Risk-constrained multi-period investment model for Distributed Energy Resources considering technology costs and regulatory uncertainties
Introduction
The adoption of behind-the-meter Distributed Energy Resources (DERs) in power distribution grids has been fast increasing during the last decades, with potential impacts in terms of grid operational costs, loss reduction, reliability and security of supply, provision of ancillary services at the distribution level, emissions reduction, and deferral of transmission and distribution network upgrades [1]. This private adoption of DERs, namely PV and storage, has been motivated by a significant decrease in technology costs [2] combined with important changes in tariff policies and solar compensation mechanisms, such as net-metering schemes [3], [4], [5] or feed-in remunerations [6], [7], which made DER economically viable for medium size consumers and microgrid owners.
However, these two factors (technology costs and DER regulatory schemes) are constantly changing and there is a significant uncertainty about their evolution in the near future. For example, when planning behind-the-meter DER investments for the next 15 or 20 years, it is difficult to anticipate deterministic trends of evolution of PV and storage asset costs. In fact, there is a significant uncertainty about the future prices of these technologies, as they typically depend on multiple aspects, such as raw material costs, the level of maturity of underlying technologies, tax incentives, and rebates, etc. Even assuming that these prices tend to decline with time, the uncertainty about the “pace” of reduction is a challenge for prosumers and microgrid owners looking for the optimal time to invest in DERs.
Similarly, there is uncertainty from the side of the DER policies that determine the revenue streams associated with these technologies. As an example, the fast adoption of DERs has initiated a regulatory discussion around solar compensation mechanisms, such as the role of net-metering policies and time-of-use tariffs or the ability of utilities to recover fixed costs in distribution grids with high penetration of DERs [8], [9], [10]. Therefore, it is expected that this discussion may lead to sudden regulatory changes in DER interconnection and compensation policies, such as the transition from net-metering to net-billing schemes [11]. As shown in [12], even small variations in solar compensation mechanism significantly impact the adoption of PV and storage technologies.
It is clear that the evolving changes in DER technologies and policy will create a new uncertainty environment in which DER adopters will plan their investments. From their perspective, postponing the procurement and installation of DERs may allow taking advantage of the decreasing trajectories of technology costs. However, while waiting for “the best moment to invest”, these potential investors might be losing important benefits and incentives coming from a favorable (DER friendly) regulatory framework. Thus, these long-term uncertainty in DER technology costs and policy trajectories introduce a new economic risk to potential DER adopters, which raises two main research questions: (i) how to plan DERs under this uncertainty environment? (ii) how to control the corresponding economic risk in the planning stage?
This paper aims to address these questions by proposing a multi-period DER investment model with economic risk constraints, considering technology costs and regulatory uncertainties.
This work expands on existing literature on behind-the-meter DER investment and planning models, traditionally used to determine the optimal portfolio and sizing of DERs assets in a building or a microgrid site, considering different costs and revenue streams [13]. Although there are some non-linear exceptions (e.g. [14]), these models are typically based on Mixed Integer Linear Programming (MILP) formulations [13], [15], [16] and have evolved over the last decade to address new challenges of DER planning and economics. Important additions to the original formulations of these investment models include the time resolution of the dispatch [17], the role of thermal loads in the optimal sizing [18], the optimal operation of multiple energy vectors [19], the security aspects of the design of electricity [20] and thermal [21] generation systems, the integration of electricity storage degradation models [22], [23], as well as the consideration of environmental objectives in the DER infrastructure planning [24].
Some of these models were also expanded to consider different types of uncertainty, such as the PV generation [25], the wind speed or the load demand [26], capturing the short-term uncertainty related to DER operations in the planning phase. The long-term aspects of planning are typically addressed through multi-period models, which determine not only the optimal portfolio and size of technologies, but also optimal timing of the investments within a planning horizon. In the context of DER investments, two multi-period planning models were presented in [27], [28], considering deterministic evolution of load and prices throughout the horizon of investment. Stochastic models for DER planning were also proposed in the context of microgrid design, using a two-stage approach [29] and particle swarm optimization [30]. In both cases, these models focus on the long-term uncertainty exclusively associated with the load growth. The multi-period technology costs and regulatory uncertainties are not considered.
An additional objective of this paper is to approach uncertainty from the risk perspective. An approach to risk in multi-year investment problems, presented in several papers that show the economic benefits of deferring the investments/upgrades till a later time in the planning horizon, is known as the “real options approach”. For example, in the DER investment case, the high volatility of fuel and electricity prices encourage the deferment of higher capacity assets [31], [32]. However, as pointed out in [32], the real options approach cannot analytically consider multiple risk factors, which may be a limitation in practical applications. Alternatively, another form of dealing with uncertainty in this context is quantifying multiple economic realizations using a risk measure, and guaranteeing that it falls below a specified threshold [33], [34]. Conditional Value-at-Risk (CVaR), due to its linear property, has been widely used to capture risk in various DER optimization problems. For example, on DER operations, [35] seeks to minimize a microgrid operational cost in addition to a corresponding CVaR component. In [36], CVaR is used to limit the risk associated with the operational cost of a scheduling problem for a wind-integrated smart multi-carrier energy hub, considering wind generation, electrical, and thermal demands as uncertainty parameters. In the context of power generation investment and planning, [37] uses a CVaR constraint to limit total investment and operational costs, considering fossil fuel prices and hydrological inflows as potential risk sources, while [38] employs CVaR to control the imbalance between energy generation and demand caused by uncertainty from wind and solar output and demand. Specifically in DER planning, CVaR has been used to capture risk where the uncertainty comes from electricity and gas prices [39]. The authors consider two different types of hedges: physical hedge (DER on-site investment) and financial hedge (gas/electricity futures). However, the model only captures investment at the beginning of the planning horizon, which does not allow the study of multi-year long-term uncertainties, such as the ones associated with DER technology costs and regulation.
