Market Applications and Uncertainty Handling for Virtual Power Plants

Abstract

Virtual power plants achieve the flexible scheduling and management of power systems by integrating distributed energy resources such as renewable energy sources, energy storage systems, and controllable loads. However, due to the instability of renewable energy generation, load demand fluctuations, and market price uncertainty, virtual power plants face a gigantic challenge operating and participating in electricity markets. First, this paper outlines the functions and uncertainties of virtual power plants; then, it describes the uncertainties of virtual power plants in terms of aggregation, participation in market bidding, and optimal dispatch; finally, it summarizes the review.

1. Introduction

With the global power system transitioning towards decarbonization and sustainability, virtual power plants (VPPs), as a new type of energy management and optimization technology, have gradually been widely used [1]. Shimon Awerbuch first proposed the concept of VPPs in 1997 [2]. Due to differences in resource conditions and policy environments, VPPs in various regions have developed diverse technical approaches and operational modes.

In Europe, the increasing share of wind power and photovoltaics (PVs) each year results in greater uncertainty in renewable energy output, which leads to increased volatility in power generation and intensified price fluctuations in the electricity market. Projects such as the EU FENIX project [3], the EU Virtual Fuel Cell Power Plant project [4], and the German professional virtual power plant project [5] initiative have introduced advanced meteorological and load forecasting technologies. By creating a highly interactive control platform that integrates distribution and transmission grids, these projects effectively address real-time power deviations caused by fluctuations in wind and solar power generation, as well as demand-side loads. This has improved the robustness of system operations and the stability of the grid [6].

The development of virtual power plants in North America has increasingly focused on demand response and the integration of renewable energy. This approach addresses the unpredictability between user behaviour and energy supply. Since demand response relies on user participation and timely implementation, and user behaviour is often difficult to predict accurately, virtual power plants in North America typically employ dynamic pricing, incentive mechanisms, and real-time monitoring tools during the dispatch process to minimize discrepancies in response. Additionally, large-scale local wind and solar projects are often dispersed, and their generation outputs can fluctuate rapidly due to changing weather conditions. To manage this variability, forecasting models and distributed energy management techniques are integrated into the architecture of virtual power plants. This integration allows for flexible time-sharing scheduling and market bidding to accommodate uncertain renewable generation. Moreover, price signals are utilized to guide load-side regulation, thereby enhancing the overall operational economics and reliability of the system [7].

In recent years, China’s virtual power plants have made positive progress in coping with the uncertainty of resource diversity and load fluctuations. For example, the State Grid Jibei virtual power plant responds to the risk of inter-regional power supply and demand imbalance by accessing and controlling cross-regional diverse resources in real time; the State Power Investment Corporation (SPIC) Suzhou virtual power plant adopts high-precision meteorological and load-forecasting models and implements hierarchical aggregation and rolling optimization to dynamically adjust the output plan and mitigate the impacts of power generation and load-side uncertainties. The Jiangsu megawatt-scale residential virtual power plant, with the help of big data and Internet of Things (IoTs) technology, realizes the intelligent regulation and control of residential home appliances and staggered power consumption to cope with the operational uncertainty caused by load fluctuations. Suzhou Virtual Power Plant has a total adjustable load of 20,000 kW, with a single station regulation response speed of seconds and an accuracy of over 90%. These demonstration projects show the huge potential of virtual power plants in technological innovation, resource optimization and integration, and green and low-carbon development, and they provide valuable experience and reference for the challenge of uncertainty in the context of global energy transition [8]. The development and application of virtual power plants inevitably face multiple uncertainties, such as the stochastic nature of the grid output of multiple renewable resources, the stochastic nature of load demand, and the direction of power market prices. Demonstration projects generally make use of high-precision forecasting, real-time monitoring, optimal scheduling, etc., to resolve the risk of supply–demand balance and the economic benefits brought about by uncertainties as far as possible.

As shown in Figure 1, virtual power plants are becoming an important part of the smart grid as a new type of energy management and optimal dispatch technology. Through mechanisms such as resource aggregation, market bidding, and optimal dispatch, virtual power plants integrate and manage flexible resources, such as dispersed renewable energy sources, energy storage systems, and controllable loads, so that they have market competitiveness similar to that of traditional power plants and can effectively participate in the electricity market [9]. However, due to the instability of renewable energy output [10], the volatility of load demand [11], the uncertainty of market price [12] and other uncertainties, virtual power plants are facing a lot of challenges in their actual operation and effectively coping with uncertainties in resource aggregation; market bidding and optimal scheduling are used to improve the stability and economy of virtual power plants and have become the focus of current research.

To systematically explore the operational mechanisms and coping strategies of VPPs in an uncertain environment, this paper conducts an analysis centred on three core aspects: resource aggregation, market bidding, and optimal dispatch. Based on existing research, it also presents the related prospects. The structure of the full text is as follows: Starting from the perspective of resource integration, Section 2 dissects two aggregation models: one oriented towards market profits, and the other aimed at system stability. It reveals the impact mechanism of multi-source uncertainties, such as renewable energy output and load demand, on aggregation efficiency. Section 3 focuses on the power market environment and, from the dimensions of the previous day market, real-time market, and demand response, explores the optimization path of bidding strategies for virtual power plants under the dual pressures of price fluctuations and supply–demand imbalances. Section 4 further delves into dynamic decision-making, combining machine learning and robust optimization techniques, to propose a dispatch model that balances economic efficiency and robustness, addressing the challenges of uncertainties across multiple time scales. Section 5 systematically reviews the advantages and limitations of existing uncertainty handling methods and points out future research trends from the directions of the joint optimization of multiple uncertainties, algorithm efficiency, and deep integration of artificial intelligence. This paper reviews the literature to date on uncertainty handling in resource aggregation, market bidding, and optimal scheduling processes for virtual power plants. It compiles the current methods and technical tools for dealing with uncertainty in resource aggregation, market bidding, and the optimal dispatching process, aiming to provide lessons and references for the uncertainty-coping strategies of virtual power plants in the future.

2. Virtual Power Plant Resource Aggregation

A virtual power plant, as an aggregator of distributed energy resources, can efficiently schedule and manage multiple forms of energy, such as renewable energy sources, energy storage devices [13], and demand response resources. Figure 2 shows the flow of virtual power plant aggregation.

2.1. Resource Aggregation for Market Returns

Based on the purpose of resource aggregation, virtual power plants are classified into two categories: one is resource aggregation with the purpose of market revenue, and the other is resource aggregation with the goal of power system stability and security [14]. The subjects of the two types of virtual power plants are different, with the former being dominated by aggregators and the latter being dominated by grid management organizations such as distribution grid operators (DSOs), transmission grid operators (TSOs), and independent system operators (ISOs).

The virtual power plant forms a competitive scheduling entity that can participate in the market by aggregating different types of distributed energy resources, such as renewable energy, energy storage, electric vehicles, and loads. A general optimization model for resource aggregation with market returns can be expressed as a profit maximization problem. The model aims to maximize market returns through the optimal dispatch of different types of distributed energy resources within a virtual power plant [15]. Specifically, the objective is to optimize by maximizing the product of the market electricity price and the power output of each distributed energy resource at each point in time, minus the operating cost. The basic constraints are as follows:

Power balance constraint: This requires that the total power output at each point in time is equal to the sum of the demand and the required spare capacity [16]; Device operation constraint: The output power of each distributed energy resource is between its minimum and maximum power range. These constraints ensure that the virtual plant is dispatched to meet the power demand, taking into account the need for spare capacity and ensuring that the power output of each resource is within the allowed range [17].

