*2.2. Principle of UPQC's Shunt Converter Control*

The control unit of the shunt converter processes the voltage signal of the UPQC's DC-link capacitor *Cdc*, Figure 1, in order to obtain the conductance signal. This signal gives crucial information needed to produce the reference for the source current. The conductance signal can be used to obtain the current reference signal as well for the shunt active power filter (SAPF) as for UPQC's shunt converter.

In general, the compensated load may be nonlinear, time variable, passive or active, of single or polyphase structure with or without the neutral conductor, unbalanced, etc. From this perspective applying an universal method for obtaining the signal of equivalent conductance would be beneficial. Such an universal method, which allows this signal calculation as a function of amount of energy stored in the active filter's reactance elements, has been proposed in [8]:

$$\mathbf{g}(t) = \frac{(W\_{APF0} - w\_{APF}(t))(N\_{SF} + 1)}{T\_{st}V\_S^2} \tag{1}$$

where: *g*(*t*) is the instantaneous load equivalent conductance signal; *WAPF*<sup>0</sup> is initial amount of energy, which has been stored in all UPQC's reactance elements during UPQC initialization procedure; *wAPF*(*t*) is amount of energy stored in these elements at instant *t*; *NSF* is the ratio of amount of energy delivered to the load from the supply source with respect to energy that is simultaneously delivered to the load from UPQC's reactance elements—After each instant of change of load active power until the moment of achieving a new stead state by UPQC; *Tst* is a user dependent parameter that may be utilized to define UPQC time response on change of load active power; *VS* is source voltage rms.

The Equation (1) can be simplified to the form that only information on a part of total amount of energy stored in the UPQC is taken into account: namely that is stored in its DC-link capacitor:

$$\log(t) = \frac{\mathbb{C}\_{\rm dc} \Big(V\_{\rm C0}^2 - v\_{\rm dc}^2(t)\Big) (\mathcal{N}\_{\rm SF} + 1)}{2T\_{\rm st}V\_{\rm S}^2} = K\_V \Big(V\_{\rm C0}^2 - v\_{\rm dc}^2(t)\Big) (\mathcal{N}\_{\rm SF} + 1) \tag{2}$$

where *Cdc* is capacity of DC-link capacitor, *VC*<sup>0</sup> is its initial (i.e., after UPQC initialization procedure, see also *WAPF*<sup>0</sup> in Equation (1)) voltage and *vdc*(*t*) is its voltage at instant *t*, and where:

$$K\_V = \frac{C\_{dc}}{2T\_{st}V\_S^2} \tag{3}$$

It is characteristic for the discussed control technique that the DC-link capacitor voltage is not controlled to be constant. On the contrary, the "freewheeling" capacitor voltage is an input signal for obtaining the conductance signal. The *KV* factor gives a proportion between a signal related to the DC-link capacitor voltage and the conductance signal. The *KV* factor has a practical meaning: it may be used as the gain coefficient of a simple P-type regulator in the active filter's control unit. No other signal converters of DC-link capacitor voltage are needed to obtain the conductance signal (Equation (2)).

There is a parameter *Tst* in the denominator of Equation (3). By changing this parameter the user can control the UPQC's shunt converter inertial response on any change of load active power. By increasing/decreasing magnitude of this parameter more/less energy of each change of load active power can be buffered by DC-link capacitor. In other words, the *Tst* parameter can be used to regulate the energy flow between the source and the load in order to stabilize (or average) the source active power.

Having the conductance signal the reference for source current can be determined by the relationship:

$$
\dot{v}\_S^\*(t) = \mathcal{g}(t)v\_{1S}(t) \tag{4}
$$

where *v*1*S*(*t*) is fundamental component signal of source voltage. This component can be obtained in many ways (e.g., using filtration or PLL based techniques).

