SELECTION OF VOLTAGE, FREQUENCY, AND TIME SETPOINTS FOR AN AUTOMATIC SEPARATION DEVICE OF A CHP PLANT

Postgraduate Student V. I. STAROSTIN

At present, a process is under way of merging individual power systems into unified ones. In many cases, power systems are interconnected by weak intersystem ties. In the absence of main intersystem lines at voltages of 400–500 kV, such ties are, as a rule, double-circuit 110 kV transmission lines supplying substations of an electrified railway. In this case the exchange-power flows between power systems are relatively small, since their limit is determined by the static-stability margin.

Changes in intersystem power flows, irregular oscillations caused by traction loads, disconnection of large generating capacities, and sudden application of large loads can lead to a violation of static stability and, as a consequence, to a deep drop in voltage and frequency. Statistics show that during 1960–1962, in the unified power system of Western Siberia alone, 26 cases of stability violations of intersystem power transmission lines were recorded [1].

At the CHP plant under study, operating conditions caused by loss of static stability in the power system and by a sharp decrease in voltage and frequency were repeatedly created, one of which led the CHP plant to a complete shutdown. The process of oscillation of frequency and voltage, when they decrease simultaneously, has a strong effect on the operation of auxiliary-service mechanisms and, above all, on the operation of feedwater electric pumps. This is explained by the fact that they have a fan-type resisting torque and operate with a large back pressure.

Modern high-pressure boiler units with a small drum volume, operating together with electric feed pumps 5Ts-10 or other high-pressure pumps, even with a slight loss of pump capacity caused by a decrease in the number of revolutions, must after a few minutes be disconnected from the steam lines when the limiting lower water level in the boiler drums is reached.

Thus, the question of automatic separation devices (ASD) in the scheme of electrical connections must acquire considerable importance and be regarded as a measure for improving the reliability of power-system operation.

The following requirements must be imposed on automatic separation devices (ASD) existing at a number of power stations:

1. The ASD must automatically separate one generator or several generators onto the station-service buses and separate consumer blocks for their independent operation from the grid.

2. The operating time of the ASD must be such that it is not actuated by disturbances of system operating conditions that do not threaten shutdown of the boiler units, and so that it operates before the boiler units must be shut down as a result of loss of output of the feed electric pumps.

3. The ASD must be reliable, simple to operate and adjust, and must possess universality.

It is appropriate to note that instantaneous application of a command pulse for ASD operation under emergency conditions is inadmissible for the reason that any separation of generators is associated with disturbance of the existing balance of active and reactive powers, which places the remaining system under still more severe conditions. In addition, the real possibility of failure of some control circuit of the circuit-breakers increases, taking into account the great branching and responsibility of the ASD circuits.

In practice there have been cases in which a disturbance of the operating condition of the power system was restored faster than the time setting assigned for the ASD, and therefore unnecessary operation was prevented.

Since the personnel of power stations and of the Central Relay Protection and Automation Service experience difficulties in selecting voltage, frequency, and time settings for the ASD, this article proposes a fundamentally new method of selection, taking into account the operating conditions of the electrical scheme and of the thermomechanical equipment of the station-service auxiliaries of power stations. In selecting the settings, the analysis is based on a graphical-analytical calculation for a specific typical high-pressure CHP plant, and it can be used for other analogous CHP plants. For power stations having modes, equipment, scheme, and layout different from the calculated ones, the calculation method may be used.

For analysis of the operation of the feed installation together with the boiler units, two problems should first be solved:

1. Determine the torques of the electric motor of the feed installation at nominal parameters and at reduced values of voltage and frequency.

2. Determine the resistance torques of the feed pump as a function of the rotational speed.

Determination of the Torques of the ATM-2000-2 Electric Motor and the Resistance Torques of the 5Ts-10 Pump

At high-pressure CHP plants, as the drive for 5Ts-10 feed pumps, the ATM-2000-2 electric motor has become predominantly widespread: 2000 kW, 3000/6000 V, 2980 rpm, 460/230 A.

This electric motor has two versions: manufactured by Sachsenwerk (GDR) and by the Novosibirsk Turbogenerator Plant (NTGZ). The characteristics of the electric motors of both versions almost coincide, which leads to identical electromagnetic torques within the range of slip from \(S = 0\) to the critical \(S = S_k\) (the stable part of the characteristic). Since, in calculating the values of the torques, they are required only within this slip range—

…then in this case they may be considered of the same type, disregarding a certain difference in the starting characteristic.

The construction of the basic characteristic \(M=f(S)\) is carried out on the basis of catalog data and factory tests in no-load and short-circuit conditions. It should be noted that finding the reduced active resistance of the rotor and the inductive resistances of the rotor and stator by the method proposed by I. A. Syromyatnikov [2], at two values of slip \(S=0\) and \(S=1\), is considerably more accurate than with other known methods. This is especially true of ATM-series electric motors, which have small operating slips and possess a whole series of special features (the phenomenon of saturation and displacement of current in the rotor cage, the influence of the magnetic bandage).

