2. Unit commitment renewable energy sources and distribution network

In order to ensure the security and reliability of the power supply from RES and the network, electrical resources must be planned and effectively controlled. The large distribution network consists of many elements including generators, transmission lines, transformers and circuit breakers. New RES green energy sources are co-opted or integrated into a distribution system or smart grid system including other DC/DC converters and DC/AC converters and must then be scheduled for microsystem operation. In addition, market structure and real-time energy pricing need to be assessed. For stable operation of the micro-network, it will be necessary to plan electricity generation and supply it to the system load for every second of the intelligent area operation—Rohan Island (Prague 8, Czech Republic) (see Figure 1). Energy sources for large energy systems consist of water, nuclear energy, fossil fuels, renewable energy sources such as solar energy (photovoltaic systems) as well as green energy such as fuel cells, biomass and combined heat and power (CHP

#### Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

or also known as cogeneration). These resources must be managed and synchronised to meet the load demand of the microprocessor.

The load requirement of the RES and electricity grids is cyclical and has a peak daily demand for hours and minutes of the week, that is, weekly peak demand for each month and monthly peak demand for the year. Figures 4 and 5 show the course of electricity demand in our intelligent area on Mondays and Thursdays.

The energy resources must be optimised to meet the peak demand of each load cycle, so that the total cost of generating and distributing electricity is minimised. The power system operator must plan the power sources of the grid and equipment to meet the different load conditions.

Systemic load has a general mathematical formulation. This load gradually increases during the day and then decreases during the night. The cost of the generated power of individual RES sources is not the same for all sources. Therefore, there is a higher effort to produce more energy at the least cost in units. In addition, several network lines connect one electrical network to another neighbouring power grid. These are called interconnections between networks. When exporting power from one power system to an adjacent power supply system through a connecting line, balanced power is considered a load; and conversely, when such power is imported, it is considered energy production. Flow control through these network distributions is

Figure 4. Electricity demand—Monday.

Figure 5. Electricity demand—Thursday.

2. Unit commitment renewable energy sources and distribution network

Figure 3.

66

Figure 2.

Zero and Net Zero Energy

Example of a municipal power station [9].

Microcosm of fictitious RES intelligent regions of Rohan Island [8].

In order to ensure the security and reliability of the power supply from RES and the network, electrical resources must be planned and effectively controlled. The large distribution network consists of many elements including generators, transmission lines, transformers and circuit breakers. New RES green energy sources are co-opted or integrated into a distribution system or smart grid system including other DC/DC converters and DC/AC converters and must then be scheduled for microsystem operation. In addition, market structure and real-time energy pricing need to be assessed. For stable operation of the micro-network, it will be necessary to plan electricity generation and supply it to the system load for every second of the intelligent area operation—Rohan Island (Prague 8, Czech Republic) (see Figure 1). Energy sources for large energy systems consist of water, nuclear energy, fossil fuels, renewable energy sources such as solar energy (photovoltaic systems) as well as green energy such as fuel cells, biomass and combined heat and power (CHP preprogrammed (software) based on safe operation and economic indicators. In order to control the energy flow through the connection lines within the transmission at a given frequency of the system, the concept of the control error is introduced (area control error, ACE) and is defined as [10].

$$A\_{\rm CE} = \Delta P\_n - \beta \Delta f \tag{7}$$

to control the turbine control valves. In order to achieve reasonable regulation (i.e. ACE reduced to zero), system load requirements are sampled every few seconds. The second objective is to fill energy consumption in the prescribed sample at each minute and to allocate the varying load between the different units to minimise operating costs. This assumes that the load demand remains constant over each period. Figure 7 shows the AGC block diagram. The AGC also manages the connected micro-networks in a large interconnected power grid. The microgrid concept assumes the grouping of loads in the area within various micro-projects, such as photovoltaics, biomass and combined CHP, acting as a single control network. For the local grid, this cluster becomes the only discernible burden. When the micro-network is connected to the grid, microprocessing voltage is controlled by the local grid. In addition, the frequency of the electrical network is controlled by the operator of the electrical network. The microgrid cannot change the voltage of the bus network and the frequency of the power supply. Therefore, if the microwave network is connected to the local grid, it becomes part of the network and is subject to network failures. The AGC control system is designed to monitor

The economic supply is expressed in a mathematical process where the required electricity production from the grid including the RES within the micro-network of the intelligent region, Rohan Island, is divided between individual energy sources within the operating RES micro-networks, and thus by minimising defined cost criteria [4], it is subject to both load and operating constraints or penalties.

For each specified load over time (see Figures 4 and 5) the power of each RES power plant, including electricity from the distribution grid (i.e. each production unit within the power plant), is calculated to minimise the total cost of fuel required to operate the system load [3]. The problem of economic supply is traditionally formulated as an optimisation with quadratic cost objective functions [11, 24]:

Ci <sup>þ</sup> BiPgi <sup>þ</sup> AiP<sup>2</sup>

gi (8)

PDi þ Ploss ¼ 0 (9)

f Pg <sup>¼</sup> <sup>∑</sup> Ng

Control software—Automatic power generator control (AGC) RES [10].

∑ Ng

i¼1

i�1

Pgi � ∑ ND i¼1

s:t Vmin ≤V ≤Vmax Pgmin ≤Pg ≤Pgmax

system load fluctuations.

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

2.1 Economic delivery

Figure 7.

69

where

$$
\Delta P\_n = P\_2 - P\_1
$$

$$
\Delta f = f\_{mf} - f\_{mer}
$$

and P2 is the planned power between two power nets; P1 is the actual power output between two network nets; fRef is the reference frequency, that is, the nominal frequency; fmer is the actual measured frequency of the system; and β is frequency distortion.

The AGC software (automatic generation control) is designed to achieve the following activities (Figure 6):


The above conditions are subject to additional limitations that may be introduced in network security considerations, such as loss of power in the line or in the generator.

The first objective is to solve the additional controller and the distortion concept. Parameter β is defined as frequency distortion and is the so-called debug factor that is set when implementing AGC. In the case of a small change in load on the microsystem in the intelligent area, it leads to proportional changes in the system frequency.

For this reason, a bug in a controlled area ACE ¼ ΔPn � βΔf provides each space with information on load changes and controls an additional smart zone controller

#### Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

to control the turbine control valves. In order to achieve reasonable regulation (i.e. ACE reduced to zero), system load requirements are sampled every few seconds.

The second objective is to fill energy consumption in the prescribed sample at each minute and to allocate the varying load between the different units to minimise operating costs. This assumes that the load demand remains constant over each period. Figure 7 shows the AGC block diagram. The AGC also manages the connected micro-networks in a large interconnected power grid. The microgrid concept assumes the grouping of loads in the area within various micro-projects, such as photovoltaics, biomass and combined CHP, acting as a single control network. For the local grid, this cluster becomes the only discernible burden. When the micro-network is connected to the grid, microprocessing voltage is controlled by the local grid. In addition, the frequency of the electrical network is controlled by the operator of the electrical network. The microgrid cannot change the voltage of the bus network and the frequency of the power supply. Therefore, if the microwave network is connected to the local grid, it becomes part of the network and is subject to network failures. The AGC control system is designed to monitor system load fluctuations.