A variable component may appear in conductance signal (Equation (2)) if the load current contains a non-active component. Since UPQC compensates such component with the use of energy stored in its reactance elements (Equation (1)) this cause an oscillating component in DC-link capacitor voltage (Equation (2)). This component can distort the reference (Equation (4)). In order to eliminate impact of this component on the reference (Equation (4)) the continuous signal (Equation (2)) should be transformed into the stepwise waveform. To do this the signal (Equation (2)) is sampled at the very end of each subsequent period *Tm* of source voltage cycle. Then each sample is hold for the next period *Tm*+1, [8]. Application of such sample-and-hold procedure causes a "step-by-step" UPQC's shunt converter action in that every change in load active power is practically entirely buffered with energy stored in the DC-link capacitor. For such method of full-buffering of energy flow the *NSF* parameter, see Equations (1) and (2), should be set to zero. As the result the source-to-load flow of energy is delayed for one period *T* and the stepwise form of the conductance signal applied for a *Tm* period is given by:

$$G\_{T\_m} = \frac{\mathcal{C}\_{dc} \Big(V\_{\mathcal{C}0}^2 - \nu\_{\rm dc}^2 (T\_{m-1})\Big)}{2T\_{\rm st}V\_{\mathcal{S}}^2} \tag{5}$$

where: *vdc*(*Tm-*1) is capacitor *Cdc* voltage at the end of (*m*-1)th period *T*.

Finally, on the base of Equations (4) and (5) the source current reference signal *iS \** for period *Tm* is:

$$\mathbf{u}\_{S,T\_m}^\*(t) = G\_{T\_m} \mathbf{v}\_{1S}(t) \tag{6}$$

It should be emphasized that during compensation the following inequality has to be satisfied:

$$
\upsilon\_{dc}(t) \gg \upsilon\_S(t) \tag{7}
$$

If this condition is not satisfied the UPQC dynamics can be insufficient. In an extreme case, when *vdc*(*t*) < *vS*(*t*), the UPQC action may become even harmful.

#### *2.3. Principle of UPQC's Series Converter Control*

Source voltage waveform may deviate from its fundamental component due to wide range of physical phenomena existing in the grid. They may be considered as voltage harmonics, flicker, swell or sag, or pulse transients. There are specialized devices to overcome power quality problems that are related to voltage disturbances. The dynamic voltage restorer (DVR) seems to be the most economical solution in this field, [22]. However, UPQC's series converter can maintain the load voltage *vL* to be close to the fundamental component *v*1*<sup>S</sup>* of the source voltage *vS*.

Independently of the reason of voltage distortion its shape bettering can be performed with the use of the same conductance signal-based control method considered. In other words, there is no need to identify the reason or spectrum of the source voltage distortion. In any case it is sufficient to inject the adequate voltage correction *vadd* in series with the source voltage *vS* (Figure 1). To produce appropriate voltage correction *vadd* the series converter generates (using energy stored in the DC-link capacitor) the current flow through the converter's side winding of the injecting transformer. The hysteresis controller compares load voltage to its reference, i.e., the source voltage fundamental component, and steer switches action of the series converter in order to keep this voltage near this reference. As the result the required voltage *vadd* appears across the grid side winding of the injecting transformer.

Voltage and current distortion components may be considered as nonactive ones. Therefore, while compensating and being in the steady state, both UPQC converters impact the compensated voltage/current runs using nonactive power only, i.e., without change of mean magnitude of DC-link capacitor energy (if skip energy loss in the UPQC circuitry). In such situation the load conductance signal is still constant and, consequently, source current amplitude is constant as well. This observation is important from the perspective of the considered control method.

However, for the control method considered each change of load active power cause change of the conductance signal. Also energy losses in UPQC circuitry influence the total load-and-UPQC active power, so they impact the conductance signal (Equation (5)). It can be then said that there are no changes of signals (Equations (5) and (6)) when load active power is constant and the UPQC's series converter compensates only for higher harmonics of source voltage. On the contrary, the signals (Equations (5) and (6)) get new magnitude when the series converter counteracts change of source voltage rms, or if there is a change in source voltage harmonic content. As a result the source is loaded higher/lower in order to maintain constant voltage rms across load terminals.