The calculation of the curves \(M=f(S)\) was performed for nominal values of phase voltage and frequency, reduced voltage values \((0.9U_{\text{н}},\ 0.8U_{\text{н}},\ 0.7U_{\text{н}})\) and nominal frequency, reduced frequency values of 49, 48, 47, 45 Hz and nominal voltage, and, finally, for the most frequently encountered case, when voltage and frequency are reduced simultaneously in such a way that

\[ \frac{U}{f}=\text{const}. \]

In determining this dependence, one may use the simplified formula for the ratio of the torque to the nominal torque

\[ m=\frac{M}{M_{\text{н}}} = \frac{ 2b_{\text{н}}\cdot \dfrac{K'_u}{K'_f} }{ \dfrac{S_k}{K_f S}+\dfrac{K_f S}{S_k} } \tag{1} \]

\[ K_f=\frac{f}{f_{\text{н}}} \quad\text{— frequency ratio;} \]

\[ K_u=\frac{U}{U_{\text{н}}} \quad\text{— voltage ratio;} \]

\[ b_{\text{н}} \quad\text{— ratio of the maximum torque, determined graphically from the curve } M=f(S) \text{ at nominal voltage and frequency;} \]

\[ S_k \quad\text{— critical slip, determined graphically for the nominal operating condition or by the formula:} \]

\[ S_k= \frac{G_1 R'_{20}} {\sqrt{R_1^2+\left(X_1+C_1X'_2\right)^2}} \tag{2} \]

Figure 1 presents a series of curves \(M=f(S)\) at nominal and reduced values of voltage and frequency. To make it possible to study the starting conditions of reserve pumps, in addition to these voltages a phase voltage equal to \(0.925U_{\text{н}}\), i.e., 3210 V, was adopted, to which there corresponds a proportional reduction of frequency to 46.25 Hz.

To determine the pump resistance torques at different speeds, it is necessary to calculate the operating conditions of the feedwater installation. At the CHP plant under study, 10 boiler units of the TP-230 type are installed, with a nominal capacity of 230 t/h, a nominal drum pressure of 110 ata, and a superheated-steam temperature of 510°. The feedwater installation consists of 9 feedwater electric pumps of type 5Ts-10, with a guaranteed capacity of 270 m³/h and

Fig. 1. Dependence of the driving torque of the ATM-2000-s motor and of the resisting torque of the 5Ts-10 pump on slip at various values of frequency and voltage: curves 1—\(U_n\); 2—\(0.9U_n\); 3—\(0.8U_n\); 4—\(0.7U_n\); 5—49 Hz, \(U_n\); 6—48 Hz, \(U_n\); 7—47 Hz, \(U_n\); 8—45 Hz, \(U_n\); 9—49 Hz, 3400 [[unclear: unit]]; 10—48 Hz, 3330 [[unclear: unit]]; 11—47 Hz, 3260 [[unclear: unit]]; 12—46.25 Hz, 3210 [[unclear: unit]]; 13—45 Hz, 3120 [[unclear: unit]]; 1–7—353, 334, 300, 260, 220, 180, 140 t/h.

with developed head of 1570 m w.c. The minimum pressure in the feed main is 130 atm. The temperature of the feedwater in the pump is 158°C.

The feedwater installation in normal operation works according to a rational schedule, in which the selection of the number of operating pumps is reduced to determining, for various feedwater flow rates, the operating modes of the feed electric pumps with the minimum expenditure of electric power for their drive.

The calculated operating modes of the feedwater installation are taken as: minimum—the capacity of one pump, 140 t/h; maximum—the capacity of one pump, 334 t/h. The maximum, most severe, mode is fixed from the materials of the technical department and, as a rule, coincides with one of the last months of the year.

Such a mode occurred in December, when all 10 boiler units at the station were operating with a total capacity of 1910 t/h. In this case, taking into account 5% continuous blowdown, the quantity of water pumped will be 2012 t/h.

For this quantity of feedwater, on the basis of the rational schedule, 6 pumps were in operation, each with a capacity of 334 t/h.

The calculation of the operation of the feedwater installation under disturbances of the operating mode due to a decrease in frequency and voltage is based on a graph of the dependence of the pump head, power, and efficiency on the feedwater flow rate. The pump characteristics are taken, on the one hand, from the factory characteristics of the 5Ts-10 pump, which passed stand tests, and, on the other hand, from the test materials for the same type of pump having the lowest efficiency. From the data of these tests, averaged characteristics \(Q-H\), \(Q-P_2\), \(Q-\eta\) were constructed, shown in Fig. 2 by thick lines. Consequently, the selected averaged characteristics between pumps with high and low efficiency reflect the operation of the entire feedwater installation and agree with the averaged characteristics obtained by ORGRES during testing of 5Ts-10 pumps at a number of power stations [3].

