the multi-area optimal power flow (MAOPF), which can preserve the information privacy and operational independence of each area. The MAOPF problem is decomposed into a series of subproblems for individual areas by the dual dynamic programming (DDP) algorithm, and the Benders cut-based value functions are used to reflect the impacts of one area’s decisions to the subsequent areas. The optimal solution of MAOPF can be obtained in a decentralized fashion, requiring only a limited amount of information exchange among neighbor areas. Moreover, a parallel processing technique is designed to avoid the waiting process of the basic DDP algorithm, thus accelerating the computing speed of the proposed decentralized algorithm. Compared with the existing decentralized algorithms, the proposed algorithm has better performance in terms of convergence and computational efficiency. In addition, there is no need for parameter tuning. Case studies on several IEEE test systems and a real 2298-bus system demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

• A framework for DER aggregator to participate in day-ahead market considering security check is proposed. • A single-leader-multi-follower Stackelberg game model is established. • A linearized power flow model of DS with substation transformer tap is proposed. • An A-RBRD algorithm is proposed to solve the Stackelberg game model. • Performance of the model and algorithm are verified using a constructed and a realistic T&D system. With increasing distributed energy resources (DERs) integration, the strategic behavior of a DER aggregator in electricity markets will significantly affect the secure operation of the distribution system. In this paper, the interactions among the DER aggregator, energy and reserve markets, and distribution system are investigated through a single-leader-multi-follower Stackelberg game model with the DER aggregator as the leader and the independent system operator and distribution system operator as the followers. To guarantee the operation security of the distribution system, security check problems under three different scenarios are involved in the follower level, which is linearized using a mixed-integer linearized power flow model. Then, using the strong duality theorem, the proposed model is converted into a bi-level mixed-integer linear (BMILP) programming model with only mixed-integer linear follower-level problems. Next, an accelerated relaxation-based bi-level reformulation and decomposition algorithm is proposed to solve the BMILP problem. Finally, case studies are carried out on a constructed integrated transmission and distribution (T&D) system and a practical integrated T&D system to verify the effectiveness of the proposed model and algorithm. The simulation results indicate that the available downward reserve of the DER aggregator will decrease with the security limitation of the distribution system. [ABSTRACT FROM AUTHOR]

• A mixed-integer linear model for coordinated scheduling of integrated T&D systems is proposed. • An improved Lipschitz dynamic programming-based decentralized algorithm is proposed for the decentralized model. • Two strategies for introducing reverse norm cuts are proposed to improve convergence. • A curve-fitting approach is proposed to obtain pre-defined lower bounds of the value functions for acceleration. • Performance of the proposed algorithms are verified using a constructed and a practical T&D system. In this study, we propose an improved Lipschitz dynamic programming-based decentralized algorithm for the coordinated scheduling of integrated transmission and distribution (T&D) systems, considering unit commitments in a transmission system and the AC power flow and discrete control devices in distribution systems. In this algorithm, reverse norm cuts are introduced iteratively to approximate the value functions of subproblems of distribution systems, which are formulated as mixed-integer linear programming models. Based on the characteristics of subproblems of distribution systems, two strategies for introducing the reverse norm cuts in the subproblem of the transmission system are developed to improve the convergence. Furthermore, to further accelerate the proposed decentralized algorithm, a curve-fitting approach is designed to obtain the pre-defined approximate lower bounds of the value functions of distribution systems at each scheduling time period, which are formulated as a linear constraint set with integer variables. Finally, case studies are conducted on a constructed integrated T&D system and a practical integrated T&D system to verify the accuracy and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy resource (DER) integrations. However, existing online algorithms have the following limitations: 1) Correction-only algorithms ignore the time-varying characteristics of the optimization problem; 2) Prediction-correction algorithms cannot handle nonlinear OPF problems; 3) Most algorithms only consider the application of single-phase cases. This paper addresses the above limitations by proposing a novel measurement-based prediction-correction online distributed OPF algorithm for multi-phase ADNs. This algorithm is based on an improved multi-phase linearized alternating current (AC) power flow model that takes advantage of the voltage measurements to improve the approximation accuracy. In each sampling period, the proposed algorithm first performs a limited number of correction steps, iterating the incremental variable based on the current outputs of DERs and the voltage measurements to track the optimal solution. The DERs then execute the resultant incremental output powers. After forecasting the time-varying parameters, the proposed algorithm performs a few prediction steps to seek a better starting point for the correction steps before the next sampling. Numerical test results of the modified IEEE 37-bus and 123-bus distribution systems demonstrated that the proposed algorithm can track the optimal solution of the time-varying nonlinear OPF problem more accurately than existing online algorithms, even in extra-high penetration scenarios (≥200%). • Time-varying nonlinear optimal power flow (OPF) problems are studied. • Distributed energy resources such as photovoltaics and wind turbines are considered. • An improved multi-phase linearized alternative current power flow model is proposed. • A measurement-based prediction-correction online distributed algorithm is proposed. • Test results show the proposed algorithm outperforms state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

