Conditions for the Joint Operation of an Inverter, Synchronous Machines, and a Load

V. K. Shcherbakov and R. S. Zainulina

I

Introduction

The receiving end of a direct-current power transmission line may, in the general case, include an inverter (a converter of direct current into alternating current), synchronous generators operating in parallel with the inverter, reactive-power generators (synchronous compensators and capacitors), and a load (motors, furnaces, lamps, etc.).

The adjusted operation of all these elements of the receiving end presupposes that, with unchanged voltage in the network of the receiving end of the power transmission, the inverter and the synchronous generators must supply as much active power as is required by the load, on the one hand, and, on the other hand, the synchronous generators, synchronous compensators, capacitors, and other possible reactive-power generators must supply as much reactive power as is required by the inverter and the load.

A possible deviation of the voltage from its nominal value in the receiving network will inevitably cause a change in the magnitude of the powers supplied and consumed by the elements of the receiving end and, as a consequence, the appearance of an imbalance of active and reactive powers in the network, a further change in the network voltage, etc.

Such a situation may be expected in view of the relative independence of the magnitude of the active power supplied and the reactive power consumed by the inverter from the behavior of the network load. If the generators of active and reactive power, in the steady-state regime, supply to the network exactly as much power as is required of this power by the load plus the losses in the network, then there is no such relationship between the powers supplied and consumed by the inverter, on the one hand, and by the load, on the other hand. Once adjusted, the correspondence between the inverter and the load can easily be disturbed when the voltage deviates from its nominal value.

Under certain conditions and up to a certain limit, synchronous generators and synchronous compensators can serve as a buffer between the inverter and the load and, under definite conditions, can help restore equilibrium in the network of the receiving end of the power transmission when the network voltage has changed. In other cases it is necessary to resort to special regulating means that at every given moment ensure the balance of active and reactive powers in the network of the receiving end.

Below is set forth a method for investigating the conditions for the joint stable operation of an inverter, generators, compensators, and a load, applied—

relative to the particular case when the power of the electric transmission is taken equal to the power of the other sources of active power in the receiving-end network; the characteristics of the generators and compensators are taken as typical for large modern machines; a certain average typical load is taken into account.

II

Characteristics of the Active and Reactive Powers of the Network Elements

Fig. 1 shows the connection diagram of the elements. For simplicity, all elements are connected directly to the same buses.

First, the behavior of each element is considered separately when the voltage on the common buses is varied, and then in their mutual relation.

Fig. 1. Receiving end of a direct-current electric transmission

Synchronous generators

The total power of the synchronous generators is taken equal to the power of the inverter. The generators are sources of commutation voltage for the inverter; they determine the frequency in the network and the shape of the voltage curve on the receiving-substation buses.

Within small limits of voltage variation, it may be assumed that the active power of the generator does not change with voltage variation.

Fig. 2. Reactive-power curve of the generator

Fig. 2 gives the dependence of the reactive power of a generator with synchronous reactance \(x_d = 1.1\), \(\cos \varphi = 0.85\), on voltage. The curve is constructed on the basis of the circle diagram under the assumption that, at nomi-

at rated voltage, the inverter supplies rated reactive power. As can be seen, a generator of conventional design, without excitation control and previously operating at the rated power factor, reduces its reactive-power output when the voltage on the buses to which it is connected is lowered or raised. A synchronous generator increases its reactive-power output when the bus voltage is lowered only in the case where the generator has previously been operating underloaded with respect to reactive power; but even then the positive regulating effect is very small.

Synchronous compensators

The dependence of the reactive power supplied on the bus voltage is shown in Fig. 3. The curve was obtained from the circle diagram for a compensator with synchronous reactance $x_d = 1.8$, for excitation corresponding to the rated reactive power of the compensator.

The behavior of a synchronous compensator during fluctuations of bus voltage depends on the degree of its prior loading. A synchronous compensator loaded with rated reactive power has, accordingly, high excitation and, when the voltage drops, reduces the reactive power supplied and does not help maintain the voltage at its former level.

In Fig. 4 the reactive-power curves of a synchronous compensator at different excitation are given. Curve 2 corresponds to operation of the compensator at half load. As the curve shows, the synchronous compensator increases the reactive power supplied when the voltage on the buses decreases, but even in this case it contributes little to maintaining the voltage at its former level without the intervention of regulating devices.

Fig. 3. Reactive-power curve of a synchronous compensator

Fig. 4. Reactive-power curves of a synchronous compensator at different excitation.

Load

The usual composition of the load is: asynchronous and synchronous motors, furnaces, mercury rectifiers, lighting, and household load. Asynchronous motors are the main part of the load, accounting for more than 50% of it. Therefore they determine the course of variation of the active and, especially, reactive powers of the entire load as the voltage on the load buses changes.