The construction of characteristics for different numbers of pump revolutions is carried out according to the proportionality formulas:

\[ \frac{Q_2}{Q_1}=\frac{n_2}{n_1}; \quad \frac{H_2}{H_1}=\left(\frac{n_2}{n_1}\right)^2; \quad \frac{P_2}{P_1}=\left(\frac{n_2}{n_1}\right)^3 \]

These families of characteristics are shown in Fig. 2. A complete characteristic of the operation of the feed pumps can be given only when the characteristic of the feed network is known. The working head developed by the pump consists of the static and dynamic heads and is expressed by the equation:

\[ H=H_{\text{st}}+H_{\text{dyn}} \tag{3} \]

The height from the pump axis to the water level in the drum is 28 m, and to the water level in the 6 ata deaerator is 20 m; then

\[ h_1\gamma=28\cdot0.91=25.5 \ \text{m w.c.}; \qquad h_2\gamma=20\cdot0.91=18.2 \ \text{m w.c.} \]

where \(\gamma\) is the density of water in t/m³.

\[ H_{\text{st}}=1090+25.5-50-18.2=1047 \ \text{m w.c.} \]

The dynamic head, which characterizes the resistance of the network, depends on the degree of opening of the feed valve with the unchanged state of the other valves in the feedwater tract. The degree of opening of the feed valve, controlled by an electronic automatic regulator, is deter-

Fig. 2. Dependence of head, power, and efficiency on the capacity of the feed pump at various rotational speeds.

is determined by the capacity necessary to maintain the constancy of the water level in the boiler drum. To determine the characteristic of the network with the feed valve fully open, the initial point of the main characteristic \(Q—H\) is chosen at a pressure in the feed network of 120 atm. The setting for starting the standby pumps is made for this pressure. If the pressure in the network is below 120 atm, the supply of water to the boilers practically ceases. Corresponding to this, the head developed will be equal to 1132 m water column.

In this case the throughput capacity of the feed valve is the greatest and is determined from the \(Q—H\) curve by a capacity of 353 t/h. Then the dynamic head is:

\[ H_{\text{dyn}} = H - H_{\text{st}} = 1132 - 1047 = 85 \text{ m water column}. \]

For this degree of opening of the feed valve, the head at any specified pump capacity is calculated by the formula:

\[ H = H_{\text{st}} + H_{\text{dyn}}\left(\frac{Q}{Q_{353}}\right)^2 \text{ m water column}. \]

For a degree of opening of the feed valve corresponding to another capacity, the head developed by the pump and the dynamic head are determined analogously. Figure 2 presents a series of parabolic curves characterizing the network for various degrees of opening of the feed valve. These curves proceed from the point of static head and terminate on the main characteristic \(Q—H\).

From the characteristics of the pump and of the network, a graph is constructed of the dependence of the resistance torques on the rotational speed:

\[ M = 0.975 \frac{P_2}{n} 10^3 \text{ kgm} \tag{4} \]

\[ P_2 = \frac{Q \cdot H}{102 \cdot 3600 \, \eta} 10^3 \text{ kW}. \tag{5} \]

The useful power on the shaft can be determined not only by calculation, but also from the \(Q—P_2\) curves for different rotational speeds. With a decrease in the rotational speed and the limiting degree of opening of the feed valve, the capacity will decrease to a value determined by the point of intersection of the speed characteristic with the network characteristic. For smaller values of the degree of opening of the feed valve, determined by the capacity in the range from 140 to 353 t/h, the calculation is performed in the same manner, and the resistance-torque curves are plotted in Fig. 1. The point of intersection of the curve of the driving torque and the resistance torque determines the rotational speed at which a specified pump capacity is ensured.

Using Fig. 2, one can construct a graph of the dependence of capacity on rotational speed. The construction is performed taking into account the limiting capacity of 353 t/h, from the points of intersection of the speed characteristics \(Q—H\) with the network characteristic. When the rotational speed of the pump is reduced below nominal, no loss of capacity will occur until the rotational speed corresponding to the point of intersection of the network characteristic, with the feed valve fully open, and the speed characteristic \(Q—H\) is reached. In this case the feed valve will begin to open to its limiting value. With a further reduction in rotational speed,

productivity will begin to decrease. This dependence is presented in Fig. 3.

The processes occurring in the feed-water installation can be analyzed after the weight of the water in the cylindrical layer in the boiler drum has been determined.

