1. Introduction
With the development of the multi-energy system, more and more different energy sectors are coupled together, such as the integrated electrical network and natural gas network (IEGN). Meanwhile, the distributed multi-generation solutions, especially the combined cooling, heat, and power (CCHP), have proliferated. CCHP plants facilitate the interaction between the electricity and gas networks, and promote the efficiency and environmental friendliness of the IEGN as a whole [
1,
2,
3]. However, the increasingly more frequent interactions that are caused by the CCHP plants may challenge the coordination and mutual accommodation of the IEGN [
2,
3]. In particular, it greatly influences the linepack reserve in the natural gas network [
4,
5], which plays an important role in supporting the gas turbines to ramp up and down, and to serve the balancing needs in the electrical network, and thus may harm the safe operation of the IEGN [
6,
7,
8].
The CCHP plant, whereby various energy conversion devices are installed to supply multi-energy (ME) demands (electricity, heat, and cooling) from multiple input energy sources (natural gas, electricity, and so on), provides redundant energy generation options and energy pathways inside. For example, heat could be produced with electricity (in electrical heaters), or fuel (in combustion groups); cooling could be generated from electricity (in electric chillers) or heat (in absorption chillers) [
9,
10,
11]. Hence, various generation combinations can be used to supply the ME demands, which will cause different energy exchanges with the interconnected energy networks. According to the specific generation combination, the ME demand can be supplied through electricity alone, or through natural gas alone, or both. The generation combinations can be optimally chosen, and shift with purposes, while meeting the ME demands [
11]. This flexible energy dispatch shift of the CCHP plants provides extra flexibility to the IEGN and demonstrates the significant potential in optimizing the operation performance of the IEGN. Traditional energy management studies regarding the CCHP plants only consider limited types of ME devices in the modelling process, however the flexibility that is brought by the redundant generation options, especially the internal energy dispatch shift, has been rarely considered in the energy management of the CCHP plants so far.
Nonetheless, this flexible energy dispatch manners of the CCHP plant will frequently change the energy distribution both in the electrical network and the natural gas network, which will change the linepack reserves in the gas network. At the same time, not only the normal gas turbines, the flexible energy dispatch of many ME devices, such as the combined cycle gas turbine (CCGT), require enough linepack reserves as well. Therefore, the linepack reserve should be jointly considered in the energy management of the CCHP plants in order to promote both the efficiency and the safety of the IEGN. If not, not only the flexible energy dispatch of the CCHP plant may be hindered from realization, but also the gas turbines may be prevented from balancing the demands in a power system, which may undermine the operating reserve adequacy and threatens the safety of the IEGN [
4,
5]. Besides, as the development of the IEGN, the electrical networks are more and more dependent on the fast-response flexibility provided by the gas turbines and the linepack reserve. For instance, it is more and more used by system operators to balance the stochastic renewable energy sources [
12]. Many studies regarding the linepack reserve are mainly about securing the safe operation of the natural gas network, as far as the authors know, the linepack reserve has not been literally considered in the energy management of the IEGN with CCHP plants yet, although its impact on the IEGN management is huge. Therefore, lineack reserve should be an integral part of the energy management of the IEGN.
