Bases of calculation and design of asynchronous diesel generators for autonomous system of power supply

The article discusses the characteristics of diesel generator sets currently used in autonomous power supply systems. The modes of operation of synchronous generators and their overload capacity are analyzed. The overloading capacity of diesel generator sets (DGS) can be significantly increased when used as an electromechanical energy converter of asynchronous generators (AG). The initial algorithm for their selection involves calculating the optimal value of the rotor speed and choosing the range of rotation frequency. The value of the optimal value of the rotational speed is determined depending on the method of maintaining the constancy of the current frequency when calculating the parameters of an autonomous asynchronous semiconductor cascade, which is understood as an AG together with its excitation and control system. The dependences of individual terms of electrical power losses on the operating mode of an autonomous asynchronous semiconductor stage are considered. After determining the optimal speed, the possible AG power is selected. Then, from a number of powers, its nominal power is selected. After determining the rated power, the minimum and maximum values of the rotational speed, it is possible to determine the optimal operating modes of the diesel generator set with the AG. As a criterion of optimality, the specific effective fuel consumption of the diesel generator set is taken. This approach to the choice of the type of diesel generator set when designing autonomous power supply systems requires a detailed consideration of the technical and economic characteristics of the units. The proposed design principles can ensure the most complete use of the positive properties of a diesel engine and an electromechanical energy conversion system, as a result of which to improve the technical and economic characteristics of autonomous power supply systems.


Introduction
The success of the operation of commercial and municipal facilities (CMO) largely depends on the uninterrupted operation of technical life support systems, the most important of which is the guaranteed power supply system (GES).
SGEP is designed to ensure uninterrupted supply of all consumers of KMO with electricity in accordance with established standards that determine the requirements for the quality of electricity in case of emergency outages from main sources.
As the most reliable and economical in such systems, diesel generator sets (DGU) with aggregate power from 5 to 4000 kW have become widespread. Synchronous machines (SM) [3] are used as  [3], which sometimes perceive uneven and unstable load, which are harmful modes for the operation of the generator.
The article proposes a method for adjusting the SGEP generator to a sharply variable characteristic of the network using an asynchronized generator with a variable speed. The reliability and efficiency of the autonomous power supply systems depend significantly on the type and operating modes of the drive motor of the power source. The choice of the motor for the drive of synchronous (SG) and asynchronous (AG) generators should be made on the basis of the characteristic features of their operation. For any type of generator, the correct choice of the engine provides for a detailed analysis of its limiting and external characteristics together with the energy characteristics of the generator [1,2].

Materials and methods
Currently, autonomous power supply systems use, as a rule, diesel engines developed for transport installations. Such diesel engines have all-mode speed controllers п, which ensure stable operation in a wide range of п from п min to п max The characteristics of such motors can be as shown in Figure 1, where the еf curve represents the full external characteristic, the аb and dc curves are the upper and lower limiting characteristics. In accordance with the definitions of these characteristics, the figure of the аbcdа determines the field of possible modes that do not have any restrictions on the duration of work. The operation of the engine according to the external characteristic is possible only during the limitations on the duration of operation (up to 1-2 hours). In this regard, the shaded areas of the figure еf3dе should be understood here as a field of modes in which the duration of continuous operation and the total operating time during operation are limited. All modes falling into this shaded field can be considered as overload modes; knowing this, you can choose the power and speed of the drive generator [3,4]. And in Figure 2 shows a universal characteristic and the field of possible modes of operation of a diesel engine with an asynchronous generator (AG).   When using a synchronous generator, its rotation frequency nc is selected depending on the number of pairs of generator poles and the frequency of the generated current f. So, at f = 50 Hz, the synchronous rotation frequency n c can take one of the following values: 3000, 1500, 1000, 750, 500, 375, 300, 250, 200 rpm, etc. Based on the mass requirements -the overall parameters of the power plant, the value of n c is selected (it is obvious that п min < n c < п max ) and then the possible rated power of the generator Р nom is determined [5]. Figure 1 it is clearly seen that at n c the rated power of the generator can be equal to P' nom = N е2 η g (1) where N е2 -engine power according to the limiting characteristic at п = n c ; η g -generator efficiency.
