Nash-Q learning-based collaborative dispatch strategy for interconnected power systems

Proliferated integration of variable renewable resources, especially wind power, in multi-area power systems brings about critical needs to coordinate balancing resources over the whole interconnected system. This paper proposes a coordination methodology in the real-time electricity market between regional interconnected power systems. The new method optimally dispatches generating units, determines interregional energy trading, and allocates regulation reserve throughout the entire system. The balancing resources in participating areas are shared and more effectively used to tackle the wind power uncertainty by means of a combined automatic generation control system. In order to comply with the existing operating philosophy of regional electricity markets, the augmented Lagrangian relaxation along with alternative direction method of multipliers are applied to provide a fully decentralized procedure with limited data interchanges between neighboring regions. Performance of the proposed method is examined on a two-area 6-bus and the modified three-area IEEE 118-bus test systems. The results confirm the applicability and effectiveness of the proposed model in providing flexible energy trading, regulation sharing, improved economic efficiency, and increased ability to integrate variable renewable energy into the power systems.

Dispatch results depend on the forecast wind power in an electric power grid. High levels of uncertainty in wind power lead to large forecast errors (FEs). Wind power FE creates an imbalance between power load demand and supply, which poses risks to the power grid. To minimise the risk caused by uncertainty in wind power, FE was analysed. The actual and forecast power of wind generations were studied to determine which factors had strong relationships with FE. After being analysed by principle component analysis, these factors were used to build an assessment model to estimate FE. According to the output of the assessment model, risk factor (RF) was defined to evaluate the risk‐level associated with wind power. Moreover, based on a grid including wind generation and fossil fuel‐fired power plants, a dispatch model was built to account for the cost of fossils fuels and RF. This dispatch model was studied to find strategies for decreasing the impact of wind power on the grid. The results from their research will increase the safety and reliability of power grids with uncertain levels of wind power and promote the widespread use of wind power.

This paper presents an adjustable interval optimization model for the energy and reserve clearance while treating the wind power variation and uncertainty. Instead of conventional predicted intervals (PIs), adjustable intervals (AIs) as subsets of PIs are proposed as more judicious choices for economically covering wind uncertainties. Ramp-capability reserve is modeled to ensure the existence of sufficient ramp capability needed to follow up wind power variation within AIs. However, realization of wind power beyond AIs, which is no longer compensable by ramp-capability reserve, would necessarily lead to either load shedding or wind spillage. In order to optimally determine AIs, apart from the energy and reserve procurement costs, the costs associated with load shedding and wind spillage are incorporated in the objective function. The confidence level theory is employed as well for tuning the robustness and conservatism of the final solution. Performance of the proposed method is examined on several case studies on an 8-bus and modified IEEE 118-bus test systems. Sensitivity analyses are conducted to specify the impacts of important parameters on the obtained solution. The results confirm the applicability and effectiveness of the proposed methodology.

Considering the increased interactions between power grids and natural gas grids, this study presents a chance‐constrained maintenance scheduling model for integrated gas‐electric grids with wind energy integration. Given the uncertainties of wind power, the loss of wind power probability is modelled as a chance constraint, ensuring the high utilisation of wind power. To overcome the adversities caused by the non‐linear and non‐convex models of natural gas systems, a piecewise linear approximation method is employed to transform the non‐linear models into a group of mixed integer linear models. A big‐M formulation method is used to construct inequality constraints for lines/pipelines to be under maintenance. In addition, unit commitment is also coordinated to achieve the best maintenance strategies. The proposed chance‐constrained stochastic programming model is converted into an equivalent deterministic programming model via a strong extended formulation for the sample average approximation by leveraging the star‐inequalities. Several tests on a four‐node natural gas system with a six‐bus power system and a 20‐node natural gas system with a modified IEEE 118‐bus power system demonstrate the effectiveness of the proposed model.

Chapter 4 - Data-driven robust stochastic optimization for power systems operations

Multi-objective optimization dispatching of a micro-grid considering uncertainty in wind power forecasting

Research on peak load shifting for hybrid energy system with wind power and energy storage based on situation awareness

A new multi-timescale optimal scheduling model considering wind power uncertainty and demand response

A minimum cost production model which can be used to account economical energy exchange between utilities and evaluate production cost saving in multiple area interconnected systems is proposed in this paper. A fast probabilistic production simulation model is used to determine the thermal incremental cost of each system separately. Based on the thermal incremental cost of each subsystem, a nonlinear optimization model which minimizes the total production cost of the whole interconnected systems is used to determine the economical energy exchanges in the interconnected systems. Then total production cost and cost saving are for whole interconnected systems and each system. The minimum cost principle based on Lagrange multipliers is proposed to solve this nonlinear optimization problem. The tie line capacity limit and energy loss are included in the energy exchange process. Hourly loads are used in the model. The thermal incremental cost of each system and the energy exchanges between interconnected systems are evaluated hour by hour. Then a period summary report is produced. The proposed minimum cost model has been incorporated into FEPSS (Fast Electricity Production Simulation System) package. The Pacific Power Corporation, Australia has used this model to study power system interconnections in Southeast Australia. >

With the large-scale wind power integration, the uncertainty of wind power poses a great threat to the safe and stable operation of the system. This paper proposes dynamic economic dispatch problem formulation in thermal power system incorporating stochastic wind and small-hydro (run-in-river) power, called thermal-wind-small hydropower system (TWSHS). Weibull and Gumbel probability density functions are used to calculate available wind and small-hydro power respectively. An improved differential evolution algorithm based on gradient descent information (DE-GD) is proposed to solve the dynamic economic dispatch (DED) problem considering uncertainty of wind power and small-hydro power, as well as complicated constraints in TWSHS. Based on the traditional differential evolution algorithm, the gradient information of the objective function is introduced after the mutation process to enrich the diversity of the population, thus increasing the possibility of convergence to the global optimization. Generation scheduling is simulated on a TWSHS with the proposed approach. Simulation results verify feasibility and effectiveness of the proposed method while considering various complex constraints in the thermal-windsmall hydropower system.