#### 2.1 Economic delivery

preprogrammed (software) based on safe operation and economic indicators. In order to control the energy flow through the connection lines within the transmission at a given frequency of the system, the concept of the control error is introduced

> ΔPn ¼ P<sup>2</sup> � P<sup>1</sup> Δf ¼ fref � f mer

and P2 is the planned power between two power nets; P1 is the actual power output between two network nets; fRef is the reference frequency, that is, the nominal frequency; fmer is the actual measured frequency of the system; and β is

The AGC software (automatic generation control) is designed to achieve the

• Compensation of the surface energy load of the given area, that is, distribution of nodes, links and load schedule, thus controlling the system frequency Δf

• Distribution of changing loads between generators minimising operating

The above conditions are subject to additional limitations that may be introduced in network security considerations, such as loss of power in the line or in the

is set when implementing AGC. In the case of a small change in load on the microsystem in the intelligent area, it leads to proportional changes in the system

Control software—Automatic power generator control (AGC) RES [10].

The first objective is to solve the additional controller and the distortion concept. Parameter β is defined as frequency distortion and is the so-called debug factor that

For this reason, a bug in a controlled area ACE ¼ ΔPn � βΔf provides each space with information on load changes and controls an additional smart zone controller

ACE ¼ ΔPn � βΔf (7)

(area control error, ACE) and is defined as [10].

where

Zero and Net Zero Energy

frequency distortion.

costs

generator.

frequency.

Figure 6.

68

following activities (Figure 6):

The economic supply is expressed in a mathematical process where the required electricity production from the grid including the RES within the micro-network of the intelligent region, Rohan Island, is divided between individual energy sources within the operating RES micro-networks, and thus by minimising defined cost criteria [4], it is subject to both load and operating constraints or penalties.

For each specified load over time (see Figures 4 and 5) the power of each RES power plant, including electricity from the distribution grid (i.e. each production unit within the power plant), is calculated to minimise the total cost of fuel required to operate the system load [3]. The problem of economic supply is traditionally formulated as an optimisation with quadratic cost objective functions [11, 24]:

$$f\left(P\_{\mathcal{g}}\right) = \sum\_{i=1}^{N\_{\mathcal{g}}} \left(C\_i + B\_i P\_{\mathcal{g}i} + A\_i P\_{\mathcal{g}i}^2\right) \tag{8}$$

$$\sum\_{i=1}^{N\_{\tilde{\mathbf{g}}}} P\_{\mathbf{g}i} - \sum\_{i=1}^{N\_D} P\_{Di} + P\_{loss} = \mathbf{0} \tag{9}$$

$$s.t. \ V\_{min} \le V \le V\_{max}$$
 
$$\mathbf{n} \qquad \dots \qquad \dots$$

$$P\_{\mathcal{g}min} \le P\_{\mathcal{g}} \le P\_{\mathcal{g}max}$$

Figure 7.

Control software—Automatic power generator control (AGC) RES [10].

#### Zero and Net Zero Energy

where Ng is the total output produced from all RES, ND is the total power consumed, Pzt is the total power loss in the system, xið Þt is the energy state of the IT sources over time t (see functions (10), Pgi is the power output of the RES, PDi is the power consumed, Pgi,min is the minimum power of the RES source, Pgi,max is the maximum power of the RES source, Pg is the rated power of the RES source, V is the voltage of the RES source, Vmin is the minimum voltage of the source of RES and Vmax is the maximum voltage of the RES source.

If independent variable Pg (function argument) Pgi, that is, power of the IT resources in time t and xið Þt , is the energy state of the IT source over time t, we get the basic relationship of the cost function:

$$f\left(P\_{\mathcal{S}}(t), \mathbf{x}(t)\right) = \sum\_{i=1}^{N\_{\mathcal{E}}} \sum\_{t=1}^{T} \left(\mathbf{C}\_{i} + B\_{i} P\_{\mathcal{g}^{i}}(t) + A\_{i} P\_{\mathcal{g}^{i}}^{2}(t)\right) \bullet \boldsymbol{\varkappa}\_{i}(t) \tag{10}$$

depending on the higher output), [CZK/MW], for example, Ci ∙ Pi ¼ ½ � CZK , and B are costs that are dependent on the second output of power (e.g. joule heating losses are greater with a larger current passing through the conductor). Joule heat is then

t [J]. Further, heat is lost in iron and friction CZK=MW<sup>2</sup> a PG is the power

Restrictive conditions include balances and imbalances according to energy algorithms, as well as generator, bus, voltage and current flow limitations. This is solved through analytical programming, such as nonlinear programming (NLP), quadratic programming (QP) and linear programming (LP), Newton's method, inner point method (IPM) and decision support such as the analytic hierarchy process (AHP). We use alternative methods such as evolutionary programming (EP) [12], genetic algorithms (GA) [13], taboo searching [14], neural networks [15], optimisation of particle flocks [16, 17], the stochastic optimisation algorithm simulated annealing (SA) [18, 29] and adaptive dynamic programming (ADP) which are passive learning

Resource deployment, or operational planning function, is sometimes referred to as "pre-delivery". In the overall RES resource management hierarchy [11], resource deployment is coordinated with the planning of economic supply and maintenance and production over time. Scheduling resource deployment covers the scope of the decision on the hourly operation of the power system with a horizon of 1 day–1 week. Resource planning covers the hourly operation of the RES system with a horizon

methods to improve the performance of the economic delivery algorithm.

a. Restrictions of RES operation and cost per unit of RES resource

While respecting constraints and unexpected stochastic variables, certain assumptions are made when compiling a mathematical statement of resource sorting. These may include, for example, rotary reserves of electricity currents, equipment for respective initial reserves under the conditions of a boiler (in the case of biomass) or partial formulation with the commencement of operation. The first constraint is that realistic electricity production must be greater than the sum of the total electricity consumption (power) of consumers in the intelligent Rohan

Pcel is the total required power (net demand) [MW]. a Pres is the total power

The RES micro-network should maintain a certain power reserve; then the cap

gi � Pres

Pgið Þt ≥Pcel þ Prez (13)

gi (14)

c. Restrictions of running the power plant in terms of RES

d.Restrictions on the local network (micro-networks) RES

Island area, including required power reserves, or the sum is equal to

∑ Ng

i¼1

Pmax gi <sup>¼</sup> Pcap

of the power reserve must be modified in some way. Hence

2.2 Resource assignment (unit commitment)

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

of 1 day–1 week. We take into account:

reserve in [MW].