The normal level of the evaporation surface is 50 mm below the diameter of the drum. The limiting lower level is 180 mm below the diameter. Performing the necessary calculations, we determine the volume of water in this layer, equal to 2.88 m³. At \(t=316^\circ\) and \(\gamma=0.666\ \text{t/m}^3\), the weight of the water in the cylindrical layer will be:

\[ G = V \cdot \gamma = 2.88 \cdot 0.666 = 1.52\ \text{t}. \]

Dependence of the change in feed-water flow rate on the decrease in the turbine speed

The operating characteristics of steam turbines at power stations are calculated on the basis of the normal speed corresponding to the standard frequency of 50 Hz. The selected frequency variation range of 50–45 Hz entails a change in turbine speed from 3000 to 2700 rpm, and for such a decrease in speed it is impossible, directly from the regulating characteristics, to determine the change in steam flow rate, and consequently also in feed-water flow rate. In analyzing this dependence it is assumed that the heat load of external consumers and in-house auxiliary needs remains unchanged, and that district-heating turbines having extractions are considered as operating in the condensing mode.

The increase in the steam flow rate through the turbines when the speed decreases occurs for two reasons:

1. Due to an increase in the degree of opening of the turbine regulating valves.

2. As a result of deterioration of the turbine efficiency.

When the turbine speed decreases, their regulating system acts to open the regulating valves, owing to which the steam flow rate increases. The nature of the increase in steam flow rate is taken from the materials of factory tests of the regulating systems of various types of turbines installed at the CHP plant under study. Figure 4 shows the dependence of the travel of the servomotor of the high-pressure cylinder on the rotor speed of turbine VPT-25-3 [4]. As is seen from the graph, this dependence is expressed by the equation of a straight line not passing through the origin:

\[ n = KX + n_0 \tag{6} \]

where
\(n_0\) — a constant value equal to 3171 rpm;
\(K = \operatorname{tg}\varphi\) — the tangent of the angle of inclination, equal to \(-1.8\);
\(X\) — servomotor travel in mm;
\(n\) — the speed at which the servomotor travel is determined.

To construct the dependence of the steam flow rate through the turbine on speed, it is necessary to know the share of steam consumption accounted for by the turbine of the given type. With a total steam production of 1910 t/h for all 10 boiler units, the steam consumption by the turbines will amount to:

Fig. 3. Dependence of output on the rotational speed of the feed pump.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

VPT-50-2    350 t/h · 1 = 350 t/h
VPT-25-3    180 t/h · 4 = 720 t/h
VR-25     280 t/h · 3 = 840 t/h
    Total:      1910 t/h

For other values of the total steam extraction, there will be a proportional distribution of the steam load among the turbogenerators. Since the travel of the servomotor of the MCV has a linear dependence on the turbine speed and is determined by the tangent of the slope of a straight line, the dependence of steam consumption on rotor speed will therefore also be a straight line, for which the following linear equation is valid:

\[ D=\frac{n-n_1}{K}+D_1 \quad (\text{t/h}) \tag{7} \]

\(D\) — the steam consumption being determined at various rotor speeds;
\(D_1\) — steam consumption at rated speed;
\(n_1\) — rotor speed at rated frequency;
\(n\) — rotor speed at which the steam consumption is determined.

In Fig. 5 this dependence is expressed by straight line 1. If the initial steam load of the turbine differs from the values indicated above, then, using equation (7), one can obtain a series of parallel straight lines, or static characteristics, whose displacement is determined by the servomotor travel. On this basis, straight lines 2, 3, 4, 5 are constructed for the initial load of the VPT-25-3 turbine, respectively: 160, 140, 120, 100 t/h.

For the VPT-50-2 turbine, these same dependences are determined analogously on the basis of factory test data [5] and are shown in Figs. 6 and 7. For steam turbines, the limit of the regulating capacity of the valves is determined by the degree of governing nonuniformity, equal to:

\[ \delta = 4\% \pm 1\% \]

\[ \delta=\frac{n_1-n}{n}; \quad n=n_1(1-\delta)=3000\cdot 0.95=2850\ \text{rpm}. \]

At this speed, the regulating valves are fully opened, and with a further decrease in speed the steam consumption does not increase. In Fig. 5 this limit is shown for the VPT-25-3 turbine by a vertical secant line, and in this case the steam consumption will be 264 t/h at an initial steam load of 180 t/h.

In addition to the regulating capacity of the valves, the turbine steam consumption is limited by the flow capacity of the regulating valves and steam lines. For the VPT-25-3 turbines it is 220 t/h, and for the VPT-50-2, 410 t/h [6].

Thus, at a speed of the VPT-25-3 turbine below 2930 rpm and a steam load of 180 t/h, the steam consumption will be constant and limiting.