Finally, as an important conclusion it can be said, that all energy relations between the UPQC's series converter and the rest of the system considered can be supervised by the control unit of the UPQC's shunt converter and there is no operational incompatibility between both converters.

#### **3. Studies for UPQC Standard Operation**

The considered control method has been extensively verified by means of computer simulation. The IsSpice software (Intusoft, San Pedro, CA, USA) has been used. During some analyses performed the deformation of source voltage and load current often went beyond the voltage and current runs encountered in practice. They caused strong overload of UPQC circuitry. This approach, attractive in simulation studies, allows to assess the usability area of the considered UPQC control method.

In this paper simulation studies are divided into two parts. The first one, Section 3, considers UPQC standard operations, i.e., compensation for nonactive current and improving the voltage waveform on load terminals. The second part, Section 4, describes additional UPQC functionalities that arise if the conductance signal control method is used. In particular, this section considers the possibility of using UPQC as a distribution center for locally generated power.

For all analyses performed the same supply source characteristic and UPQC circuitry were used:


(5) A high-pass passive LC(R) filter has been added in parallel to the UPQC's shunt converter in order to diminish flow of high-frequency component of the compensating current into the supply source branch.

### *3.1. Basic Examination of the Control Method. Turning UPQC and Load On and O*ff

Achieving the steady state after turning the UPQC or load on and off is considered in this Subsection. Analyses of selected signals of the network after switching the load on and off gives information on correctness of source-and-load energy balancing performed by UPQC. This energy balancing is crucial for the studied UPQC control method.

For all analyses carried out in this subsection the load is a thyristor power controller. It is composed of a 10 Ω resistor in series with two thyristors in antiparallel connection. Both thyristors are fired symmetrically with phase angle of π/2. This load brings in abrupt load power changes and wide harmonic spectrum for load current that can be difficult to compensate by SAPF and UPQC devices.

### 3.1.1. Turning UPQC's Shunt Converter On

Since the shunt converter controls the source current it is also responsible for the total power delivered to the whole UPQC-and-load network. In particular, it controls also the source current component that is related to energy dissipated in all UPQC's circuitry. For this reason the shunt converter should be turned on no later than the series one. The process of turning the shunt converter on is shown in Figures 2 and 3, and then characterized with the use of basic electrical load and UPQC parameters collected in Tables 1 and 2.

In Figure 2 source voltage *vS*(*t*), source current *iS*(*t*) and the conductance signal *G*(*Tn*)—According to Equation (5), are shown as waveforms 1, 2 and 3, respectively. Before the time instant *t* = 400 ms the source-and-load circuit acts in the steady state. The UPQC is inactive yet and does not impact the source-load energy transmission. Then the shunt converter is turned on at instant *t* = 400 ms. Until this moment the DC-link capacitor voltage is of its initial magnitude *VC*0, so the conductance signal (Equation (6)) is null. For that reason for the whole period *T* starting at this moment the load is powered using energy stored in UPQC reactance elements, practically solely from its DC-link capacitor. Therefore the source current is practically null. At the end of this period *T*, i.e., at *t* = 420 ms, the load equivalent conductance related to this period can be calculated and then used to produce the reference signal (Equation (6)) for the next period *T*, i.e., for time period 420 ms–440 ms.

**Figure 2.** Shunt converter turning on. Source voltage: run 1, source current: 2, conductance signal: 3. Y scale for conductance signal is 45 mS/div.

**Figure 3.** Shunt converter turning on process. DC-link capacitor voltage: waveform 1, and load equivalent conductance signal: waveform 2.

**Table 1.** Compensated load basic electrical parameters just before (for 380 ms–400 ms) and after (for 400 ms–460 ms) the instant (at 400 ms) of turning the shunt converter on.


VLoad and ILoad are voltage and current rms on load terminals, SLoad and PLoad are load apparent and active powers, PFLoad is load power factor, WLoad is energy consumed by load, GLoad is load equivalent conductance equal to PLoad/(VLoad) 2.

**Table 2.** UPQC-and-load subcircuit basic electrical parameters before (380 ms–400 ms) and after (400 ms–460 ms) the instant (at 400 ms) of turning the shunt converter on.


