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Strategic Decision-Making Coping with Uncertainties and Strategic Interplays
The ever-increasing uncertainties due to volatile and uncertain renewable generation have been inevitably bringing about high operational risk. To counter this, many approaches, such as robust optimization, stochastic optimization, chance-constrained optimization, and distributionally robust optimization, to name a few, have been applied to power system planning and operation. However, there is still a lack of an in-depth understanding of the underlying mechanism of uncertainty accommodation. On the other hand, transactive energy and multi-energy system integration allow numerous participants to act as decision-makers. The strategic behaviors of decision-makers significantly complicate the decision-making. All these problems call for the innovation of decision-making theories for future energy and power systems.
Noticing that the interplays between decisions and uncertainties determine the system's uncertainty accoomodability, We converted the decision-making problems into non-cooperative games and turned to analyze the equilibrium strategies. This idea leads to a unified game-theoretic framework for decision-making to cope with uncertainties due to high-penetration renewables and strategic interplays among multiple decision-makers. Here we highlight some of our results in the following three aspects.
Mathematically characterizing accommodability of uncertain renewable generation
Game-theoretic decision-making for optimally accommodating uncertainty
Sophsiticated equilibrium analysis considering strategic behaviors in energy trading
Characterizing accommodability of uncertain renewable generation
A Zero-Sum Game Perspective
Dispatchable/Admissible Region & Operational Risk
Admissible region in terms of small-signal stability
We extended the classic concept of feasible region in the injection space to incorporate uncertain power injections from volatile renewable generation, mathematically depicting the condition that controllable injections can eliminate all the possible power imbalance caused by uncertain injections. Furthermore, my work reveals that the projection of the extended region to the subspace of uncertain injections identifies all possible uncertainties that can be accommodated, which is referred to as the dispatchable region [1]. Moreover, given a specific uncertain set (e.g., by prediction), the intersection of the uncertainty set and the dispatchable region identifies the capability of the system to accommodate uncertain injections, which is called the admissible region [2]. Uncertainties outside the admissible region lead to operational risk. This fundamental work provides a geometric characterization of uncertainty accommodability with a simple but profound understanding, and also benefits the understanding of operational risk and operational flexibility from a game-theoretic perspective[3]. As a natural generalization, we further extended this concept to the admissible region considering small-signal stability [4].
[1] W Wei, F Liu, S Mei, Dispatchable Region of the Variable Wind Generation, IEEE Transactions on Power Systems, 2015, 30 (5): 2755-2765.
[2] C Wang, F Liu*, J Wang, et al., Risk-Based Admissibility Assessment of Wind Generation Integrated into a Bulk Power System, IEEE Transactions on Sustainable Energy, 2016, 7 (1):325-336.
[3] J Li, F Liu*, Z Li, et al., Grid-side flexibility of power systems in integrating large-scale renewable generations: A critical review on concepts, formulations and solution approaches, Renewable and Sustainable Energy Reviews, 2018(93): 272-284.
[4] Y Pan, S Mei, F Liu*, et al., Admissible Region of Large-Scale Uncertain Wind Generation Considering Small-Signal Stability of Power Systems, IEEE Transactions on Sustainable Energy, 2016, 7(4): 1611-1623.
Game-theoretic decision-making for accommodating uncertainty
The work above implies that decision-making under uncertainties is essentially a multi-move, zero-sum game. In this game, the uncertainty and the flexibility serve as two players who are maximizing/minimizing the operational risk. Hence, its equilibrium strategies result in the "best" strategies to hedge against the risk arising from uncertainties. This inspiring principle further leads to efficient algorithm design for solving various kinds of complicated decision-making problems of power systems with high-penetration uncertain renewables, ranging from planning[5], day-ahead dispatch[6], and real-time operation[7].
