Urban integrated energy system stochastic robust optimization scheduling under multiple uncertainties

Virtual power plant (VPP) has gradually become a key technology to the increasing penetration of renewable energy. The uncertainty and variability of renewable energy and load demand pose significant challenges to the efficiency and stability of VPP's operation. In this paper, a data-driven two-stage stochastic robust optimization (SRO) scheduling model is proposed for a VPP considering wind power, solar power, load demand, and market price uncertainties. The objective is to maximize the profit of the VPP in the energy market and minimize the total system cost of the VPP in the reserve market under the worst-case realization of the uncertainties. The Dirichlet process mixture model (DPMM) and variational inference algorithm are employed for constructing the data-driven uncertainty ambiguity set considering the correlations among multiple uncertainties. The tailored column-and-constraint generation algorithm is developed to solve the SRO model iteratively by reformulating the second stage with the application of the Karush-Kuhn-Tucker conditions. Results from a case study illustrate the effectiveness and superiority of the proposed model.

Motor vehicles have been identified as a growing contributor to air pollution, such that analyzing the traffic policies on energy and environment systems (EES) has become a main concern for governments. This study developed a dual robust stochastic fuzzy optimization—energy and environmental systems (DRSFO-EES) model for sustainable planning EES, while considering the traffic sector through integrating two-stage stochastic programming, robust two-stage stochastic optimization, fuzzy possibilistic programming, and robust fuzzy possibilistic programming methods into a framework, which can be used to effectively tackle fuzzy and stochastic uncertainties as well as their combinations, capture the associated risks from fuzzy and stochastic uncertainties, and thoroughly analyze the trade-offs between system costs and reliability. The proposed model can: (i) generate robust optimized solutions for energy allocation, coking processing, oil refining, heat processing, electricity generation, electricity power expansion, electricity importation, energy production, as well as emission mitigation under multiple uncertainties; (ii) explore the impacts of different vehicle policies on vehicular emission mitigation; (iii) identify the study of regional atmospheric pollution contributions of different energy activities. The proposed DRSFO-EES model was applied to the EES of the Beijing-Tianjin-Hebei (BTH) region in China. Results generated from the proposed model disclose that: (i) limitation of the number of light-duty passenger vehicles and heavy-duty trucks can effectively reduce vehicular emissions; (ii) an electric cars’ policy is enhanced by increasing the ratio of its power generated from renewable sources; and (iii) the air-pollutant emissions in the BTH region are expected to peak around 2030, because the energy mix of the study region would be transformed from one dominated by coal to one with a cleaner pattern. The DRSFO-EES model can not only provide scientific support for the sustainable managing of EES by cost-effective ways, but also analyze the desired policies for mitigating pollutant emissions impacts with a risk adverse attitude under multiple uncertainties.

In this paper, the model of strategic wind power offering in the day-ahead (DA) market is proposed considering the uncertainties of wind power production, and price forecasting of DA and real-time (RT) market. The wind power deviation in the RT market is settled with the two-price mechanism based on the deviation direction and the relation between the locational marginal prices (LMPs) of DA and RT. Instead of using the point forecasting for the DA and RT LMPs, the uncertainties of LMP forecasting are modeled. In addition, the correlation between the forecasting errors of DA and RT LMP are directly modeled instead of generating the correlated scenarios. Finally, the optimal offered quantity of wind power in the DA market is derived using the probability theory based on the probabilistic wind power forecasting. The case study using the price data of actual DA and RT from Midcontinent Independent System Operator (MISO) validates the effectiveness of the proposed model. It shows that the correlation of the forecasting errors of DA and RT LMP has a significant impact on the wind power quantity offered by DA and revenue results.

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

In this paper, a Casualty Collection Points (CCPs) location problem is formulated as a two-stage robust stochastic optimization model in an uncertain environment. In this modelling approach, the network design decisions are integrated with the multi-period response operational decisions where the number of casualties with different levels of injuries coming from the affected areas is uncertain. Furthermore, the transportation capacity for the evacuation of casualties to CCPs and hospitals is also uncertain. To solve this complex problem, a robust sample average approximation method with the feasibility restoration technique is proposed, and its efficiency is examined through a statistical validation procedure. We then evaluate the proposed methodology in the backdrop of a hypothetical case of Bhopal gas tragedy (with the same hazard propagation profile) at the present day. We also report the solution robustness and model robustness of 144 instances of the case-study to show the proficiency of our proposed solution approach. Results analysis reveals that our modelling approach enables the decision makers to design a humanitarian logistic network in which not only the proximity and accessibility to CCPs are improved, but also the number of lives lost is decreased. Moreover, it is shown that the proposed robust stochastic optimization approach converges rapidly and more efficiently. We hope that our methodology will encourage urban city planners to pre-identify CCP locations, and, in the event of a disaster, help them decide on the subset of these CCPs that could be rapidly mobilised for disaster response.

