**8. An algorithm of simulation model construction for integrated multi-carrier energy systems**

A general approach to constructing a simulation model of an integrated multicarrier energy system and to solution of different problems with its help can be represented as follows [21, 22] (see **Figure 7**).

Input data about the studied integrated multi-carrier energy system is prepared including the matrices of parameters of individual energy systems (their network topologies, electric and hydraulic resistances of electric lines and pipelines), as well as vectors of nodes parameters (electric power and heat generations, loads, storages, etc.).

The necessity to use of two libraries of integrated energy system elements was noted earlier in Section 6. An algorithm for simulation model construction of integrated multi-carrier energy system selects required model of the next element from the point of view of individual energy system topology (depending on the element type) either from library of typical elements in Matlab/Simulink software or from additional library, which includes the energy hubs models. After that required model attaches to necessary node (nodes for energy hub model) of integrated energy system. As it is noted in Section 6, the energy hub model has several inputs and several outputs, which connect different individual energy systems into integrated multi-carrier energy system.

As we said in Section 6, above mentioned procedure creates so called basic part of integrated energy system simulation model. It is necessary to work out an additional part for simulation model, which represents the specifics of concrete calculated problem (see Section 6).

Matlab/Simulink software contains the object-oriented programming language, which has used for construction of integrated multi-carrier energy system simulation model. **Figure 7** represents simplified flow chart of the basic part of discussed algorithm taking into account three individual energy systems: electric power, heat and gas supply systems.

*Simulation Modeling of Integrated Multi-Carrier Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.99323*

## **9. Illustrative case study**

An integrated energy system is considered including the electricity and heat supply systems of a block of 9 dormitories of a University campus. The diagram of the electric network of the integrated energy system is shown in **Figure 8**, the diagram of the heat network is topologically about similar, since each dormitory is a consumer of both electricity and heat. The diagram of the heat network is not given, since the load of heat pipelines in the problem solved does not including, but, on the contrary, decreases, i.e., there are no network constraints on heat transfer.

In **Figure 8** FS is feeding substation, the nodes 11, 12, 13, 14, 15 are transformer substations 6/0.4 kV.

**Figures 9** and **10** indicate the total annual electricity and heat consumption curves for the entire block of dormitories, respectively. We assume that thermal energy is consumed only for heating. The daily heat load curve is uniform. The irregularity factor of daily electrical load curve is 0.4 (the ratio of the load value during the night minimum period from 23:00 to 7:00 to the peak load value). Daily curves of heat and electrical load are the same for all dormitories.

We consider the conditions for preventing overload of the electrical network. To this end, the total load power during the night minimum of the daily load curve, including its power level plus the amount of power consumed to convert electricity into heat, should not exceed the daily maximum load. In this case, the load flow in the electrical network will not change and there will be no overloads.

**Table 1** shows monthly data on the parameters of electricity supply to consumers on the University campus.

The values of daily maximum load are used to calculate the values of conventional maximum possible electricity consumption of the campus per month with the formula:

$$E\_{\text{mon. max}} = \left(P\_{\text{day.max}} \cdot \text{24}\right) \cdot \text{30},\tag{12}$$

**Figure 8.** *Diagram of the electrical supply system.*

#### *Simulation Modeling of Integrated Multi-Carrier Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.99323*

#### **Figure 9.**

*Electricity consumption of 9 dormitories.*

**Figure 10.** *Heat consumption of 9 dormitories.*

where *Emon:* max is the maximum possible conventional value of electricity consumption per month; *Pday:* max is a daily maximum load.

The amount of electricity that can be converted into heat (conversion potential) is determined by:

$$E\_p = E\_{mon.\,\max} \cdot 0, \mathbf{6} \cdot \mathbf{0}, \mathbf{3} \mathbf{3}, \tag{13}$$

where *Ep* is the potential for converting electricity into heat per month; coefficient 0.6 reflects the share of free power within the night minimum load; coefficient 0.33 determines the share of duration of the night minimum daily load curve (8 hours), during which electricity is paid for at the minimum night rate.

Conversion of electricity into heat is carried out according to the relationship:

$$\mathbf{1 kWh} = \mathbf{0}, \mathbf{0}0086 \text{ Gcal.}$$

In **Table 1**, the last two columns indicate two options for the amount of electricity to be converted to heat: the entire (100%) conversion potential and 50% of this potential.


**Table 1.**

*University campus power consumption data.*

Following the current pricing system for electricity and heat, electricity rates are differentiated throughout the day: a preferential night rate from 23:00 to 7:00 is \$ 0.011 per kWh. Heat rate is \$ 20.6 per Gkal.

