Optimal Operation Strategy of Large-scale CHP in District Heating System

Abstract

In the landscape of Korea, having numerous industrial complexes and densely populated residential areas and showing evident seasonal changes, district heating systems (DHS) with large-scale combined heat and power plants (L-CHP) are widely utilized. L-CHP is a combined system consisting of a backpressure turbine and an extraction-condensing turbine. It can transition the operation mode according to the heat and electric load situation, unlike small-scale CHP (S-CHP), which has a single operation mode. This paper defines the physical constraints and the outputs of heat and electricity for L-CHP’s operation modes and intermediate modes, which are the transition processes between operation modes. In addition, a novel optimal scheduling model of DHS based on mixed integer linear programming (MILP) is presented. The DHS comprises L-CHP and auxiliary facilities such as a peak load boiler and electric/thermal storage systems. To demonstrate the proposed optimization model, case studies are conducted with a sample DHS responding to the seasonal heat demands and Korean electricity market prices. The simulations are performed using IBM’s CPLEX Studio IDE 12.8.0.

Appendices

Appendix

A Objective Function

$$\begin{aligned} \max \left\{ \sum _{t \in \mathbb {T}} \left[ {\lambda _{t} P(t) + \psi _{t} Q(t) - C(t)} \right] \right\} \end{aligned}$$

(A.1)

$$\begin{aligned} P(t) = \sum _{m \in \mathbb {M}} P_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} p_{n}^{chp}(t) + P_{D}^{ESS}(t) - P_{C}^{ESS}(t) , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.2)

$$\begin{aligned} Q(t) = \sum _{m \in \mathbb {M}} Q_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} q_{n}^{chp}(t) + Q_{D}^{ACC}{(t)} - Q_{C}^{ACC}{(t)} + Q^{PLB}{(t)} , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.3)

$$\begin{aligned} C(t) = \sum _{m \in \mathbb {M}} C_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} c_{n}^{chp}(t) + SUC(t) + SUD(t) + C^{PLB}(t) , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.4)

$$\begin{aligned} C_{m}^{CHP}(t)= & {} \rho _{t}^{CHP} \left\{ a_{m} P_{m}^{CHP}(t) + b_{m} Q_{m}^{CHP}(t) + c_{m} u_{m}^{CHP} (t) \right\} ,\nonumber \\{} & {} \times \forall m \in \mathbb {M} \ , \forall t \in \mathbb {T} \end{aligned}$$

(A.5)

$$\begin{aligned} c_{n}^{chp}(t) = \rho _{t}^{CHP} \left\{ a_{n} p_{n}^{chp}(t) + b_{n} q_{n}^{chp}(t) + c_{n} v_{n}^{chp} (t) \right\} , \ \forall n \in \mathbb {N} \ , \forall t \in \mathbb {T} \end{aligned}$$

(A.6)

$$\begin{aligned} SUC(t) = SUC \cdot y(t) , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.7)

$$\begin{aligned} SDC(t) = SDC \cdot z(t) , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.8)

$$\begin{aligned} C^{PLB}(t) = \rho _{t}^{PLB} \cdot {Q^{PLB}(t)}/{\eta ^{PLB}} , \ \forall t \in \mathbb {T} \end{aligned}$$

(A.9)

B Constraints

1.1 B.1 Constraints on Heat Balance

$$\begin{aligned} \sum _{m \in \mathbb {M}} Q_{m}^{CHP}(t) \!+\! \sum _{n \in \mathbb {N}} q_{n}^{chp}(t) \!+\! Q^{PLB}(t) \!=\! HL_{t} - Q_{D}^{ACC}(t) \!+\! Q_{C}^{ACC}(t)\ , \quad \forall t \in \mathbb {T} \end{aligned}$$

(B.1)

1.2 B.2 Constraints on the Status of L-CHP’s Operation Mode

$$\begin{aligned} \sum _{m \in \mathbb {M}} u_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} v_{n}^{chp}(t) = 1 \ , \quad \forall t \in \mathbb {T} \end{aligned}$$

(B.2)

1.3 B.3 Constraints on the Direction of L-CHP’s Mode Transition

$$\begin{aligned} u_{m}^{CHP}(t)+ & {} \sum _{h \in \mathbb {H}} u_{h}^{CHP}(t) + \sum _{i \in \mathbb {I}} v_{i}^{chp}(t) \le U \cdot \left\{ 1 - u_{m}^{CHP} (t-1) \right\} \nonumber \\+ & {} 1 \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.3)

$$\begin{aligned} u_{m}^{CHP}(t)+ & {} \sum _{h \in \mathbb {H}} u_{h}^{CHP}(t) + \sum _{i \in \mathbb {I}} v_{i}^{chp}(t) \ge L \cdot \left\{ 1 - u_{m}^{CHP} (t-1) \right\} \nonumber \\+ & {} 1 \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.4)

$$\begin{aligned} v_{n}^{chp}(t)+ & {} \sum _{j \in \mathbb {J}} u_{j}^{CHP}(t) \le U \cdot \left\{ 1 - v_{n}^{chp} (t-1) \right\} \nonumber \\+ & {} 1 \ , \ \forall n \in \mathbb {N} , \forall t \in \mathbb {T} \end{aligned}$$