After determining Р' no m , the nearest Р nom is selected from the range determined by GOST 12139-84, subject to the condition Р no m ≤ Р' nom . In the case of using SG, diesel engines must operate according to the regulatory characteristic with a slope of 2-6%. Moreover, the regulator is usually adjusted so that п = п с at N e ≈ 0,5 N eном where N enom = Р nom /η g . Thus, the field of possible modes of operation of a diesel generator (DG) is narrowed to a narrow band, indicated in Fig. 1 hatched line 51'2'34 '. It can also be seen here that, due to the slope of the regulatory characteristic, the overload capacity of the DG slightly decreases (the power at points 2 'and 4' is less than at points 2 and 4). The maximum power of the DG at overload N n is determined from the condition N e nom < N п < N e max (2) The overload capacity of diesel generator sets (DGU) can be significantly increased when used as an electromechanical energy converter AG [6][7][8][9][10]. The peculiarity of such diesel generators is the ability to operate with variable speed and the algorithm for their selection is as follows. At the beginning, the optimal value of п opt is calculated and the range of change in the rotational speed Δn is selected. The value of п opt is determined depending on the method of maintaining the constant frequency of the current f at n=var when calculating the parameters of an autonomous asynchronous semiconductor stage (AAPC), which is understood as an AG together with its system of excitation and control. Energy is supplied to the AG stator in two ways: electromechanically from the internal combustion engine shaft and electromagnetic through the rotor circuit from the excitation system. Generator electromagnetic power [10][11][12] Р el = N e + Р el , (3) where N е -is the effective power of the diesel engine (mechanical power); Р el -electrical power of the excitation system. The components of the electromagnetic power are: At a synchronous rotation frequency (п=п с ), s=0 and N e =Р e . If s ≠ 0, then the change in the mechanical energy supplied to the AG rotor should be compensated by the change in the power supplied from the excitation system. Since in AAPK the excitation energy of the AG is also obtained due to the effective power of the engine, then N e = P g +∑ΔР, (6) where P g -generator power ΔР -the sum of all losses in the AAPC. Let us consider the dependences of the individual terms ∑ΔР on the AAPK operating mode. Additional and mechanical losses in the AG ΔР д.м АГ depend on the AG power and its rotor speed. This dependence can be represented as where ΔР a.m AG(0) -additional and mechanical losses of AG at s = 0; k -coefficient of proportionality.
Additional and mechanical losses in the pathogen ΔР a.m.p depend on the power of the pathogen in about the same way as in the AG. If we also take into account the fact that the power of the pathogen depends on Δn, then  Losses in the excitation system of the exciter ΔР e.e in the general case, the greater, the lower the rotor speed n r of the exciter, since with a decrease in n r it is necessary to increase the excitation current. They can be represented as ΔР e.e = ΔР e.e(0) (1+s)γ, (9) where ΔР e.e(0) -losses in the excitation system of the exciter at s = 0; γ -coefficient of proportionality. The losses in the exciter can also be represented as where ΔР exc(0) -losses in the exciter at s = 0; β -proportionality coefficient, taking into account the scheme and operating mode of the exciter at the current sliding module | s | [10][11][12][13].
Stator copper loss ΔР c.s , rotor ΔР c.r. losses in the stator steel ΔР s.s. are practically independent of slip. Losses in rotor steel ΔР s.r. proportional to the rotor current frequency f r and can be represented as: ΔР s.r. = ΔР s.r(1) q |s| (11) where ΔР s.r(1) is the loss in the rotor steel at s = 1; q -proportionality coefficient.
These losses can be represented as the sum of all losses in AG ∑ΔР AG = ΔР a.m AG (0) (1+ k)+ ΔР c.s + ΔР c.r + ΔР s.s (13) and losses in the AG excitation system ∑ΔР exc = ΔР a.m.p (0) (k+ αΔs+ α)+ ΔР e.e(0) γ+ ΔР inv + ΔР exc(0) β (14) In accordance with the accepted designations of efficiency: AG η AG , excitation systems AG η exc and AAPC η AAPC can be expressed by the equations: where |Р r | -active power module of the AG rotor, as a sum Р r = Р r(0) + Р g s (16) In the formula (16) Р r(0) -the active power of the rotor at s = 0. The formula for η ААPC taking into account (15) The active power of the rotor Р r together with the reactive power Q p determine the total power 2 2 r r HP Q  of the synchronous exciter, which in turn determines the mass, dimensions and efficiency of the AG excitation system. The synchronous exciter is selected so that its rated apparent power H nom is not less than the required Н max (H nom >H max ) at s = s max .