In recent years, for the market optimization of VPP resource aggregation, researchers have proposed a variety of optimization mechanisms and modelling methods, and the literature [18] proposes a VPP-DER aggregation mechanism based on the algorithm of the National Resident Matching Program (NRMP), which adopts a two-layer optimization model to improve market adaptive capacity, with the upper layer constructing the global optimization model to maximize the social benefits, and the lower layer optimizing the individual based on the local information of distributed resources. The resource aggregation strategy improves the market competitiveness of DER resources. Ref. [19] investigates the role of Deferrable Loads (DLs) in VPP resource aggregation and constructs flexible scheduling windows and time-coupling constraints for DLs to optimize the scheduling synchronization of different DER resources.

2.2. Resource Aggregation Targeting Power System Stability and Security

A virtual power plant can not only be optimized by aggregating different types of distributed energy resources, such as renewable energy, energy storage, electric vehicles, and loads, with the goal of market returns, but it can also serve as an important tool for enhancing grid stability and security [20]. As a highly flexible scheduling entity, a virtual power plant can improve the reliability, stability, and security of the power system, ensure the balance of supply and demand, reduce frequency fluctuations and network congestion, and enhance the risk-resistant capability of the grid through the intelligent scheduling of distributed resources. At this point, the optimization objective of virtual power plant resource aggregation can be modelled as a system stability and security maximization problem, which mainly considers frequency regulation capability, load balancing capability, and standby capacity optimization.

In recent years, for aggregation that targets power system stability and security, researchers have focused on improving the frequency and voltage stability of the grid, especially in virtual power plant (VPP) resource scheduling. Ref. [21] proposes an active dynamic aggregation model for the resource co-ordination of distributed integrated energy systems (DIMSs) through a two-stage robust optimization algorithm, which is solved by a column and constraint generation (CCG) algorithm to ensure the stability of the system under different operating states. By simulating the joint dispatch of wind, PV, and storage systems, this study verifies that the optimization method can provide efficient frequency support in the case of grid load changes, thus enhancing the dynamic response capability of the grid. In addition, ref. [22] addresses the specific impact of VPP involvement in grid stability and proposes an aggregation model based on electromagnetic transient simulation for analyzing the role of VPP in transient frequency and voltage stability. The study employs electromagnetic transient (EMT) simulation and incorporates the IEEE 39-bus test system for validation, and the results show that the method can effectively analyze the impact of DER resources on the transient stability of the grid and optimize the dynamic regulation strategy of VPP resources on short time scales.

In recent years, blockchain technology has been introduced into VPP resource aggregation management to improve scheduling transparency and co-ordination efficiency. Ref. [23] designs a blockchain-based VPP consensus mechanism using smart contracts for distributed resource transaction optimization. The study combines Hyperledger Fabric for experimental testing, and the results show that the co-ordination efficiency of VPP resource scheduling is improved, information security increases, and the risk of data fraud is reduced by adopting the blockchain mechanism.

2.3. Considering Uncertainty in Resource Aggregation

Uncertainty in virtual power plant resource aggregation arises from four primary sources, as shown in Figure 3 below:

(1)

Uncertainty in renewable energy generation:

Renewable energy power generation is highly affected by meteorological conditions, and its power output is highly stochastic. Wind speed variations lead to instability in wind power generation, and PV power generation is affected by solar radiation, cloud cover, and other factors, making power generation randomly volatile [24].

(2)

Uncertainty in load demand:

The volatility of customer load demand is highly influenced by customer behaviour, which is affected by a variety of factors, such as the time of day, season, economic activity, temperature, etc., making it difficult to make accurate short-term forecasts [25]. Electricity price is the main factor that affects the revenue of virtual power plants.

(3)

Uncertainty in electricity spot market prices:

Electricity prices in the spot market are highly volatile and directly affect the revenue of virtual power plants. Prices in the electricity spot market are determined by market supply and demand, which change frequently and are difficult to predict [12].

(4)

Uncertainty of electric vehicle charging and discharging:

Access to electric vehicles introduces a new source of uncertainty, with stochastic charging and discharging behaviours that are influenced by driver habits, electricity price fluctuations, and the distribution of charging infrastructure [26].

Aiming at the problem of renewable energy generation uncertainty, ref. [27] proposes a virtual power plant dispatchable power aggregation method based on a two-stage self-adaptive robust optimization method, focusing on solving the uncertainty of wind and solar output. Copula theory is used to generate a joint output scenario of wind and solar power for the uncertainty of wind and solar power generation. Two-stage adaptive robust optimization (ARO) is used, with the first stage being the “current decision”, where an initial decision is made based on the possible range of uncertainty to determine the optimal range of the dispatchable power aggregation area for the VPP. The second stage is “wait and see”, which is based on the decision made in the first stage and is adjusted in the second stage according to the actual situation and more real-time information. This means that the decision in the first stage is based on the maximum range of the dispatchable power area, but the second stage can adjust the strategy to new situations based on future information. Traditional robust optimization usually needs to consider the effects of all uncertainty scenarios, resulting in a very high number of scenarios to be processed and high computational complexity, while ARO reduces the computational complexity of the problem by dividing the optimization problem into two stages. The first-stage decisions can be made more roughly, while the second-stage adaptations are made only when necessary, thus making the solution process more efficient. The dispatchable range of this method is 163.6 MWh, which is 12% larger than that of the traditional method and improves robust feasibility.

Aiming at the impact of renewable energy and market price uncertainty on the risk of virtual power plants, ref. [28] proposes a multi-energy dynamic aggregation optimization model for virtual power plants based on the Improved Cuckoo’s Algorithm (CS-EO), which focuses on solving the risk impacts of renewable energy outputs and electricity market price uncertainty on virtual power plants. By introducing conditional value-at-risk as a risk metric, the article uses a scenario approach to simulate uncertainties in wind energy, PV, and market electricity prices, combined with risk preference coefficients, to provide a more robust decision-making model for the capacity allocation of virtual power plants, quantifying uncertainty risks through 64 combined scenarios. The results show that when the risk coefficient L increases from an aggressive value (0.05) to a conservative value (2.0), the number of wind turbines decreases by 90.6%, the PV array decreased by 72.4%, the total cost increased by 17.2%, but the CVaR risk decreased by 23.8%, validating the effectiveness of CVaR in risk-cost trade-offs; the improved cuckoo algorithm (CS-EO) converged 40% faster than the standard CSA.

In addition to risk metrics, ref. [29] focuses on dealing with uncertainty in resource aggregation, particularly concerning spare capacity and the volatility of wind generation. By designing a two-stage optimization model, the first stage uses a hybrid stochastic Minimum Maximum Regret (MMR) model to cope with the uncertainty in spare capacity and market price and optimize the offer strategy of VPPs according to the previous day market. The second stage then dynamically adjusts the confidence intervals of wind power generation through an adaptive algorithm to reduce the conservatism of the model and optimize the real-time dispatch decision. The method effectively balances the market price fluctuation and uncertainty of wind power generation to ensure that VPPs can flexibly respond to the changing market environment, thus improving economic efficiency and operational reliability. Ref. [30] constructs a VPP aggregation model considering network constraints and DERs time-series coupling constraints, and it proposes some VPP performance parameters to characterize and quantify regulation capability. Additionally, an uncertainty aggregation that considers the time-series coupling characteristics of variables was constructed, and an aggregation method under uncertainty scenarios was proposed based on a two-stage robust optimization model. The regulation capability of VPPs in frequency regulation and spinning reserve is exploited to improve the feasibility of practical applications. Moreover, the revenue of the VPP increased by 29.5%.

