Search

A modern power system is characterized by a stochastic variation of the loads and an increasing penetration of renewable energy generation, which results in large uncertainties in its states. These uncertainties bring formidable challenges to the power system planning and operation process. To address these challenges, we propose a cost-effective, iterative response-surface-based approach for the chance-constrained AC optimal power-flow problem that aims to ensure the secure operation of the power systems considering dependent uncertainties. Starting from a stochastic-sampling-based framework, 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 method, we propose, instead of using the original complicated power-system model, to rely on a polynomial-chaos-based response surface. This response surface allows us to efficiently evaluate the time-consuming power-system model at arbitrary distributed sampled values with a negligible computational cost. This further enables us to efficiently conduct an online stochastic testing for the system states that not only screens out the statistical active constraints, but also assists in a better design of the tightened bounds without using any Gaussian or symmetric assumption. Finally, an iterative procedure is executed to fine-tune the optimal solution that better satisfies a predefined probability. The simulations conducted in multiple test systems demonstrate the excellent performance of the proposed method.

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To estimate the uncertainty in the stochastic economic dispatch (SED) problem for the purpose of forecasting, the conventional Monte-Carlo (MC) method is prohibitively time-consuming for practical applications. To overcome this problem, we propose a novel Gaussian-process-emulator (GPE)-based approach to quantify the uncertainty in SED considering wind power penetration. Facing high-dimensional real-world data representing the correlated uncertainties from wind generation, a manifold-learning-based Isomap algorithm is proposed to efficiently represent the low-dimensional hidden probabilistic structure of the data. In this low-dimensional latent space, with Latin hypercube sampling (LHS) as the computer experimental design, a GPE is used, for the first time, to serve as a nonparametric, surrogate model for the original complicated SED model. This reduced-order representative allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus test system reveal the impressive performance of the proposed method.

A modern power system is characterized by an increasing penetration of wind power, which results in large uncertainties in its states. These uncertainties must be quantified properly; otherwise, the system security may be threatened. Facing this challenge, we propose a cost-effective, data-driven approach to assessing a power system's load margin probabilistically. Using actual wind data, a kernel density estimator is applied to infer the nonparametric wind speed distributions, which are further merged into the framework of a vine copula. The latter enables us to simulate complex multivariate and highly dependent model inputs with a variety of bivariate copulae that precisely represent the tail dependence in the correlated samples. Furthermore, to reduce the prohibitive computational time of traditional Monte-Carlo simulations that process a large amount of samples, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model through a Bayesian-learning framework. To accelerate the convergence rate of this Bayesian algorithm, a truncated polynomial chaos surrogate, which serves as a highly efficient, parametric Bayesian prior, is developed. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. Results of simulations that are performed on several test systems reveal the impressive performance of the proposed method in the probabilistic load-margin assessment.

Polynomial-chaos-expansion-based surrogate models have recently been advocated in the literature for power system dynamic parameter estimation. Regarding the estimation of the uncertain generator parameters, a Bayesian inference framework has been proposed based on a polynomial-based reduced-order representation of the synchronous machines using assumed parameter values. Then, the non-Gaussian posterior probability distribution functions (pdfs) of these parameters are recovered through the stochastic sampling approach efficiently. However, facing very large parameter errors, the reliability of the surrogate model decreases, yielding biased estimation results. To overcome this problem, this article develops a hierarchical Bayesian inference framework that processes the measurements provided by phasor measurement units, while making use of multifidelity surrogates together with the importance sampling method. The latter allows us to estimate in an efficient manner the posterior pdfs of the uncertain parameters through the normalized weights of the prior samples. To improve the accuracy of the posterior pdfs, an adaptive procedure is further adopted in the importance sampling for the gradual evolution of its proposal functions. The new proposals assist in fine-tuning the sample space and thereby help to construct surrogates with higher fidelity. Through an iterative process, this approach is able to estimate accurately and efficiently non-Gaussian posterior pdfs of the uncertain generator parameters subject to gross errors.