(B.5)

$$\begin{aligned} v_{n}^{chp}(t) + \sum _{j \in \mathbb {J}} u_{j}^{CHP}(t) \ge L \cdot \left\{ 1 - v_{n}^{chp} (t-1) \right\} + 1 \ , \ \forall n \in \mathbb {N} , \forall t \in \mathbb {T} \end{aligned}$$

(B.6)

$$\begin{aligned} \sum _{k \in \mathbb {K}} v_{k}^{chp}(t) \le U \cdot \left\{ 1 + u_{m}^{CHP} (t) - u_{m}^{CHP} (t-1) \right\} \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.7)

$$\begin{aligned} \sum _{k \in \mathbb {K}} v_{k}^{chp}(t) \ge L \cdot \left\{ 1 + u_{m}^{CHP} (t) - u_{m}^{CHP} (t-1) \right\} \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.8)

$$\begin{aligned} \sum _{i \in \mathbb {I}} v_{i}^{chp}(t) - 1 \le U \cdot \left\{ 1 + u_{m}^{CHP} (t) - u_{m}^{CHP} (t-1) \right\} \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.9)

$$\begin{aligned} \sum _{i \in \mathbb {I}} v_{i}^{chp}(t) - 1 \ge L \cdot \left\{ 1 + u_{m}^{CHP} (t) - u_{m}^{CHP} (t-1) \right\} \ , \ \forall m \in \mathbb {M} , \forall t \in \mathbb {T} \end{aligned}$$

(B.10)

$$\begin{aligned} \sum _{j \!\in \! \mathbb {J}} u_{j}^{CHP}(t \!+\! MIT_{n} \!-\! 1) \!\le \! U \cdot \left\{ 1 \!-\! v_{n}^{chp} ( t \!-\! MIT_{n} \!-\!1 ) \right\} \!+\! 1 \ , \ \forall n \in \mathbb {N} \ , \forall t \in \mathbb {T} \end{aligned}$$

(B.11)

$$\begin{aligned} \sum _{j \in \mathbb {J}} u_{j}^{CHP}(t \!+\! MIT_{n}\! -\! 1) \ge L \cdot \left\{ 1 \!- \!v_{n}^{chp} ( t \!-\! MIT_{n} \!-\!1 ) \right\} \!+\! 1 \ , \ \forall n \!\in \! \mathbb {N} \ , \forall t \!\in \! \mathbb {T} \end{aligned}$$

(B.12)

1.4 B.4 Constraints on the Production Limits of L-CHP and PLB

$$\begin{aligned} P_{m}^{min} \cdot u_{m}^{CHP}(t) \le P_{m}^{CHP}(t) \le P_{m}^{max} \cdot u_{m}^{CHP}(t) \ , \quad \forall m \in \mathbb {M} \ , \forall t \in \mathbb {T} \end{aligned}$$

(B.13)

$$\begin{aligned} p_{n}^{min} \cdot v_{n}^{chp}(t) \le p_{n}^{chp}(t) \le p_{n}^{max} \cdot v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \forall t \in \mathbb {T} \end{aligned}$$

(B.14)

$$\begin{aligned} Q_{m}^{min} \cdot u_{m}^{CHP}(t) \le Q_{m}^{CHP}(t) \le Q_{m}^{max} \cdot u_{m}^{CHP}(t) \ , \quad \forall m \in \mathbb {M} \ , \forall t \in \mathbb {T} \end{aligned}$$

(B.15)

$$\begin{aligned} q_{n}^{min} \cdot v_{n}^{chp}(t) \le q_{n}^{chp}(t) \le q_{n}^{max} \cdot v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \forall t \in \mathbb {T} \end{aligned}$$

(B.16)

$$\begin{aligned} Q_{1}^{CHP} = \alpha _{1}^{(1)} P_{1}^{CHP}(t) + \beta _{1}^{(1)} u_{1}^{CHP}(t) \ , \quad m = 1 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.17)

$$\begin{aligned} Q_{2}^{CHP} \le \alpha _{2}^{(1)} P_{2}^{CHP}(t) + \beta _{2}^{(1)} u_{2}^{CHP}(t) \ , \quad m = 2 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.18)

$$\begin{aligned} Q_{2}^{CHP} \le \alpha _{2}^{(2)} P_{2}^{CHP}(t) + \beta _{2}^{(2)} u_{2}^{CHP}(t) \ , \quad m = 2 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.19)

$$\begin{aligned} Q_{2}^{CHP} \ge \alpha _{2}^{(3)} P_{2}^{CHP}(t) + \beta _{2}^{(3)} u_{2}^{CHP}(t) \ , \quad m = 2 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.20)

$$\begin{aligned} q_{n}^{chp} \le \mu _{n}^{(1)} p_{n}^{chp}(t) + \omega _{n}^{(1)} v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.21)

