*2.1. The Research Object*

Both discussed methods for discharge measurement—pressure-time and volumetric gauging method—were used for performance tests of a reversible hydrounit in a Polish pumped-storage power plant (PSPP). The considered plant is equipped with four similar reversible hydraulic machines (pump-turbines) working under the head of approximately 440 m and generating/consuming power over 120 MW.

The artificial head water reservoir is connected to pump-turbines using two underground penstocks, branching close to the inlets of the pump-turbines, prior to the shut-off ball-valves. The pump-turbines are connected via the tailrace tunnel with the surge tank to the tail water tank. A schematic diagram of the PSPP flow system with its main dimensions is shown in Figure 1.

**Figure 1.** Flow system of the pump-turbine.

### *2.2. The Volumetric Gauging Method*

Determining discharge using the volumetric gauging method consists in measuring the volume of water Δ*V* flowing through the tested hydraulic machine during time Δ*t*. The discharge is determined using of the following formula:

$$Q\_V = \frac{\Delta V}{\Delta t} = \frac{V \Big(z \Big(t\_f\big)\big) - V \big(z \big(t\_0\big)\big)}{t\_f - t\_0} \tag{1}$$

where Δ*V* [m3] stands for measured increase or decrease in volume of water in the head water reservoir, Δ*t* = *tf* −*t*<sup>0</sup> [s]—the time interval in which the increase/decrease in water volume occurred, and *z*—level of water in the head reservoir.

When using the volumetric gauging method, there are several issues that can significantly affect the accuracy of the measured flow rate [11,18]. The main task is to determine the relationship between the volume and the water level of the reservoir *V*(*z*). This relationship should be determined on the basis of precise reservoir geometry measurements (particularly useful for artificial reservoirs) or accurate bathymetric scanning. The issue of determining the reservoir volume also involves measuring the water level in this reservoir.

In common situations, transmitters designed to control this level usually included in the power plant equipment are not suitable for use in the volumetric gauging method as they have a wide measuring range and low accuracy class. In order to achieve low uncertainty of measurements, the change in the water level in the reservoir should be determined using special methods. The schematic diagram of the proposed method is shown in Figure 2. Its most important element is measuring the increase in water level Δ*z* in the power plant reservoir by means of a precise transducer measuring the

pressure difference in the reservoir and a constant pressure level set using small auxiliary tank, hung at the appropriate height. The configuration of such an installation should ensure the possibility of carrying out an approximately one-hour measurement at a fixed operating point of the tested hydrounit.

**Figure 2.** The water level change measurement technique used in the volumetric gauging method.

The proposed method allows for the significant reduction of the measurement uncertainty giving an additional possibility for taking into account the unfavorable phenomenon of water surface waving occurring during the tests. This phenomenon can affect the results of the measured flow rate in the most significant way. Traditional ways for measuring the water level used in the volumetric gauging method cannot ensure required accuracy of discharge measurements. Using a measuring system with appropriate characteristics and applying linear regression for the results of measuring the level of water in the reservoir leads to eliminate the effect of water waving on measurement results (Figure 3). It's worth pointing out that it is very important to base the regression line on the boundaries selected at the extreme points of the peaks or valleys of the differential pressure signal. This is a prerequisite for obtaining the correct final flow measurement results.

**Figure 3.** The volumetric gauging method—basic rules of flow rate determination.

Owing to the solutions applied, a very narrow uncertainty range was possible to achieve and the results of its estimation are presented in the next chapter of the paper. The uncertainties (standard and expended) were estimated according to the procedure described in Appendix B that was developed basing on the general recommendations presented in [19].

#### *2.3. The Pressure-Time Method*