Coordinated Planning under Uncertainties
Coordinated Planning under Uncertainties
Aggregating uncertainties in generation and ramping in Equivalent load duration curve
Robust Risk-Constrained UC
Robust Risk-Constrained UC
Different strategies leading to different accommodabilities
Realtime Robust Dispatch
Realtime Robust Dispatch
Dispatchability under given cost of real-time dispatch
[5] J Li, Z Li, F Liu*, H Ye, X Zhang, S Mei, N Chang, Robust Coordinated Transmission and Generation Expansion Planning Considering Ramping Requirements and Construction Periods, IEEE Transactions on Power Systems, 2018, 33 (1), 268-280
[6] C Wang, F Liu*, J Wang, F Qiu, W Wei, S Mei, S Lei, Robust Risk-Constrained Unit Commitment with Large-scale Wind Generation: An Adjustable Uncertainty Set Approach, IEEE Transactions On Power Systems, 2017, 32 (1), 723-733.
[7] Wei Wei, Liu Feng, Mei Shengwei, Real-Time Dispatchability of Bulk Power Systems with Volatile Renewable Generations, IEEE Transactions on Sustainable Energy, 2015, 6 (3), 738-747
Equilibrium analysis considering strategic behaviors in energy trading
When other sectors like heating are integrated into power systems, different stakeholders with interest conflicts are likely to adopt strategic decisions. Our studies addressed this problem via the equilibrium analysis considering participants’ strategic behaviors[8][9]. By comprehensively characterizing the strategic interplay among the participants, we showed that multi-lateral trading could create additional market competition to endow the energy prices with elasticity, rendering more reasonable prices. I also investigated the optimal package contract of multiple energies under asymmetric information and revealed the distortion of contract prices [10].
[8] Y Chen, W Wei, F Liu*, et al., Energy Trading and Market Equilibrium in Integrated Heat-Power Distribution Systems, IEEE Transactions on Smart Grid, 2019, 10 (4), 4080 - 4094.
[9] C Wang, W Wei, J Wang, F Liu*, S Mei, Strategic Offering and Equilibrium in Coupled Gas and Electricity Markets, IEEE Transactions on Power Systems, 2018, 33 (1), 290-306.
[10] Y Chen, W Wei, F Liu*, et al., Optimal contracts of energy mix in a retail market under asymmetric information, Energy, 2019, 165: 634-650.
The proliferation of distributed energy resources creates opportunities to form local/community markets for transactive energy. I have been focusing on the potential of energy sharing among prosumers. Our work showed that the sharing scheme could achieve nearly social optimal efficiency without central coordination [11]. Furthermore, we designed a generalized demand bidding mechanism for energy sharing with desirable properties of the market equilibria [12], and a distributed equilibrium-seeking algorithm with experimental verification[13]. These works provide fundamental understandings and insights that benefit the energy sharing market design.
[11] Y Chen, W Wei, F Liu*, et al., Analyzing and validating the economic efficiency of managing a cluster of energy hubs in multi-carrier energy systems, Applied Energy, 2018, 230: 403-416.
[12] Y Chen, S Mei, F Zhou, S Low, W Wei, F Liu*, An Energy Sharing Game in Prosumers based on Generalized Demand Bidding: Model and Properties, IEEE Transactions on Smart Grid, 2020, 11 (3): 2055-2066.
[13] Z Wang, F Liu*, Z Ma, et al., Distributed generalized nash equilibrium seeking for energy sharing games in prosumers, IEEE Transactions on Power Systems, 2021, 36 (5): 3973-3986.
A personal account of the effort with my collaborators is summarized in [14]. We expect these results could shed new light on the mechanism design underpinning the market and operation of future energy and power systems.
[14] Shengwei Mei, Feng Liu, Wei Wei, Engineering Game Theory and Its Applications to Power Systems, Science Press, Beijing, China,2016. (in Chinese)
Strategic trading behaviors in heat-power systems
Coupled electricity and natural gas markets
Engergy sharing stucture and mechanism
Applications
The developed assessment and dispatch algorithms have been deployed to partly function the “Robust Dispatch and Control Platform” of Qinghai provincial power grid of China. So far, the Qinghai power grid has installed 8.4GW wind generation, 16.4GW PV generation, 12GW hydro generation, and 3.8GW coal-fired generation. The wind and PV generation capacity is about 61% of the total installed capacity. Since most hydro generations are run-of-the-river, the coal-fired generation plays a crucial role in providing flexible regulation capacity. Hence it is challenging to accommodate such a large-scale renewable generation. Nevertheless, the platform has successfully supported Qinghai provincial power system to accommodate over 65.3 billion kWh of electricity generated by wind and PV in the past three years. It also partially supported the Qinghai power grid's 3-day, 7-day, and 15-day demonstrative operation with nearly 100% renewables (including hydropower)[15].
