**3.3.1 Baseline scenario results and effect of mountainous observation ingestion**

The baseline scenario is that defined considering observations taken by the reduced MisT network formed by ANZA, BRUN, LAPR, PRCO, MGRA and DANI stations. For the October week, tomographic reconstructions were carried out considering ZWDs observed by the reduced MisT network observations taken during 12–18 October. The good agreement between measured and estimated ZWD time series evaluated above NAND during this period and for this scenario is shown in Fig. 4, while some statistics are given in column A of Table 2. Since data from the two mountainous receivers (BISB and BOLE in Fig. 3) were available only on 12th October, 2008, between 9.00 am and 7.00 pm, comparisons of measured and estimated ZWDs above NAND receiver were performed also considering observations taken by the reduced MisT network in this smaller period (column B of Table 2). A bias decrease of 0.4 mm is observed adding BOLE (1199 m a.s.l.) observations (see column C, Table 2) and of 1 mm adding both BOLE and BISB (1373 m a.s.l.) data (see column D, Table 2) in the input dataset. This demonstrate the necessity of measurements collected at higher altitudes which allows a best reconstruction of vertical refractivity gradients characterizing the first three atmospheric layers. The high rms error with respect the one characterizing the baseline result given in column B, Table 2, is probably due to the more noisy data acquired by the two portable mountainous receivers (this is also evidenced by the decrease in correlation observed between NAND ZWDs measurements and estimates).

used for self-consistency validation purposes ('leave-one-out' quality assessment) and are

As we have previously stated, our tomographic approach is based on two consecutive reconstruction steps. The first one (data kernel generalized inversion) creates the first guess field for the second one (algebraic tomography), which doubles the horizontal resolution (from 2x2x20 to a 4x4x20 voxels grid, i.e. means 4.5x6.5x0.5 km3). It has to be stressed that volume resolution is strictly related to the geometrical distribution of GNSS receivers and to the availability of observations. Higher resolutions would introduce an increasing number of voxels not crossed by any ray, thus worsening the final results. On the contrary, lower

Considering the available observables we were able to obtain 168 or 144 Hourly wet refractivity maps (for the October or the November week respectively). Validation is carried out considering the difference between ZWD GNSS measurements taken over NAND receiver and corresponding ZWD estimates evaluated by vertically integrating the reconstructed wet refractivity maps. Considering the entire observing period, final statistics are thus based on 168 (144) ZWD differences (measured-estimated) distribution for the October (November) week and results are given in terms of their mean values and their rms

In what follows, we will show results related to the so called baseline scenario and improvements obtained adding observations taken by mountainous receivers and from low elevation angles. Some hints about the impact of distance and height of the reconstruction

The baseline scenario is that defined considering observations taken by the reduced MisT network formed by ANZA, BRUN, LAPR, PRCO, MGRA and DANI stations. For the October week, tomographic reconstructions were carried out considering ZWDs observed by the reduced MisT network observations taken during 12–18 October. The good agreement between measured and estimated ZWD time series evaluated above NAND during this period and for this scenario is shown in Fig. 4, while some statistics are given in column A of Table 2. Since data from the two mountainous receivers (BISB and BOLE in Fig. 3) were available only on 12th October, 2008, between 9.00 am and 7.00 pm, comparisons of measured and estimated ZWDs above NAND receiver were performed also considering observations taken by the reduced MisT network in this smaller period (column B of Table 2). A bias decrease of 0.4 mm is observed adding BOLE (1199 m a.s.l.) observations (see column C, Table 2) and of 1 mm adding both BOLE and BISB (1373 m a.s.l.) data (see column D, Table 2) in the input dataset. This demonstrate the necessity of measurements collected at higher altitudes which allows a best reconstruction of vertical refractivity gradients characterizing the first three atmospheric layers. The high rms error with respect the one characterizing the baseline result given in column B, Table 2, is probably due to the more noisy data acquired by the two portable mountainous receivers (this is also evidenced by the decrease in correlation observed between NAND ZWDs

**3.3.1 Baseline scenario results and effect of mountainous observation ingestion**

error and about validation against independent data will be also given.

not included in the input dataset.

values.

**3.3 Results**

measurements and estimates).

resolutions would imply a too coarse description of the field.

Fig. 4. Time series of ZWDs measured (blue dots) and estimated (red dots) after reconstruction above NAND station, for the baseline experiment.

Table 2. Statistics of the ZWD difference (measured-estimated after reconstruction) over the NAND reference station.