The modelling analysis of the CCHP plants [
9,
10,
11], and the IEGN [
13,
14,
15], has been addressed in many publications, based on which many energy management methods are proposed [
16,
17,
18]. Based on the efficiency matrices and energy dispatch factors (EDF), Pierluigi Mancarella [
11] discusses the flexible internal energy dispatch of the CCHP plant and investigates its potential in providing real time demand response services. Ref. [
4,
19,
20,
21,
22] introduces the linepack reserve in the natural gas network. Ref. [
20,
21] define the linepack reserve as a kind of buffer that could be used without safety problem, and [
4,
22] highlights its importance as a “balancing tool” in serving the balancing needs of the IEGN. Ref. [
19] evaluates the flexibility of the IEGN by measuring the flexibility that gas turbines can provide by employing the linepack reserve in the natural gas network. Based on the steady state models of the electrical network and the natural gas network, and the security constraints in both of the networks, ref. [
16,
17,
18,
23] present several optimization models for the IEGN energy management. Ref. [
16] studies the combined economic dispatch of the IEGN. The mathematical model is formulated as an optimization problem where the objective function is to minimize the integrated gas-electricity system operation cost, and the constraints are the power system and natural gas pipeline equations and capacities. The evolutionary algorithm is applied to solve the optimization problem. A multi-objective optimization for the combined gas and electricity network expansion planning was presented in [
23]. The objectives are to minimize both the investment cost and production cost of the combined system while taking into account the N-1 network security criterion. The constraints of the optimization model include the operation and security constraints of IEGN and equality constraint that links the two networks, and the Elitist Non-dominated Sorting Genetic Algorithm II (NSGAII) is used to solve the optimization problem. Ref. [
17] incorporates the energy management of a CCHP plant into the combined economic dispatch model of the IEGN with the concept of ‘energy hub’ to minimize the total generation cost. Besides the constraints of the traditional optimal dispatch optimization model, the constraints on energy hubs are included, and the numerical methods are used to solve the optimization problem. Ref. [
18] establishes a multi-objective model for a microgrid with CCHP plant to optimize the daily operation cost, the daily environment cost, and the primary energy rate. The constraints of energy balances and devices output power are considered, and the particle swarm optimization algorithm is used to solve the model. Despite the energy management of CCHP plants are considered in [
17,
18], only one single CCHP plant and limited types of ME devices are discussed, which brought concerns: (1) The types of the considered ME devices are too few to model the flexible and shiftable energy dispatch of the CCHP plants, and to investigate its impact on the linepack reserve of the IEGN. Besides, the coordination of CCHP plants with different configurations are not considered, which impacts the operation performance of the IEGN and should be part of the energy management of the CCHP plants (2) The purposes of prior-at researches on the IEGN energy management are mainly about economy, rarely having the security of both networks considered. In particular, the linepack reserve has not been considered in the energy management of the IEGN with CCHP plants.
In light of the above issues, this paper develops an optimal energy management framework for an IEGN with multiple CCHP plants, which jointly considers the lineapck reserve in the IEGN, aiming at meeting the ME demands in a most economic, efficient, and secure way. At first, several typical ME devices are introduced and modelled with the efficiency matrices and EDFs, and based on which, the energy management of the CCHP plants, including the flexible energy dispatch, is integrated into the energy management of the entire IEGN. Then, the linepack reserve of the IEGN is modelled, and considered as an objective in the energy management framework to better secure the safety of the IEGN. When considering that the proposed optimization model is mathematically a multi-objective, mixed integer non-linear model, which cannot be easily solved with classical mathematical techniques, the NSGAII [
24] is applied to find reasonable tradeoffs. The main contributions of this paper are threefold:
The energy management of the CCHP plants, including the flexible energy dispatch is modelled, and its impact on the operation performance of the IEGN, especially the linepack reserve, is investigated and considered in the proposed energy management framework.
For the efficiency and security of the IEGN, linepack reserve in the natural gas network is modeled and is jointly considered in the energy management framework.
A multi-objective optimization model for the energy management of the IEGN is developed to simultaneously promote the profits, linepack reserve, and efficiency of the IEGN.
The rest of this paper is organized as follows.
Section 2 presents the modelling of the CCHP plants, and the linepack reserve is modelled in
Section 3. In
Section 4, a multi-objective optimization model for the energy management of IEGN is proposed and tested on an IEGN case in
Section 5. Finally, this paper is concluded in
Section 6.
4. Optimization Model for the Energy Management
Based on the models that are developed above, a multi-objective optimization model is formulated in this section. The decision variables vector
V is defined as in (21). In (21),
p and
G are the nodal pressure vector and natural gas input vector for the natural gas network,
PGT is the output vector for normal gas turbines, and
α is the EDF vector for CCHP plants.
The purpose of the proposed optimization model is to improve the profits, linepack reserve, and energy saving performance of the IEGN, simultaneously. So, the objective function comprises of three individual objectives, namely F1, F2, and F3.
F1 is modeled as the profits of the IEGN, which is the total revenue by selling electricity minus the generation cost.