With the rapid development of machine learning, more and more researchers have started to combine their research with its capabilities. Ref. [31] presents a multi-energy virtual power plant aggregation model that combines opportunity constraints with machine learning. The load demand and renewable energy generation of a virtual power plant are forecasted using machine learning methods. These forecasts provide key inputs for subsequent dispatch optimization. By learning from historical data, the machine learning model can predict future load and generation uncertainty, providing more accurate future forecasts. Chance constraints deal with forecast uncertainty by introducing probabilistic guarantees to the optimization problem. Specifically, chance constraints guarantee that system constraints are satisfied in most cases, ensuring that the dispatch outcome of the virtual plant is feasible in most cases, even in the face of imperfectly determined renewable generation. In considering the integrated management of multiple uncertainties, a robust aggregation model for multi-energy virtual power plants (MEVPPs) is proposed in ref. [32], aiming to deal with the problems related to the uncertainty of dispatch signals. The variation of system operator dispatch signals is handled by solving the max-min problem (max-min problem) and ensuring the scheduling flexibility of MEVPP. Robust modification of possible dispatch signals is performed to ensure that all signals are realized within the set power range, thus reducing the negative impact of uncertainty. Ref. [33] proposes a multi-energy virtual power plant (MEVPP) approach for co-ordinated scheduling in joint capacity, energy, and ancillary services markets, considering the integration of hydrogen facilities. The key elements of the study include an integrated framework from long-term to spot markets, including capacity, energy, and ancillary services markets, to optimize the economic profitability of the MEVPP; a co-ordination mechanism between the annual capacity plan and the daily energy and reserve plans is proposed through a two-stage stochastic planning approach incorporating conditional value-at-risk (CVaR), incorporating a daily hydrogen storage and seasonal hydrogen storage in a hybrid hydrogen storage system for short-term intra-day and long-term inter-seasonal energy complementarity and peak shaving.

A two-stage stochastic optimization model is proposed in ref. [34]: firstly, a preliminary scheduling and trading decision is made in the previous day market based on the wind power output prediction and the operational constraints of each distributed resource; subsequently, the output is flexibly adjusted, compensated, or sold in the real-time balancing market based on the actual wind power deviation using the energy storage system and the conventional units to cut down the economic cost of the prediction error and to ensure the voltage security of the distribution network in the whole.

Finally, ref. [35] handles the volatility of wind and load generation through a two-way matching model, incorporating a multi-scenario technique to optimize the co-operation between a virtual power plant and distributed energy resources to maximize the benefits of the system in an uncertain environment. In the paper, the multi-scenario technique is used to deal with the output uncertainty of wind, PV, and load within the virtual power plant. By simulating different scenarios, the impact of uncertainty on the VPP revenue model can be reflected more comprehensively, helping to optimize the adoption of the Gale–Shapley algorithm for the bi-directional matching process between VPP and DER. Ref. [36] proposes an ultra-short-term distributed photovoltaic (DPV) power prediction method based on domain adversarial graphical neural network (DAGNN), aiming at solving the power prediction problem in data-scarce scenarios in virtual power plants (VPPs). The NRMSE (Normalised Root Mean Square Error) of the DAGNN was reduced by 23.06% (15 min) to 50.55% (4 h) compared to the method with target domain data only (Method2) over the prediction range of 15 min to 4 h.

In summary, single renewable energy generation uncertainty (e.g., wind energy and PV) and multiple uncertainties (including market prices, dispatch signals, etc.) have become key research elements in virtual power plant aggregation. By combining various techniques and algorithms, such as two-stage optimization, adaptive robust optimization, scenario simulation, opportunity constraints, and machine learning, the literature has improved the flexibility and economy of virtual power plant aggregation in dealing with uncertainties to different degrees, which provides useful references for the future of large-scale distributed energy access and aggregation in the environment of multi-energy complementation.

3. Participation of Virtual Power Plants in Market Bidding

3.1. The Previous Day’s Market

Virtual power plants, as aggregators of distributed energy resources, are bidding in the previous day market to maximize economic returns by optimally dispatching resources such as wind, PV, storage, EVs, and controllable loads [37]. VPP operators need to develop a reasonable offer strategy to optimize market returns under the influence of factors such as market price uncertainty, fluctuations in renewable energy outputs, and changes in load demand [38]. The process is shown in Figure 4 below.

Scheduling optimization of virtual power plants participating in the previous day market is usually modelled as a profit maximization problem and combines power balance constraints, equipment operation constraints, and market trading constraints to form a final mathematical model based on optimization theory.

Many studies have focused on how to optimize the bidding strategies of VPPs in the previous day market to improve their market performance. Ref. [39] proposes a deep learning-based optimization method using Long Short-Term Memory (LSTM) networks for market price prediction to guide the bidding decisions of VPPs. It is shown that this method can effectively improve the market participation benefits of VPPs. Ref. [40] uses PSO-optimized Informer model (learning rate, hidden layer dimension, and other global search hyper-parameters) to improve PV and residential load forecasting accuracy (R² up to 0.88–0.91, MAE reduced by 30%), and it optimizes load forecasting by classifying the daily operation mode (weekdays/weekends/holidays) combined with the analysis of users’ behaviors (half-violin map and heat map); the MAE is further reduced by 14%, and finally, the MOPSO algorithm is used to balance economy, environmental protection, and customer satisfaction. The triple-objective scheduling scheme guarantees a voltage deviation of <2%, with a weekly revenue of RMB 260,000 and a reduction in carbon emissions by 28%. Ref. [41] presents a novel decision support system (DSS) for enhancing the long-term forecasting accuracy of a virtual power plant (VPP) in the previous day market. The study combines a bi-directional long and short-term memory (BiLSTM) network and a decision support system, aiming to address the problem of the decreasing accuracy of traditional recursive forecasting techniques in long-term forecasting. In ref. [42], the subjects with certain “price-maker” power in the market a few days previously are used to portray the bidding game and market clearing process among the power producers through the Multi-Agent Reinforcement Learning (MARL) model, and an algorithm based on MATD3 is proposed to improve the convergence speed and benefit of the bidding strategy. Ref. [43] proposes an integrated uncertainty prediction framework (En-IENN), which mainly consists of Interpretable Neural Networks (INNs) and Improved Evidence Neural Networks (IENNs). The INNs are used for feature extraction, which can clearly explain the reasons for feature selection, while IENNs are used for the prediction of uncertainty, which is achieved by minimizing the loss of the improved function to determine the evidence distribution. The En-IEN framework is more interpretable and reliable than traditional methods.

In terms of resource allocation, ref. [44] proposes a virtual power plant optimization model based on renewable energy, focusing particularly on how to optimize the resource portfolio in the previous day market. Through the effective integration of renewable resources, such as solar and wind energy, the virtual power plant can maximize the economic benefits in the market environment. Ref. [45] presents a virtual power plant bidding strategy with flexible demand-side management. The strategy optimizes the participation of virtual power plants in the previous day market by regulating peak loads and significantly improves the economic returns of virtual power plants.

3.2. Real-Time Markets

With the continuous evolution of the electricity market, the real-time market (RTM) plays a key role in ensuring the balance between the supply and demand of electricity, enhancing the efficiency of market competition and optimizing resource dispatch. Virtual power plants can participate in RTM as a whole market participant by intelligently aggregating distributed energy resources to improve market adaptability and economic returns. The operation of a VPP in RTM involves various aspects such as dispatch optimization, price response, bidding strategy, and grid co-ordination [46]. The process of virtual power plant participation in the real-time market is shown in Figure 5 below.

The bidding strategy of virtual power plants in the real-time market is also a key research area. Ref. [47] proposes a bidding strategy based on a two-tier model, in which the upper tier decides the winning bid of each power producer through market exchange, and the lower tier optimizes the bidding strategy of the virtual power plant to improve its market revenue. The strategy not only focuses on the price fluctuation of electricity but also incorporates the scheduling of load response and battery storage to adapt to the demand changes in the real-time market. Ref. [48], on the other hand, explores the optimal participation strategy in the energy market in a heterogeneous virtual power plant model based on renewable energy sources, especially in the real-time market, and the results show that the virtual power plant can effectively improve the market revenue under different weather and market scenarios.