71

b.Restrictions of RES production and reserves

<sup>Q</sup> <sup>¼</sup> RI<sup>2</sup>

output [MW].

Based on the above-defined variables, constants, mathematical approximations and mathematical structures (8) and (10), we construct two variations of the cost functions of our energy system—the physical model of the intelligent cities' energy system (Figure 2). Support is also available [8].

$$f\left(P\_{\mathcal{g}}(t), \mathbf{x}(t)\right) = \sum\_{t=1}^{T} \sum\_{i=1}^{N\_{\mathcal{g}}} \left(C\_{i} + B\_{i}P\_{\mathcal{g}^{i}}(t) + A\_{i}P\_{\mathcal{g}^{i}}^{2}(t) + \delta\_{i}(\mathbf{1} - e^{-at})\right) \bullet \boldsymbol{\varkappa}\_{i}(t) \tag{11}$$

$$f\left(P\_{\mathcal{S}}(t), \mathbf{x}(t)\right) = \sum\_{t=1}^{T} \sum\_{i=1}^{N\_{\mathcal{S}}} \left(C\_{i}P\_{\mathcal{S}^{i}} + B\_{i}P\_{\mathcal{S}^{i}}^{2}\right) \bullet \mathbf{x}\_{i}(t) + A\_{i}P\_{\mathcal{S}^{i}}\mathbf{x}\_{i}(t) \bullet \left(\mathbf{1} - \mathbf{x}\_{i}(t-1)\right) \tag{12}$$

For the sake of our experiment, we will be based on defined cost functions (12) over the entire integrated period (24 hours/day). We will separately allocate the operation and sorting of RES costs. Then we mark the cost function as F, the number of RES in the network is denoted as NG, the scheduled RES mode (24 hours) will be labelled as t ∈ f g 1; 2; …; T , the resource index is marked as i∈ 1; 2; …; Ng , the number of time moments in the given period when RES is depicted as T, the power of the IT source at time t, we denote Pgið Þt , the functional cost of the cost function f is expressed as an algebraic shape CiPgi <sup>þ</sup> BiP<sup>2</sup> gi xið Þ<sup>t</sup> ,the cost of running one of the RES is algebraic γixið Þt ∙ð Þ 1 � xið Þ t � 1 ,the start-up cost (to commence the operation of RES) in relation (12), is also expressed by the relation Di <sup>1</sup> � <sup>e</sup>�α<sup>t</sup> ð Þ<sup>∙</sup> xið Þ<sup>t</sup> ; <sup>α</sup> ¼ � <sup>Δ</sup>Ti <sup>τ</sup><sup>i</sup> ð Þt ,the cost coefficients in relation (11) and (12), are Ci, Bi, Ai, Di, respectively. ΔTið Þt and τ<sup>i</sup> the relevent cost coefficients, or the downtime and time constant of exponential increas in the start-up costs of the <sup>i</sup>-th source at time <sup>t</sup>. Ci½ � CZK , Bi½ � CZK=MW , Ai CZK=MW<sup>2</sup> �, Di½ � <sup>K</sup><sup>č</sup> , the operating costs of RES producing the output will be expressed in an algebraic relationship <sup>P</sup> <sup>¼</sup> <sup>C</sup> <sup>þ</sup> <sup>B</sup> <sup>∙</sup> <sup>P</sup> <sup>þ</sup> <sup>A</sup> <sup>∙</sup> <sup>P</sup><sup>2</sup> þ D ∙e, xið Þt is the energy state of the IT source over time t and ð Þ x1; x2; …; xn , are vector components (independently variable cost functions). Where Ng is the number of resources in the network and T the number of times or slices are considered during the day (24 hours).

We break down the cost (purpose) function (12) and express the operating costs of the RES-generating power Pg <sup>¼</sup> <sup>C</sup><sup>∙</sup> Pgi <sup>þ</sup> <sup>B</sup> <sup>∙</sup> <sup>P</sup><sup>2</sup> gi½ � CZK : This relationship is written without expressing the cost. This relationship simplifies the algorithm (12) because the generators (RES) are always in an on state xiðÞ¼ t 1: The individual variables (cost items) mean C is cost-dependent on the power output (e.g. the amount of fuel

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

where Ng is the total output produced from all RES, ND is the total power consumed, Pzt is the total power loss in the system, xið Þt is the energy state of the IT sources over time t (see functions (10), Pgi is the power output of the RES, PDi is the power consumed, Pgi,min is the minimum power of the RES source, Pgi,max is the maximum power of the RES source, Pg is the rated power of the RES source, V is the voltage of the RES source, Vmin is the minimum voltage of the source of RES and

If independent variable Pg (function argument) Pgi, that is, power of the IT resources in time t and xið Þt , is the energy state of the IT source over time t, we get

Based on the above-defined variables, constants, mathematical approximations and mathematical structures (8) and (10), we construct two variations of the cost functions of our energy system—the physical model of the intelligent cities' energy

Ci <sup>þ</sup> BiPgiðÞþ<sup>t</sup> AiP<sup>2</sup>

gi

For the sake of our experiment, we will be based on defined cost functions (12) over the entire integrated period (24 hours/day). We will separately allocate the operation and sorting of RES costs. Then we mark the cost function as F, the number of RES in the network is denoted as NG, the scheduled RES mode (24 hours) will be labelled as t ∈ f g 1; 2; …; T , the resource index is marked as

 , the number of time moments in the given period when RES is depicted as T, the power of the IT source at time t, we denote Pgið Þt , the functional

cost of running one of the RES is algebraic γixið Þt ∙ð Þ 1 � xið Þ t � 1 ,the start-up cost (to commence the operation of RES) in relation (12), is also expressed by the

(12), are Ci, Bi, Ai, Di, respectively. ΔTið Þt and τ<sup>i</sup> the relevent cost coefficients, or the downtime and time constant of exponential increas in the start-up costs of the <sup>i</sup>-th source at time <sup>t</sup>. Ci½ � CZK , Bi½ � CZK=MW , Ai CZK=MW<sup>2</sup> �, Di½ � <sup>K</sup><sup>č</sup> , the operating costs of RES producing the output will be expressed in an algebraic relationship

and ð Þ x1; x2; …; xn , are vector components (independently variable cost functions). Where Ng is the number of resources in the network and T the number of times or

without expressing the cost. This relationship simplifies the algorithm (12) because the generators (RES) are always in an on state xiðÞ¼ t 1: The individual variables (cost items) mean C is cost-dependent on the power output (e.g. the amount of fuel

We break down the cost (purpose) function (12) and express the operating costs

cost of the cost function f is expressed as an algebraic shape CiPgi <sup>þ</sup> BiP<sup>2</sup>

Ci <sup>þ</sup> BiPgið Þþ<sup>t</sup> AiP<sup>2</sup>

giðÞþt δ <sup>i</sup> 1 � e

gið Þt

�α<sup>t</sup> ð Þ

∙ xiðÞþt AiPgixið Þt ∙ð1 � xið Þ t � 1 (12)

