1 Introduction

The output of a photovoltaic (PV) power plant is affected by variable insolation, due to atmospheric effects, resulting in volatile and random characteristics [1–4]. When the grid voltage fluctuates, due to variable PV power injection or for other reasons, a PV power plant configured simply to provide active power output cannot provide reactive current to support grid voltage. However, new connection standards require the PV power plant to provide certain reactive current when disturbances are detected at point of interconnection (POI), to help maintain the voltage within the threshold range demanded by technical standards.

Currently, the reactive power sources of PV power plants include static synchronous compensators (STATCOMS) which are static reactive compensation devices, and PV inverters which can provide dynamic reactive power compensation. PV power plants are usually equipped with automatic voltage control (AVC), which can use different reactive power sources in a coordinated way. Reference [5] shows that the AVC system sets the reactive power level according to the bus voltage and total reactive load of both dispatching center and plants. The plant can regulate the POI voltage within normal range through certain strategies. Reference [6] introduces a power decoupling control strategy based on instantaneous reactive power theory, and puts forward the corresponding relation between the power components in the α–β two-phase coordinate system and the compensation current in the three-phase inverter system. It can realize inverter-based reactive power compensation and harmonic current compensation. The active/reactive power control field test and analysis of PV power plants is shown in [7]. But the paper only analyzed the reactive power control curve, carrying out no tests because of the lack of integrated control system.

PV inverters have the ability to receive AVC system instructions and adjust reactive power, as the main reactive power source of PV plant. In this paper, the reactive power output and control capability of clusters of inverters are discussed. After this analysis, a PV power plant without a STATCOM is tested on its reactive power output and control capability, and the test result is compared with the analysis. Specially, a new method to verify the plant capability to regulate voltage at POI is proposed and used.

2 Analysis on reactive power capability of PV plant

When the inverters are used as a reactive power source, reactive power output of PV power plants depends on the capability of inverters and the internal transmission loss. The loss comes from unit transformers, main transformer and collector lines. An equivalent circuit of a single inverter within the plant connected to grid is shown in Fig. 1. U gi is voltage of inverter output; U s the voltage of internal busbar; δ i the phase angle of inverter output; Xi the reactance of transformer and line; P Ii the active power of inverter; Q Ii the reactive power of inverter; S i the apparent power of inverter; P i the active power gathered in busbar; and Q i the active power gathered in busbar.

Fig. 1
figure 1

PV power plant equivalent circuit

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2.1 Inverter reactive power range

It is well known that the power equation is [8]:

$$P_{i} = \frac{{U_{s} U_{gi} \sin\,\delta_{i} }}{{X_{i} }}$$
(1)
$$Q_{i} = \frac{{U_{s} (U_{gi} \cos \delta_{i} - U_{s} )}}{{X_{i} }} = \frac{{U_{s} U_{gi} \cos \delta_{i} }}{{X_{i} }} - \frac{{U_{s}^{2} }}{{X_{i} }}$$
(2)

From (1) and (2), it is deduced that

$$P_{i}^{2} + \left( {Q_{i} + \frac{{U_{s}^{2} }}{{X_{i} }}} \right)^{2} = \left( {\frac{{U_{s} U_{gi} }}{{X_{i} }}} \right)^{2}$$
(3)

When Q i  = 0:

$$P_{i} = \sqrt {\left( {\frac{{U_{s} U_{gi} }}{{X_{i} }}} \right)^{2} - \left( {\frac{{U_{s} }}{{X_{i} }}} \right)^{2} } = \frac{{U_{s} }}{{X_{i} }}\sqrt {U_{gi}^{2} - U_{s}^{2} }$$
(4)

Equation (3) can give the range of reactive power that the inverter can supply to the bus bar:

$$- \sqrt {\left( {\frac{{U_{s} U_{gi} }}{{X_{i} }}} \right)^{2} - P_{i}^{2} } - \frac{{U_{s}^{2} }}{{X_{i} }} \le Q_{i} \le \sqrt {\left( {\frac{{U_{s} U_{gi} }}{{X_{i} }}} \right)^{2} - P_{i}^{2} } - \frac{{U_{s}^{2} }}{{X_{i} }}$$
(5)

Due to the limited apparent power of a PV inverter, the power output range is shown as the shaded region in Fig. 2. Generally, the maximum current is not allowed to exceed 1.1 I N , where I N is the nominal maximum current, and when P Ii  = 1 p.u., Q Iimax = 0.46 p.u; when P Ii  = 0, Q Iimax = 1.1 p.u.

Fig. 2
figure 2

Output characteristic of an inverter

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To maintain the active power output of PV power plants, inverters normally operate at rated active power, and therefore the reactive power output range is \(- 0.46\;{\text{p}} . {\text{u}} .\le Q_{Ii} \le 0.46\;{\text{p}} . {\text{u}} .\), which is directly tied to the limiting current of inverters.

