**10. Drawing up a combined GES scheme**

The combined scheme in **Figure 14** allows one to obtain a high-quality *SN* recognition model in view of the mutual reflection of *GOCP* ≈ *ΣGRPA* and the possibility of comparing *SOCP(t)* and *SRPA(t).* From a comparison of the parts of **Figure 14**, it follows that the synchronous detector is a 'central' element in the GESOC*P* scheme. It is known that a synchronous detector consists of a comparing element based on the multiplication or summation, a zero component filter and a threshold device. The filter turns out to be feedbacks from the *UOUT* output to the common adder. When replacing the elements covered by feedbacks in **Figures 7** and **10** with the transfer function, a more general OCP scheme is obtained in the form of a unidirectional *SN*→TS formation tree (**Figure 14**). The scheme makes it possible to solve modelling problems and smart grid information tasks [7–16].

*Automatic Control of the Structure of Dynamic Objects in High-Voltage Power Smart-Grid DOI: http://dx.doi.org/10.5772/intechopen.91664*

**Figure 14.**

*Structural schemes of GESOCP and GESRPA by signal* S(t) *and GOCP* ≈ *ΣGRPA.*

The minimum information for constructing an OCP model are two elements of the *i*OCP information part—a selective TS and a blocking TS. Also, the bundle—the signal source *SOCP(t)*and the controlled frequency generator—will be the minimum OCP model [11–13]. The generator can have amplitude, frequency and phase modulation of the output signal from the super-LFC to HFC range, depending on the problem being solved. Such OCP models minimise the time required for a single calculation. Thus, models of the OCP, RPA devices and S-detector were built. The *SOCP(t)* recovery algorithm from the OCP model can be used to decrypt the accumulated emergency files (**Figures 11**–**13**). For this, models of the ExS expert system and the diagnostic message generator are used (**Figure 4**).

### **11. Balancing structures and algorithms using game theory**

A 'balancing' task arises when considering GES schemes (**Figure 14**). According to *GOCP* ≈ *ΣGRPA*, it is possible to set the 'balance' task for the GESOCP scheme as well. The solution of the 'balancing' problem is a development of the theory of the SI method [8–11]. A numerical determination of the equilibrium point of GES schemes is proposed when considering the 'For-Against' problems for OCP and 'selectivity-blocking' using the game theory method [14]. The result is compared with the published solution through the method of dynamic functional modelling [11, 17]. This section briefly discusses the algorithm for solving the problem, designed in the form of a computing module. The problem when using computational modules is the possibility of a multivariate interpretation in the formulation of the problem and in the analysis of the results. The following aspects of the problem have emerged—(a) the need to be an expert in the specific problem being solved; (b) being sure of the possibility of using the module to solve the particular problem; and (c) it requires the presence of training and supervising samples of real semantic situations for testing and verification of results. Experience of using the module can be gained on the basis of modelling in CAD.

In the 'balancing' game, the competitors are the two root weights, *KSS selectivity* and *KSB blocking*, where the corresponding root characters are *SSS* and *SSB*. The contest is won (victory) *V*, when there is a clear victory for *KSS* or *KSB*—the correct operation of the threshold element ρN. It is lost *L* if there is 'error excessive response ρN'. The competitors have the following features, aimed at implementing the requirement to increase the stability of RPA devices in complex *SN* situations. The *KSB blocking* group always fights 'compete *KSS* and *KSB*' until they win: 'The *SSB(t)* signal is greater than *SSS(t)*' of the *blocking* group and retreats with 'error excessive


#### **Table 1.**

*Payment matrix of the participants in the 'balancing' game with example.*

operation ρN' in the case of serious injuries, with 'error excessive failure ρN'. The *KSS selectivity* group is limited by the threats of winning: 'The *SSS(t)*signal is greater than the threshold ρN'; however, if it gets to a 'complex *SN*' bout, the *selectivity* group recedes, with 'error excessive ρN failure'.

Thus, there are four game options. These appear more pronounced in a difficult *SN* situation, when there is little information for the correct operation of the threshold element ρN. The results of the game are evaluated in the form of arbitrary units (points) received or lost by the participants.

In the 'grammar *G* of one of the devices' population, we denote the share of the *blocking* group with z, and then the fraction of the *selectivity* group will be 1–z. If two competitors *KSS* and *KSB* are randomly participating in a 'one of the *SN* situations' clash, then with a probability of z × 2, they are two *KSB*; with a probability of (1–z) × 2, they are two *KSS*; and with a probability of 2 × z × (1–z), they are *KSS* versus *KSB*.

Let us designate the parameters of the 'balancing' game as damage from injury *W*, 'error excessive failure of ρN' and energy consumption *E* for the opposition 'operation-failure of ρN'. We will assume that in the 'balancing' game, the winning 'correct work ρN' is estimated as follows (**Table 1**)—victory *V* = 75 points, loss *L* = 5 points, damage from injury *W* = 150 points and energy consumption for opposing *E* = 5 points. Let us find the average number of points that competitors *KSS* and *KSB* get as a result of the 'one of the trainings *SN*' fight. The results of the 'balancing' game can be visualised in the form of a payment matrix (**Table 1**). Based on **Table 1**, on average for the *blocking* group, we get

*SB*(z) = *SH*(z) = 0.5 × (*V–W*) × z + *V*×(1*–*z) = *V–*0.5 × (*V* + *W*) × z = 75–112.5 × z. Similarly, for the *selectivity* group, we get.

*SS*(z) = *SD*(z) = *−L* × z + [0.5 × (*V–L*)*–E*] × (1*–*z) = 0.5 × (*V–L*)*–E–*[0.5 × (*V* + *L*)*–E*] × z = 30–35 × z.

The graphs of these equations in the *S–*z coordinate axes are shown in **Figure 15**. As can be seen, the winning lines 'correct work of ρN' for the groups *selectivity KSS* and *blocking KSB* intersect at the equilibrium point Ω defined by the relation:

Ω = 75–112.5 × z = 30–35 × z, z = 45/77.5 = 0.58.

**Figure 15.** *Graph of the winning line of the participants in the 'balancing' game.*

*Automatic Control of the Structure of Dynamic Objects in High-Voltage Power Smart-Grid DOI: http://dx.doi.org/10.5772/intechopen.91664*

In **Figure 15**, we choose the reliability point zRELIABILITY = 0.8 × z = 0.8 × 0.58 = 0.464. At this point, we put *SS*(z)/*SB*(z) = *KSS/KSB.* The ratio *kR* = *KSS/ KSB* = 13.76/22.8. Then.

*KSS* = *kR*/(*kR* + 1) = 0.356, *KSB* = 1/(*kR* + 1) = 0.624.