• Four discrete/continuous-time online optimal power flow algorithms are designed. • The proposed algorithms are suitable for active distribution network optimization. • The proposed algorithms are fully evaluated and compared via detailed case studies. • The proposed discrete-time prediction-correction algorithm is the most recommended. This paper discusses and analyzes the latest online algorithm applications for time-varying optimal power flow problems in active distribution networks with numerous power-electronics-interfaced distributed energy resources, which bring significant time-varying characteristics to the optimal operation of active distribution networks. Conventional offline optimization algorithms are time-consuming and unable to track time-varying optimal solutions in highly variable environments. In contrast, online algorithms are characterized by fast calculation speeds and the ability to continuously track optimal solutions, thus having great potential in solving optimization problems that vary rapidly over time. In this paper, we design online time-varying optimal power flow algorithms based on the latest online algorithms, including three discrete-time algorithms (i.e., correction-only, prediction-correction, and correction-extra correction algorithms) and one continuous-time algorithm (i.e., prediction-correction interior-point method). According to our survey of the current applications of online algorithms, this study represents the first time that discrete-time prediction-correction and correction-extra correction algorithms have been applied in solving time-varying optimal power flow problems in active distribution networks. Detailed case studies, including correctness, validity, and sensitivity analysis, are carried out on a modified IEEE 33-node system. The numerical results reveal the advantages, disadvantages, and applicability of the proposed algorithms. Moreover, the characteristics of the discrete-time and continuous-time algorithms are compared intuitively. Finally, based on the numerical results, a guide for how to select an appropriate online time-varying optimal power flow algorithm for active distribution network optimization is provided, wherein the discrete-time prediction-correction optimal power flow algorithm is the most frequently recommended choice. [ABSTRACT FROM AUTHOR]

Dispatchable distributed energy resources (DERs) in distribution networks are envisioned to aid frequency regulation for transmission systems. In this paper, a real-time optimal dispatch framework for DERs in distribution networks is designed to offer frequency regulation services simultaneously. Different from the existing research that distribution networks track uniaxially the predetermined auxiliary-services commands of the transmission system, here we regard transmission system frequency regulation as a black box and learn the parameters of its proxy satisfaction function from the perspective of DER optimization. To solve such a special optimization problem with control performance feedback, first we employ Gaussian processes to learn the satisfaction function, and, especially, build pertinent upper confidence bounds to achieve the optimal provision of ancillary services. Next, the primal-dual gradient projection process is embedded into the Gaussian process upper confidence bound algorithm to pursue the optimal DER dispatch. Accordingly, the output powers of DERs can be controlled in real-time: in disaggregate mode, they meet the goal of the distribution network; in aggregate mode, they provide a more satisfactory tie-line power flow to the transmission system. Simulations for illustrative systems are provided to validate the approach. • Real-time optimization of DNs with DERs participating in frequency regulation is studied. • A special optimal scheduling problem of DMS with control feedback from EMS is solved. • A real-time optimization algorithm that embeds the PDGP into the GP-UCB is designed. • Learning proxy function is performed concurrently with the execution of optimization. • Nodal voltage in DNs are taken into account when provide frequency regulation recourses. [ABSTRACT FROM AUTHOR]