<sup>τ</sup><sup>i</sup> ð Þt ,the cost coefficients in relation (11) and

þ D ∙e, xið Þt is the energy state of the IT source over time t

∙ xið Þt (10)

∙ xið Þt (11)

gi

xið Þt ,the

gi½ � CZK : This relationship is written

Vmax is the maximum voltage of the RES source.

f Pg ð Þ<sup>t</sup> ; x tð Þ <sup>¼</sup> <sup>∑</sup>

system (Figure 2). Support is also available [8].

i¼1

i¼1

T t¼1 ∑ Ng

T t¼1 ∑ Ng

relation Di <sup>1</sup> � <sup>e</sup>�α<sup>t</sup> ð Þ<sup>∙</sup> xið Þ<sup>t</sup> ; <sup>α</sup> ¼ � <sup>Δ</sup>Ti

slices are considered during the day (24 hours).

of the RES-generating power Pg <sup>¼</sup> <sup>C</sup><sup>∙</sup> Pgi <sup>þ</sup> <sup>B</sup> <sup>∙</sup> <sup>P</sup><sup>2</sup>

f Pg ð Þ<sup>t</sup> ; x tð Þ <sup>¼</sup> <sup>∑</sup>

Zero and Net Zero Energy

f Pgð Þ<sup>t</sup> ; x tð Þ <sup>¼</sup> <sup>∑</sup>

i∈ 1; 2; …; Ng

<sup>P</sup> <sup>¼</sup> <sup>C</sup> <sup>þ</sup> <sup>B</sup> <sup>∙</sup> <sup>P</sup> <sup>þ</sup> <sup>A</sup> <sup>∙</sup> <sup>P</sup><sup>2</sup>

70

Ng

i¼1 ∑ T t¼1

CiPgi <sup>þ</sup> BiP<sup>2</sup>

the basic relationship of the cost function:

depending on the higher output), [CZK/MW], for example, Ci ∙ Pi ¼ ½ � CZK , and B are costs that are dependent on the second output of power (e.g. joule heating losses are greater with a larger current passing through the conductor). Joule heat is then <sup>Q</sup> <sup>¼</sup> RI<sup>2</sup> t [J]. Further, heat is lost in iron and friction CZK=MW<sup>2</sup> a PG is the power output [MW].

Restrictive conditions include balances and imbalances according to energy algorithms, as well as generator, bus, voltage and current flow limitations. This is solved through analytical programming, such as nonlinear programming (NLP), quadratic programming (QP) and linear programming (LP), Newton's method, inner point method (IPM) and decision support such as the analytic hierarchy process (AHP). We use alternative methods such as evolutionary programming (EP) [12], genetic algorithms (GA) [13], taboo searching [14], neural networks [15], optimisation of particle flocks [16, 17], the stochastic optimisation algorithm simulated annealing (SA) [18, 29] and adaptive dynamic programming (ADP) which are passive learning methods to improve the performance of the economic delivery algorithm.

#### 2.2 Resource assignment (unit commitment)

Resource deployment, or operational planning function, is sometimes referred to as "pre-delivery". In the overall RES resource management hierarchy [11], resource deployment is coordinated with the planning of economic supply and maintenance and production over time. Scheduling resource deployment covers the scope of the decision on the hourly operation of the power system with a horizon of 1 day–1 week.

Resource planning covers the hourly operation of the RES system with a horizon of 1 day–1 week. We take into account:

a. Restrictions of RES operation and cost per unit of RES resource


While respecting constraints and unexpected stochastic variables, certain assumptions are made when compiling a mathematical statement of resource sorting. These may include, for example, rotary reserves of electricity currents, equipment for respective initial reserves under the conditions of a boiler (in the case of biomass) or partial formulation with the commencement of operation. The first constraint is that realistic electricity production must be greater than the sum of the total electricity consumption (power) of consumers in the intelligent Rohan Island area, including required power reserves, or the sum is equal to

$$\sum\_{i=1}^{N\_{\mathcal{g}}} P\_{\mathcal{g}i}(t) \ge P\_{\text{cell}} + P\_{\text{rxn}} \tag{13}$$

Pcel is the total required power (net demand) [MW]. a Pres is the total power reserve in [MW].

The RES micro-network should maintain a certain power reserve; then the cap of the power reserve must be modified in some way. Hence

$$P\_{\mathbf{g}^i}^{\mu a \mathbf{x}} = P\_{\mathbf{g}^i}^{\epsilon a \mathbf{p}} - P\_{\mathbf{g}^i}^{\epsilon \mathbf{e}} \tag{14}$$

Pmax gi is the maximum output power of the IT RES source [MW], Pcap gi is the production capacity power of the IT RES source (capacity) in [MW], and Pres gi is the production reserve power of the IT RES source in [MW].

$$P\_{pop} + P\_{xt} \le \sum\_{i=1}^{N} P\_{\mathcal{g}^i} - \sum\_{i=1}^{N} P\_{\mathcal{g}^i}^{res} \tag{15}$$

hj, j∈J has constraints using the algorithm. From a general point of view, the

The special-purpose function can be expressed as a sum of quadrates of the

The value of the minimised special-purpose function or the value of the

where x1, x2, …, xn has the state variables of the optimised system expressed by the special-purpose function, y1, y2, …, ym has the parameters of the optimised system

that the state variable must be higher than or equal to zero. By multiplying both sides by �1, we get a condition corresponding to the function of state variables. The

If our problem is formulated from the point of maximisation, then it is easy to make the adjustment to minimise. In that case, the situation would be the following:

> on X ⊂ Rn, if δ >0 so that for each y ∈X, yj j j j � x < δ applies f xð Þ≤ f y ð Þ:

The special-purpose function design is a very complex problem, requiring considerable experience in the subject area, and the possibilities of defining optimisation must be considered. We need to build on what is to be achieved and

We have based our experience and our research on optimisation solutions of energy systems from energy companies within the Czech Republic. Based on this we have described the physical model of the energy grid, RES microgrid (Figure 2), which corresponds to our experiment. By adjusting the algorithm (18), the relation for the restrictive condition of the cost function is gotten using relation (19) and the relation (27). The fact (reality) will be such that g xð Þ <sup>i</sup>ð Þt ≥0: Then we can write

deviations between the current parameter values and the required values

f xð Þ¼ ∑ m i¼1 yi ð Þ� x di <sup>2</sup>

optimised system parameters depends on the status vector:

d1, d2, …, dm have the required values of these parameters.