In (22), ΩCG, ΩGT, and ΩCCHP are the conventional generators set, gas-fired generators set and CCHP plants set, respectively; Pl,i is the electric load on the Bus i, PCG,j is the output of conventional generator j, PGT,k is the output of gas turbine k; aj, bj, and cj are the consumption characteristic factors of generator j; is the hourly selling price of electricity, is the hourly fuel price for power generating; and, is the hourly fuel price for heat and cooling power production.
F2 is modeled as the linepack reserve of the IEGN, as given by,
In (23), is the linepack reserve of the pipeline i. The detailed calculation process is as shown in (7)–(16).
F3 is modelled as the
PESP of the IEGN assessed by the primary energy saving indicator, as shown in (24)–(26).
WCCHP,m,
QCCHP,m, and
RCCHP,m are, respectively, the electricity, heat, and cooling output of the CCHP plant
m.
The constraints of the proposed optimization model are composed of electrical network constraints, natural gas network constraints, ME devices constraints, and linepack reserve constraints.
(27)–(29) Are electrical network constraints. (27) Represents the active and reactive power balance for each bus. (28) Represents the output limits of generators. (29) Represents the operational limits on the apparent power and the steady-state voltage magnitude. Ω
B and Ω
G denote the buses set and the generator buses set, respectively.
PGi and
QGi denote the active and reactive power outputs,
PLi and
QLi denote the active and reactive power loads,
Ui denotes the voltage magnitude of Bus
i and
θij denotes the voltage angle gap between Bus
i and Bus
j,
Gij and
Bij denote the real and imaginary parts of the
ith row the
jth column element in the nodal admittance matrix.
Sij denotes the apparent power between bus
i and bus
j.
(30)–(32) Are the natural gas network constraints. Ω
NG denotes the natural gas network nodes set. (30) Represents the natural gas flow balance for each node in the natural gas network. (31) Represents the pipeline natural gas flow function.
Si and
Di denote the natural gas injection and the natural gas load on Node
i,
Fij denotes the natural gas flow between Node
i and Node
j,
pi and
pj are nodal pressures of Node
i and Node
j, respectively.
cij is the pipeline constant. (32) Represents the operation limits on pipes and nodal pressure.
(33) and (34) are the CCHP plants constraints. In (33),
and
are the maximum output and minimum output of ME device
x in the CCHP plant CCHP
i. In (34),
and
are the energy input of CCHP
i and local ME demands,
is the energy exchange between CCHP
i and the external energy distribution networks.
(35) and (36) are constraints on the linepack reserve, which are conceived to guarantee the fluctuations that are caused by the forecasting errors either in the supply or the demand can be mitigated with the linepack reserve. [FSmax, FSmin] and [FDmax, FDmin] denote the forecasting output interval of power plants and the forecasting load interval.
Mathematically, this is a multi-objective, mixed integer non-linear problem, which cannot be easily solved by classical mathematical techniques. To address this, NSGAII [
22] is used. NSGAII is an improved version of NSGA based on Pareto optimal set, whose main loop is shown in
Figure 4. It starts by initializing the population and assigning an appropriate rank based on the fast non-dominated sorting approach. Then, reproduction operators, such as tournament selection, recombination, and mutation are used to create the offspring population. Under the elitist-preserving strategy, next generation population is generated via the competition between parent and offspring populations. The excellent individuals in the present generation are added into the next generation. More details about NSGAII can be found in [
24].
With the NSGAII algorithm, the whole computation process that is shown in
Figure 5 could be summarized as follows.
Step 1: Initialize the outputs of normal gas-fired generator buses as PGT, except the CCHP plants buses or the slack bus.
Step 2: Initialize EDF vectors for CCHP plants buses as α. Calculate electricity output W and natural gas thermal energy input F, according to the local ME demands.
Step 3: Solve the power flow of the electrical network. Calculate the natural gas demand of normal natural gas-dependent generating units for the calculation of the natural gas flow.
Step 4: Initialize the nodal pressure for all of the nodes in the natural gas network as p, the natural gas injection from natural gas sources as G. Solve the natural gas flow with natural gas demands that were calculated in the previous steps.
Step 5: NSGAII is employed to achieve the Pareto-optimal front set.