During recent decades, using wind power as one of the most substantial renewable energy sources has been vastly intensified in power systems. Increasing wind power penetration in the power grid can have both detrimental and beneficial effects. Due to the uncertain nature of wind power, the system operator is faced with many challenges to make proper decisions for the electricity market. In this paper, a probabilistic method is proposed which not only effectively manages wind power sources along with other producers, but also takes the uncertain behavior of wind power in defined intervals into account. Using wind farm information in each hour, a new approach for calculating the probability density function (PDF) in uncertainty bounds is presented. By utilizing the calculated PDF two objective functions are proposed for minimizing the total expected cost during 24 h without and with considering consumers payments. The proposed objective functions have been minimized through a two-level optimization method using three different heuristic algorithms (Teaching-Learning-Based Optimization (TLBO), Hybrid Particle Swarm Optimization and Gravitational Search Algorithm (PSO-GSA), and Ant Lion Optimization (ALO)) on an 8-bus sample transmission network. The results show the total expected cost has been decreased up to 20% in some scenarios. In addition, the proposed method can satisfy consumers by keeping their payments close to the lowest amount according to the different scenarios.

Wind power generations as a renewable source of energy have become under the spotlight of policy markets and energy providers recently. However, the technical constraints, production variability and uncertainty of wind power have limited its extensive integration into power system. Having these limitations in mind, the present paper sets for a new methodology for increasing wind power integration in deregulated electricity market. The proposed method is presented with the consideration of voltage stability assessment and wind power uncertainties. Our plan aims at maximizing social welfare and minimizing investment and annual operation cost. At the same time, we seek to overcome line constraint by taking into account wind uncertainties. In order to fulfill the aims, FACTS devices and price sensitive loads are utilized. On the other hand, a multi-objective optimization problem was used to evaluate the annual costs and outcomes of wind power investment, the optimal setting of FACTS devices, and optimal load shedding. Expected Security Cost Optimal Power Flow (ESCOPF) is used to minimize the expected total cost of system operation. To solve the proposed planning problem, Non Dominated Sorting Genetic Algorithm (NSGA-II) is exploited. Our proposed method has been applied to an IEEE30 bus test system by considering two wind scenarios. The simulation results demonstrate the efficiency of the proposed planning.

As China's wind power has been expanding, the volatility, discontinuity and uncertainty of wind power have brought great difficulties to consumption of the wind power. With the development of smart grid, it becomes possible to improve the capacity of wind power consumption by introducing real-time price and demand response theory into the market. Firstly, theories of smart meters, real-time price, and demand side response were introduced. Then taking transfer cost into consideration, a demand response model based on real-time price is proposed to optimize the load curve. At last, the wind power consumption models were built respectively according to the load curves before and after the demand response. Results show that these models can effectively reduce the abandon of wind power and increase the amount of wind power consumption.

An overlapping robust decentralized connective stabilization method based on dynamic state feedback is proposed for a kind of large-scale interconnected systems with loop topological structure. Firstly, the state space of an interconnected system is expanded by using inclusion principle of large-scale systems and the system is divided into a series of pair-wise subsystems in the expanded space. Then, the robust decentralized controllers based on dynamic state feedback for each pair-wise subsystem are designed by using LMI method and Lyapunov theory. Next, the designed repeatedly controllers for every subsystem are contracted back to the original space. Coordination of the control laws can be achieved, so that the original interconnected system is robust connectively stable. Finally, the proposed method is applied to AGC control design of a three-area interconnected power system with loop structure. Simulation results show the feasibility and superiority of the proposed method.

The uncertainty of wind power as the main obstacle of its integration into the power grid can be addressed by an accurate and efficient wind power forecast. Among the various wind power forecasting methods, machine learning (ML) algorithms, are recognized as a powerful wind power forecasting tool, however, their performance is highly dependent on the proper tuning of their hyperparameters. Common hyperparameter tuning methods such as grid search or random search are time-consuming, computationally expensive, and unreliable for complex models such as deep learning neural networks. Therefore, there is an urgent need for automatic methods to discover optimal hyperparameters for higher accuracy and efficiency of prediction models. In this study, a novel investigation is contributed to the field of wind power forecasting by a comprehensive comparison of three advanced techniques – Scikit-opt, Optuna, and Hyperopt – for hyperparameter optimization of Convolutional Neural Network (CNN) and Long Short-Term Memory Network (LSTM) models, a facet that, to our knowledge, has not been systematically explored in existing literature. The impact of these optimization techniques on the accuracy and efficiency of the CNN and LSTM models are assessed by comparing the root mean square error (RMSE) of the predictions and the required time to tune the models. The results show that the Optuna algorithm, using a Tree-structured Parzen Estimator (TPE) search method and Expected Improvement (EI) acquisition function, has the best efficiency for both CNN and LSTM models. In terms of accuracy, it is demonstrated that while for the CNN model all the optimization methods achieve similar performances, the LSTM model optimized by the Hyperopt algorithm, based on the annealing search method, results in the highest accuracy. In addition, for the first time in this research, the impact of the random initialization features on the performance of the forecasting models with neural networks is investigated. The proposed structures for deep learning models were examined to determine the most robust structure with the minimal sensitivity to the randomness. What we have discovered from the comparison of advanced hyperparameter optimization methods can be used by researchers to tune the time series-based forecasting models.