When we introduce the inequality constraint gi

For the local minimum, the following applies:

For the global minimum, the following applies

procedure of its optimisation is then as follows:

where <sup>f</sup> : <sup>X</sup> ! <sup>R</sup> <sup>a</sup> <sup>X</sup> <sup>⊂</sup> <sup>R</sup><sup>n</sup>:

what can be done.

a relationship

73

min f xð Þ for x<sup>∈</sup> <sup>R</sup><sup>n</sup> (20)

<sup>x</sup> <sup>¼</sup> ½ � <sup>x</sup>1; <sup>x</sup>2; …; xn T, (22)

min f g f xð Þ : x∈X (23)

maxf g f xð Þ : x∈ X ¼ �min f g �f xð Þ : x∈ X (24) argmax f x f g ð Þ : x∈X ¼ argminf g �f xð Þ : x∈X (25)

on X <sup>⊂</sup> <sup>R</sup>n, if foe each y∈X applies f xð Þ≤f y ð Þ (26)

: (21)

ð Þ x ≥0, the condition expresses

optimisation problem can be expressed as follows:

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

Ppop is the production power demand in [MW], Pzt is production power loss in [MW], Pgi is the total real electricity production in [MW], and Pres gi is the total reserve of electricity actually produced

$$A\_c = A\_0(1 - e^{at}) + A\_L \tag{16}$$

where Ac is the cost of running an off-line resource (resource status in a given hour) in [CZK], a is the thermal time constant, t is the time in [sec], AL is the workforce costs in [CZK], A<sup>0</sup> is the cost of running the cold boiler in [CZK] and Pmax gi is the maximum production output power of the IT source [MW].

$$A\_{ban} = A\_B t + A\_L \tag{17}$$

where AB is the costs to start a subdued resource in [CZK], t is the time in [sec] and Aban are the wage costs in [CZK].

Resource sorting belongs to the classic Lagrange relaxation technique, but the solution to the constraints is based on stochastic variables. That is why we have solved optimisation by simulated annealing as stochastic optimisation (we will not deal with this further; see [8]). Allowed cost functions are conditional when the output power produced by the local network (micro-networks) of RES in the given hour Að Þt is determined by the sum of resources turned on. We draw from a typical daily electricity consumption diagram at any given time. The optimisation algorithm works with acceptable solutions (see [8]) which can be evaluated through cost functions without the use of penalties. Then.

$$\sum\_{i=1}^{N\_{\tilde{\varepsilon}}} P\_i \mathfrak{x}\_i(t) = A(t), \text{for } t = (1, 2, \dots, 24) \text{[h]}.\tag{18}$$

#### 2.3 Optimisation of energy system special-purpose system

The design of special-purpose function f (x) is one of the most complex steps of optimisation. There is no guide or procedure of creating such a function. If we are to design such special-purpose function, we have to know what we are to achieve and what the starting point may be. When we consider our problem, we can see that, in order to achieve reliable and functional results, we have to solve it using constrained optimisation. The constrained optimisation may then be mathematically expressed as follows:

$$\begin{aligned} \text{minimalise} \, f(\mathbf{x}) \, \text{under restrictive condition } \mathbf{g}\_i(\mathbf{x}) \ge \mathbf{0}, \, i \in \mathbf{.} \, i = k' + \mathbf{1}, \dots, k\\ h\_j(\mathbf{x}) = \mathbf{0}, \, j \in \mathbf{J}, j = \mathbf{1}, \mathbf{2}, \dots, k' \end{aligned} \tag{19}$$

<sup>f</sup> : <sup>D</sup> ! <sup>R</sup>, <sup>D</sup> <sup>⊆</sup> <sup>R</sup><sup>d</sup> is defined above the definition field <sup>D</sup>, which is a continuous set of searched space, and R is a real value range. Furthermore, f,gi ahj has the functions, and I and J has the final sets of indices. The function F is a specialpurpose function; gi , i ∈I has constraints using the inequality algorithm, and

Pmax

Zero and Net Zero Energy

Pmax

as follows:

72

purpose function; gi

gi is the maximum output power of the IT RES source [MW], Pcap

production capacity power of the IT RES source (capacity) in [MW], and Pres

N i¼1

Ppop is the production power demand in [MW], Pzt is production power loss in

where Ac is the cost of running an off-line resource (resource status in a given hour) in [CZK], a is the thermal time constant, t is the time in [sec], AL is the workforce costs in [CZK], A<sup>0</sup> is the cost of running the cold boiler in [CZK] and

where AB is the costs to start a subdued resource in [CZK], t is the time in [sec]

Resource sorting belongs to the classic Lagrange relaxation technique, but the solution to the constraints is based on stochastic variables. That is why we have solved optimisation by simulated annealing as stochastic optimisation (we will not deal with this further; see [8]). Allowed cost functions are conditional when the output power produced by the local network (micro-networks) of RES in the given hour Að Þt is determined by the sum of resources turned on. We draw from a typical daily electricity consumption diagram at any given time. The optimisation algorithm works with acceptable solutions (see [8]) which can be evaluated through

The design of special-purpose function f (x) is one of the most complex steps of optimisation. There is no guide or procedure of creating such a function. If we are to design such special-purpose function, we have to know what we are to achieve and what the starting point may be. When we consider our problem, we can see that, in order to achieve reliable and functional results, we have to solve it using constrained optimisation. The constrained optimisation may then be mathematically expressed

<sup>f</sup> : <sup>D</sup> ! <sup>R</sup>, <sup>D</sup> <sup>⊆</sup> <sup>R</sup><sup>d</sup> is defined above the definition field <sup>D</sup>, which is a continuous

, i ∈I has constraints using the inequality algorithm, and

set of searched space, and R is a real value range. Furthermore, f,gi

functions, and I and J has the final sets of indices. The function F is a special-

Pgi � ∑ N i¼1 Pres

Ppop þ Pzt ≤ ∑

Ac ¼ A<sup>0</sup> 1 � e

gi is the maximum production output power of the IT source [MW].

[MW], Pgi is the total real electricity production in [MW], and Pres

production reserve power of the IT RES source in [MW].

reserve of electricity actually produced

and Aban are the wage costs in [CZK].

cost functions without the use of penalties. Then.