2.2 Transformer reactive power loss

The transformer reactive power loss includes the short-circuit loss and the no-load loss [9, 10]. It is defined as:

$$\Delta Q_{T} = \left[ {\frac{{I_{0} (\% )}}{100} + \frac{{U_{K} (\% )}}{100} \times \beta^{2} } \right]S_{e}$$
(6)
$$\Delta Q_{K} = \frac{{U_{K} (\% )}}{100} \times \beta^{2} \times S_{e}$$
(7)

where I 0 (%) is no-load current; U k (%) the short-circuit voltage; β the load factor; S e the rated capacity; ΔQ T the total reactive power loss in transformer; and ΔQ K is the load reactive power loss in transformer.

2.3 Collector lines reactive power loss

The reactive power loss in collector lines consists of line equivalent reactance and equivalent admittance. The latter is proportional to the square of applied voltage and not directly related to the transmission lines, thus not included in the calculations, therefore the line reactive power loss is:

$$\Delta Q_{L} = 3I^{2} \omega Ll$$
(8)

Therefore, the total reactive power output of PV power plant is:

$$Q = \sum {Q_{Ii} } - \sum {\Delta Q_{K} - \sum {\Delta Q_{L} } }$$
(9)

3 PV power plant reactive power control on inverters

To control reactive power PV power plants usually use an AVC system consisting of a calculator module and a reactive power distribution module. The calculator module calculates the desired reactive power demand for a PV power plant according to the voltage difference on the low-voltage side of the POI, accounting for the operating constraints of the PV power plant, and finally sets a reasonable value of reactive power. Meanwhile, the calculator module can directly receive reactive power instructions issued from the dispatch center.

The distribution module allocates the reactive power demand value, which is given by the calculator module, to reactive power sources in the PV power plant according to operating status. The flow of data in such an AVC system is shown in Fig. 3.

Fig. 3
figure 3

AVC system data flow

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The PV inverters receive AVC instructions to carry out reactive power regulation as reactive power sources. Grid-connected PV inverters usually adopt power decoupling control, which sets up outer-loop voltage and inner-loop current by converting a stationary coordinate system into a rotating coordinate system [9–12].

Under steady-state conditions, PV inverters can operate in Q u (voltage control mode), Q cosφ (power factor control mode), and Q c (reactive power control mode). The model of decoupling control is shown in Fig. 4, and the reference I qref (reactive current reference value) is decided according to the operating mode. PV inverters have the ability to receive instruction from AVC system using any operating mode and thereby participate in the grid voltage regulation.

Fig. 4
figure 4

Inverter decoupling model

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4 Standards and testing procedure

Currently, reactive power regulation of PV power plants is required by domestic and international standards. The German Federal Association of Energy and Water (BDEW) published “Generating Plants Connected to the Medium-voltage Network (Guideline for generating plants’ connection to and parallel operation with the medium-voltage network)” [13–15], in which the PV plants are expected to have the ability to regulate the voltage within a certain range. In China, National Standards GB/T 19964-2012 [16] and GB/T 29319-2012 [17], it is clearly stated that the PV plants should participate in voltage regulation according to grid voltage.

The standards require that the reactive power ability of PV plants should be tested and the test items include reactive power output capability, reactive power control capability and control mode.

Reactive power output capability testing is designed to verify the maximum inductive reactive power and capacitive reactive power. Reactive power control capability testing aims to verify the control accuracy and response time when plant receives instruction. Also the plant has to demonstrate its ability to generate reactive power under Q u , Q cosφ and Q c modes.

To perform a Q u (voltage control mode) test, it is necessary to create a voltage disturbance to simulate voltage fluctuation. However, when a PV power plant is online and generating, the grid voltage at the POI stays within narrow limits in most of the time. Moreover, the conventional device used for testing low voltage ride through (LVRT) or grid-disturbance of inverters cannot make enough disturbance because its capacity is far less than that of the PV power plant. To resolve this problem and permit an adequate Q u (voltage control mode) test, a field testing method is presented which combines transformer tap changing and AVC system adjusting.

In the following section, the reactive power capability of a 30 MW PV power plant is analyzed and field testing is carried out.

5 Field-testing result analysis

The PV power plant under test is located in China. It has 30 units of capacity 1 MW, each with two inverters stepped up through a common transformer to connect to an internal 10 kV bus bar, and finally stepped up to 110 kV through the main transformer. The PV power plant is connected to grid at 110 kV. During the test, the data recorder is installed at point A on the high-voltage side of the main transformer, as shown in Fig. 5.

Fig. 5
figure 5

Single-line diagram of the PV plant under test

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5.1 Reactive power output capability

The nominal maximum reactive output of PV inverters is ±0.55 p.u. (when the power factor equals 0.85). The internal reactive power loss which is calculated according to (6)–(9), is listed in Table 1.