#### **3.3.2 Ingestion of low elevation observations**

Considering the baseline scenario described in paragraph 3.3.1, it is clear that the improvement in the reconstruction of lower layers is strictly related to the availability of trajectories crossing (and discriminating) the lower tropospheric layers. In our tomographic reconstruction, only rays exiting from the top boundary of the analyzed 18x26 km2x10 km volume were considered. In our case, the mean elevation angle was about 30°. Since the MisT network topography is fixed, to overcome this limit and therefore improving the retrieved field, we try to ingest also low elevation trajectories which enter from the lateral boundaries of the analyzed volume. Since SWDs associated to these rays contains both a contribution of the wet refractivity field inside the considered volume (namely, the inner volume) and outside the volume (the outer volume) up to 10 km height, we modelled and removed this last quantity from the SWDs associated to low elevation (< 30°) ray before entering the tomographic approach. The wet refractivity model considered in the outer volume was obtained considering three different approaches:

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 185

(only 10 Hourly averaged ZWDs or ZTDs observations are contemporaneously available to

Fig. 5. rms of the differences between ZWDs (blue dots) or ZTDs (red dots) observed and estimated above each reference receiver, excluding data of that receiver from the input dataset before the reconstruction. All data observed by the MisT network during the entire week are taken into account. (Left) rms are plotted against the distance of the reference receiver from COMO master station. (Right) rms are plotted against the height of the reference receiver above WGS84. The degraded results obtained excluding BRUN receiver

Fig. 6. Like Fig. 5, but considering all data observed by the MisT network and by the two

First of all this analysis confirms the impact of a good height displacement of receivers in the network. Even if MisT network topography has not been optimized for the geography of the analyzed area and for tomographic applications, if we consider the impact of height in the evaluation of propagation delays, we can say that the lack of receivers placed at higher altitudes will worsen final results. In particular, considering the original MisT network, where all the receivers are more or less placed in the same layer of the map (Fig. 5) we want to highlight that, if data observed at the highest receiver (namely BISB, which is placed in another vertical layer) are not given in input to the tomography, the rms of the difference between estimated and measured zenith delays (both Wet and Total) is

mountainous receivers during the 10 hours of 12th October, 2008.

(which is the highest one) are highlighted.

generally doubled.

any receivers of the "extended" network). In this case results are shown in Fig. 6.

outer volume (this was done by a bilinear space interpolation and a linear time interpolation of the meteorological data).

Results related to this analysis are summarized in Table 3. They confirm the importance of the availability of low elevation measurements issued from different altitudes to improve the estimation of vertical refractivity gradients in such a tomographic approach. It has to be noted that the availability of external independent information (atmospheric models or, better, meteorological data) for modelling the SWD component of low elevation observations in the outer volume seems to be necessary in this case. Because of the MisT network design (receivers not homogeneously distributed in the inner volume), the internal procedure based on the coarse tomographic reconstruction (case a)) is not very effective.

Table 3. Self-consistency results considering SWD derived by low elevation observations (taken during the October week) after the application of the outer volume wet refractivity modelling strategies a., b. and c.. Results are relative to the statistics of ZWD errors (measured-estimated after reconstruction) over the NAND reference station. Results related to the baseline scenario are reported in the first column as a reference. In the last column the evident outliers due to measurements (see blue dots in Fig. 4) were removed.


**5. Simulation Results**

All simulations reported in this section have been implemented in SystemC-AMS 2.1 and run on a server installed with Intel Xeon 2.40 GHz CPU (16 cores, 2 threads each) and 128GB RAM, with Ubuntu operating system 18.04.1.

## *5.1. EES Case Study 1*

As an example case study, we used a grid-connected EES built upon the prototype of [46], and sketched on the left hand side of Figure 5. The EES includes a wind turbine, a photovoltaic (PV) array, a battery pack, various AC loads, a common DC bus, and the necessary converters. Tables 1 and 2 report the main characteristics of the EES components, in terms of rated power and costs, respectively. The right hand side of Figure 5 shows the mapping of the case study to the proposed two-layer approach. The following subsections will detail the construction of the power and cost layers.

**Figure 5.** Structure of the electrical energy system (EES) case study 1 (**left**) and result of the application of the proposed approach (**right**).

**Table 1.** Characteristics of prototype EES components.

**Table 2.** Initial capital cost and nominal lifetime of EES components.


The machine is modeled by a "SI Fundamental Synchronous Machine" block. It is a d-q model having one equivalent damper winding along *d*-axis and two equivalent damper windings along *q*-axis. The nominal field current (*I*fn) has to be defined as the field current corresponding to nominal voltage on the air gap line (*I*fq) in order to be consistent with (*L* ad) and the linear approximation used in this study.