∑ Ng

i¼1

minimalise f xð Þ under restrictive condition gi

2.3 Optimisation of energy system special-purpose system

gi is the

gi (15)

<sup>α</sup><sup>t</sup> ð Þþ AL (16)

Aban ¼ ABt þ AL (17)

PixiðÞ¼ t A tð Þ,for t ¼ ð Þ 1; 2; …; 24 ½ � h : (18)

ð Þ x ≥0, i∈ , i ¼ k<sup>0</sup>

hjð Þ¼ <sup>x</sup> <sup>0</sup>, j∈J,j <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, …, k<sup>0</sup> (19)

þ 1, …, k

ahj has the

gi is the total

gi is the

hj, j∈J has constraints using the algorithm. From a general point of view, the optimisation problem can be expressed as follows:

$$\min f(\boldsymbol{x}) \, f \boldsymbol{\sigma} \, \boldsymbol{x} \in \mathbb{R}^n \tag{20}$$

The special-purpose function can be expressed as a sum of quadrates of the deviations between the current parameter values and the required values

$$f(\mathbf{x}) = \sum\_{i=1}^{m} \left[ y\_i(\mathbf{x}) - d\_i \right]^2. \tag{21}$$

The value of the minimised special-purpose function or the value of the optimised system parameters depends on the status vector:

$$\boldsymbol{\mathfrak{x}} = \begin{bmatrix} \boldsymbol{\mathfrak{x}}\_1, \boldsymbol{\mathfrak{x}}\_2, \dots, \boldsymbol{\mathfrak{x}}\_n \end{bmatrix}^T,\tag{22}$$

where x1, x2, …, xn has the state variables of the optimised system expressed by the special-purpose function, y1, y2, …, ym has the parameters of the optimised system

d1, d2, …, dm have the required values of these parameters. When we introduce the inequality constraint gi ð Þ x ≥0, the condition expresses that the state variable must be higher than or equal to zero. By multiplying both sides by �1, we get a condition corresponding to the function of state variables. The procedure of its optimisation is then as follows:

$$\min \left\{ f(\mathbf{x}) : \mathbf{x} \in X \right\} \tag{23}$$

where <sup>f</sup> : <sup>X</sup> ! <sup>R</sup> <sup>a</sup> <sup>X</sup> <sup>⊂</sup> <sup>R</sup><sup>n</sup>:

If our problem is formulated from the point of maximisation, then it is easy to make the adjustment to minimise. In that case, the situation would be the following:

$$\max \{ f(\mathbf{x}) : \mathbf{x} \in X \} = -\min \left\{ -f(\mathbf{x}) : \mathbf{x} \in X \right\} \tag{24}$$

$$\arg\max \{ f(\mathbf{x}) : \mathbf{x} \in \mathbf{X} \} = \arg\min \{ -f(\mathbf{x}) : \mathbf{x} \in \mathbf{X} \} \tag{25}$$

For the local minimum, the following applies:

$$on \ X \subset \mathbb{R}^n, \text{if } \begin{array}{l} \delta > 0 \text{ so that} \\ \text{for each } y \in X, \ ||y - \mathbf{x}|| < \delta \text{ } applies \text{ $f(\mathbf{x}) \le f(\mathbf{y})$ .} \end{array}$$

For the global minimum, the following applies

$$on \, X \subset \mathbb{R}^n, \text{ if } f \text{e } e \text{ach } y \in X \, applies \, f(x) \le f(y) \tag{26}$$

The special-purpose function design is a very complex problem, requiring considerable experience in the subject area, and the possibilities of defining optimisation must be considered. We need to build on what is to be achieved and what can be done.

We have based our experience and our research on optimisation solutions of energy systems from energy companies within the Czech Republic. Based on this we have described the physical model of the energy grid, RES microgrid (Figure 2), which corresponds to our experiment. By adjusting the algorithm (18), the relation for the restrictive condition of the cost function is gotten using relation (19) and the relation (27). The fact (reality) will be such that g xð Þ <sup>i</sup>ð Þt ≥0: Then we can write a relationship

$$\log(\varkappa\_i(t)) = \sum\_{i=1}^{N\_\sharp} P\_i \varkappa\_i(t) - A(t) \ge 0 \tag{27}$$

min f xð Þ¼ ; g f xð Þþ a ∑

fg Xð Þ¼ f Xð Þþ ag<sup>2</sup>

ply. Because <sup>g</sup><sup>2</sup> is a negative number, there is a power when <sup>γ</sup>ð Þ<sup>t</sup> <sup>&</sup>gt; <sup>∑</sup><sup>i</sup>

suitable definition of the constraining conditions may be selected.

and the deviation of production from consumption.

we have achieved a suitable solution.

Experimental solution:

consumption.

75

negative and positive slope.

(29) and (30), we get a modified algorithm [23] as follows:

then w (31) are the same in the algorithm (31).

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

following function, fg:

When applying definition 1, limiting the conditions (27) and the relationship (28) to the target function fg Xð Þ or by applying definition 1 and conditions (27),

where ag2ð Þ <sup>X</sup> is the so-called penalty of the non-required electrical power sup-

We are looking for an <sup>x</sup> allowing us to minimise functions f Xð Þþ ag2ð Þ <sup>X</sup> :In such case we solve Eq. (31) by minimising cost function f(X) and maximising the penalty defined as function ag<sup>2</sup>ð Þ <sup>X</sup> . The result of summing the two functions up is the

We used the minus sign in algorithm (32) as we intend to maximise functional prescription μð Þ g Xð Þ : Function g xð Þ defines the output stability of the system, which is why we may set it to zero. This function thus ranges from 0 to 1 and μ is fuzzy zero. Both constraining conditions (31) and (32) may be compared, and the most

When function fg Xð Þ approaches the minimum, which is our intent, we achieve a stable power output balance. Our objective is to minimise both the operation costs

Note: If the power consumption of a given area of "Rohanský ostrov" smart urban area is higher than the production, there will be a minus sign on the right side of Eq. (27) (it will be a negative number). Then we will focus on mathematical expression (28); if the value of expression (27) is very small, that is, close to zero,

1. We start from (32), focusing on penalising unsolicited power supply to the smart area from the local RES microgrid. Weight a (coefficient) defines the conditions of the cost function. In numerical ratio, it is set to such value that

a.We set a low permissible deviation between power generation and

b.We define the source organisation so that the required output at a given

c. We accept a small permissible deviation which we mark ΔP (Figure 8) and accept expression (33), which is the function of the chart showing

the ratio of costs and balances mutually approximately set off.

2. Next, we define the condition of extending the admissible solution.

time was as near as possible to the required consumption.

Let us define the membership function as X ¼ 0, which is a classical set, and μA : X ! h i 0; 1 as the representation [21]. A fuzzy set will then be a

function value of the target function (31) must be artificially reduced or increased;

m i¼1 gi <sup>2</sup>

ð Þ x (30)

Pgixið Þt . The

ð Þ X ≈ min (31)

fg Xð Þ¼ f Xð Þ� aμð Þ g Xð Þ (32)

where xiðÞ¼ t ð Þ x1ð Þt ; x2ð Þt ; …; x7ð Þt :Dependency x ! ðÞ¼ <sup>t</sup> ð Þ <sup>x</sup>1ð Þ<sup>t</sup> ; <sup>x</sup>2ð Þ<sup>t</sup> ; …; <sup>x</sup>7ð Þ<sup>t</sup> depends on the state of the source at a given hour,

where ∑Ng <sup>i</sup>¼<sup>1</sup>Pixið Þ<sup>t</sup> represents the state of the power generator at time <sup>t</sup> and <sup>γ</sup>ð Þ<sup>t</sup> represents the energy consumption forecast for a given hour.