Our research works have won several awards, including the first prize for Scientific and Technological Progress Award by the China Renewable Energy Society (CRES) and the grand prize for Power Technological Innovation Award by the China Electricity Council (CEC).
[15] L Dong, Y Li, F Liu, et al. Development Path and Practice of Regional Fully Clean Power Supply: A Case of Qinghai Province, Journal of Global Energy Interconnection, 2020, 3 (4): 385-392. (in Chinese)
Qinghai Provincial Power Grid
Dispatch Platform of Qinghai Provincial Power Grid
Fully Clean Energy Operation (3-, 7, 15-day demonstrative operation)
Key Projects
I received the project “Game-Theoretic Methodology for Accommodating and Dispatching Large-Scale Renewable Generations” from the National Science Foundation of China (NSFC, 2011-2013). NSFC evaluated my project as “excellent.” Due to these research works, I was selected as one of the core members of the “Innovation Group” in power systems awarded by NSFC (2013-2019). In 2018, noticing our research works, NSFC formally set “Engineering Game Theory” as an emerging research direction. Furthermore, I am acting as the principal investigator of a sub-project of the Joint Major Research Fund in Smart Grids sponsored by NSFC and State Grid Corporation of China (2020-2023), “Supply-Demand Balance Mechanism and Methodologies Enabling Renewable Energy Dominated Power Systems.” This project aims to extend the current work to future renewable-dominated power systems concerned with interdependence between decisions and uncertainties (endogenous uncertainties).
Ongoing Work: Game-Theoretic Approach to Addressing Exogenours/Endogenous Uncertainties
In a power system integrated with a very high penetration of uncertain renewables, renewable generation must be responsible for flexible regulation. In this situation, the decision variables themselves become uncertain, leading to a dependency between decisions and uncertainties and thus significantly complicating the decision-making problem. We have conducted primary research on this topic, paying particular interest to specific problems[S1][S2]. We are trying to extend our previous results built on conventional decision-independent uncertainties (or exogenous uncertainties) to decision-dependent uncertainties (or endogenous uncertainties), including the concept of admissible region and the solution algorithms [S3]. We expect to utilize the developed game-theoretic methodologies to push the power system to extremely high penetration of renewable generation with guaranteed security. Essentially, it casts into a Nash-Stackelberg-Nash hierarchical game involving decision-dependent uncertainties [S4]. We expect this work could provide fundamental theoretical tools with insights into the decision-making under complicated uncertainties, particularly for future energy and power system with very high-penetration renewables.
This work is supported by the sub-project of the Joint Major Research Fund in Smart Grids sponsored by NSFC and State Grid Corporation of China, “Supply-Demand Balance Mechanism and Methodologies Enabling Renewable Energy Dominated Power Systems.”
[S1] Y Zhang, F Liu*, et al., Robust Scheduling of Virtual Power Plant under Exogenous and Endogenous Uncertainties, accepted by IEEE Transactions on Power Systems, online access
[S2] Y Zhang, F Liu*, Y Su, Y Chen, et al. Two-Stage Robust Optimization under Decision Dependent Uncertainty, accepted by IEEE/CAA Journal of Automatica Sinica.
[S3] Y Su, Y Zhang, F Liu*, et al. Robust Dispatch with Demand Response under Decision-dependent Uncertainty, 2020 IEEE Sustainable Power and Energy Conference (iSPEC), 2122-2127
[S4] Y Zhang, F Liu*, et al., On Nash-Stackelberg-Nash Games under Decision-Dependent Uncertainties: Model and Equilibrium, accepted by Automatica, https://arxiv.org/abs/2202.11880
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