In India, Short term open access (STOA) in transmission and distribution provides a range of opportunities to the market players. Sellers and buyers can transact power bilaterally through over the counter contracts or bid collectively through the power exchanges in Day Ahead Market (DAM). Real Time Market (RTM) was introduced in India from 01.06.2020. This has created a new opportunity for the electricity market players for trading in real time with a lead-time of 1.5 hours. RTM provides 48 bidding windows over a day. This provides additional flexibility for last mile portfolio optimization. This paper attempts to analyze the impact of coexistence of DAM and RTM to derive further inferences. It provides an insight to the relationship of the Market Clearing Price (MCP) of DAM and RTM. Trend of MCP of DAM and RTM is analyzed with respect to variation in demand.

Decisions for a variable renewable resource generator’s commitment in the energy market are typically made in advance when little information is obtainable about wind availability and market prices. Much research has been published recommending various frameworks for addressing this issue. However, these frameworks are limited as they do not consider all markets a producer can participate in. Moreover, current stochastic programming models do not allow for uncertainty data to be updated as more accurate information becomes available. This work proposes two decision-making frameworks for a wind energy generator participating in day-ahead, intraday, reserve, and balancing markets. The first framework is a two-stage stochastic convex optimization approach, where both scenario-independent and scenario-dependent decisions are made concurrently. The second framework is a series of four two-stage stochastic optimization models wherein the results from each model feed into each subsequent model allowing for scenarios to be updated as more information becomes available to the decision-maker. In the simulation experiments, the multi-phase framework performs better than the single-phase in every run, and results in an average profit increase of 7%. The proposed optimization frameworks aid in better decision-making while addressing uncertainty related to variable resource generators and maximize the return on investment.

Robust bidding strategy for aggregation of distributed prosumers in flexiramp market

The electrical power system has the uncertainty in its operation process, from this brings the demand forecast can with actual demand existence certain deviation. The balanced from the electricity generation and the load demand may brought to be, by using of the day-ahead and real-time electricity market transaction mechanism and the demand real-time adjustment electricity generation. At the same time, to manifest the demand-side fully in the market competition function, a revised bidding strategy was studied for the demand-side under the day-ahead and real-time market, making use of two stage decision method of the newsvendor problem. The example had indicated this method had feasible.

Wind power bidding is critical for wind power producers operations in an electricity market. Due to the uncertainly and variability of wind power output, some markets impose a penalty on the deviation between the wind power bids in the day-ahead market and the real wind power output in the realtime market. The objective of a wind power producers bidding problem is to maximize the producers profit while minimizing the penalty and ensuring the output from its wind farms can be utilized to the largest extent. In this paper, we present a wind power bidding strategy based on chance-constrained optimization. The chance constraint is used to define the probability that certain amount of wind power bid into the market can be accepted. We formulate the problem as a chance-constrained two-stage (CCTS) stochastic optimization program. The second stage represents the many possible realizations of wind power output by scenarios. We also consider pumped-storage hydro power plants as storage to accommodate the fluctuation of wind power. Sample Average Approximation (SAA) is used to solve the problem. Numerical examples are also provided.

“Comparing merit order effects of wind penetration across wholesale electricity markets”

The increasing penetration rates of wind power in power systems bring challenges to the dynamic economic dispatching. This paper proposes a Robust Stochastic Optimization (RSO) model to handle the uncertainty of wind power in dynamic economic dispatch. Based on the event-wise ambiguity set and event-wise recourse adaptation, the RSO model has generality and enables the ambiguity set to be constructed irrelatively to the specific problem. Furthermore, by introducing the detail-variables, the adjustment of event-wise ambiguity set of the RSO model can reduce the conservativeness. To the dynamic economic dispatch problem, simulations studies on the IEEE 118-bus system and IEEE 300-bus system verify that 1) RSO model is flexible and adjustable; 2) RSO model has excellent performance under different penetration rates of wind power; 3) Compared with the results of Robust Optimization (RO) and Stochastic Optimization (SO), RSO model can balance the economy and robustness effectively; 4) The RSO model has better performance in dealing with the small sample volume of wind power data.

Optimal bidding strategy of a virtual power plant in day-ahead energy and frequency regulation markets: A deep learning-based approach

In this paper, a two-stage stochastic optimization strategy is proposed for microgrids to optimize the energy bids for the day-ahead (DA) and real-time (RT) balancing market, considering the price elasticity of load demands. The uncertainty of energy prices in DA and RT market, output power of renewable energy resources and load demands are considered and modeled in this paper. The price elasticity of load demands is considered and modeled. The objective of the proposed strategy is to minimize the total cost, including the energy cost in both the DA and RT market, the total generation cost of DG units, the discharging cost and the cost of demand response. Comprehensive case studies based on the codes and data of PJM power market show that the proposed strategy can minimize the total cost of the microgrid.

Forecast value considering energy pricing in California