For the VPT-50-2 turbine this limiting steam consumption will occur at 2955 rpm and below, if the initial steam load was 350 t/h. In this connection it is appropriate to note the following feature. Investigation of emergency modes caused by frequency reduction, using the readings of self-recording instruments registering the steam consumption of the turbines, frequency, pressure, and steam temperature, showed that the limiting values of steam consumption are influ—

a number of factors (the pressure and temperature of the steam ahead of the turbines in emergency conditions, the degree of frequency fluctuation). The complexity, or more precisely the impossibility, of taking these circumstances into account forced the author to abandon them and to consider the increase in steam consumption under the calculated, most severe conditions from the standpoint of their effect on the operation of the boiler units and the feed installation. This is all the more correct since the calculated limiting values of consumption are special cases and, under certain circumstances, may occur. The steam consumption by back-pressure turbines of the BP type is determined by the “behavior” of the heat consumer. Regardless of a reduction in the number of turbine revolutions, the heat load of the consumers—especially during the first period after a disturbance of the regime—will remain practically unchanged, and for those turbines that are on the back-pressure limiter, a reduction in the number of revolutions will not change the steam consumption at all. Those turbines that have the possibility of regulation and operate in parallel with one another in supplying steam to a common header will practically not increase the steam load, but only redistribute it among themselves. This redistribution is obviously caused by the nonuniformity of the regulation setting and by other reasons.

Therefore it should be assumed that, with a constant steam load of the external consumers, the total steam consumption by the BP turbines will remain constant when the number of turbine revolutions decreases. This same conclusion is confirmed by practical data and observations both in emergency and in normal conditions. A quantitative estimate of the increase in steam consumption by the turbines due to deterioration of turbine efficiency is of no interest in the present calculation, since when the turbine speed is reduced to 2500 rpm the steam consumption increases by 3.3%, and at 2900 rpm only by 0.7%.

Determination of the emergency shutdown time of boiler units as a function of frequency and voltage

Knowing the weight of water in the cylindrical layer and using Figs. 1 and 3, one can construct a graph of the dependence of the emergency shutdown time of the boiler units on the reduction in frequency and voltage for various capacities of the feed pumps.

The calculation sequence adopted is as follows:

1. From the known values of reduced voltage or frequency, or of a proportional reduction in both quantities, the new number of revolutions of the pump is found from Fig. 1.

2. From the curve in Fig. 3, for the given pump capacity and the new number of revolutions, the value of the reduced capacity is determined.

3. From the static characteristics in Figs. 5 and 7, the increase in steam consumption by the turbines is determined, with recalculation to the quantity of feedwater falling on one feed pump.

4. From the value of the reduced capacity, taking these reasons into account, the emergency shutdown time of the boiler units is calculated:

\[ t_{\text{a.k.}}=\frac{60G}{Q_{\text{nach.}}-\left(Q_{\text{kon.}}-Q'\right)}\,m \quad (\text{min}) \tag{8} \]

where
\(G\) is the weight of water in the cylindrical layer in the boiler drum;
\(Q_{\text{nach.}}\) is the pre-emergency capacity of the feed pump;
\(Q'\) is the capacity of the feed pump caused by the reduction in its number of revolutions;

\(Q'\) — increase in steam (feedwater) consumption due to a decrease in turbine speed;

\(m\) — ratio of the number of operating boiler units to the number of operating pumps.

Thus, for example, for the operating condition \(f=45\) Hz; \(U=3120\) V and \(Q_{\text{fw}}=2012\) t/h, \(Q_{\text{steam}}=1910\) t/h; \(Q_{\text{init.}}=334\) t/h with 6 operating pumps.
\(Q_{\text{final}}=275\) t/h; \(n_{\text{final}}=2686\) rpm.

The increase in steam consumption by the turbines, according to the balance of distribution of the steam load among them:

VPT-50-2 \((410-350)=60\) t/h; VPT-25-3 \((220-180)\cdot4=60\) t/h

The increase in steam consumption by the turbines, according to the balance per distribution pump:

\[ Q'=\frac{60+160}{6}=36.7\ \text{t/h}. \]

Emergency shutdown time of the boiler units:

\[ t_{\text{em. b}}=\frac{1.52\cdot60}{334-(275-36.7)}\cdot\frac{10}{6}=1.58\ \text{min}. \]

For another feedwater-installation capacity and other operating conditions, the calculation is performed in the same way.

In Fig. 8 the curves are plotted for the operating conditions:

1 — \((45\ \text{Hz};\ 3120\ \text{V})\), 2 — \((47\ \text{Hz};\ 3260\ \text{V})\), 3 — \((48\ \text{Hz};\ 3330\ \text{V})\),

4 — \((49\ \text{Hz};\ 3400\ \text{V})\) and

for the case of operation of the feedwater installation with no reserve. In actual practice, when the normal operating condition is disturbed, one or several standby pumps are started automatically (if ATS is available) or manually, if the voltage drop is of such a magnitude that it allows them to run up. Under the same operating condition and with the start of one standby pump, only

\[ Q_{\text{final}}=275\cdot\frac{7}{6}=321\ \text{t/h} \quad\text{and}\quad m=\frac{10}{7} \]

change.