In this letter, a novel Gaussian process emulator is proposed, for the first time, to conduct the probabilistic power-flow calculation. Based on Bayesian inference, a Gaussian process emulator is trained and served as a nonparametric, reduced-order model of the nonlinear power-flow model. This emulator allows us to evaluate the time-consuming power-flow solver at the sampled values with a negligible computational cost. The simulations reveal the excellent performance of this method.

The flow characteristics of reactor fuel assembly always intrigue the designers and the experimentalists among the myriad phenomena that occur simultaneously in a nuclear core. In this work, the visual experimental method has been developed on the basis of refraction index matching (RIM) and particle image velocimetry (PIV) techniques to investigate the detailed flow characteristics in China fast reactor fuel subassembly. A 7-rod bundle of simulated fuel subassembly was fabricated for fine examination of flow characteristics in different subchannels. The experiments were performed at condition of Re = 6500 (axial bulk velocity 1.6 m/s) and the fluid medium was maintained at 30 °C and 1.0 bar during operation. As for results, axial and lateral flow features were observed. It is shown that the spiral wire has an inhibitory effect on axial flow and significant intensity of lateral flow mixing effect is induced by the wire. The root mean square (RMS) of lateral velocity fluctuation was acquired after data processing, which indicates the strong turbulence characteristics in different flow subchannels. Keywords: Lateral flow mixing strength, PIV measurement, Flow characteristics analysis, China fast reactor fuel subassembly

In this work, we develop a polynomial-chaos-expa- nsion (PCE)-based approach for decentralized dynamic parameter estimation through Bayesian inference. Using this approach, the non-Gaussian distribution of the inverted parameters is obtained. More specifically, we first represent the decentralized generator model with the PCE-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through Metropolis-Hastings (M-H)-based Markov chain Monte Carlo (MCMC). Then, we propose a two-stage hybrid Markov chain Monte Carlo (MCMC) to recover a posteriori distribution of the decentralized generator model parameters. In the first stage, we use the gradient-enhanced Langevin MCMC algorithm to characterize an intermediate posterior parameter distribution. This algorithm is computationally scalable to the high-dimensional parameter space. Based on the intermediate posterior distribution, during the second stage, we use the adaptive MCMC algorithm to fine-tune the strong correlations between the parameters. Finally, the fully recovered a posterior distribution is obtained in the end. The simulation results show that the proposed PCE-based hybrid MCMC algorithm can accurately and efficiently estimate the high-dimensional generator dynamic model parameters with full probabilistic distribution provided.

The risks associated with rare events threatening the security of power system operation are of paramount importance to power system planners and operators. To analyze the risks caused by high-impact, low-frequency rare events, an immensely large number of samples are typically required for the Monte-Carlo (MC) method on the high-fidelity power system model to achieve a sufficient accuracy, thereby rendering this approach computationally prohibitive. To handle this problem efficiently, it is desirable to construct a surrogate model for the power system response. However, the straightforward MC sampling of the low-fidelity surrogate can lead to biased results in the low-probability tail regions that are vital to risk assessment. Moreover, a single surrogate is unable to handle the topology uncertainties caused by random branch outages. To overcome these issues, we propose a hybrid multi-surrogate (HMS) method based on the polynomial chaos expansion (PCE) with low-probability tail events reevaluated by the high-fidelity model through a probabilistic analysis. This method improves the computational efficiency of the MC method for rare-event risk assessment by leveraging multi-fidelity models while retaining the desired accuracy. Simulations conducted in three test systems verify the excellent performances of the HMS method.