To the best of our knowledge, there is no multi-period planning model for behind-the-meter DERs which explicitly addresses technology costs and regulatory uncertainties. As discussed above, such model is key to help prosumers and microgrid owners plan their investment strategies in an increasing uncertainty environment around DER policy and regulation as well as around technology maturity and costs of DER assets, particularly PV and storage technologies. To fill this gap, this paper presents a multi-period investment and planning model with economic risk constraints that is able to generate consistent DER procurement strategies in this uncertainty environment. Specifically, the proposed model calculates the optimal investment in PV, batteries, and conventional distributed generation assets in each year of a planning horizon, taking into account the uncertainty in technology costs of solar and storage technologies, as well as in fuel pries and solar compensation policies. Finally, the model allows the investor to impose economic risk constraints to the problem, both in an annual basis and in the horizon of the investments. The paper uses a case study, comprising investments in a large building in California, to show how different types of economic risk constraints can affect the size of DER assets as well as the optimal schedule of the investments.
This paper is structured as follows. Section 2 presents the formulation of the model to determine an optimal portfolio for electricity generation subject to cost-risk balance. Section 3 presents a case study and discusses the numerical results. Section 4 concludes and proposes directions for future work.
Section snippets
Methodology
The optimization model considers 3 types of long-term uncertainty: (i) trajectories of electricity and fuel prices, describing the uncertainty associated with the evolution of the energy markets; (ii) scenarios of technology costs, representing the uncertainty around the maturation of PV and storage technologies; (iii) scenarios of evolution of the DER regulation policies, in particular the magnitude and structure of the solar compensation mechanisms. Considering the multiple combination of
Case study
This section presents a case study to illustrate how the proposed model can find the optimal multi-year DER investment strategy, considering PV, storage and two types of natural gas generators. The program is solved by CPLEX using a computer with 8 GB of RAM and a 2.3 GHz Quad-Core processor.
Conclusion and future works
This paper presents a stochastic multi-period investment and planning model with economic risk constraints facing an uncertainty environment around DER technology costs and regulatory policies. The model is capable of generating consistent risk-constrained optimal DER investment strategies for a multi-year horizon.
As shown in the results, such strategies can be translated into “cost vs risk” solutions to support the decisions of prosumers and microgrids owners, who are interested in investing
CRediT authorship contribution statement
Thanh To: Formal analysis, Investigation, Software, Methodology, Writing – original draft. Miguel Heleno: Conceptualization, Supervision, Writing – review & editing. Alan Valenzuela: Software, Supervision, Validation.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
References (51)
- et al.
Integrating distributed generation into electric power systems: A review of drivers, challenges and opportunities
Electr Power Syst Res
(2007) - et al.
The impact of rate design and net metering on the bill savings from distributed PV for residential customers in California
Energy Policy
(2011) - et al.
Customer-economics of residential photovoltaic systems (part 1): The impact of high renewable energy penetrations on electricity bill savings with net metering
Energy Policy
(2014) - et al.
Configuring residential PV net-metering policies – a focus on the mediterranean region
Renew Energy
(2017) How feed-in remuneration design shapes residential PV prosumer paradigms
Energy Policy
(2017)- et al.
Combining feed-in tariffs and net-metering schemes to balance development in adoption of photovoltaic energy: Comparative economic assessment and policy implications for European countries
Energy Policy
(2017) - et al.
What drives profitability of grid-connected residential PV storage systems? A closer look with focus on Germany
Energy Econ
(2018) - et al.
On the benefits of behind-the-meter rooftop solar and energy storage: The importance of retail rate design
Energy Econ
(2020) - et al.
Future-proof tariff design: Recovering sunk grid costs in a world where consumers are pushing back
Energy Econ
(2018) - et al.
Alternatives for current net metering policy for solar PV in the netherlands: A comparison of impacts on business case and purchasing behaviour of private homeowners, and on governmental costs
Renew Energy
(2020)
Self-consumption for energy communities in Spain: A regional analysis under the new legal framework
Energy Policy
Optimal investment and scheduling of distributed energy resources with uncertainty in electric vehicle driving schedules
Energy
Coordinated short-term scheduling and long-term expansion planning in microgrids incorporating renewable energy resources and energy storage systems
Energy
Sandia’s microgrid design toolkit
Electr J
Resilience and economics of microgrids with PV, battery storage, and networked diesel generators
Adv Appl Energy
A mixed integer linear programming approach for optimal DER portfolio, sizing, and placement in multi-energy microgrids
Appl Energy
Battery aging in multi-energy microgrid design using mixed integer linear programming
Appl Energy
Environmental and economic optima of solar home systems design: A combined LCA and LCC approach
Sci Total Environ
Long-term sizing of rural microgrids: Accounting for load evolution through multi-step investment plan and stochastic optimization
Energy Sustain Dev
Multi-year stochastic planning of off-grid microgrids subject to significant load growth uncertainty: overcoming single-year methodologies
Electr Power Syst Res
Optimal investment strategies in decentralized renewable power generation under uncertainty
Energy
Investment and upgrade in distributed generation under uncertainty
Energy Econ
Conditional value-at-risk for general loss distributions
J Bank Financ
Solving corrective risk-based security-constrained optimal power flow with Lagrangian relaxation and benders decomposition
Int J Electr Power Energy Syst
Co-optimization of energy and reserve in standalone micro-grid considering uncertainties
Energy
Cited by (5)
A multi-criteria decision-making framework for distributed generation projects investment considering the risk of electricity market trading
2023, Journal of Cleaner ProductionEconomic analysis of the feller buncher in Brazilian Eucalyptus plantations: modeling with time series
2023, International Journal of Forest Engineering