Calculations show that for frequencies of 47, 48, and 49 Hz the operating condition is restored in different times by starting one standby pump. When the frequency drops below 46.5 Hz, two standby pumps must be started in order to restore normal operation. In Fig. 8, curve 5 is used to determine the emergency shutdown time of the boiler units when the frequency drops to 45 Hz, and curve 6 when the frequency drops to 47 Hz and one standby pump is started. It is of interest to note that, at normal frequency and a maximum pump capacity of 334 t/h, the overturning torque will occur when the voltage drops to \(0.66U_{\text{n}}\). In this case the feedwater pumps will stop, and the water in the boiler drums will fall to the limiting level in 27 s (see formula 8):

Determination of the run-up time of standby feedwater electric pumps at different voltages on the auxiliary-service sections

The run-up time of the standby feedwater pumps introduces a substantial correction into the selection of time setpoints for the ASD. This time depends primarily on the magnitude of the voltage on the auxiliary-service buses, which is below nominal as a result of the general voltage drop in the system and due to the starting of the pump (pumps).

When determining the reduction in voltage caused by the starting of a pump, the ordinary equivalent circuit of the electrical circuit from-

Fig. 8. Time of emergency tripping of boiler units as a function of frequency and voltage in the power-supply scheme for the auxiliary equipment. Curves 1 for frequency 45 Hz; 2—47 Hz; 3—48 Hz; 4—49 Hz; 5—45 Hz and start-up of one standby pump; 6—47 Hz and start-up of one standby pump.

the pump motor up to the distribution device of generator voltage, whose busbars may be assumed in the calculation to have unlimited power. At the CHP plant under study, the voltage at the s/n section from the start-up of the standby pump decreases to a value of \(0.925\,U_{\text{n}}\), and, taking into account the overall voltage reduction in the system, it will have the following values: at \(0.9\,U_{\text{n}}\)—80%, \(0.8\,U_{\text{n}}\)—71%, \(0.7\,U_{\text{n}}\)—62%.

Determination of the acceleration time of the feed pump at reduced voltages in the system and nominal frequency is carried out by a graphical method, on the basis of the constructed dependences of torque on slip for various values of the reduced voltage and of the resisting torque at the maximum pump capacity of 334 t/h (Fig. 9). It should be noted that the torque curves were constructed by calculation only in the slip range \(S = 0 \div 0.05\). In this case the calculated values of the active and inductive resistances do not change, and the torque curves coincide with the actual ones.

Construction of the starting characteristic of the ATM-2000-2 by calculation is fundamentally impossible because of the impossibility of taking additional losses into account.

Therefore, the torque curves for the range of these slips were taken for different values of the reduced voltage from experimental materials [7]. The resisting-torque curve of the feed pump (7) in Fig. 9 during starting with the gate valve closed was likewise taken from experimental materials. The resisting torques of the pump with the check valve open were determined by calculation above. The point of intersection of the resisting torques with the gate valve closed corresponds to a slip of 0.287, or to a rotor speed of 2140 rpm. Consequently, at this speed the check valve will open during starting. The dependence of torque on slip (curves 1, 2, 3, 4, 5, 6) is taken for the voltages on the motor, respectively, \(1.0\,U_{\text{n}}\), \(0.925\,U_{\text{n}}\), \(0.9\,U_{\text{n}}\), \(0.83\,U_{\text{n}}\), \(0.8\,U_{\text{n}}\), \(0.7\,U_{\text{n}}\), at nominal frequency. From the graphical analysis it is seen that the motor can accelerate during starting if the voltage on it is not less than \(0.83\,U_{\text{n}}\).

The curves of excess, or dynamic, torque \((2', 3', 4')\) were constructed for voltages of, respectively, \(0.925\,U_{\text{n}}\), \(0.9\,U_{\text{n}}\), \(0.83\,U_{\text{n}}\) by the graphical method, as the difference of ordinates between the torque and the resisting torque at the calculated capacity of 334 t/h. In the same Fig. 9 the resisting-torque curves from \(1''\) to \(12''\) are indicated, corresponding to capacities: 353, 334, 320, 300, 280, 260, 247, 220, 200, 180, 160, 140 t/h.

The acceleration time of the electric pump is determined by the method of successive intervals

\[ t_{\text{p}} = -T_j\left(\frac{-\Delta S_1}{m_{\text{ex.}1}} + \frac{-\Delta S_2}{m_{\text{ex.}2}} + \ldots \frac{-\Delta S_n}{m_{\text{ex.}n}}\right) \tag{9} \]

\(T_j\)—the mechanical time constant of the unit;

\[ T_j = \frac{GD^2_{\text{red.}}\, n_1^2}{364\,P_{\text{n}}} = \frac{0.324 \cdot 3000^2}{364 \cdot 2000} = 4\ \text{s}. \tag{10} \]

\[ GD^2_{\text{red.}} = GD^2_{\text{mot.}} + GD^2_{\text{p.}} = 0.31 + 0.0138 = 0.324\ \text{t}\cdot\text{m}^2 \]
—the flywheel moment of the unit.