Table 1 Reactive power loss
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Therefore, when the PV plant generates at full power, the theoretical reactive power output is:

$$Q = \sum {Q_{Ii} } - \sum {\Delta Q_{K} - \sum {\Delta Q_{L} } } { = 6} . 1 9 7\,{\text{ MVar}}$$
(10)
$$\frac{Q}{{Q_{N} }} = 0.2\;{\text{p}} . {\text{u}} .$$
(11)

During the test period, the maximum irradiation is 533 W/m2 while the output active power of PV power plant is P 0 = 16 MW. The reactive power output capability is tested at every 10 % step of P 0 and the result is shown in Fig. 6. Q C is the capacitive reactive power of PV power plant, and Q L is the inductive reactive power of PV power plant.

Fig. 6
figure 6

Reactive output capability

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It can be seen from Fig. 6 that the maximum Q C of plant reaches almost 0.48 p.u. when the irradiation is low, and the maximum Q L of plant reaches almost 0.53 p.u. The reactive power output is slightly less than calculated because of the loss, nevertheless, the output capability meets the standards requirements.

5.2 Reactive power control capability

The reactive power control capability is carried out when the active power is about 50 % P 0. The plant is set to follow the reactive output curve 0-Q C -Q L -0 and the result is shown in Fig. 7. The reactive power step response times are shown in Table 2, and it can be seen that the plant has the reactive power control capability, and the response time is lesser than 10 s. The results meet the requirement in GB/T 19964-2012 and GB/T 29321-2012.

Fig. 7
figure 7

Reactive control capability

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Table 2 Response time for reactive power control
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5.3 Reactive power control mode

In this section, tests are reported for Q u mode (voltage control) and Q cosφ mode (power factor control) respectively.

  1. 1)

    Q u mode (voltage control)

Before the test, PV power plant is set to operate under Q u mode (voltage control). The reference voltage is set to 1.0 Un and the threshold to ±2 % by the AVC system, which means the system monitors voltage at the POI and will regulate voltage exceeding the range of 0.98–1.02 U n by adjusting inverters’ reactive outputs. The main transformer is provided with an on-load tap changer, which has a short-circuit impedance of 10.8 %. The transformer has ±10 adjustment range with 1.25 % increments.

During the test, the voltage is adjusted to exceed the limits using the on-load tap changer, and the response of the inverters is recorded and analyzed.

As shown in Fig. 8, by adjusting the on-load tap changer, the bus voltage is raised over the threshold value. At this time the plant calculates and dispatches the reactive power to inverters, to stabilize voltage in the normal range.

Fig. 8
figure 8

Voltage and reactive current (over 5 min)

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By the detailed view in Fig. 9, it can be seen that the reactive current changed after the voltage rise over the threshold value in several seconds. The reactive power and response time is calculate and shown in Table 3.The response time is measured from the voltage changing over preset value.

Fig. 9
figure 9

Voltage and reactive current (over 7 s)

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Table 3 Q u mode test result
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  1. 2)

    Q cosφ mode (power factor control)

When plants operate under Q cosφ mode, the system keep monitoring the power factor at the POI, and calculates and dispatches instructions to the inverters, so that they generate reactive power to make the power factor equal to a requested value.

During the test, the plant firstly was asked to adjust cosφ from 1.0 to 0.95, then 5 min later to adjust cosφ from 0.95 to 1, and finally after another 5 min to adjust the power factor from 1 to −0.95.

The bus voltage, reactive power, power factor at the low voltage side (10 kV) of the first test is shown in Fig. 10.

Fig. 10
figure 10

10 kV voltage, reactive power and power factor when AVC requests power factor from 1 to 0.95

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The figure shows that the reactive power increases after the AVC system sent out the power factor set value. The power factor changed from 1 to 0.965 after a delay of 1.6 s.

Then the power factor is set from 0.965 to 1, and the result is shown in Fig. 11. The power factor changed from 0.965 to 0.999 after a delay of 1.2 s.

Fig. 11
figure 11

10 kV volage, reactive power and power factor when AVC requests power factor from 0.95 to 1

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After that, the power factor is set from 1 to −0.95 and the result is shown in Fig. 12. The figure shows that it takes 1.2 s to make power factor change from 1 to −0.968.

Fig. 12
figure 12

10 kV voltage, reactive power and power factor when AVC requests power factor from 1 to −0.95

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The accuracy of unit power factor is very good, but the accuracy of plant is poor, which could be caused by several reasons: ① it could be caused by reactive power losses which may be larger than expected in Table 1; ② it is assumed that the sum of inverters’ output is less than multiplication of single inverter because of the deviation of phase angle. And further experiments are planned to be performed to reveal the real reason.

Obviously, the power factor control accuracy needs to be improved, but the field test proves that the plant has the ability to work under Q u mode (voltage control) and Q cosφ mode (power factor control).

6 Conclusion

In this paper, reactive power output capacity and control capability of PV plants, using inverters without other compensating device, are theoretically analyzed. The maximum capacity and inductive reactive power control are tested using a 30 MW PV power plant and compared with theoretical value. Voltage control and power factor control operating modes are demonstrated. A new testing method is proposed which combines the AVC system and an on-load tap changer to make voltage disturbances to verify voltage control mode.