Parameters i ∈ 1; 2; …; Ng � � stand for source indexes. NG represents the number of sources in our microgrid (which is 7). Variable t∈ f g 1; 2; …; T represents the time the connected sources spend in the defined mode, and Pgið Þt is the output of the source at time t.

#### 2.4 Penalty function

The optimisation algorithm works with acceptable but inadmissible solutions. The penalising function is zero in terms of standard requirements. For one criterion, it has a non-zero value and is positive.

If we add a penalty function to the cost function, then we get an algorithm that is only optimally suitable for local searches in terms of effectiveness. We see this if we exit from [19, 20]; then we can apply a suitable approach to penalising cost functions.

In the first instance Let us define meanings. Definition 1: Consider functions f, g, and suppose some values of the function g (x) belong to D (f). To every such value u ¼ g xð Þ∈ D fð Þ, assign y = f (u) = f (g (x)). This defines the function h (x) = f (g (x)), which we will call function f, g and mark it h=f � g Note: G is the first function and the second is F. The penalising function is the function of unsolicited power supply:

$$f\left(P\_{\mathcal{S}}(t), \mathbf{x}(t)\right) = \left(f(X) + a\right) \bullet \prod\_{i=1}^{m} c\_i^{b\_i} \tag{28}$$

where x tðÞ¼ <sup>X</sup> <sup>¼</sup> f g <sup>x</sup>1; <sup>x</sup>2; …; xD ,D= 7 minimises the function f Pg ð Þ<sup>t</sup> ; x tð Þ � � � f costð Þ X which is a purposeful function, ci ¼ 1:0 þ si ∙ gi ð Þ X jestli gi ð Þ X >0, nebo ci ¼ 1 jinak si ≥1, bi ≥1; min ð Þþ f Xð Þ a>0:

The individual parameters have the following meaning: a ensures load function f Pgð Þ<sup>t</sup> ; x tð Þ � � take negative values. Parameter <sup>a</sup> is set to high. Constant si is applied to the functional transformation, and bi is searching for duplicate hypersurfaces. Limited values gi ð Þ X will be lower than higher for values si and bi. Very often with parameters like s=1 and b=1, the penalty works satisfactorily. This is an external penalty function that links penalties with condition violations. Penalties only apply outside of acceptable solutions. The external penalty is the one that uses exceeding quadrate measures as a penalty [21]. We have a limited minimisation function [22]; then

$$\min f(\mathbf{x}); \mathbf{g}\_i(\mathbf{x}) \le \mathbf{0}, i = \mathbf{1}, \dots, m; h\_j(\mathbf{x}) = \mathbf{0}, j = \mathbf{1}, \dots, l, j$$

We will replace

$$\min f(\mathbf{X}, \mathbf{g}) = f(\mathbf{X}) + a \sum\_{j=1}^{l} h\_j^2(\mathbf{X}) + a \sum\_{i=1}^{m} \left(\mathbf{g}\_i\right)^2(\mathbf{X}) \tag{29}$$

where a ¼ a1, a2, …, a ! ∞ apr hjð Þ¼ x 0, j ¼ 1, …, l; we will get

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

g xð Þ¼ <sup>i</sup>ð Þt ∑

where xiðÞ¼ t ð Þ x1ð Þt ; x2ð Þt ; …; x7ð Þt :Dependency x

represents the energy consumption forecast for a given hour.

depends on the state of the source at a given hour,

where ∑Ng

Zero and Net Zero Energy

source at time t.

2.4 Penalty function

unsolicited power supply:

ited values gi

We will replace

then

74

it has a non-zero value and is positive.

Parameters i ∈ 1; 2; …; Ng

Ng

i¼1

sources in our microgrid (which is 7). Variable t∈ f g 1; 2; …; T represents the time the connected sources spend in the defined mode, and Pgið Þt is the output of the

The optimisation algorithm works with acceptable but inadmissible solutions. The penalising function is zero in terms of standard requirements. For one criterion,

If we add a penalty function to the cost function, then we get an algorithm that is only optimally suitable for local searches in terms of effectiveness. We see this if we exit from [19, 20]; then we can apply a suitable approach to penalising cost functions. In the first instance Let us define meanings. Definition 1: Consider functions f, g, and suppose some values of the function g (x) belong to D (f). To every such value u ¼ g xð Þ∈ D fð Þ, assign y = f (u) = f (g (x)). This defines the function

h (x) = f (g (x)), which we will call function f, g and mark it h=f � g Note: G is the first function and the second is F. The penalising function is the function of

where x tðÞ¼ <sup>X</sup> <sup>¼</sup> f g <sup>x</sup>1; <sup>x</sup>2; …; xD ,D= 7 minimises the function f Pg ð Þ<sup>t</sup> ; x tð Þ � � �

The individual parameters have the following meaning: a ensures load function f Pgð Þ<sup>t</sup> ; x tð Þ � � take negative values. Parameter <sup>a</sup> is set to high. Constant si is applied to the functional transformation, and bi is searching for duplicate hypersurfaces. Lim-

parameters like s=1 and b=1, the penalty works satisfactorily. This is an external penalty function that links penalties with condition violations. Penalties only apply outside of acceptable solutions. The external penalty is the one that uses exceeding quadrate measures as a penalty [21]. We have a limited minimisation function [22];

ð Þ X will be lower than higher for values si and bi. Very often with

ð Þ x ≤0, i ¼ 1, …, m; hjð Þ¼ x 0, j ¼ 1, …, l,

<sup>j</sup> ð Þþ X a ∑

m i¼1 gi � �<sup>2</sup>

l j¼1 h2 Ym i¼1 c bi

ð Þ X jestli gi

<sup>i</sup> (28)

ð Þ X >0, nebo ci ¼

ð Þ X (29)

f Pg ð Þ<sup>t</sup> ; x tð Þ � � <sup>¼</sup> ð Þ f Xð Þþ <sup>a</sup> <sup>∙</sup>

f costð Þ X which is a purposeful function, ci ¼ 1:0 þ si ∙ gi

1 jinak si ≥1, bi ≥1; min ð Þþ f Xð Þ a>0:

min f xð Þ; gi

min f Xð Þ¼ ; g f Xð Þþ a ∑

where a ¼ a1, a2, …, a ! ∞ apr hjð Þ¼ x 0, j ¼ 1, …, l; we will get

<sup>i</sup>¼<sup>1</sup>Pixið Þ<sup>t</sup> represents the state of the power generator at time <sup>t</sup> and <sup>γ</sup>ð Þ<sup>t</sup>

� � stand for source indexes. NG represents the number of

PixiðÞ�t A tð Þ≥ 0 (27)

! ðÞ¼ <sup>t</sup> ð Þ <sup>x</sup>1ð Þ<sup>t</sup> ; <sup>x</sup>2ð Þ<sup>t</sup> ; …; <sup>x</sup>7ð Þ<sup>t</sup>

$$\min f(\mathbf{x}, \mathbf{g}) = f(\mathbf{x}) + a \sum\_{i=1}^{m} \left(\mathbf{g}\_i\right)^2(\mathbf{x}) \tag{30}$$

When applying definition 1, limiting the conditions (27) and the relationship (28) to the target function fg Xð Þ or by applying definition 1 and conditions (27), (29) and (30), we get a modified algorithm [23] as follows:

$$f\mathbf{g}(X) = f(X) + a\mathbf{g}^2(X) \approx \min \tag{31}$$

where ag2ð Þ <sup>X</sup> is the so-called penalty of the non-required electrical power supply. Because <sup>g</sup><sup>2</sup> is a negative number, there is a power when <sup>γ</sup>ð Þ<sup>t</sup> <sup>&</sup>gt; <sup>∑</sup><sup>i</sup> Pgixið Þt . The function value of the target function (31) must be artificially reduced or increased; then w (31) are the same in the algorithm (31).