Fig. 9. Determination of the acceleration time of the electric feedwater pump when the voltage drops in the auxiliary-service circuit.

\(\Delta S\) — the slip intervals into which the graph is divided;

\(m_{\mathrm{i.z}}\) — the ratio of the surplus torques within these same intervals to the nominal value.

For voltages \(0.925 U_{\mathrm{n}}\), \(t_{\mathrm{p.n}} = 9.1\) sec; \(0.9 U_{\mathrm{n}}\) — 11.2 sec; \(0.83 U_{\mathrm{n}}\) — 23.2 sec.

Selection of Voltage, Frequency, and Time Setpoints for the ASD

The starting element of the ASD, responding to a decrease in voltage, frequency, or both quantities simultaneously and having time delays, must send a command pulse to the program device, which acts on the control circuits of the circuit breakers both of the main circuit and of the auxiliary-services circuit.

1. By voltage. A reduction in the voltage at the electric motor leads to a slight reduction in the speed of the supply electric pump and, consequently, in its capacity. Even such a deep voltage dip as \(0.7 U_{\mathrm{n}}\), with a pump capacity of 334 t/h, causes a decrease in speed from 2980 to 2952 rpm (Fig. 1), which amounts to 1%. With such a reduction in speed, no loss of capacity at all will occur, owing to the reserve in the degree of opening of the feed valve. Therefore there is no need to set a voltage setpoint.

2. By time. For the starting element of the ASD, the selection of time setpoints is reduced to accounting for the time of emergency shutdown of boiler units, the starting of standby feed pumps, and the operating time of intermediate relays in the output circuits and of circuit breakers. In addition, a time margin must be taken into account, considering the natural error of the calculation and the psychological state of the operating personnel when the water level in the boiler drums decreases.

Proceeding from this, it seems reasonable to take the margin factor within the range \(1.33 \div 2\). \(K_{\mathrm{z}} = 1.33\) means that the command pulse for starting the ASD will be issued, after subtracting the starting time of the standby pumps and the operating time of the intermediate relays and circuit breakers, when 75% of the water of the cylindrical layer of the boiler drum has been lost.

\[ \frac{t_{\mathrm{av.k}}}{K_{\mathrm{z}}} = \frac{t_{\mathrm{av.k}}}{1.33} = 0.75 t_{\mathrm{av.k}} \]

Thus, the range of variation \(K_{\mathrm{z}} = 1.33 \div 2\) is relatively small and determines the difference in the time of issuing the command pulse, in accordance with the value \((0.75 \div 0.5)t_{\mathrm{av.k}}\).

The value of the margin factor changes the frequency nonselectivity zone and affects the choice of time setpoints, but has no effect on the dead zone. The reliability factor \(K_{\mathrm{n}}\), which determines the different conditions for starting standby pumps (degree of packing of the glands, general condition of the unit), as in many calculations, is taken equal to 1.1.

In general form, the formula for determining the ASD time delay, taking into account all the factors listed, will be:

\[ t = \frac{t_{\mathrm{av.k}}}{K_{\mathrm{z}}} - \left(K_{\mathrm{n}} t_{\mathrm{p.n}} + t_{\mathrm{sx}}\right) \ \text{(sec.)} \tag{11} \]

where

\[ t_{\mathrm{p.n}} \text{ — starting time of the standby feed pumps;} \]

\[ t_{\mathrm{sx}} \text{ — operating time of the intermediate relays of the output circuits and of the circuit breakers.} \]

According to experimental data it is about two sec.

3. By frequency. Under both maximum and minimum load conditions of the feed installation, the curves of the emergency shutdown time of the boiler units when only the frequency is reduced and when the frequency and voltage are reduced simultaneously practically coincide; therefore, to simplify the circuit, the setpoint may be specified only by frequency. Taking into account the large scatter in the emergency shutdown time when the frequency changes within the limits of \(50 \div 45\) Hz, it is advisable to make the starting element of the automatic separation device (ASD) two-stage.

Allowance for the presence of dead zones and nonselectivity zones with respect to frequency must be the determining factor in selecting the setpoints. If the setpoint of the first stage is specified as 45 Hz and that of the second as 48 Hz, then, on the one hand, within the frequency range \(50 \div 48\) Hz there is a dead zone, while, on the other hand, within the frequency setpoints of stages I and II there is a nonselectivity zone. The proper selection of frequency setpoints can be made after determining the dead zones and nonselectivity zones.

When determining the dead zone it is necessary to know the specified frequency setpoint. A sufficient initial condition for determining the nonselectivity zone is the dependence of the boiler-unit shutdown time on frequency. This dependence is determined from Fig. 8 for a pump capacity of 334 t/h and is curve 1 in Fig. 10. If the frequency setpoints for the first and second stages are initially taken as 45 and 48 Hz, respectively, then for this frequency range the operating time of the ASD, without allowance for the safety factor, is determined by formula (11), on the basis of which curve 2 in Fig. 10 is constructed.