3.3. Demand Response

With the development of the smart grid, demand response has become an important means to optimize power system operation and balance supply and demand. By aggregating distributed energy sources, energy storage systems, and controllable loads, virtual power plants enable them to participate in power trading as an overall market player, improving the flexibility and economic efficiency of the grid [49].

Ref. [50] proposes a VPP model based on demand response to optimize the balance between electricity demand and generation by integrating renewable energy sources and flexible loads, which in turn improves the stability of the grid. Ref. [51] designs a demand response scheme with incentives, aiming to optimize the operating cost of VPPs and enhance consumer benefits by motivating consumers to participate in demand response. Meanwhile, ref. [52] proposes a virtual power plant scheduling control method considering price-driven demand response, and the model can effectively regulate the consumers’ electricity consumption behavior to achieve the effect of load shaving and peak filling. Ref. [53] introduces a risk-constrained stochastic planning approach in its study, aiming at co-ordinating cooling and heating loads with renewable energy generation to reduce the operating cost of VPPs and guarantee power quality. Ref. [54] proposes a two-tier optimal scheduling method for a multi-energy virtual power plant (VPP) with source-load synergy. The upper-layer model optimizes the load side through time-sharing tariffs and controllable load dispatch, while the lower-layer model optimizes the generation output of each distributed power source according to the upper-layer model. This approach aims to cope with the volatility and intermittency problems caused by renewable energy sources, such as wind and PV, connected to the grid to reduce the phenomenon of wind and PV abandonment and improve the security and stability of grid operation.

3.4. Consideration of Uncertainty in Market Bidding

As shown in Figure 6, virtual power plants have been subject to uncertainty in market bidding, especially regarding how to cope with the volatility of renewable energy and changes in market prices [55]. As the complexity of the market environment increases, the offer strategy of virtual power plants in the electricity market becomes particularly complex [56]. To cope with these uncertainties, virtual power plants need to adjust their bidding strategies in both the previous day and real-time markets, and risk management mechanisms need to be introduced to ensure stable returns for virtual power plants [57].

Recent studies have proposed a variety of optimization methods to cope with market uncertainty and resource constraints, especially in the bidding and scheduling decisions of virtual power plants, where the handling of uncertainties in renewable energy output, load demand, and power prices has received increasing attention. For example, ref. [58] deals with the uncertainty of wind power and PV power generation by modelling the joint probability distributions of these two energy sources using the Clay–Copula functions. The article adopts a robust optimization method and introduces a constraint violation probability to regulate the impact of market uncertainty on the bidding strategy of virtual power plants. The model can adjust the bidding strategy according to the risk preference of the decision-maker by choosing different robust control coefficients and constraint violation probabilities, and the optimization process ensures that the virtual power plants can obtain a stable and acceptable economic return, even in a market environment with high uncertainty. It has the advantage of balancing stability and economy by dynamically adjusting the strategy through the risk preference coefficient. However, the Copula function has limited ability to model high-dimensional data correlation and relies on historical data distribution assumptions.

In a further extension of the coupled renewable energy and electricity market uncertainty problem, ref. [46] models the uncertainty in wind power generation and electricity market prices through LASSO regressions and Markov processes. Electricity market prices are modelled through a time series model, which first decomposes prices into deterministic trends (LASSO regression estimates deterministic trends in electricity prices) and stochastic fluctuations. Then, a Markov process is utilized to capture both the stochastic and long-term trends in electricity price volatility. In particular, forecast errors in wind energy production and stochastic fluctuations in market electricity prices are modelled. To cope with the aforementioned uncertainties in wind energy production and electricity prices, the article employs the stochastic dual dynamic programming (SDDP) algorithm to solve a multi-stage stochastic optimization problem. Decisions at each stage depend on the current resource state and future market information. The article uses a scenario lattice to discretize the uncertain stochastic process and optimizes the decisions at each stage by recursively computing the post-decision value function. Based on actual operational data from the Spanish electricity market and wind farm operational data from 2013 to 2015, the model’s effectiveness was validated through a 365-day out-of-sample backtesting. The results showed that compared to a pure previous day market strategy, the proposed model could achieve an annualized increase in revenue of over EUR 100,000. In terms of risk control, the nested CVaR model optimizes the tail risk of weekly returns from EUR −3891 to EUR −2068, reducing risk exposure by 40%. However, the extreme risk of wind power forecast errors still requires long-term mitigation through portfolio management. At the algorithmic level, under the ADDP framework, the average solution time for daily decision-making problems is only 65 s, fully meeting the decision-making time window of over 2 h in the intraday market.

As the complexity of the problem increases, researchers have begun to consider the combination of multiple uncertainties, for example, the joint uncertainty of load, market price, and wind energy. Ref. [59] investigates the demand response strategy of VPPs in market bidding, especially how to cope with the bidding strategy under the uncertainty of renewable energy output, load demand, and market price. The article proposes a model of a multi-stage bidding strategy based on the stochastic programming theory, which applies to the participation of VPPs in day-ahead, intraday demand response, and real-time power markets. This model takes into account the uncertainty of renewable energy output, customer load demand, and market prices. The model adapts to the uncertainties in different markets by optimizing at multiple stages to more accurately reflect the operational strategy of the VPP, which can help the VPP develop a more robust bidding strategy in an uncertain market environment. It has the advantage that multi-stage optimization improves strategy robustness and adapts to different market rules. Further insights from a Chinese VPP case study reveal that there is an economic inflection point of 30 MWh for demand response capacity (DRcap); below this value, each additional 10 MWh of DRcap increases profits by an average of 8.2%, whereas above this value, returns diminish due to excessively high procurement costs; under a 25% wind power forecast error scenario, setting DRcap to 20 MWh can increase VPP bidding volume by 18% compared to the baseline while reducing operational costs by 15% through off-peak charging of energy storage and 7% through bilateral negotiated procurement (average price $44.4/MWh). However, the model assumes that market stages are independent and ignores cross-stage coupling risk.

Similarly, ref. [60,61] proposes a two-stage robust optimization model that integrates distributed energy resource and demand uncertainty and handles bidding in different markets at two key stages, with the first being the regulation service contract (decided at least 1 week in advance) and the second being the previous day market bidding contract (decided the day before). Robust optimization ensures that the VPP can make optimal decisions in the face of future uncertainty, further improving the profitability of the virtual power plant in the energy and regulation service markets. The article integrates the regulation service and the previous day market bidding contract in the same optimization framework, and it handles multiple contracts simultaneously through a two-stage robust optimization model, which enables the VPP to make flexible strategy adjustments between the two markets, thus improving the overall economic efficiency of the VPP more effectively and solving the problem of handling the regulation service and the bidding contract separately in the traditional approach. Its strength lies in the flexibility of the optimization framework to adapt to multiple contract types and enhance comprehensive revenue. The limitation is that reconciliation service contracts need to be determined 1 week in advance, and the real-time response capability is insufficient. Ref. [62] describes the composition structure of the VPP and its coupling with multiple markets in detail, including the energy market, the FRP market, the carbon quota market, and the green certificate market. In order to address the uncertainty of renewable energy output, the article adopts a two-stage stochastic optimization approach, which takes into account the probability and uncertainty of different scenarios in the upper model, helping the VPP to more accurately assess the risks encountered in the bidding process. Finally, the article verifies the effectiveness of the proposed model through an arithmetic example analysis. The simulation results show that the introduction of the carbon quota and green certificate markets increases the proportion of renewable energy output in the electricity market for the VPP by 9.4%. For the same generation size, the profit of a high proportion of renewable energy VPPs in the ECG market is higher than that of conventional VPPs by EUR 24,780.57. This suggests that the proposed model is effective in facilitating the low-carbon energy restructuring of VPPs and improving their profitability.