VSource and ISource are voltage and current rms on UPQC terminals, ISource THD is source current THD factor, SUPQC<sup>+</sup>Load and PUPQC<sup>+</sup>Load are UPQC-and-load apparent and active powers seen on UPQC terminals, PFUPQC<sup>+</sup>Load is UPQC-and-load subcircuit power factor, WUPQC<sup>+</sup>Load is energy delivered to UPQC-and-load subcircuit from source, ΔWDCCap is change of energy stored in DC-link capacitor, GSignal is signal of load equivalent conductance calculated accordingly to Equation (5).

The whole "static" change of the capacitor voltage takes place in two steps: the first step from 599.7 V (sample taken at time *t* = 400 ms), down to 589.3 V (sample taken at *t* = 420 ms) and then the second step from 589.3 V for sample taken at *t* = 420 ms down to 588.4 V at *t* = 440 ms. There are two main reasons of this two-step process of energy balancing:


Finally, after the two-step updating of the conductance signal magnitude the whole network achieves the steady state.

There are basic electrical parameters characterizing load and UPQC action, related to waveforms shown in Figures 2 and 3, collected in Tables 1 and 2. They characterize the load and source work, respectively.

The load work is buffered through the UPQC. Therefore, variations in load action are "seen modified" from the perspective of the supply source. In particular, there are two major changes, which are seen from this perspective, that occur in whole load-and-UPQC circuitry action at *t* = 400 ms and then 20 ms later. These changes are related to the periodical updating of the conductance signal, see Equation (5) and comments to Figures 2 and 3.

It is noteworthy, that there is no difference in UPQC operation if the order of turning on the load and UPQC is reversed, that is, when UPQC is already active at the moment when the load begins its work. Similarly, at this moment the DC-link capacitor voltage equals its initial magnitude and the going magnitude of the conductance signal is zero. Consequently, the energy flow is buffered by UPQC with all consequences on UPQC action already described above.

#### 3.1.2. Turning UPQC's Series Converter On

The series converter starts its action at *t* = 800 ms (Figure 4), when the network operates in the steady state and the shunt converter is already active. Since for the control method considered no time is needed for analysis of source voltage spectrum its distortion can be compensated immediately. This compensation cause change in harmonic components of DC-link capacitor voltage, waveform 2 in Figure 4. Although compensation for harmonics does not require the use of active power an increase of mean magnitude of the capacitor voltage can be observed. This is due to change of load active power being result of elimination of higher harmonics power from the total active power of the load.

Change in mean value of capacitor voltage causes change in magnitude of conductance signal (Equation (5)). Therefore, appropriate change of source current amplitude can be also observed. Changes of source-UPQC-load system parameters, related to Figures 4 and 5, are collected in Tables 3 and 4.

Just after turning the series converter on, at *t* = 800 ms, there is a drop of load active power resulting from eliminating load voltage distortion. As a consequence a part of source current turns out to be "excessive" with respect to going load and UPQC energy demand. Energy of this excessive current is stored in the DC-link capacitor increasing its voltage/energy. Therefore, on the base of Equation (5) the conductance signal is recalculated to a new magnitude at the beginning of the next *T* period. From this instant, i.e., for *t* = 820 ms, possibly delayed by the corrections described in the commentary next to Figure 2, the whole network reaches a new steady state.

**Figure 4.** Series converter turning on. Load voltage: waveform 1, and DC-link capacitor voltage: waveform 2.

**Figure 5.** Series converter turning on process. Source current: waveform 1, and conductance signal: waveform 2.

**Table 3.** Basic parameters describing load action before (780 ms–800 ms) and after (800 ms–860 ms) the instant (800 ms) of turning the series converter on.


VLoad THD [%] is load voltage THD factor and other parameters are defined as for Table 1.


**Table 4.** Basic parameters describing load action before, (780 ms–800 ms) and after (800 ms–860 ms) the instant (800 ms) of turning the series converter on. All parameters are defined as for Table 2.