Fig. 5. Curves of the active and reactive powers of a composite load

Figure 5 gives the curves of active and reactive powers of a composite load, compiled by Teploelektroproekt. The curves show that, when the voltage on the buses is reduced, a mixed load favors maintaining the voltage at the former level, considerably reducing the reactive power consumed.

Inverter

It is assumed that the power of the inverter is equal to the power of the other sources of active power at the node, and that the mercury valves of the inverter installation are connected according to a double three-phase bridge circuit, the most acceptable in high-voltage and high-power installations.

Fig. 6. Curves of the reactive power of the inverter

Fig. 7. Curves of the active power of the inverter

On the basis of the external characteristic of the inverter, curves of the active and reactive powers of the inverter were obtained for three values of the firing advance angle and for constant voltage at the beginning of the line, Figs. 6 and 7.

Increasing the advance angle of the inverter leads to an increase in the active power delivered and in the reactive power consumed by the inverter. At \(\beta = 60^\circ\), the absolute value of the reactive and active powers is almost twice as large as at \(\beta = 30^\circ\).

As the inverter lead angle changes, the ratio of active to reactive powers changes. At \(\beta = 60^\circ\), the reactive power consumed by the inverter is much greater than the active power delivered by it to the network. The operating lead angles of the inverter lie between angles of \(30^\circ\) and \(60^\circ\).

III

Balance of Reactive Power in the Receiving-End Network

The sources of reactive power at the node are synchronous generators and synchronous compensators. Graphical addition of the reactive-power curves of synchronous machines gives the curve of the variation of the total reactive power produced at the node with the variation of the voltage on the buses, Fig. 8, curve 1.

The consumers of reactive power at the node are the complex load and the inverter. Graphical addition of the reactive-power curves of the inverter and the load gives the resultant curve of the variation of the reactive power consumed by all elements of the node with the variation of the voltage on the common buses, Fig. 8, curve 2.

The elements of the node are selected so that at the nominal voltage on the buses there is equilibrium of power; therefore the reactive-power curves of the sources and consumers intersect at point \(M\). Point \(M\) is the point of normal operation of the elements of the node. As the course of curves 1 and 2 shows, when the voltage deviates from the nominal value in one direction or the other, the ratio of the reactive power of consumers and sources changes. When the voltage on the buses is reduced by approximately 10%, an excess of reactive power is preserved; when the voltage is increased, on the contrary, a deficiency of reactive power arises. These two conditions completely determine the stable operation of the system at point \(M\) under possible static deviations of the voltage from its nominal value.

Fig. 8. Resultant curves of the reactive power of sources and consumers

When the voltage is reduced by more than 10%, the reactive power required by the consumers proves to be greater than the power that the sources can supply. There is a shortage of reactive power at the node. The consequence of this will be a further reduction of the voltage on the buses and the collapse of the system.

IV

Balance of Active Power in the Receiving-End Network

In the absence of regulating devices in the elements of the node, as the voltage on the common buses changes, the equilibrium of active power is also disturbed.

If, for two elements of the network—the load and the generators—the active power changes little with a change in voltage, then the active power delivered by the inverter to the network changes rather sharply. The sources of active power at the node are the synchronous generators and the inverter.

The active-power characteristics of the inverter and of the generators are shown in Fig. 9, curve 2.

Line 1 in Fig. 9 represents the change in active power consumed by the mixed load. Within the voltage-variation limits under consideration, the active power of the load changes very little. The resultant curves of the active power of the sources and consumers intersect at point \(M\), corresponding to the rated voltage on the buses and representing the normal operating point. At this point there is equilibrium of active power.

Fig. 9. Resultant curves of the active power of sources and consumers

It is evident from Fig. 9 that, when the voltage is reduced by \(1\text{–}5\%\), the equilibrium is disturbed: the active power that the sources can deliver proves to be greater than the active power required by the consumer. As a result of the voltage reduction, the inverter takes on an additional active load, while the generators are unloaded. When the voltage is increased, on the contrary, owing to the reduction in the active power delivered by the inverter to the network, the generators will be heavily loaded. If the load on the generators is within permissible limits, they will remain in operation. If not, they will be disconnected by overload protection. As a result, the system breaks up.

V

Conclusion

1. Above, a general method has been given for investigating the conditions for joint operation of the elements of a system connected to a direct-current transmission line.

2. At the same time, the investigation carried out for certain particular, but sufficiently typical, values of the parameters of the network elements has shown that, evidently, in most cases stable operation of the system is impossible without the intervention of the corresponding regulating devices.

3. It is important to note, however, that under static voltage variations permissible in normal operation \((\pm 5\%)\), in the case analyzed, the equilibrium of reactive power is maintained without intervention of regulating devices.

4. The results of such an investigation of the behavior of the inverter, synchronous machines, and load as applied to a specific case make it possible to formulate quite definite requirements for the regulating devices of all elements of the node.

5. The investigation carried out above must be supplemented by consideration of the behavior of the system when the load at the receiving end changes.