On this basis, ref. [63] establishes a stochastic adaptive robust scheduling model considering a central air-conditioning system (CACS) and multiple markets, which uses a stochastic planning method to deal with the uncertainty of electricity market price, and it is combined with an adaptive, robust method to solve the uncertainty of PV power output; adaptive robust optimization reduces the over-conservatism of traditional robust optimization using phased decision-making according to different markets, which makes the VPP able to flexibly adjust its strategy when part of the uncertainty is known.

Ref. [64] proposes an improved electricity price prediction method based on large-scale language modelling (LLM) and market sentiment analysis to address the challenge of increased electricity price volatility following the introduction of the 5-min settlement (SMS) mechanism in Australia’s National Electricity Market (NEM). The adoption of the 5-min settlement mechanism by the NEM from October 2021 has led to more frequent and complex electricity price fluctuations, and traditional machine learning models (e.g., LSTM and GRU) [65] find it difficult to accurately predict short-term electricity prices due to their reliance on historical data and insufficient resolution. Electricity prices are affected by the supply–demand balance, participants’ bidding behavior, and market sentiment, and new methods need to be integrated to improve prediction accuracy. Based on the original Conditional Time Series Generative Adversarial Network (CTSGAN), a spike confusion matrix loss function is introduced to enhance the prediction ability of spike tariffs (>600 AUD/MWh) by balancing the false positive rate (FPR) and false negative rate (FNR). The outputs of the bidding behavior and market sentiment proxies are also integrated as input conditions. The RMSE of the LLaMa3 8B proxy (29.92) is significantly lower than that of the conventional model (GRU: 193.51; LSTM: 86.27), and it is more accurate in forecasting, especially for large generators and fossil energy players. This study provides an innovative solution for the accurate prediction of highly volatile electricity markets by fusing the semantic analysis capabilities of LLM with the temporal modelling advantages of generative adversarial networks.

In dealing with more complex market uncertainties, a flexible, robust optimization method is proposed in ref. [66] to optimize the bidding strategies of renewable energy virtual power plants in multiple markets, taking into account the output uncertainties of wind energy, PV power generation, and energy storage. The article innovatively introduces the concept of asymmetric uncertainty, which breaks through the limitation of the traditional robust optimization method, which assumes the uncertainty to be symmetrically distributed. By modelling the uncertain parameters as asymmetric distributions, the method more realistically reflects the market price fluctuations and output uncertainty of renewable energy sources (e.g., wind power and PV). In this way, the model can capture the actual market situation more accurately, improving the accuracy of forecasting and making the bidding strategy more flexible and adaptable to actual market uncertainty. This approach not only handles more complex market environments and uncertainties but also enables optimal dispatch in multiple markets, thus improving the economic efficiency and market competitiveness of VPPs. Meanwhile, the method’s simplified, robust optimization structure and high computational efficiency make it more feasible and practical in practice.

At the same time, researchers have begun to try to link electricity with other markets to achieve more comprehensive revenue optimization. Ref. [67] proposes a multi-time-stage joint power-carbon market bidding strategy model, which aims to optimize the bidding strategy of virtual power plants in power and carbon markets, especially in the previous day market, real-time market, carbon market, and green certificate market. The article deals with the uncertainty of electricity prices in the power market, prices in the carbon market, and supply and demand in the green certificate market through a two-stage optimization model. The first stage is previous day market bidding based on market forecasts and electricity demand, in which virtual power plants need to develop electricity purchase and sales strategies based on forecasts of electricity prices, the carbon market, and the green certificate market; the second stage uses real-time market dispatch when VPPs adjust to the decisions made in the first stage and the actual market situation. By optimizing across multiple time phases, the VPP can respond more flexibly to real-time power price fluctuations and demand changes.

In addition, ref. [68] effectively handles uncertainty in the virtual power plant bidding process, especially regarding renewable energy sources, through interval optimization methods. Most traditional methods use scenario analysis or probability distributions to model uncertainty, which usually requires a large number of computational scenarios and assumes that the uncertainty parameters conform to a certain distribution. With the interval optimization approach, by using the number of intervals (i.e., ranges of uncertain parameters represented by left and right boundaries), the method can efficiently represent the uncertainty in the output of renewable energy sources without relying on distributional assumptions. Each uncertain variable is represented through an interval, the range of which is determined by the minimum and maximum values, and the median value represents the expected value. To better handle uncertainty in the optimization process, the article introduces the pessimism parameter. Pessimism controls the decision-maker’s acceptance of uncertainty, and higher pessimism implies higher risk tolerance. By adjusting the pessimism degree, the VPP can optimize the bidding strategy by making effective profit and risk trade-offs in the face of uncertainty.

Finally, ref. [69] uses scenario trees and scenario lattices to describe uncertainty. Scenario trees are used to characterize the uncertainty in PV generation, while scenario lattices are used to characterize the uncertainty in demand response. The article proposes a new method to generate a scenario lattice of electricity demand for demand response data predicted by machine learning techniques, which is better adapted to new forecasting models than traditional scenario generation methods. Ref. [70] effectively reduces uncertainty in VPP optimization runs by proposing a new deep reinforcement learning probabilistic predictor based on quantile regression deep deterministic policy gradient (QRDDPG) for describing possible scenarios of wind power and electricity prices within a confidence interval. In addition, a reward function based on unbalanced samples is constructed to efficiently evaluate the strategy scores of the actor network in the DDPG. The proposed VPP operating profit increases by 18.69%, and the emissions and voltage deviations decrease by 3.42% and 10.44%, respectively. This proves the superiority of the proposed probabilistic prediction method.

In summary, the optimization problem of virtual power plants in the market offers involves the handling of multiple uncertainties. From singular uncertainties to multiple uncertainties, researchers have adopted various methods, such as robust optimization, stochastic programming, interval optimization, etc., aiming to enhance the economic efficiency and stability of virtual power plants in the electricity market. Although these studies have made significant progress in theory, how to deal with multiple uncertainties in complex market environments in practical applications remains an important direction for future research.

4. Optimized Scheduling of Virtual Power Plants

4.1. Optimize Scheduling Strategy

With the development of virtual power plant technology, how to optimize the scheduling strategy of VPPs to improve their market competitiveness and economic efficiency has become a hot topic of current research. In recent years, researchers have proposed a variety of optimized scheduling strategies to solve the co-operative scheduling problem of different types of VPP resources [71].

Ref. [72] proposes a VPP optimal dispatch method for large-scale new energy access to the grid, aiming to reduce deviation penalties and improve the expected profit of VPPs through a compensation mechanism, as well as to optimize the real-time balance of VPPs through a dispatch model. On this basis, ref. [73] proposes a multi-energy VPP scheduling framework that integrates scheduling strategies for electricity and natural gas markets and reduces the curtailment ratio of renewable energy sources through optimization strategies to improve the competitiveness of VPPs in the market.

Ref. [74] provided an improved genetic algorithm for the voltage control scheduling of VPPs, aiming to improve the stability and security of the power grid. By incorporating voltage control requirements in the optimization process, the model can achieve optimal scheduling of the grid and ensure stable power output. In ref. [75], by reviewing a variety of optimal scheduling methods, the economic scheduling problem of a VPP is explored, and a scheduling model based on mixed integer linear programming (MILP) is proposed. The method focuses on the resource aggregation efficiency of the VPP, reducing unnecessary energy waste by optimizing the scheduling scheme and effectively improving the overall economic efficiency of the system. Ref. [76] presents a power market-oriented VPP dispatch model that optimizes the economics of VPPs by considering the dispatch of conventional generating units and energy storage devices. Ref. [77] quantifies uncertainty using a network state-based scenario-reduction strategy. Due to the large scale of the optimization problem, with many variables and complex constraints, it is difficult for traditional centralized methods to solve it directly. For this reason, this paper proposes a distributed optimization algorithm based on multi-temporal trend decoupling. By decoupling the charging and discharging models of the energy storage system in time, an effective decomposition and solution of the large-scale optimization problem is achieved.

