Optimal operation of flexible heating systems for reducing wind power curtailment

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Flexibility in a heating system refers to the ability of regulating its heat consumption/supply/storage from time to time, which indirectly affects the corresponding electricity production and consumption. Through an optimal use this kind of ability, integration challenges for wind power such as curtailment can be addressed. In the paper, a series of flexibility options in the heating system are modeled and investigated, including extraction combined heat and power plant, electric boiler, electric heat pump (HP), heat storage and demand response management of the heat load. Based on a mathematical model developed for achieving an optimal dispatch of the heating system, heating systems with various configurations of flexibility options can be investigated regarding their contribution to wind power curtailment. A practical case study is presented to validate the proposed solution, with eight configuration scenarios defined to represent the existing and other possible system setups. The results show that there is a huge potential of using the flexibility from the heat sector to support wind power integration, and the potential can be affected by the seasonal variations of energy demand, wind profile and technical parameters like efficiency of the HP. Further, contribution of different flexibility options to wind power integration is different in regards to the achieved operation-scale techno-economic performance.

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Combined heat and power


District heating


Demand side management


Electric boiler


Extraction CHP


Electric heat pump


Heat storage


Point of common coupling

\( \varvec{t} \in {\mathbf{T}} \) :

Time intervals

τ :

Subset of t

n :

Number of consecutive time intervals during which period the total amount of regulated heat demand equals to zero

\( \lambda_{P,t}^{\text{imp}} \), \( \lambda_{P,t}^{\exp } \) :

Price of electricity import and export during time interval t

\( \lambda_{{{\text{chp}},t}} \) :

Fuel price during time interval t

\( \lambda_{{{\text{wind}},t}}^{\text{cur}} \) :

Penalty price of wind power curtailment during time interval t

\( \left( {\varvec{a}_{1} ,\varvec{a}_{2} ,\varvec{a}_{3} ,\varvec{a}_{4} ,\varvec{a}_{5} ,} \right) \) :

Parameter coefficients for estimating the fuel consumption of the ECHP plant

(A, B, C, D):

Generic boundary points denoting the operation region of the ECHP plant, each point contains a pair of values of electricity and heat outputs

\( \varvec{C}_{\varvec{v}} /\varvec{C}_{\varvec{m}} \) :

Slope for line DC//line BC used for defining the operation boundary of an ECHP plant

\( \overline{{P_{\text{chp}} }} \)/\( \underline{{P_{\text{chp}} }} \), \( \overline{{Q_{\text{chp}} }} \)/\( \underline{{Q_{\text{chp}} }} \) :

Maximum/minimum electricity/heat output of the CHP plant

\( \overline{{Q_{\text{hp}} }} \)/\( \underline{{Q_{\text{hp}} }} \) :

Maximum/minimum heat output of the HP

\( \overline{{Q_{\text{eb}} }} \)/\( \underline{{Q_{\text{eb}} }} \) :

Maximum/minimum heat output of the EB

\( \overline{{R_{s} }} \)/\( \underline{{R_{s} }} \) :

Maximum/minimum storage capacity of the HS

\( \overline{{P_{{{\text{ex}},t}}^{\text{imp}} }} \)/\( \overline{{P_{{{\text{ex}},t}}^{\exp } }} \) :

Maximum electricity import/export between the district energy system and the external electricity grid during time interval t

\( P_{d,t}^{{}} \) :

Electricity demand of the district energy system during time interval t

\( P_{{{\text{wind}},t}}^{\text{plan}} \) :

Planned production of wind power during time interval t

\( Q_{d,t}^{\text{plan}} \) :

Planned heat demand during time interval t

\( \overline{{\delta_{d,t}^{\text{down}} }} \) / \( \overline{{\delta_{d,t}^{\text{up}} }} \) :

Maximum flexible heat demand for down/up regulation as percentage of the planned heat demand during time interval t

\( \varvec{\eta}_{\varvec{s}} \), \( \varvec{\eta}_{{{\mathbf{eb}}}} \), \( \varvec{\eta}_{{{\mathbf{grid}}}}^{\varvec{P}} \), \( \varvec{\eta}_{{{\mathbf{grid}}}}^{\varvec{Q}} \) :

Storage efficiency of the HS, conversion efficiency of the EB, and energy loss coefficient of electricity/heat grid during energy transmission


Coefficient of performance of the HP

\( C_{{{\text{chp}},t}} \) :

Fuel cost of the CHP plant during time interval t

\( f_{{{\text{chp}},t}} \) :

Fuel consumption of the CHP plant during time interval t

\( P_{{{\text{ex}},t}}^{\text{imp}} \)/\( P_{{{\text{ex}},t}}^{\exp } \) :

Electricity exchange (import/export) between the district energy system and the external grid during time interval t

\( P_{{{\text{wind}},t}}^{\text{shed}} \)/\( P_{{{\text{wind}},t}}^{r} \) :

Curtailed/real production of wind power during time interval t

\( P_{{{\text{grid}},t}}^{\text{loss}} \)/\( Q_{{{\text{grid}},t}}^{\text{loss}} \) :

Electricity/heat grid loss during time interval t

\( P_{{{\text{chp}},t}} \)/\( Q_{{{\text{chp}},t}} \) :

Electricity/heat production of the CHP plant during time interval t

\( P_{{{\text{eb}},t}} \)/\( Q_{{{\text{eb}},t}} \) :

Electricity consumption/heat production of the EB during time interval t

\( P_{{{\text{hp}},t}} \)/\( Q_{{{\text{hp}},t}} \) :

Electricity consumption/heat production of the HP during time interval t

\( Q_{{{\text{loss}},t}} \) :

The amount of heat loss of the HS during time interval t

\( Q_{d,t}^{r} \) :

Heat demand during time interval t after regulation

\( Q_{s,t}^{{}} \) :

The amount of heat charged/discharged during time interval t

R s,t :

The stage of heat energy level within the HS by time interval t

U ex,t :

Binary variable equals to 1 if the district energy system exports electricity


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Sun, T., Zhang, T., Chen, Z. et al. Optimal operation of flexible heating systems for reducing wind power curtailment. Electr Eng (2020) doi:10.1007/s00202-020-00919-6

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  • Combined heat and power
  • District heating, electric heating
  • Flexible heat demand
  • Optimal dispatch
  • Wind power integration