Standardized modelling and economic optimization of multi-carrier energy systems considering energy storage and demand response
Introduction
At present, the global power consumptions mainly rely on the fossil fuels [1], [2]. The fossil energy crisis and environmental pollution have become the two critical issues that threaten the human long-term survival and development. Therefore, it is significant to explore a new energy supply and consumption pattern, which will promote the living of human being. Therefore, the multi-carrier energy system (MES), which can highly improve the efficiency of energy supply and consumption, is proposed and widely discussed recent years [3], [4], [5]. However, compared with the conventional power grid, the MES contains a variety of energy systems, such as electricity, natural gas, and heat, so that the unified optimization calculation is more difficult to be carried out [5]. The fast and accurate calculation of MES planning scheme and optimal operation state becomes a significant topic.
For analysing and modelling of MES, the concept of energy hub (EH) was proposed by the Swiss Federal Institute of Technology in 2007, which described the energy input, output, storage, and coupling relationships in the MES [6]. The EH model, which includes dispatch factors, combines the input energy and output energy by using the coupling matrix [7], [8], [9], [10]. Generally, the EH model is widely adopted in the study of the optimal operation state and planning scheme of MES [11], [12], [13], [14], [15], [16], [17], [18]. For example, [11], [12] applied the EH model into the industrial study; [13] discussed a cost-emission of fuel cell/PV/battery hybrid energy system based on EH model by using -constraint method and fuzzy satisfying approach; [14], [15] analyse the energy management and optimal planning and sizing of the components in the multi-carrier energy system through the EH model; [16] discussed a multi-objective framework for analysing the environment and economy performance of big users with demand response considered by using the EH model; [17], [18] studied the method for calculating the optimal operation of MES of the micro energy grid level based on the EH model.
One important aspect for the MES study is a standardized modelling method of the EH model. In [19], the authors have proposed a method to calculate the coupling matrix of the EH model based on a path searching method. However, with the increase number of energy devices in MES, it will be more complicated to calculate the coupling matrix of EH model. Further, the formulation involves dispatch factors, which leads to a nonlinear optimization problem. In previous studies, in order to easily calculate the coupling matrix of EH model integrated with energy storage, it is usually assumed that the energy storage is installed at the input or output side of the EH model [6], [20], [21]. However, in the actual MES, the energy storage can be installed anywhere. Therefore, the energy storage should be arbitrarily located in the coupling matrix of the EH model to reflect practical situations. Also, the concept of demand response in MES should be expanded. There are two types of demand response in MES: (1) flexible energy load in each time interval [22] and (2) shifting load from one energy form to another [23], [24]. Every type should be considered in the EH model. The nonlinearity of the economic optimization EH model is mainly caused by two reasons: (1) variable efficiency of energy conversion devices (inherent nonlinearity of energy conversion devices); (2) EH model introduces dispatch factors into the coupling matrix (structure nonlinearity of energy hub). The first type of nonlinearity can be solved by using piecewise linear approximations (PWLA) method in [25]. For simple EH model, the nonlinearity caused by dispatch factors can be solved by the variable substitution method in [6]. However, the method cannot be used for eliminating the nonlinearity of a complex EH model caused by dispatch factors. Therefore, in the most of complex study cases [26], [27], [28], the optimization of the EH model still becomes a nonlinear optimization problem, even the efficiency is constant. Overall, it is necessary to propose a simple and standardized modelling and calculation method for EH model.
To bridge these gaps, this paper proposes an efficient multi-step modelling and calculation method for the EH model based on graph theory. The main contributions of the paper are:
- (1)
A multi-step standardized modelling method is proposed for the multi-carrier energy systems based on the EH model. The complex EH model can be divided into several simple EH models by using the proposed method, which reduce the difficulty of establishing the coupling matrix of a complex EH model directly. The coupling matrix of complex EH model can be obtained by multiplying the coupling matrix of each simple EH, which can also avoid the large matrix calculation of the traditional modelling method. The complexity of large matrix calculation (includes matrix inversion) is much higher than several simple matrices multiplying. This is the main reason that the traditional modelling method is generally used for small-scale systems.
- (2)
The proposed model is highly decoupled. So, if the several devices in the multiple energy system are replaced, it is less complicated to update the coupling matrix compared with using the existing energy hub modelling method. Because the complex energy hub is divided into several simple energy hubs, we can only focus on the simple energy hub that have devices replaced.
- (3)
The nonlinearity of a complex EH model caused dispatch factors can be eliminated by using variable substitutions based on the proposed method. The proposed model separates the complex EH model into several simple EH models. The variables substitution is added into each simple EH model to avoid the nonlinearity brought by dispatch factors.
- (4)
The energy storage, demand respond and renewable energy are all integrated in the coupling matrix of EH model in this paper. The location of energy storage is extended to anywhere of EH model and the concept of demand response is also expanded.
Section snippets
Basic definitions of EH model
EH is an interface between consumers, energy producers, transportation infrastructures and storage equipment, which can describe the coupling and switch relationship of each energy flow in the process of distribution, conversion and storage. The EH model includes different kinds of energy conversion devices, such as combined heating and power (CHP) units [29], [30], furnace, heat pumps, gas-fired or electrical boilers, absorption or compression chiller and different types of storage etc. To
The relationship between the CEH model and SEH model
If each path (from input terminals to output terminals) of CEH model contains the same number of nodes, the CEH model can be separated into several SEH models, which is called separable CEH model, as shown in Fig. 5. However, the required condition of separable CEH model is very strict. In the practical energy network, most of CEH models cannot be separated directly. To change inseparable EH models separable, the real nodes arrangement and virtual nodes insertion methods are proposed in this
The linearization of EH model
In order to eliminate the nonlinearity in formula (4), the variables of (4) is replaced by using (19).
After variable substitutions, (4), (5), (6) can be transformed to (18), (19),From (19), (20), (21), it can be seen that in each SEH model, the expression functions can be transformed to a
Case introduction
To study the applicability and efficiency of the proposed method, it is implemented in modelling and optimal dispatch of a residential district in Guangzhou over a 24-h time interval. Fig. 8 illustrates the EH model of the residential district, which consists of a transformer (T), a CHP unit, a furnace (F), an electric heater (EHe), a compression chiller (CC), an absorption chiller (AbC), a heat storage (HS), an electricity storage (ES). The load demand is mainly characterized in the summer
Optimization case introduction
Table 1, Table 2 list the parameters of the energy converters and energy storage of this system. The day ahead electricity price used in this case is referred to [19]. Gas price are assumed to be constant, as shown in Fig. 11. The energy demands are divided into fixed critical load curves and deferrable load curves, as shown in Fig. 12. According to the analysis of the energy demand characteristics of district in Guangzhou, 24-h time period of residential energy loads usually can be divided
Conclusions
This paper proposes a multi-step standardized modelling and calculation method for EH model based on graph theory. The proposed modelling method adopts the multi-step modelling method to reduce the difficulty of setting up the coupling matrix of EH model directly. In addition, the storage device can be considered as extra input energy, which can expand the location of storage devices at anywhere of EH model. The concept of demand response programming in MES are also discussed and integrated in
Acknowledgements
This study is supported by the National Key Research and Development Program of China, China (2016YFB0901900) and Guangdong Power Grid Power Dispatching and Control Centre (GDKJQQ20161179).
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