In the context of multi-energy scheduling, a model predictive control (MPC)-based VPP scheduling methodology is proposed in ref. [78], focusing on reducing power scheduling costs through rolling optimal scheduling on multiple time scales. The model further optimizes VPP scheduling using the particle swarm optimization algorithm, which results in significant cost reduction. Ref. [79] proposes a rural VPP architecture containing biomass power generation, wind–solar interconnection, an energy storage system, and demand response loads, adopting a two-stage distribution robust optimization model; it introduces fuzzy sets to describe the uncertainty distribution information and combines with Dual Vertices Fixing (DVF) algorithm to efficiently solve non-convex optimization problems to avoid the excessive conservatism of traditional methods.

Overall, existing research on virtual power plant scheduling optimization mainly focuses on idealized scheduling models to improve resource usage efficiency and system economics through static optimization strategies. It still faces challenges such as computational complexity and practical applicability.

4.2. Considering Uncertainty in Optimal Scheduling

As an important mechanism for power dispatching, virtual power plants are not only capable of integrating a variety of distributed energy resources such as wind, solar, and energy storage devices but also of effectively coping with the uncertainty problems in the power system. However, in actual operation, virtual power plants face a variety of uncertainty factors, which mainly originate from market price fluctuations, the volatility of renewable energy output, and changes in power load. To improve the operational efficiency and economy of virtual power plants, researchers have proposed a variety of optimal scheduling methods.

Many studies focus on dealing with a single type of uncertainty. For example, ref. [80] proposes a model predictive control (MPC)-based optimal scheduling method for virtual power plants that takes into account market price fluctuations and uncertainty in wind power generation. Prediction errors are compensated by introducing a feedback-correction mechanism, which allows the MPC to make real-time corrections based on data from actual operations to cope with real-time system changes and uncertainties. The advantage is that MPC rolling optimization improves the dynamic adjustment ability and reduces the impact of short-term prediction errors. The limitations are the high requirement of computational resources and the insufficient handling of multi-timescale coupling problems.

Similarly, ref. [81] presents a data-driven, two-stage stochastic robust optimization (SRO) scheduling model for virtual power plant optimization that takes into account multiple uncertainties such as wind power, PV generation, load demand, and market price. The article uses the Dirichlet Process Mixing Model (DPMM) and variational inference algorithms to construct the uncertainty set, taking into account the correlation between wind power, PV, and load demand. This approach effectively extracts and models the intrinsic relationships of uncertain data, reflecting the correlation between multiple uncertainties more flexibly and accurately than traditional methods, thus avoiding the limitations of a single hypothetical distribution. The model makes pre-dispatch decisions in the first stage to determine the optimal arrangement of energy markets and reserve capacity and adjusts to the actual situation in the second stage to minimize adjustment costs. With this two-stage robust optimization structure, the method solves the problem that single-stage robust optimization models are usually overly conservative, and it can adjust the system’s operation strategy more efficiently in the face of a variety of worst-case uncertainties. The advantages are that DPMM flexibly captures the nonlinear relationships between variables and avoids single distribution assumptions. The limitations are the slow convergence of the variational inference algorithm and limited practicality in large-scale scenarios. Case studies validate the effectiveness of the model and algorithm; as wind power uncertainty budgets increase from 0 to 12, the VPP reserve declarations show a downward trend, and net costs rise significantly, indicating that the system needs to retain more ramping resources to cope with wind power fluctuations, and increased robustness comes at a higher conservative cost. Further analysis of the impact of reserve energy prices reveals that higher prices prompt VPPs to proactively increase reserve capacity and energy declarations (with the highest increase reaching 23%), either by sacrificing day-ahead energy market revenues or increasing traditional power plant costs to hedge against the risks of reserve deployment uncertainty. This highlights the regulatory role of economic incentives in robust decision-making.

As the complexity of the problem increases, researchers have begun to consider the joint effects of multiple uncertainties and propose more sophisticated optimization methods. For example, ref. [82] proposes a new stochastic adaptive robust optimization (SARO) model for optimal scheduling of virtual power plants when participating in day-ahead energy and standby markets. The innovation of the article focuses on how to deal with uncertainty in the optimal scheduling process, especially involving external uncertainty and internal uncertainty. The external uncertainties mainly include the market price and the availability of wind power generation, which are determined by the external environment and are not affected by the scheduling decisions of the virtual power plant. The article models these uncertainties through a scenario-based stochastic programming approach and uses conditional value-at-risk (CVaR) to manage the risks associated with these uncertainties. This approach helps to optimize VPP decisions under different market conditions to cope with price volatility and wind power output uncertainty. Internal uncertainty refers to the uncertainty in the scheduling requests that VPPs face when providing standby capacity, and the scope of these requests varies according to the decisions of the VPP. The SARO model employs a decision-dependent polyhedral set of uncertainties, which allows the set of uncertainties to be adjusted as the decisions are made and reduces over-conservatism. This approach is more practical and flexible than traditional robust optimization methods based on user-preset budget parameters. The advantage is that decision-making relies on uncertainty sets to reduce conservatism and improve scheduling flexibility, and the limitation is that extreme scenario generation relies on manual pre-determination and lacks automated extrapolation capabilities. Case studies demonstrate that thermal/cooling system inertia regulation significantly enhances flexibility; when the PMV constraint range is expanded, heating demand decreases by 12%, and thermal load energy storage potential is enhanced; in buildings with increased equivalent thermal resistance R, cooling load decreases by 18%, highlighting the role of thermal inertia in enhancing ‘cooling storage’ capacity. In the most adverse scenario, the overlap of low PV output (8:00–11:00 and 17:00–18:00 below 2 MW) and peak electricity demand (7:00–11:00 exceeding 15 MWh) forces the system to purchase electricity during peak hours. At this point, demand response (DR) shifted 12% of electricity consumption to off-peak hours (6:00–12:00 and 20:00–22:00), effectively reducing peak-hour costs by 15%, keeping the total cost of the economic mode at CNY 31,998. In the carbon emission optimization mode, due to the higher carbon emission intensity of gas turbines compared to purchased electricity, the system actively limits GT output. increasing electricity purchases to 29.18 MWh. Although this results in a 2.5% increase in carbon emissions compared to the economic mode (to 0.7087 t), it demonstrates the trade-off mechanism between economic and environmental objectives.

Based on this idea, ref. [83] further extends the optimal scheduling scenarios and proposes a two-stage robust optimal scheduling method for multi-energy virtual power plants (MEVPPs), which takes into account both the volatility of the PV output and the uncertainty of the electric load, aiming to optimize the economics of the virtual power plants and reduce the carbon emissions. The two-stage optimization framework is divided into an outer layer optimization and an inner layer optimization, where the main objective of the outer layer optimization is to determine optimal scheduling decisions such as power purchases, sales, and load shifts by considering the worst-case PV output and electric load scenarios. The inner-layer optimization ensures that the objectives are achieved even in the worst-case scenarios by generating worst-case scenarios and adapting the dispatch strategy based on them. These methods demonstrate how to improve the dispatch efficiency and economics of virtual power plants by combining multiple uncertainties.