To restore normal operation when the frequency is reduced within \(46.5 \div 45\) Hz, it is necessary to start two standby feed pumps, with the starting time of each, in the most unfavorable case, equal to 23.2 sec. The starting of the second standby pump at a frequency of 46.5 Hz determines in Fig. 10 the appearance of a horizontal threshold.

When determining the ASD operating time with allowance for safety factors, the following curves have been constructed: \(3—(K_z = 1.33)\); \(4—(K_z = 1.5)\); \(5—(K_z = 1.75)\); \(6—(K_z = 2)\).

The nonselectivity zones depend on the following causes:

1. Specified frequency setpoints.
2. Safety factors.
3. Capacity of the feed pump in normal operation.
4. Number of standby pumps being started.

As can be seen from Fig. 10, at \(K_z = 1.33\) and the initially specified frequency setpoints \(f_I = 45\) Hz; \(f_{II} = 48\) Hz, the nonselectivity zone of the second stage will be determined by a perpendicular to the time axis up to its intersection with curve 2. This intersection point corresponds to a frequency of 47 Hz; therefore, the nonselectivity zone has the range \(47 \div 45\) Hz, and when the frequency decreases within this range the second stage, although it will come into operation, will nevertheless cause the ASD to operate with a time greater than that required for releasing water from the boiler drums. It is not difficult to determine the nonselectivity zone for other values of \(K_z\) as well; as \(K_z\) increases, this zone will decrease. It is undesirable to have a nonselectivity zone, especially at frequencies close to the setpoint of the first stage, since operation of the ASD in this case will be meaningless. According to the reliability condition, it is required that the operating frequency zone of the first stage overlap—

Fig. 10. Determination of the zones of nonselectivity and frequency insensitivity for the automatic separation device (ADU).

would be, with the operating frequency zone of the second stage of the order of \(0.25\ \text{Hz}\); then the operating frequency zone of the first stage will have boundaries \(46 \div 44.25\ \text{Hz}\) (points “v” and “g”), and that of the second stage \(47.5 \div 45.75\ \text{Hz}\) (points “a” and “b”), if \(K_3=1.75\) is adopted for the first stage and \(K_3=2\) for the second. The intersections of the perpendiculars dropped from points “a” and “v” with the time axis give the time setpoints for the ASD. Thus, when detuning from the zones of nonselective operation, the frequency and time setpoints should be selected as follows:

\[ \begin{array}{lll} \text{Stage I} & f=46\ \text{Hz}; & t=18\ \text{s},\\ \text{Stage II} & f=47.5\ \text{Hz}; & t=60\ \text{s}. \end{array} \]

Using the curves of Fig. 10, and specifying the frequency setpoint of the second stage, the reserve factor, and the frequency of the overlap zone, one can determine the frequency setpoint of the first stage and the operating time of these stages. The principal disadvantage in selecting the frequency and time setpoints is the presence of an insensitivity zone (dead zone), which in the present calculation lies practically within the frequency range \(49 \div 47.5\ \text{Hz}\). The insensitivity zone can be avoided by a number of measures: raising the frequency setpoint of the second stage, introducing a third stage into the scheme, operational measures of a system-conditions nature, and manual starting of the ASD from the control board without time delay. Comparing the calculation results, one may conclude that when the frequency decreases to within \(45\ \text{Hz}\), the thermomechanical processes proceed intensively and are, to some extent, comparable in time with the processes occurring in the electrical circuit. When the frequency decreases to within \(48\ \text{Hz}\), the thermomechanical processes proceed considerably more slowly. For the time element of the ASD, the best option should be considered the use of a motor time relay of type \(E\text{—}512\) or \(E\text{—}513\), on which independent setpoints can be made not only for 2 but also for 3 stages.

REFERENCES

1. Portnoi M. G., Rudenko Yu. N., Yasnikov V. N., Consolidation of the power systems of Siberia by weak tie lines, Elektricheskie stantsii, No. 5, 1963.

2. Syromyatnikov I. A., Operating Conditions of Asynchronous and Synchronous Electric Motors, Gosenergoizdat, 1963.

3. Kirsh A. K., Shishkin A. G., Reduction of electric-power consumption for the supply of feedwater by the pumps of Ts-40 of the Berdyansk Mechanical Plant, BTI, 1961.

4. Ural Turbine-Mechanical Plant, Description of the control systems of turbine VPT-25-3.

5. Leningrad Metal Plant, Description of the control systems of turbine VPT-50-2.

6. Materials of Ts. K. B., Increasing the electrical and thermal capacity of operating power stations by modernizing the main equipment, 1962.

7. Ivanova O. V., Self-starting of feed pumps of high-pressure CHP plants, Elektricheskie stantsii, No. 2, 1958.