In this case, at s ≠ s max , a decrease in η c.в will take place. and the more, the greater the difference |s| from | s max |. Thus, it can be shown that η s.exc. = f(Δs). Considering that the synchronous exciter and the inverter are series-connected elements of the excitation system η exc = η s.exc. η inv , where i η inv -the efficiency of the inverter, which depends on s, i.e., η inv = f 1 (s).  f(s, Δs). The complex nature of the dependence η ААPC = f(s,Δs) does not allow to unambiguously determine the optimal slip values s opt and the range of its change Δs. Therefore, first of all, in DGS with AG, the synchronous rotation frequency п с is selected.
Then, according to equation (17), taking into account dependence (18), they are determined by the values of η ААPC for different s. The optimal value is taken as s = s opt , at which η ААPC reaches a maximum, and from s opt it is determined n оpt =n c (1+ s opt ) (19) Then, knowing Δs or setting its values in relation to s opt , we find s opt , at which the average value of η ААPCΔs reaches a maximum. The values of s and Δs are chosen optimal if the product А = η ААPC η ААPCΔs reaches its maximum (A = A max ). After determining n оpt , the possible power of the AG is determined where N е2 -the effective engine power in terms of the limiting characteristic at п = n оpt (ordinate of point 2 in Figure 2).
Then the rated power of АГ Р nom is selected from a range of capacities. Here it is only necessary to fulfill the following condition: where N' еnom -the engine power according to the limiting characteristic; η ААPC -efficiency at п = n мах (s = s мах ). Suppose that the selected nominal power of the AG corresponds to the engine power N еnom , determined by the ordinate of point 1 in Fig. 2. According to the value of this power, п min is determined based on the need to ensure stable operation of the diesel engine in the event of a surge in the rated load on the engine operating at N е =0 and п=n min . This condition can be fulfilled if, at п = n min , the engine power according to the external characteristic is N е ext >N еnom . Then It is known that if the stability of the current frequency f in a diesel generator set with an AG is ensured in the zone of variation of the rotational speed 0,5 n с < n < 1,5 n с , then at п' тiп <0,5 n с the value

Results and discussion
After determining Р nom , п тiп and п тax , it is possible to determine the optimal operating modes of the diesel generator set with AG. As a criterion of optimality, it is advisable to take the specific effective fuel consumption of diesel generators. Knowing the economic characteristics of a diesel engine and AAPC, it is possible by calculations to estimate the effective efficiency or specific effective fuel consumption of the diesel generator set b i at various speed and load modes and build lines of equal specific costs (isolines) in coordinates N en. Typically, such isolines have the form shown in Fig. 2 by thin lines, where b 1 < b 2 < b 3 <…< b n . With the known dependences b=f(N e , n), it is graphically or analytically easy to determine the law of optimal regulation in Figure 2, which is represented by the БВ line passing in the zone of minimum specific fuel consumption. Taking into account the limitations of the limits of the change in the speed of rotation, the regulation of n in the entire range of variation of N e will be optimal along the АBCD line, where the AB and CD lines are regular characteristics at the setting п тiп and п тax , respectively. A narrow strip in the vicinity of the shaded line ABCD represents the field of optimal operating modes of the DGS and AG.
When operating a diesel generator set with optimal speed control, not only high efficiency is achieved, but also its overload capacity is significantly increased. This is clearly seen when considering Figure 2. Here, the part of the field of possible modes of operation of DGS with AG, limited by the figure 15D31, differs in that N e > N eном and can be considered as a field of overload modes. At the same time, some part of the field of overload modes of the diesel generator set lies below the limiting characteristic of the engine. In connection with these overloads of DGS with AG, it is advisable to divide into two groups -allowing long-term operation and short-term. The magnitude of the short-term overload can be determined by the formula max () max max AAPC n n e sh t nom enom AAPCnom Here N e max -the diesel power according to the external characteristic at п = n max ; η ААPC(п= nmax) and η ААPCnom -efficiency of AAPK at N e max and N e nom , respectively. The installed capacity of all diesel generators in an autonomous power supply system should, in addition to providing consumers, allow maintenance of individual diesel generators without interrupting the power supply to consumers. Therefore, the total rated power of the DGS 1 ins n nom i P   is chosen so that when the most powerful DG is stopped, the remaining operating power will provide reliable power supply to consumers. For this purpose, the following conditions must be met: where n уст -the number of installed diesel generators; max nom P -the rated power of the most powerful DG. P base -base generator power.