We are looking for an <sup>x</sup> allowing us to minimise functions f Xð Þþ ag2ð Þ <sup>X</sup> :In such case we solve Eq. (31) by minimising cost function f(X) and maximising the penalty defined as function ag<sup>2</sup>ð Þ <sup>X</sup> . The result of summing the two functions up is the following function, fg:

$$f\mathbf{g}(X) = f(X) - a\mu(\mathbf{g}(X))\tag{32}$$

We used the minus sign in algorithm (32) as we intend to maximise functional prescription μð Þ g Xð Þ : Function g xð Þ defines the output stability of the system, which is why we may set it to zero. This function thus ranges from 0 to 1 and μ is fuzzy zero. Both constraining conditions (31) and (32) may be compared, and the most suitable definition of the constraining conditions may be selected.

When function fg Xð Þ approaches the minimum, which is our intent, we achieve a stable power output balance. Our objective is to minimise both the operation costs and the deviation of production from consumption.

Note: If the power consumption of a given area of "Rohanský ostrov" smart urban area is higher than the production, there will be a minus sign on the right side of Eq. (27) (it will be a negative number). Then we will focus on mathematical expression (28); if the value of expression (27) is very small, that is, close to zero, we have achieved a suitable solution.

Experimental solution:

	- a.We set a low permissible deviation between power generation and consumption.
	- b.We define the source organisation so that the required output at a given time was as near as possible to the required consumption.
	- c. We accept a small permissible deviation which we mark ΔP (Figure 8) and accept expression (33), which is the function of the chart showing negative and positive slope.

Let us define the membership function as X ¼ 0, which is a classical set, and μA : X ! h i 0; 1 as the representation [21]. A fuzzy set will then be a

microgrid at a distance of up to 50 km from our fictitious urban area. Continuous and reliable power supply is provided by two high-voltage lines with various switchboards guided from both independent directions. Table 1 lists the costs,

Electricity consumption estimates are based on the values of the total usable floor area of all the buildings in the area, and for the estimation of electricity type consumption, specific consumption and consumption values of electricity for months per year for individual types of buildings and the total electricity consumption per year are given in Table 2, including financial costs [26–28]. Table 3 shows

Unit State PN A B C

FV1 1 140 190 0.50 170 FV2 0 260 190 0.50 230 FV3 0 100 190 0.50 123 FV4 1 50 190 0.50 110 FV5 1 4 190 0.50 95 Biomass 1 1 300 0.40 173 Cogeneration plant 0 1–4 80 0.10 85

[Off/on] mw [CZK/MW] [CZK/MW2

] CZK

characteristics and technical constraints of individual sources.

Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

Note: Pn is the output rate of the RES-based power plant with a simulation of 0.7.

] is the specific electricity consumption per floor area in m<sup>2</sup>

is electricity consumption per year, PPV [kWp] is photovoltaic power."

Building types and their specific and total consumption.

, Wp, year [kWh / m<sup>2</sup>

], Wsp [kWh]

RES parameters in micro-networks (local RES) [8].

Table 1.

"Note: Wp [kWh / m<sup>2</sup>

Table 2.

77

coordinated pair A ¼ ð Þ X; μA : Set X will be the universe of fuzzy set A, and μA will be the membership function of fuzzy set A. For each x∈X,real number μA xð Þ is the level or degree of the membership of element x in fuzzy set A; μA xð Þ will be interpreted the following way:


In our case, g(X) expresses the deviation of the stable output balance which is why we seek to set it to zero. Number x∈X is selected arbitrarily from fuzzy set A, and μg is a function of fuzzy set A (where the admissible deviation is defined). It is obvious that for each x∈X, real number μ (g (X)) may be called the membership level or degree of element x in fuzzy set A.

We describe and compare the expressions x � g Xð Þ and μA Xð Þ� μð Þ� g Xð Þ . Then, μð Þ g Xð Þ can be expressed as follows:

$$\mu(\lg(\mathbf{X})) = (\Delta P - |\lg(\mathbf{X})|) / \Delta P \text{ in case when}$$

$$\mathbf{g}(\mathbf{X}) \in \langle -\Delta P, \Delta P \rangle \tag{33}$$

$$\mu(\lg(X)) = 0 \text{ in case when } \lg(X) \notin \langle -\Delta P, \Delta P \rangle \tag{34}$$

Expressions (33) and (34) and Figure 8 allow us to assume that ΔP¼0, by which the constraining condition is fulfilled (see μðð Þ¼ g Xð Þ 1). Eq. (32) is optimised by its subsequent minimisation or maximisation (μ¼0 ǎz 1). Fuzzy number "μ" will always be small, and we may achieve that using number a (therefore we maximise function f(X)). At this moment, we may say that we have solved the optimisation of our task for the purposes of other applications, for example, in order to minimise the special-purpose function.

### 3. Experiment

Let us assume the fictitious smart city (intelligent area of Rohan Island) which consists of a complex of intelligent residential, administrative and public buildings with a wide range of civic amenities (Figure 1).

The energy concept of the area under consideration is clearly focused on local renewable energy sources (FV1, FV2, FV3, FV4 and FV5) assembled together with biomass and cogeneration systems (Figure 2), including TS-DS 22/0.4 kV power station, RMS, (Figure 2), located in the underground floor of KU02. This is a RES

#### Optimising Energy Systems in Smart Urban Areas DOI: http://dx.doi.org/10.5772/intechopen.85342

microgrid at a distance of up to 50 km from our fictitious urban area. Continuous and reliable power supply is provided by two high-voltage lines with various switchboards guided from both independent directions. Table 1 lists the costs, characteristics and technical constraints of individual sources.

Electricity consumption estimates are based on the values of the total usable floor area of all the buildings in the area, and for the estimation of electricity type consumption, specific consumption and consumption values of electricity for months per year for individual types of buildings and the total electricity consumption per year are given in Table 2, including financial costs [26–28]. Table 3 shows