The speed and field voltage supply of the experimental tests must be imposed in the simula‐ tion. A clock and lookup tables are used to assign test data values to each simulation time step. The initial rotor position and fault time are chosen such that the experimental and simulated short circuits are synchronized. When the synchronous machine block is used in discrete simulation, a small parasitic resistive load is required at the machine terminals to avoid numerical oscillations. Figure 8 shows the Simulink block diagram used to simulate a short circuit.

The optimization process is implemented with the "fmincon" function of the optimization tool of Matlab. It allows finding the minimum value of constrained nonlinear multivariable problems. There are no particular constraints imposed in the optimization problem, except that all variables must be nonnegative. The field and armature currents of both three-phase and line-to-line short circuits are optimized simultaneously. Results are presented in Table 3.

**Figure 8.** Simulation block diagram

### **3.3. Validations**

The parameters identified by the SSFR and reverse identification methods are presented in Table 3. To evaluate the transient responses of the d-q model, we used the Matlab/Simulink block "SI Fundamental Synchronous Machine" with the parameter values identified using experimental SSFR and reverse identification methods. We compared the field and armature responses to a three-phase short circuit and to a line-to-line short circuit (both with neutral not connected). The field current was approximately equal to 0.22 A (0.44pu). As seen in Figures 9a and 10a, the model is able to reproduce the armature current's waveform. In Figure 10b, the field current's general behavior is well represented. However, the oscillations are less damped in the case of simulated data compared to test data.

**Table 3.** d-q model parameters of the laboratory machine ܮଶ୯ 3.7 81 mH

 **Figure10: Line-to-line short circuit with a field current equal to 0.22 A**

 **Figure 9: Three-phase short circuit with a field current equal to 0.22 A Figure 9.** Three-phase short circuit with a field current equal to 0.22 A

 **Figure 9: Three-phase short circuit with a field current equal to 0.22 A**

ܴୟ 156 156 m mH 9.5 9.1 ܮ ܴୢ 187 186 m mH 2.26 2.95 ୢܮ ܴଵୢ 712 390 m ܮଵୢ 0.692 0.113 mH ܴଵ୯ 1.616 0.871 ܮଵ୯ 132 0.98 mH ܴଶ୯ 1.17 2.379 ܮଶ୯ 3.7 81 mH

 **Figure10: Line-to-line short circuit with a field current equal to 0.22 A Figure 10.** Line-to-line short circuit with a field current equal to 0.22 A

#### This section presents the coupled-circuit modeling method and illustrates its application for **4. Coupled-circuit model**

**4 Coupled-circuit model**

magnetic couplings between every electrical circuit in a machine. Compared to the d-q standard model presented earlier, it is a higher-order model that can take account of the spatial harmonics [8]. **4.1. Modeling method**  This section presents the coupled-circuit modeling method and illustrates its application for the simulation of the generator under study. This method allows the modeling of the magnetic couplings between every electrical circuit in a machine. Compared to the d-q standard model presented earlier, it is a higher-order model that can take account of the spatial harmonics [8].

the simulation of the generator under study. This method allows the modeling of the

### **4.1. Modeling method**

The behavior of a polyphase machine can be represented by several electrical circuits that are magnetically coupled. Depending on the discretization level, each individual circuit can be equivalent to a winding or a coil or a conductor or a part of a massive conductor having a constant current density. Generally, the selected circuits correspond to the stator phases, the rotor field, and the rotor damper winding [16]. The magnetic saturation is not taken into account in this section, but an improvement of the model using a simple method is presented in section 6.

The method we present does not introduce a reference frame transformation and the stator has a fixed angle. Each electrical circuit is linear and can be modeled by a resistance and several inductances that depend on the rotor angular position *θ*. The mutual inductances between the stator and the rotor alternate relative to the rotor position. Other inductances may also vary around a mean value relative to the space harmonics caused by rotor or stator slotting or saliency.

The set of circuit equations can be written in a vector matrix form as shown in (1). The elements of matrix *L* (*θ*) provide the magnetic couplings in the stator, in the rotor, and between them (2):

Simulation Methods for the Transient Analysis of Synchronous Alternators http://dx.doi.org/10.5772/61604 271

$$
\begin{bmatrix} V \ \end{bmatrix} = \begin{bmatrix} R \end{bmatrix} \begin{bmatrix} I \ \end{bmatrix} + \frac{\mathbf{d} \begin{bmatrix} \begin{bmatrix} L \ \end{pmatrix} \begin{bmatrix} I \ \end{bmatrix} \begin{bmatrix} I \ \end{bmatrix}}{\mathbf{d}t} \tag{1}
$$

