A multivariate dimension-reduction method for probabilistic power flow calculation

Wind farms commonly cluster in regions rich in wind resources. Thus, correlation of wind speeds from different wind farms should not be ignored when modeling a power system with large wind energy penetration. This paper proposes a probabilistic optimal power flow (POPF) technique based on the quasi-Monte Carlo simulation (QMCS) considering the correlation of wind speeds using copula functions. In this paper, a copula function is used to model the dependent structure of random wind speeds and their forecast errors. QMCS is employed in the sampling procedure to reduce computation burden. The proposed method is applied in probabilistic power flow (PPF). Furthermore, the PPF is used in the POPF problem that aims at minimizing the expectation and downside risk of fuel cost simultaneously. Simulation studies are conducted on a modified IEEE 118-bus power system with wind farms integrated in two areas, and the results show that the accuracy and efficiency are improved by the proposed method.

Probabilistic power flow with topology changes based on deep neural network

In recent years, the increasing integration of renewable energy and electric vehicles has exacerbated uncertainties in power systems. Operators are interested in identifying potential violation events such as overvoltage and overload via probabilistic power flow calculations. Evaluating the violation probabilities requires sufficient accuracy in tail regions of the output distributions. However, the conventional Monte Carlo simulation and importance sampling typically require numerous samples to achieve the desired accuracy. The required power flow simulations result in substantial computational burdens. This study addresses this challenge by proposing a surrogate-assisted importance sampling method. Specifically, a high-fidelity radial basis function-based surrogate is constructed to approximate the nonlinear power flow model. Subsequently, the surrogate is embedded in the conventional importance sampling technique to evaluate the rare probabilities with high efficiency and reasonable accuracy. The computational strengths of the proposed method are validated in the IEEE 14-bus, 118-bus, and realistic 736-bus systems through comparisons with several well-developed methods. The comparisons provide a reference for system operators to select the appropriate method for evaluating violations based on the intended applications.

Renewable energy sources, such as wind and photovoltaic solar, have been increasingly integrated into electricity grids. They have introduced additional uncertainty to power systems along with uncertainty due to stochastic nature of demand. Traditional deterministic power flow does not provide sufficient information for the calculation and analysis of such power systems; therefore, to manage such uncertainties, probabilistic power flow methodologies need to be used. This paper presents a cumulant-based probabilistic power flow approach in which we develop a technique to deal with various probability distributions that represent different sources of uncertainty in power systems. The proposed approach is caried out on the modified IEEE-14 bus test system, showing good performance in comparison with the result obtained by Monte Carlo simulation.

With the rapid growth of renewables, probabilistic optimal power flow (POPF) has become an important tool to analyze uncertainties in power systems. However, POPF calculation involves repeatedly solving the optimization problem. The computational efficiency has been a major bottleneck for its practical application in power industries. This letter proposes a novel method to significantly improve the efficiency of POPF calculation while maintaining the desired accuracy. The IEEE 30-bus, IEEE 118-bus, and practical utility 661-bus systems are used to demonstrate the effectiveness of the proposed method.

Facing stochastic variations of the loads due to an increasing penetration of renewable energy generation, online decision making under uncertainty in modern power systems is capturing power researchers' attention in recent years. To address this issue while achieving a good balance between system security and economic objectives, we propose a surrogate-enhanced scheme under a joint chance-constrained (JCC) optimal power-flow (OPF) framework. Starting from a stochastic-sampling procedure, we first utilize the copula theory to simulate the dependence among multivariate uncertain inputs. Then, to reduce the prohibitive computational time required in the traditional Monte-Carlo (MC) method, we propose to use a polynomial-chaos-based surrogate that allows us to efficiently evaluate the power-system model at non-Gaussian distributed sampled values with a negligible computing cost. Learning from the MC simulated samples, we further proposed a hybrid adaptive approach to overcome the conservativeness of the JCC-OPF by utilizing correlation of the system states, which is ignored in the traditional Boole's inequality. The simulations conducted on the modified Illinois test system demonstrate the excellent performance of the proposed method.

In a modern power system, stable operation of the electrical system is a major concern. For the stable operation of power system, it is desirable to access the effect of unforeseen events and identification of more sensitive nodes. The most outstanding job of distribution engineers is to simulate the power system for corrective action. Probabilistic power flow (PPF) is a tool that can effectively access the performance of power system network over most of its working conditions taking into account the unforeseen events. In this paper, a new PPF model is developed to evaluate power system network taking into account the uncertainty with input random variables, such as wind energy, loads, generation outage, and branch outage. This model is based upon the two well-known methods, Monte Carlo simulation (MCS) and point estimation method (PEM). For the sake of, computational efficiency and results accuracy Box-Muller sampling equation was used with MCS and $2m+1$ concentration scheme was used with PEM. The proposed model was investigated by using modified IEEE 14-bus standard test system.