While traditional stochastic programming can handle fluctuations in wind and solar power output, it has limited ability to regulate the rigid constraints of ‘heat-driven power generation’ in combined heat and power (CHP) systems. In response, ref. [84] proposes dynamic reconfiguration technology for electro–thermal coupled systems as a new path to cross-energy flexibility gains for virtual power plants (VPPs). In energy systems dominated by CHP (where CHP accounts for 13% of electricity and 60% of heating loads in China), traditional VPP scheduling is constrained by the rigid ‘heat-driven power generation’ constraint. However, seasonal reconfiguration of the heat network optimizes valve topology to release the regulatory capacity of CHP units, forming a ‘source-load’-co-ordinated wind power absorption mechanism. The S-BD parallel solving algorithm divides 40 scenarios into independent subproblems, using a penalty function to drive the cutting plane for unified processing of feasibility and optimality cuts, significantly improving computational efficiency; in the P6H8 system, the solving time was reduced from 79.57 s to 50.87 s. Actual system verification in Jilin Province demonstrates that this strategy increases VPP wind power installed capacity by 100%, reduces curtailment penalty costs by 46.7%, and lowers total investment costs by 13.3%. These data confirm that dynamic thermal network restructuring creates additional flexibility resources for VPPs through spatio-temporal load migration. Future research should further explore the application of multi-network coupled affine regulation mechanisms in enhancing resilience under extreme scenarios.

To further improve the modelling accuracy of uncertainty, the wind speed PDF model (probability density function model) proposed in ref. [85] can more accurately describe wind speed uncertainty and its impact on wind power generation. The article not only uses the Weibull distribution to model wind speed uncertainty but also improves the accuracy of wind speed prediction by fitting the long-term wind speed data with a normal distribution through the wind speed PDF model (DWP-RSS model). Specifically, the DWP-RSS model improves wind speed prediction accuracy by discretizing the wind speed data, and each wind speed interval is represented using a normal distribution and weighted according to the probability of each interval. This approach provides more accurate wind speed prediction for virtual power plant dispatch optimization, which can effectively deal with the uncertainty of wind power generation and reduce the impact of prediction errors on dispatch decisions.

Additionally, to handle multiple uncertainties at the source and load sides simultaneously, a new optimal scheduling method for a multi-energy virtual power plant (MEVPP) is proposed in refs. [86,87], aiming to solve the challenges posed by multiple uncertainties. By combining stochastic optimization and robust optimization, these approaches propose a two-stage robust stochastic optimization model that mainly deals with source-side and load-side uncertainties. The authors describe the uncertainty in wind and PV power generation using a basis uncertainty set with a robust adjustment factor. This uncertainty set is flexibly adapted to scenarios with different fluctuation magnitudes by adjusting the robust adjustment coefficients, thus avoiding the overly conservative dispatch results of traditional methods. With this approach, the fluctuations of wind and PV outputs can be modelled more accurately, and the risk of the dispatch results can be reduced. Load uncertainty mainly comes from the demand for multiple energy sources such as electricity, heat, cooling, and natural gas. The article employs the Wasserstein Generative Adversarial Network (WGAN-GP) to generate load scenarios, which are combined with the K-medoids clustering method to downscale the generated scenarios and select the most representative ones. This approach avoids assuming a probability distribution on load data and improves the practicality and accuracy of load scenario generation.

Ref. [88] proposes the ‘interval prediction-mechanism coupling-hierarchical optimization’ method; it is based on improved variational modal decomposition (IVMD) and fuzzy information granularity (FIG) to reconstruct the source load data interval, combined with improved echo network (IESN) and ARIMA models to predict nonlinear/linear components (with 100% coverage), quantifying carbon emission reduction benefits through a green certificate–carbon trading coupling mechanism (offsetting 246.43 t of CO₂). This scheme achieves a net profit of CNY 464,657 at a 95% confidence level and reduces carbon emissions by 31.39%. Complementing this technically, ref. [89] reveals the profound impact of building physical characteristics on uncertainty; the vertical thermal dynamic model it constructs shows that ignoring building height leads to heating imbalance (high-rise users experience reduced flow due to friction losses, with temperatures exceeding limits by 24.66 °C), while quantifying the floor water pressure-flow relationship lays the foundation for precise scheduling of building thermal inertia. At the risk synergy level, ref. [90] utilizes CVaR-Copula theory to quantify losses from wind and solar prediction errors (reducing risk costs by 23.8%) and designs an electricity–heat–carbon multi-market P2P trading mechanism; ref. [89] further introduces a CVaR risk-aversion strategy, dynamically balancing costs and extreme risks through the coefficient $\beta$ (CVaR decreases by 12.3% when $\beta$ = 0.4), which provides a universal risk hedging tool for multi-energy systems. In terms of improving solution efficiency, ref. [90] employs an improved ADMM-GBS algorithm (reducing solution time by 613 s), while ref. [89] proposes TSA-AD-ADMM asynchronous optimization; by asynchronously updating residual adaptive penalty parameters and boundary information, computational time is compressed to 658 s (a 70.8% speedup) in the P33D12 system, and together, these two approaches push the boundaries of distributed solution efficiency.

In summary, the uncertainty problem in virtual power plant scheduling has attracted a great deal of research. Although a single uncertainty model is theoretically effective in optimizing virtual power plant scheduling, a comprehensive model considering multiple uncertainties is more practical in complex practical application scenarios. Future research should continue to explore the scheduling strategies under extreme uncertainty conditions in-depth and consider more practical constraints to improve the adaptability and scheduling efficiency of virtual power plants.

5. State-of-the-Art Analysis and Outlook of Uncertainty Handling Methods for Virtual Power Plants

5.1. Analysis of the Current Situation

Currently, virtual power plants have made significant progress in addressing uncertainty problems and have developed rich theoretical and practical experiences. However, with the diversification of distributed energy resources and the complexity of the electricity market environment, virtual power plants still face multiple uncertainties during operation. These factors include the stochastic nature of renewable energy sources, the volatility of load demand, the frequent changes in power market prices, and the stochastic nature of electric vehicle charging and discharging behaviors. Although researchers have proposed various optimization methods to address these uncertainties, challenges such as high computational complexity, limited prediction accuracy, insufficient method versatility, and inadequate real-time response capability persist at this stage. Specifically, the uncertainty problem of virtual power plants can be analyzed in more detail in terms of both types and treatment methods.

First, starting from the types of virtual power plant uncertainties, the current virtual power plant uncertainties can be categorized as follows, as shown in

Table 1. Classification of uncertainty types.

Type of Uncertainty	Bibliography
Renewable energy contribution	[10,24,27,28,36]
Market price	[12,58,64]
Load requirement	[11,25,40,54]
Electric vehicle charging and discharging	[26,40,45,73]
Combining multiple uncertainties	[33,59,62,70,88]

below:

(1)

Uncertainty of renewable energy output: The output of wind power and PVs has obvious randomness and volatility and is greatly affected by meteorological factors. In the actual operation process, these random fluctuations make forecasting and scheduling more difficult, especially in extreme weather conditions. Safe and stable operation is still a huge challenge.

(2)

Uncertainty of load demand: The randomness of user behavior and economic activities makes it difficult to forecast load accurately. Although the existing methods can improve the forecasting accuracy to a certain extent, it is still necessary to further improve the adaptability of the model and the accuracy of the forecast.

(3)

Uncertainty of market price: Spot market price fluctuations are frequent and large, directly affecting the economic efficiency of virtual power plants. Although the study proposes a variety of forecasting methods, the problems of real-time operation and accuracy have not been solved well.

(4)

Uncertainty of EV charging and discharging behavior: User driving habits, tariff strategies, charging facility layouts, and other factors make it difficult to accurately predict charging and discharging behaviors, and the current method has not yet comprehensively covered the reality of complex practical scenarios.

(5)

Integration of multiple uncertainties: The joint processing method of multiple uncertainties proposed by existing research still has the problems of high computational complexity and insufficient real-time response in practical applications.

Secondly, virtual power plants use a variety of methods for uncertainty handling, each with its advantages and limitations, as shown in

Table 2. Classification according to uncertainty-handling methods.