Power grids include entities such as home-microgrids (H-MGs), consumers, and retailers, each of which has a unique and sometimes contradictory objective compared with others while exchanging electricity and heat with other H-MGs. Therefore, there is the need for a smart structure to handle the new situation. This paper proposes a bilevel hierarchical structure for designing and planning distributed energy resources (DERs) and energy storage in H-MGs by considering the demand response (DR). In general, the upper-level structure is based on H-MG generation competition to maximize their individual and/or group income in the process of forming a coalition with other H-MGs. The upper-level problem is decomposed into a set of low-level market clearing problems. Both electricity and heat markets are simultaneously modeled in this paper. DERs, including wind turbines (WTs), combined heat and power (CHP) systems, electric boilers (EBs), electric heat pumps (EHPs), and electric energy storage systems, participate in the electricity markets. In addition, CHP systems, gas boilers (GBs), EBs, EHPs, solar thermal panels, and thermal energy storage systems participate in the heat market. Results show that the formation of a coalition among H-MGs present in one grid will not only have a significant effect on programming and regulating the value of the power generated by the generation resources, but also impact the demand consumption and behavior of consumers participating in the DR program with a cheaper market clearing price.

This paper develops a new response-surface-based Bayesian inference approach for power system dynamic parameter estimation of a decentralized generator using phasor-measurement-unit measurement. The response surface for the decentralized generator model is formulated through a polynomial-chaos-based surrogate. This surrogate allows us to efficiently evaluate the time-consuming dynamic solver at parameter values through a polynomial-based reduced-order representation. In addition, a polynomial-chaos-based analysis of variance is performed to screen out model parameters while ensuring system observability. In dealing with sampling the non-Gaussian posterior distribution for the parameters, the Metropolis-Hastings sampler is adopted. The simulations conducted in the New England system under different system events show that the proposed method can achieve a speedup factor of two orders or magnitude compared with the traditional method while providing full probabilistic distribution of model parameters and achieving the same level of accuracy.

The generalized polynomial chaos (gPC) method recently advocated in the literature, exhibits impressive efficiency and accuracy in probabilistic power flow (PPF) calculations of small-scale power systems. However, it suffers from the “curse of dimensionality” and can only be applied to systems with input random variables that follow a set of standard probability distributions. This paper overcome these weaknesses by developing a hierarchical polynomial chaos analysis of variance (ANOVA) method that shows excellent performances in terms of accuracy, efficiency, rationality, and adaptability, for small- to large-scale power systems. By proving the equivalence between the polynomial chaos expansion and the ANOVA decomposition, which is executed at no extra computational cost, the dimensionality of the polynomial chaos expansion can be adaptively reduced to improve the computational efficiency of the generalized polynomial chaos method in high-dimensional problems. Furthermore, by resorting to the Stieltjes procedure, it is extended to any assumed probability distributions of the input random variables. Simulation results carried out on the IEEE 118-bus system and the 1354-bus European high voltage system with correlated renewable energy generations reveal that the developed method outperforms the generalized polynomial chaos method and the Monte Carlo (MC) method while being compatible with real-time applications in power systems.

In this study, a dynamic two-level framework is proposed to model investment incentives in a multi-carrier energy market from a strategic company’s point of view. Capacity payment and firm contract are assumed as investment incentives to encourage the strategic producer to invest in generation units. In addition, financial incentives to invest in combined heat and power (CHP) include tax rebate and loans. Strategic company’s behavior is considered as a two-level model so that, in the first level, the objective function is to maximize the profit of the strategic producer by participating in an energy hub market. The strategic producer can invest in transmission lines, generation units, CHP, and gas furnace. In the second level, the aim is to maximize a multi-carrier energy social welfare encompassing heat, gas, and electric energy. In this model, units invested by rival companies are modeled using possible scenarios. Electric energy loads in this energy hub system are envisaged to be elastic, while heat loads are assumed to be inelastic to the market price. On the other hand, gas loads are indirectly elastic to the price. Besides, in the proposed framework, DC power flow and an exact gas flow model with the linearized Weymouth equation are used. The proposed model is implemented on two case studies including 6-bus system, and an energy hub system encompassing 24-bus IEEE RTS power system and 10-node natural gas system.