• A robust optimization for small-signal stability constrained optimal power flow (SSSCOPF-RO) model of a power system considering the dynamic characteristics and uncertain power output of DFIGs is established. • The SSSCOPF-RO model is transformed into an SDP model using the semi-definite relaxation (SDR) and McCormick envelop relaxation (MER) techniques to improve the convergence and computational efficiency. • The bilayer robust optimization model is transformed into a single-layer optimization model based on dual programming theory to be directly solved by commercial solvers. • Results show the high efficiency, accuracy and robustness of the proposed method. When substantial wind power generation is integrated into the power system, the low rotational inertia and uncertain power output of wind turbines pose a great challenge to the small-signal stability (SSS) of power system operation. In this paper, considering the dynamic model of a doubly fed induction generator (DFIG) and the uncertainty of wind power, we establish a bilayer robust optimization of the SSS constrained optimal power flow (SSSCOPF-RO) model for a power system with DFIGs. It uses Lyapunov's second theorem to describe the SSS constraint. By the semi-definite relaxation and McCormick envelope relaxation techniques, we transform the inner-layer optimization of the SSSCOPF-RO model into a semi-definite program (SDP) model to improve the convergence reliability and computational efficiency of solving the model. Based on the dual optimization theory, the inner-layer SDP model is converted into its dual SDP model, and the bilayer robust optimization model is transformed into a single-layer optimization model, which can be solved using the solver MOSEK in the software CVX. Finally, case studies were conducted on IEEE 9-, 39-, and 118-bus systems to validate the proposed method. The obtained optimal solution of the transformed single-layer optimization model could ensure the SSS of the system under the uncertain fluctuation of DFIGs' active power output and effectively reduce the network loss cost, and the results indicate the effectiveness and robustness of the proposed model. [ABSTRACT FROM AUTHOR]

• A hybrid node-branch OPF model for calculating the SVSM of ITDNs is proposed. • Different reactive power-voltage control modes and uncertainty of RESs are considered. • Two distributed bi-level OPF models for the SVSM interval of ITDNs are established. • The ADMM algorithm is used to obtain the SVSM interval of ITDNs distributedly. • Results on different ITDNs show the accuracy and efficiency of the proposed method. To accurately and efficiently calculate the static voltage stability margin (SVSM) interval of integrated transmission and distribution networks (ITDNs) considering the uncertain fluctuation of renewables, a distributed bi-level optimal power flow (OPF) calculation method based on the alternating direction method of multipliers for the SVSM interval of ITDNs is proposed in this paper. Due to the different structure characteristics of transmission network (TN) and distribution network (DN), a hybrid node-branch OPF method for calculating the SVSM of ITDNs is proposed, which has better convergence than the traditional node OPF method. Different reactive power-voltage control modes of renewable energy stations (RESs) are also considered in the calculation. Considering the uncertain fluctuation of RESs, two distributed bi-level OPF models for calculating the upper and lower bounds of the SVSM interval of ITDNs are established. Based on the alternating direction method of multipliers, the SVSM interval bounds of ITDNs can be obtained by solving the sub-optimization models and transmitting the boundary coupling variables and the load growth parameter between the TN and multiple DNs iteratively until the given convergence criterion is satisfied. Test results on two ITDNs, the modified IEEE 39–33 & 69 bus system and an actual 2285-bus ITDNs, demonstrate the high computation accuracy and efficiency of the proposed distributed bi-level OPF method compared with other calculation methods. [ABSTRACT FROM AUTHOR]