In general terms, the following relations are valid:

$$C\_{\epsilon} = E\_p \cdot t\_3,\tag{14}$$

*Ce* is the cost of electricity before conversion into heat.

$$C\_{t\eta} = E\_t \cdot t,\tag{15}$$

*t* is heat tariff; *Et* is thermal energy. The following relations are valid:

$$\mathbf{C}\_{\epsilon} = \mathbf{C}\_{\epsilon n} + \mathbf{C}\_{\epsilon d},\tag{16}$$

$$\mathbf{C}'\_{\epsilon} = \mathbf{C}\_{\epsilon n} + \mathbf{C}'\_{\epsilon n} + \mathbf{C}\_{\epsilon d},\tag{17}$$

$$\mathbf{C}\_{t} = \mathbf{C}\_{t\mathbf{n}} + \mathbf{C}\_{td},\tag{18}$$

$$\mathbf{C}'\_t = \mathbf{C}\_{tn} - \mathbf{C}'\_{tn} + \mathbf{C}\_{td},\tag{19}$$

$$\mathbf{C}'\_{en} < \mathbf{C}'\_{tn},\tag{20}$$

where *Сen* is cost of electricity before conversion at night; *Сed* is cost of electricity before conversion to daytime; *Ct* is cost of thermal energy before conversion; *Сtn* is the cost of thermal energy at night; *Сtd* is the cost of thermal energy in the daytime; *C*0 *<sup>e</sup>* is cost of electricity after conversion; *C*<sup>0</sup> *en* is cost of electricity at night after conversion; *C*<sup>0</sup> *<sup>t</sup>* is cost of thermal energy after conversion; *C*<sup>0</sup> *tn* is the cost of thermal energy after conversion at night.

*Simulation Modeling of Integrated Multi-Carrier Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.99323*

The results of the calculations of the considered options are presented in **Figures 11** and **12**.

Let us return to the condition of preventing the electrical network overloads, formulated above. An analysis of the transfer capability and loading of individual ties lines in the case of electricity conversion into heat, according to the condition assumed, shows that this loading is not the same (see **Table 2**).

It is important to estimate some limiting volume of conversion of electricity into heat at night taking into account the possibilities of electrical network. These possibilities depend on free transfer capabilities of ties and permissible loading of transformers on feeding substation. Required parameters of electrical network and basic load flow calculation without consideration of active losses you can see on the **Table 2**. Consumption load at night which found on the previous stage (basic load flow) for each consumer is 490 kW. The permissible loading of transformers on


**Table 2.**

*Required parameters of electrical network and basic load flow.*

feeding substation is 6000 kW. Let us consider, that cable lines from transformer substations 6/0.4 kV to import of electricity into building do not have the limits of transfer capabilities. As for limiting volume of heat supply for each consumer, let us to consider 380 kW after re-calculation into converted electricity.

Let us formalize optimization problem as following:

Objective function:

$$
\Delta P\_{\rm FS} \to \max,\tag{21}
$$

Subject to:

$$
\Delta P\_{\rm FS} \le \Delta P\_{\rm FSLim},
\tag{22}
$$

$$P\_{\vec{\eta}} \le P\_{\vec{\eta}/\text{lim }}.\tag{23}$$

$$P\_{kheat} \le P\_{kheat\text{ lim }\text{s}}.\tag{24}$$

$$
\Delta P\_{\rm FS}^{l+1} = \Delta P\_{\rm FS}^{l} + h \frac{\Delta P\_{\rm FS}^{l}}{\mathbf{1}/\Delta P\_{\rm ij}},\tag{25}
$$

$$
\Delta P\_{\vec{\eta}} = P\_{\vec{\eta}\,\mathrm{lim}} - P\_{\vec{\eta}},\tag{26}
$$

where Δ*PFS* is additional power for conversion into heat; *Pij* lim is transfer capability of tie *ij, i, j* = 1, 2, 3; *Pkheat* lim is top re-calculated to electricity level of heat for consumer.

*k, k* = 1–9; *h* is the step of optimization; *l* is the number of iteration. The second member in right part of (25) is the similar to gradient of objective function.

Several beginning steps of optimization are along the ray 10–11 to use the possibility for additional conversion of electricity into heat. The results of these iterations are 380 kW for consumer 2 and 380 kW for consumer 3 as the additional converted volumes of electricity. These volumes along the ray 10–11 are top volumes for additional conversion. One next iteration deals with the ray 10–12, where it is possible to use 380 kW for consumer 5 and the rest on this ray 250 kW (2100– 1470 – 380 = 250) for consumers 1 or 4. The iteration along the ray 10–14 allows to use 140 kW additional converted electricity (2100–1960 = 140) for consumers 6 or 7 or 8 or 9.

It is possible to see, that we could use more electricity for additional conversion into heat, but the problem is in hhe electrical network limitation.

#### **10. Conclusion**

Creation of the integrated multi-carrier energy systems is progressive trend in development of energy supply systems. Joint expansion of individual energy systems leads to enhancement of economic efficiency and reliability of energy supply to consumers. It is necessary to have the efficient tools for expansion planning and operation management and control of integrated multi-carrier energy systems.

*Simulation Modeling of Integrated Multi-Carrier Energy Systems DOI: http://dx.doi.org/10.5772/intechopen.99323*

Energy hub concept is progressive way for modeling and simulation of integrated energy systems, but there are some problems in determination of the coefficients of connection of each individual input and each individual output of the energy hub simulation model.

This Chapter represents new approach to solve above mentioned problems based on the possibilities of Matlab/Simulink software taking into account the elements of energy hub concept. The main idea of suggested approach deals with the construction of simulation model of integrated multi-carrier energy system considering the models of simple typical elements from the Matlab/Simulink library and complicate energy hub models from additional library, which is created based on Matlab/Simulink software possibilities.

Illustrative case study shows the efficiency of suggested approach.
