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ABSTRACT
In the face of the ever-increasing pressure on climate change, recent decades witnessed booming interests in the integrated energy systems (IES) consisting of intermittent renewable energy and dispatchable power sources, such as reformed gas-fed solid oxide fuel cells (SOFC). However, optimization of system design and operation is challenging due to the system complexity, inevitable couplings, and various constraints. To this end, this paper proposes a comprehensive model to describe integrated energy systems with combined cooling, heating, and power (CCHP). Optimal economic performance is formulated as the objective function. Constraints are derived based on the safety and operation requirements. The problem is solved by developing a two-stage stochastic programming framework to achieve the optimized results in terms of both design and operation. The second stage concerns the operation scheduling given the operation plan and stochastic characteristics, based on which the first stage concerns the design planning to realize the prescribed CCHP capacity. Considering the computation complexity of the second stage, the stochastic characteristics are represented by selected scenarios. And to present the mutual influence of energy demands and climate conditions, the time sequence correlation among energy demands and renewable energy availability is considered in the clustering-based scenario selection technique. To solve the proposed two-stage framework, the real-coded genetic algorithm and mixed integer linear programming method are applied in the first and second stages, respectively. A case study in San Francisco is carried out to verify the effectiveness of the proposed method, providing some intuitive guidance for future IES operation and system planning.
Nomenclature
| IES | = | integrated energy system |
| SOFC | = | solid oxide fuel cell |
| CCHP | = | combined cooling, heating and power |
| MILP | = | mixed integer linear programming |
| LHS | = | Latin Hypercube Sampling |
| = | Symbols | |
| = | economic cost | |
| = | unit cost | |
| = | unit cost of electricity | |
| = | unit cost of natural gas energy | |
| = | components capacity | |
| = | coefficient of performance | |
| = | original data | |
| = | normalized original data | |
| = | electricity | |
| = | global horizontal irradiance | |
| = | heating | |
| = | each year during the project lifetime | |
| = | dimensions of stochastic parameters | |
| = | large constant number | |
| = | project lifetime | |
| = | scenario number of the expansion scenarios | |
| = | scenario number of the cluster | |
| = | probability | |
| = | part-load ratio | |
| = | lower triangular matrix in the Cholesky decomposition | |
| = | consumed natural gas energy | |
| = | interest rate | |
| = | random order matrix | |
| = | scenario set | |
| = | original scenario set | |
| = | expansion scenario set | |
| = | objective scenario set | |
| = | upper limit of the renewable components’ capacity | |
| = | wind speed | |
| = | continuous operation variables | |
| = | binary variables | |
| = | binary operation variables | |
| = | Greek symbols | |
| = | shape parameter | |
| = | scale parameter | |
| = | irradiance absorption efficiency | |
| = | standard deviation | |
| = | replacement coefficient | |
| = | efficiency | |
| = | cost converting coefficient | |
| = | stochastic parameters | |
| = | rank correlation matrix of R | |
| = | operation equality constraints | |
| = | components capacity constraints | |
| = | operation inequality constraints | |
| = | set of all the components | |
| = | Subscripts/superscripts | |
| = | absorption chiller | |
| = | average | |
| = | batteries | |
| = | each cluster | |
| = | cut-in wind speed | |
| = | cut-out wind speed | |
| = | each type of energy demands | |
| = | electrical chiller | |
| = | energy error in the conservation constraints | |
| = | exported electricity through the grid | |
| = | converting future cost to present cost | |
| = | feasible components’ capacity | |
| = | heat pump | |
| = | heat recycling | |
| = | charging status | |
| = | investment | |
| = | imported electricity through the grid | |
| = | initial expansion scenario set | |
| = | unit investment cost | |
| = | each component | |
| = | unit maintenance cost | |
| = | upper boundary of the interval | |
| = | lower boundary of the interval | |
| = | discharging status | |
| = | operation | |
| = | penalty term in the objective function | |
| = | converting present cost to annual cost | |
| = | approximated constant efficiency part-load interval | |
| = | photovoltaic devices | |
| = | replacement indicator | |
| = | rated parameters | |
| = | unit replacement cost | |
| = | each scenario | |
| = | solar heater | |
| = | solar energy | |
| = | heat storage | |
| = | each time step | |
| = | total annual cost | |
| = | wasted energy | |
| = | wind energy | |
| = | wind turbines |
Acknowledgments
This work was supported by National Natural Science Foundation of China under Grant 51936003 and 51806034, the Natural Science Foundation of Jiangsu Province, China, under Grant BK20211563.
Author contributions
Y. Zhang: Conceptualization and Methodology
J. Jiang: Software and Review
K. Chen: Writing and Formal Analysis
L. Sun: Supervision and Validation
Disclosure statement
No potential conflict of interest was reported by the author(s).