• •A FFHE method combining with the Pade approximation to calculate the post N -1 contingency SVSM is proposed. • •The approximate power series expression and the rational fraction expression of the post-contingency SVSM are obtained. • •The contingency instability degree of severe N -1 contingencies can be calculated. • •Results show the accuracy and robustness of the proposed method. A calculation technique for the static voltage stability margin (SVSM) under N -1 contingency based on the fast and flexible holomorphic embedding (FFHE) and Pade approximation (PA) methods is proposed. The technique can also obtain the approximate analytic function between the post N -1 contingency SVSM and the pre-contingency SVSM. Using the contingency parameter as an embedded variable, the relationship between the post N -1 contingency SVSM and the pre-contingency SVSM is approximately described in the form of power series. By constructing the FFHE matrix equation, the values of state variables at the pre-contingency static voltage stability limit point are taken as the 0th order coefficients. The FFHE matrix equation is solved to obtain the higher order coefficients from the lower order coefficients step by step. Thereby the power series expression of post N -1 contingency SVSM is obtained. In addition, by using the PA method, the approximate rational fraction expression of the post-contingency SVSM which can improve the convergence and accuracy of the power series can be obtained. Test results for the IEEE 39-bus system and an actual 1559-bus power grid demonstrate that the proposed method to calculate the post-contingency SVSM has high accuracy and strong robustness compared with the optimal power flow and continuation power flow methods. The average relative errors of the proposed method in the two cases are 0.58155% and 1.0862%. The strong robustness is reflected in the fact that there is no need to repeatedly select the initial value for calculation under different contingencies. [ABSTRACT FROM AUTHOR]

• The interval of the SVSM of ITDNs is calculated. • A DCC method for SVSM central value based on polynomial approximation is proposed. • A DCC method of the affine interval algorithm for SVSM fluctuation is proposed. • Results show the accuracy and efficiency of the proposed method. The uncertain power output of renewable energy stations (RESs) will result in the uncertain fluctuation of the static voltage stability margin (SVSM) of a power system with centralized and distributed RESs integrated to the transmission network (TN) and distribution networks (DNs), respectively. A decomposition and coordination calculation (DCC) method is proposed to determine the SVSM interval of integrated transmission and distribution networks (ITDNs) using intervals to describe the uncertain RES outputs. First, based on the polynomial approximation expressions of the injected power of the boundary bus with respect to its voltage and the load growth parameter of each DN, the DCC of continuation power flow between TN and DNs is executed to obtain the central value of the SVSM interval of ITDNs. Next, the affine interval algorithm is used to calculate the SVSM fluctuation interval caused by the uncertain RES output intervals. The block bordered-diagonal form and Gaussian elimination method are used to execute the DCC of the first-order sensitivities of SVSM with respect to RES outputs, and alternating iterations between TN and each DN are used to execute the DCC for optimizing the contractive noise symbol intervals. The proposed DCC method can efficiently calculate the SVSM interval of ITDNs in which lots of DNs are integrated with distributed RESs. Test results on two ITDNs, one composed of modified IEEE systems and the other an actual 2285-bus power grid, demonstrate the correctness and efficiency of the proposed method compared with the centralized algorithm and the Monte Carlo method. [ABSTRACT FROM AUTHOR]

• A dynamic energy management model for maximizing the expected-cost realization-probability. • A novel approximate dynamic programming algorithm designed to solve the proposed model. • Transformation of the DEM model into the Markov decision process. • Decomposition of the mixed-integer nonlinear programming problem into small nonlinear programming problems. Dynamic energy management (DEM) is being recognized as an important tool for the economical and efficient operation of microgrid. This paper proposes an expected-cost realization-probability (ECRP) optimization approach for the DEM of microgrid. In the model, the expected cost is taken as an economic goal to find the schedule with the maximum ECRP (i.e., the maximum probability of obtaining an actual operation cost which is lower than this economic goal). It is a stochastic mixed-integer nonlinear programming (MINLP) problem composed of the AC power flow, battery operation characters and logical variables. To solve this NP-hard problem, an ECRP-based approximate dynamic programming is proposed. The original MINLP problem is decomposed into small nonlinear programming subproblems to facilitate the solution. And the ECRP-based value function is formed to describe the relationship among the decisions of subproblems, which helps to obtain the near-optimal decision in a decomposed manner. Simulation examples presented on a real microgrid indicate that the ECRP of the proposed method is higher than those of the other two comparison algorithms. [ABSTRACT FROM AUTHOR]