Quantifying the uncertainty of the renewable energy generation units and loads is critical to ensure the dynamic security of next-generation power systems. To achieve that goal, the time-consuming Monte Carlo simulations are usually used, which is not suitable for online dynamic analysis of large-scale power systems. To circumvent this difficulty, two uncertainty quantification approaches using polynomial-chaos-based methods are proposed and investigated. The first approach is the generalized polynomial chaos method that is able to reduce the computing time by three orders of magnitude compared with Monte Carlo methods while achieving the same accuracy. We find that this approach is very useful for short-term power system dynamic simulations, but it may produce unreliable results for long-term simulations. To address the weakness of that approach, we present the second method, namely the multi-element generalized-polynomial-chaos method. It is seen that this method is more accurate and more numerically stable than the generalized polynomial chaos method. Since the uncertainties of the renewable energy generation units and loads can follow very different distributions, we extend the Stieltjes’ recursive procedure that allows us to derive the orthogonal basis functions for any assumed probability distribution of the input random variables. Extensive simulations carried out on the WECC 3-machine 9-bus system and the New England 10-machine 39-bus system reveal that our proposed approaches are able to produce comparable accuracy as the Monte Carlo based method while achieving significantly improved computational efficiency for both stable and unstable power system operating conditions.

The increasing penetration of renewable energy along with the variations of the loads bring large uncertainties in the power system states that are threatening the security of power system planning and operation. Facing these challenges, this paper proposes a cost-effective, nonparametric method to quantity the impact of uncertain power injections on the load margins. First, we propose to generate system uncertain inputs via a novel vine copula due to its capability in simulating complex multivariate highly dependent model inputs. Furthermore, to reduce the prohibitive computational time required in the traditional Monte-Carlo method, we propose to use a nonparametric, Gaussian-process-emulator-based reduced-order model to replace the original complicated continuation power-flow model. This emulator allows us to execute the time-consuming continuation power-flow solver at the sampled values with a negligible computational cost. The simulations conducted on the IEEE 57-bus system, to which correlated renewable generation are attached, reveal the excellent performance of the proposed method.

The increasing penetration of renewable energy resources in power systems, represented as random processes, converts the traditional deterministic economic dispatch problem into a stochastic one. To solve this stochastic economic dispatch, the conventional Monte Carlo method is prohibitively time consuming for medium- and large-scale power systems. To overcome this problem, we propose in this paper a novel Gaussian-process-emulator-based approach to quantify the uncertainty in the stochastic economic dispatch considering wind power penetration. Based on the dimension-reduction results obtained by the Karhunen-Lo\`eve expansion, a Gaussian-process emulator is constructed. This surrogate allows us to evaluate the economic dispatch solver at sampled values with a negligible computational cost while maintaining a desirable accuracy. Simulation results conducted on the IEEE 118-bus system reveal that the proposed method has an excellent performance as compared to the traditional Monte Carlo method.

This paper develops a polynomial-chaos-expansion (PCE)-based approach for decentralized dynamic parameter estimation. Under Bayesian inference framework, the non-Gaussian posterior distributions of the parameters can be obtained through Markov Chain Monte Carlo (MCMC). However, the latter method suffers from a prohibitive computing time for large-scale systems. To overcome this problem, we develop a decentralized generator model with the PCE-based surrogate, which allows us to efficiently estimate some generator parameter values. Furthermore, the gradient of the surrogate model can be easily obtained from the PCE coefficients. This allows us to use the gradient-based Langevin MCMC in lieu of the traditional Metropolis-Hasting algorithm so that the sample size can be greatly reduced. Simulations carried out on the New England system reveal that the proposed method can achieve a speedup factor of three orders of magnitude as compared to the traditional method without losing the accuracy.

The constant need to reduce emissions in the automotive sector has driven the electrification of powertrain and chassis. To comply with this trend and decrease the bound even further, the present paper proposes the use of hydraulic regenerative shock absorbers for automotive suspension systems. The conversion of linear into angular motion and the suitable control of an integrated electric machine allow to transform part of the vibrational energy into electricity. In these damping devices, the key element is the motor-pump unit that is interfaced onto a conventional hydraulic cylinder architecture. Hence, the proposed research focuses on this component by investigating different design aspects in all the domains of interest. The objective is to optimize the energy conversion efficiency of the unit without affecting its damping control property. To give means of validation, a motor-pump prototype is built and experimentally characterized through a dedicated test rig.