As a matter of course, the unprecedented ascending penetration of distributed energy resources (DERs), mainly harvesting renewable energies (REs), is concomitant with environmentally friendly concerns. This type of energy resources are innately uncertain and bring about more uncertainties in the power system, consequently, necessitates probabilistic analyses of the system performance. Moreover, the uncertain parameters may have a considerable level of correlation to each other, in addition to their uncertainties. The two point estimation method (2PEM) is recognized as an appropriate probabilistic method in small scale or even medium scale problems. This paper develops a new methodology for probabilistic optimal power flow (P-OPF) studies for such problems by modifying the 2PEM. The original 2PEM cannot handle correlated uncertain variables but the proposed method has been equipped with this ability. In order to justify the impressiveness of the method, two case studies namely the Wood & Woollenberg 6-bus and the Mathpower 30-bus test systems are examined using the proposed method, then, the obtained results are compared against the Monte Carlo simulation (MCS) results. Comparison of the results justifies the effectiveness of the method in the respected area with regards to both accuracy and execution time criteria.

In this paper, a power flow calculation method for real bipolar voltage source converter (VSC) based high voltage direct current (HVDC) grid is proposed, which is applicable for the system operating in symmetric mode and asymmetrical mode. An optimization method for the asymmetrical mode is proposed to increase the safety and reliability of the system. The simulation results verify that the power flow calculation method possesses high precision and the optimization method works effectively.

Guest Editorial: Situational awareness of integrated energy systems

Uncertainty parameters of battery energy storage integrated grid and their modeling approaches: A review and future research directions

Due to the lack of the support from the main grid, the islanded hybrid ac/dc microgrid will more likely cause the power flow severe fluctuation and even the microgrid to be split once a serious contingency occurs. To maintain the security and stability of the system under such a condition, this paper proposes a new static security risk assessment of the islanded hybrid ac/dc microgrid considering that the hybrid ac/dc microgrid was split. First, this paper presents a static security analysis criterion to determine the post-contingencies splitting scheme and a new load-shedding strategy to achieve power balance of subsystems. On this basis, a probabilistic power flow calculation method based on Levenberg-Marquardt with a nonmonotone line search (LMNL) algorithm is applied to calculate the probabilistic power flow of the islanded subsystems. Finally, the probability distribution of static security risk assessment indexes, including the dc loss load risk, ac loss load risk, and interlinking converter (ILC) active power limit violation risk, are obtained. The simulation results on the test system demonstrate the necessity of considering the hybrid ac/dc microgrid was split, and prove the feasibility and effectiveness of the proposed method.

Power systems optimization under uncertainty: A review of methods and applications

To evaluate the impact of the randomness and correlation of photovoltaic (PV) and load on AC/DC systems with a multiport current flow controller (M-CFC), this paper proposes a probabilistic optimal power flow calculation for AC/DC systems based on a nonparametric kernel density estimation. First, according to the M-CFC model, the DC power flow calculation method with M-CFC was deduced, and its influence on line loss was analyzed. Second, a nonparametric kernel density estimation with an adaptive bandwidth was used to accurately describe the probability distribution of the PV and load, and correlation samples of the PV and load were obtained by the mixed copula function. Then an optimization model that considers system loss and static security was established, and a fast nondominated sorting genetic algorithm based on the elite strategy (NSGA-II) was used to calculate the multi-objective probability optimal power flow of the AC/DC system. Finally, a case study was performed on the modified IEEE39 bus system using measured PV and load data. We verified the nonparametric kernel density estimation with an adaptive bandwidth can better adapt to random component uncertainty, and M-CFC can improve the static security of the system.

Most existing carbon emission management strategies only control the total carbon emission without focusing on both the regional carbon emission and the stochastic properties of the system. Correlated regional loads and unpredictable renewable energies in the power system make regional carbon emission management (RCEM) increasingly challenging and necessary. A complex multi-objective RCEM model based on probabilistic power flow (PPF) considering correlated variables is contributed in this paper. The three objective functions to be minimized are 1) the cost of electricity generated, 2) the total carbon emission, and 3) the carbon emission difference among regions which reflects the regional carbon emission imbalance from the supply side. A new clonal selection algorithm (CSA) coupled with a fuzzy satisfying decision method and an extended 2 m +1 point estimate method (PEM) is proposed to solve this multi-objective RCEM model. The proposed method is illustrated through IEEE 30-bus, IEEE 118-bus and simplified Shanghai case studies. The proposed model can help reduce the total carbon emission, control regional carbon emission, prevent probabilistic congested lines from overloading, and choose the most suitable region for wind farms (WFs).