Method Type	Bibliography	Applicability Analysis
Robust optimization	[21,29,43,61,66]	This approach is suitable for situations where it is essential to confirm that the system operates within constraints, even under extreme scenarios, such as environments with strict requirements for grid frequency and voltage stability. The main advantage of this method is its strong robustness against extreme uncertainties. However, traditional methods often compromise economic efficiency due to their conservative nature.
Stochastic optimization	[24,34,38,59,70]	It is suitable for scenarios that need to simulate the probability distribution of multiple scenarios in a refined way (e.g., previous day market bidding). Scenario-generation techniques (e.g., Monte Carlo simulation and cluster dimensionality reduction) can improve the model accuracy under multiple uncertainty couplings, but the computational complexity increases significantly when the number of scenarios is too large.
Machine learning and opportunity constraints	[31,36,40,52,64]	It is suitable for scenarios that require high-precision prediction and probabilistic constraints for co-optimization (e.g., load demand prediction and scheduling). Machine learning (e.g., LSTM and reinforcement learning) can improve prediction accuracy, and the chance constraints ensure system reliability through probability thresholds, but the model’s generalization ability is limited by the quality of the training data, and it may fail under unexpected events.
Improved heuristic algorithms	[19,28,74,79]	Suitable for complex non-convex optimization problems (e.g., multi-objective resource aggregation). Improved heuristic algorithms (e.g., cuckoo algorithms and genetic algorithms) are flexible, but the speed of convergence and the quality of the solution depend on parameter settings.
Statistical methods	[27,46,58,86]	Suitable for scenarios where uncertainty correlations need to be modelled (e.g., joint wind-light output distribution). Copula function, LASSO regression, and other methods can effectively extract statistical relationships between variables but have limited ability to handle high-dimensional data or nonlinear relationships.
Interval optimization	[47,68,77]	Suitable for scenarios where the range of uncertainty is well defined but the distribution is unknown (e.g., conservative scheduling decisions). Interval numbers simplify uncertainty characterization, but the results are biased towards conservatism.
Adaptive robust optimization	[30,44,57,82]	Suitable for scenarios where decisions need to be dynamically adjusted in stages (e.g., multi-timescale market bidding). Reduces conservatism through two-stage optimization, but it requires high real-time data updating and computational speed.

below:

(1)

Robust optimization: Robust optimization aims to ensure the safety and reliability of the system in the worst case, but its computational complexity is high, and the results are usually conservative, which may reduce the efficiency of resource use. However, this conservatism can be mitigated and the efficiency of resource utilization can be improved by setting the uncertainty reasonably and combining other methods.

(2)

Stochastic optimization: Stochastic optimization handles uncertainty finely through multi-scenario analysis and can effectively analyze different possible scenarios. However, as the number of scenarios increases, the computational complexity of the model increases significantly, which may make it difficult to meet the real-time application requirements. Scenario-reduction techniques and scenario-screening methods can effectively reduce computational complexity.

(3)

Machine learning and chance constraints; Machine learning improves prediction accuracy, and chance constraints guarantee the reliability of the system. However, machine learning models have limited generalization ability and perform poorly in the face of unexpected events or untrained data.

(4)

Improved heuristic algorithm: Heuristic algorithms possess a high degree of flexibility and adaptability, but the results are less stable and susceptible to the initial values and parameter settings of the algorithm. To overcome this limitation, a more robust algorithmic framework or a mixture of other deterministic algorithms can be used.

(5)

Statistical methods (Copula/LASSO regression, etc.): Statistical methods can effectively analyze the correlation between data, but their performance is limited in the processing accuracy of high-dimensional data and complex scenes. The prediction accuracy of statistical methods can be significantly improved by data preprocessing and dimension-reduction techniques.

(6)

Interval optimization: Interval optimization methods are simple to compute and easy to understand and implement, but the results are usually conservative and may reduce the economic efficiency of the system. The use of dynamic interval adjustment strategies can effectively improve this problem.

(7)

Adaptive robust optimization: Adaptive robust optimization can dynamically adjust the decision according to real-time information, but the real-time response speed still needs to be further improved in practical applications. Improving the execution efficiency of the algorithm and adopting fast-solving techniques can effectively alleviate this problem.

5.2. Outlook

Given the current problems and challenges in uncertainty handling in virtual power plants, future research can focus on the following aspects:

(1)

Joint optimization with multiple uncertainties:

Most of the current studies deal with a single or a few uncertainty factors separately and do not study the uncertainty of virtual power plants. In the future, further attention should be paid to the linkage effect of multiple uncertainty factors, including renewable energy output, load fluctuation, power market price, and electric vehicle charging and discharging, and a comprehensive optimization model and solution method should be proposed to enhance the adaptive ability of virtual power plants to the complex uncertainty environment.

(2)

Efficient and real-time optimization algorithms:

The currently used methods, such as robust optimization, stochastic optimization, and interval optimization, despite their significant theoretical effects, have too high computational complexity and insufficient real-time response capability in practical applications, which limits their application scope. Future research needs to explore algorithms and models with lower computational complexity and faster solution speeds to improve the responsiveness and reliability of virtual power plants in actual operation.

(3)

Deep integration of artificial intelligence techniques and uncertainty handling:

Machine learning, especially deep learning techniques, has shown great potential in the field of prediction. However, at this stage, machine learning models are still deficient in generalization ability and face unexpected events. Future research can deeply explore the integration of emerging machine learning techniques, such as reinforcement learning and self-supervised learning, with optimization methods to improve the generalization performance of prediction models and their responsiveness to unexpected events.

(4)

Uncertainty risk management system development:

Future research should be devoted to constructing a perfect uncertainty risk management system, including risk quantification, risk conduction path analysis, and risk early-warning mechanisms, to realize a reasonable balance between the economy and stability of virtual power plants, reduce operation risk, and improve operation efficiency.

6. Conclusions

As a core carrier for integrating distributed energy resources, the core value of VPPs lies in transforming uncertainty into an elasticity advantage of system operation through flexible scheduling and intelligent decision-making. In this paper, a systematic study shows that the technology path of virtual power plants in dealing with renewable energy fluctuations, load demand stochasticity, and market price uncertainty presents three main features: multi-method co-optimization (e.g., integration of robust optimization and machine learning), multi-timescale decision-making (day-ahead and real-time market dynamics adjustments), and multi-objective trade-offs (economy, stability, and low-carbon performance). Although the existing methods perform well in singular uncertainty scenarios, there are still bottlenecks such as model conservatism and real-time response lag in multiple uncertainty coupling (e.g., extreme weather super-imposed on market mutation) and cross-regional resource synergy. Future research needs to break through the following key areas:

(1)

Analysis of endogenous coupling mechanisms of multiple uncertainties: Existing models mostly regard uncertainties as external perturbations, ignoring the dynamic correlation between source, load, storage, and price (e.g., bi-directional impacts of EV charging and discharging behaviors and fluctuations in electricity price). A dynamic coupling framework based on causal reasoning needs to be constructed to reveal the uncertainty conduction path and improve risk prediction capability.

(2)

Collaboration between lightweight algorithms and edge intelligence: Aiming at the problem of the high computational complexity of robust optimization, a layered optimization architecture combining federated learning and edge computing can be explored to realize millisecond responses in the ‘prediction-decision-execution’ link so as to meet the demand of the high proportion of renewable energy connected to the grid.

(3)

Market–carbon synergistic mechanism design: The existing bidding strategy focuses on electricity price risk and lacks a dynamic response to external policies such as the carbon market and green certificate trading. It is necessary to construct a multi-dimensional market game model of electricity–carbon and green certificates to quantify the impact of policy fluctuations on the return of virtual power plants.

(4)

Enhanced resilience under extreme scenarios: Current research mostly assumes that uncertainty obeys a smooth distribution, making it difficult to cope with climate anomalies or black swan events. Complex system theory can be introduced to design a full-cycle resilience scheduling framework of ‘prevention-adaptation-recovery’, which can be combined with digital twin technology to realize extreme scenarios.