$$\begin{aligned} q_{n}^{chp} \le \mu _{n}^{(2)}p_{n}^{chp}(t) + \omega _{n}^{(2)} v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.22)

$$\begin{aligned} q_{n}^{chp} \ge \mu _{n}^{(3)}p_{n}^{chp}(t) + \omega _{n}^{(3)} v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.23)

$$\begin{aligned} q_{n}^{chp} \ge \mu _{n}^{(4)}p_{n}^{chp}(t) + \omega _{n}^{(4)} v_{n}^{chp}(t) \ , \quad \forall n \in \mathbb {N} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.24)

$$\begin{aligned} 0 \le Q^{PLB}(t) \le Q_{PLB}^{max} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.25)

1.5 B.5 Constraints on ACC

$$\begin{aligned} 0 \le u_{C}^{ACC}(t) + u_{D}^{ACC}(t) \le 1 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.26)

$$\begin{aligned} 0 \le Q_{C}^{ACC}(t) \le Q_{C}^{max} \cdot u_{C}^{ACC}(t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.27)

$$\begin{aligned} 0 \le Q_{D}^{ACC}(t) \le Q_{D}^{max} \cdot u_{D}^{ACC}(t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.28)

$$\begin{aligned} 0 \le ACC(t) \le ACC^{max} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.29)

$$\begin{aligned} ACC(t) = Q_{C}^{ACC}(t) - Q_{D}^{ACC}(t) + ACC(t-1) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.30)

$$\begin{aligned} \sum _{l = t}^{t+{MUT_{C}^{ACC}}-1} u_{C}^{ACC}(l) \ge MUT_{C}^{ACC} \cdot \left[ u_{C}^{ACC}(t) - u_{C}^{ACC}(t-1)\right] \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.31)

$$\begin{aligned} \sum _{l = t}^{t+{MUT_{D}^{ACC}}-1} u_{D}^{ACC}(l) \ge MUT_{D}^{ACC} \cdot \left[ u_{D}^{ACC}(t) - u_{D}^{ACC}(t-1)\right] \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.32)

1.6 B.6 Constraints on ESS

$$\begin{aligned} 0 \le u_{C}^{ESS}(t) + u_{D}^{ESS}(t) \le 1 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.33)

$$\begin{aligned} 0 \le P_{C}^{ESS}(t) \le P_{C}^{max} \cdot u_{C}^{ESS}(t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.34)

$$\begin{aligned} 0 \le P_{D}^{ESS}(t) \le P_{D}^{max} \cdot u_{D}^{ESS}(t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.35)

$$\begin{aligned} 0 \le ESS(t) \le ESS^{max} \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.36)

$$\begin{aligned} ESS(t) = P_{C}^{ESS}(t) - P_{D}^{ESS}(t) + ESS(t-1) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.37)

1.7 B.7 The other Technical Constraints of L-CHP

$$\begin{aligned} z(t) - y(t) = u_{0}^{CHP}(t) + u_{0}^{CHP}(t-1) \le 1 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.38)

$$\begin{aligned} y(t) + z(t) \le 1 \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.39)

$$\begin{aligned} \left[ \sum _{m \in \mathbb {M}} P_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} p_{n}^{chp}(t) \right] - \left[ \sum _{m \in \mathbb {M}} P_{m}^{CHP}(t-1) + \sum _{n \in \mathbb {N}} p_{n}^{chp}(t-1) \right] \\ \\ \le \left[ y(t) + z(t) \right] \cdot P_{m}^{max} + \left[ 1 - u_{0}^{CHP}(t-1) + u_{0}^{CHP}(t) \right] \cdot RU \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.40)

$$\begin{aligned} \left[ \sum _{m \in \mathbb {M}} P_{m}^{CHP}(t-1) + \sum _{n \in \mathbb {N}} p_{n}^{chp}(t-1) \right] - \left[ \sum _{m \in \mathbb {M}} P_{m}^{CHP}(t) + \sum _{n \in \mathbb {N}} p_{n}^{chp}(t) \right] \\ \\ \le \left[ y(t) + z(t) \right] \cdot P_{m}^{max} + \left[ 1 - u_{0}^{CHP}(t-1) + u_{0}^{CHP}(t) \right] \cdot RD \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.41)

$$\begin{aligned} \sum _{s = t-MUT+1}^{t} y(s) \le \left\{ \sum _{m \in \mathbb {M}} u_{m}^{CHP} (t) + \sum _{n \in \mathbb {N}} v_{n}^{chp} (t) \right\} - u_{0}^{CHP} (t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.42)

$$\begin{aligned} \sum _{s = t-MDT+1}^{t} z(s) \le 1- \left\{ \sum _{m \in \mathbb {M}} u_{m}^{CHP} (t) + \sum _{n \in \mathbb {N}} v_{n}^{chp} (t) \right\} + u_{0}^{CHP} (t) \ , \ \forall t \in \mathbb {T} \end{aligned}$$

(B.43)