Minimizing Wind Power Curtailment and Carbon Emissions by Power to Heat Sector Coupling—A Stackelberg Game Approach

Abstract

This paper proposes a Stackelberg game approach to minimize both the wind power imbalances and carbon emissions by harnessing demand response (DR) of residential heating loads fed by electricity or district heating (DH) options. The problem is formulated as a bilevel optimization model. An aggregator (leader) at the upper level aims at minimizing the mismatch between electricity demand and wind power while mitigating the carbon emissions arising from the DH system. The aggregator owns a wind farm and is responsible for controlling the DH generation through a combustion-based source and a deep well heat pump system (DWHP), which converts power into heat by utilizing wind power and replacing combustion-based DH. The aggregator submits bonuses to the households (followers) at the lower level incentivizing them to modify their consumption profile. The households receive the bonus offers and consequently decide how to optimize their net electricity and DH energy payments via an upward or downward DR strategy. The uncertainties associated with wind power and heating loads are considered using a stochastic programming framework. Long term thermal performance of the DWHP is studied separately. Results prove that the proposed bilevel framework enables significant reductions in wind power imbalances, carbon emissions, and energy payments. INDEX TERMS Stackelberg game, demand response, district heating, deep well heat pump, bilevel optimization, power to heat, sector coupling

Optimizing Power and Heat Sector Coupling for the Implementation of Carbon-Free Communities

“…The two-capacity building model is accurate enough to estimate the space heating load of a detached house or an apartment building [10,12,23]. The model evaluates the heating demand by capturing the indoor air dynamics relative to the outdoor air temperature variation.…”

“…Constraint (10) states that the stored thermal energy can hover within specified limits only, while Equation (11) guarantees that the final energy level of the thermal storage is greater than or equal to the initial level. Constraint (12) maintains the energy balance of the deep borehole by ensuring that the total heat energy extracted from the borehole is equal to the heat energy injected over a yearly operating cycle. Although the borehole reaches a steady-state operation in 10-15 years of continuous operation, maintaining such energy balance is quite necessary for long-term operation.…”

“…In order to linearize the quadratic term in Equations ( 13) and ( 14), special ordered sets of type 2 (SOS2) variables are employed in Equations ( 16) and (17). SOS2 is a set of variables in which at most two variables take nonzero values, and these variables are adjacent to each other [12,32]. The base of the quadratic term, i.e., a continuous variable, is first represented as a sum of a finite number of breakpoints weighted with SOS2 variables, as in Equation (16).…”

“…The aggregator operated the resources optimally to minimize the thermal storage size, while covering the DH demand through P2H conversion, only. The calibrated two-capacity model parameters of the prototype house are listed in Table 1 [11,12]. The rated power of the heating unit for each house was distributed around a mean value of 7 kW, while the mean house area was 180 m 2 .…”

“…In our previous work [12], the P2H option was considered, along with the DR of space heating in a short-term operation-planning model enabling aggregator and households to communicate with each other to achieve mutual benefits. However, in order to account for events concerning high wind days or even very low wind days in P2H application for DH demand, thermal storage is certainly required, as endorsed in the literature.…”