Treynor Ratio guided risk-return model for TSO-DSO mutualism considering energy and price volatility

M. Jisma, Vivek Mohan, Mini Shaji Thomas, Siqi Bu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


Treynor Ratio (TR), a reward to volatility measure in finance, is used to quantify excess return per unit risk taken by the investor, where risk implies volatility in returns relative to market portfolio return. In this paper, TR is modified (TREP) to suggest the hourly weight of each risky energy asset at which it is worth using in the transmission and distribution levels to sustain the volatility of the market and to yield reasonable returns to both TSO and DSO. Uncertainties in the wind and solar energy sources pose energy-risk and fluctuations in grid power price poses financial risk, and both impact the TSO-DSO profit trade-off. Here, beta is used as the risk measure that evaluates the effect of uncertainty in each energy source on operators’ profit relative to the collective effect of all the energy sources available in the system. When risk is modelled using absolute measures like standard deviation or variance which are independent of market portfolio returns, it discourages risky assets more, to keep a risk-averse profile. By co-optimizing TREP values of TSO and DSO, more realistic portfolios are built by maximizing their expected profits per unit risk in relative terms. The resultant portfolio utilizes higher share of distributed energy resources (DERs) and renewable energy, thereby improving the role of DSOs in the market. The operators’ returns are found to be closer to the market portfolio returns at risks well within the market portfolio risk level.

Original languageEnglish
Article number100852
JournalSustainable Energy, Grids and Networks
Publication statusPublished - Dec 2022


  • Beta
  • DSO
  • Optimization
  • Renewable energy
  • Risk
  • Treynor Ratio
  • TSO

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Renewable Energy, Sustainability and the Environment
  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Treynor Ratio guided risk-return model for TSO-DSO mutualism considering energy and price volatility'. Together they form a unique fingerprint.

Cite this