( ) s1 s12 s1n s1r1 s1r2 s1rm s 21 s2r1 sn 1n sn-1rm Snm RS n m sn 1 snn 1 sn snr 1 snrm-1 snrm RS mn mn r r1s1 r1s2 r 1sn r2s1 rm LM M M M M M M M M [L ] M M M L M MM L M L MM M M M q - ´ ´ - ´ ´ é ù é ù ê ú ê ú ê ú ê ú ê ú ê ú ê ú ê ú é ù é ù ë û ëê ú ê û ë úû = = ê ú é ù éù ë û ë û ëû L L OO M OO M MOO MOO L L L OO M MOO r 1 r 12 r1m r 21 -1sn rm-1m rms1 rmsn-1 rmsn rm 1 rmm-1 rm LM M M M M MM M ML é ù ê ú é ù é ù ê ú ê ú ë û ë û ë û L OO M MOO L L (2)

To represent the movement and the variation of current, we may express (1) in the following manner, where Ω is the rotor angular speed:

$$
\mathbb{E}\left[\boldsymbol{V}\right] = \left[\boldsymbol{R}\right]\left[\boldsymbol{I}\right] + \Omega\left\{\frac{\mathbf{d}[L(\boldsymbol{\theta})]}{\mathbf{d}\,\theta\_{\mathrm{m}}}\right\}\left[\boldsymbol{I}\right] + \left[L(\boldsymbol{\theta})\right]\left\{\frac{\mathbf{d}\left[\boldsymbol{I}\right]}{\mathbf{d}\,\boldsymbol{t}}\right\}.\tag{3}
$$

The voltage on each circuit must be imposed to solve (3) and find the derivative of all currents (4):

$$\frac{\mathbf{d}\left[\boldsymbol{I}\right]}{\mathbf{d}t} = \left[\boldsymbol{L}(\boldsymbol{\theta})\right]^{-1} \cdot \left[\boldsymbol{\left[\boldsymbol{V}\right]} - \left(\left[\boldsymbol{R}\right] + \boldsymbol{\Omega} \frac{\mathbf{d}\left[\boldsymbol{L}\left(\boldsymbol{\theta}\right)\right]}{\mathbf{d}\boldsymbol{\theta}\_{\rm m}}\right) \left[\boldsymbol{I}\right]\right] \tag{4}$$

The circuit equations to account the stator star or delta connection and the damper bars connected in a grid or cage design. Figure 11 presents an example of circuit for the rotor damper bar connections connected by shorting-ring impedances (*R*ri, *L* ri) in a cage design. The unknowns of the circuit problem are the mesh currents (*J*i ), and the matrix *L* (*θ*) and *R* must be modified as detailed in Ref. [16].

Now that the circuit model is defined, the values of the inductance *L* (*θ*) and resistance *R* matrix have to be identified. The identification of the resistance matrix is straightforward and depends on the section of the conductor and its length. The values in the inductance matrix must be identified for a given number of angular positions (*θ*). Some authors propose an analytical approach to estimate the inductance curves using winding functions [8, 17]. It assumes that the permeance of iron is infinite. Another way to avoid additional simplifications is to use a finite element method [18], as proposed in this study.

For analysis purposes, the time required for this identification is quite well compensated by its increased precision. The identification is done with 2D finite element simulation with static

**Figure 11: Equivalent circuit for a rotor cage for the damper winding Figure 11.** Equivalent circuit for a rotor cage for the damper winding

general, and accurate identification of the inductance curves.

0 1 0 0

magnetic couplings, with high efficient variable-step solvers.

magnetic field resolution. The permeability of the magnetic material must be a constant (no magnetic saturation) and the extremity effects (magnetic flux leakage in the third direction) are neglected. They could be considered in a 3D simulation. This method allows a fast, general, and accurate identification of the inductance curves. Now that the circuit model is defined, the values of the inductance ሾܮሺߠሻሿ and resistance ሾܴሿ matrix have to be identified. The identification of the resistance matrix is straightforward and depends on the section of the conductor and its length. The values in the inductance matrix must be identified for a given number of angular positions (ߠ(. Some authors propose an

From the inductance curves, we can evaluate their first and second derivatives curves [18]. Linear interpolation in these curves is an efficient method to estimate the inductance value and its derivative value for any rotor position. Knowing the inductance values of two discrete rotor positions (*θ*0 and *θ*1), one can compute the inductance value for any rotor position *θ* between *θ*0 and *θ*1 using (5): analytical approach to estimate the inductance curves using winding functions [8], [17]. It assumes that the permeance of iron is infinite. Another way to avoid additional simplifications is to use a finite element method [18], as proposed in this study. For analysis purposes, the time required for this identification is quite well compensated by its increased precision. The identification is done with 2D finite element simulation with static

magnetic field resolution. The permeability of the magnetic material must be a constant (no

$$\text{for } \theta\_0 < \theta \le \theta\_1 \qquad \mathcal{L}(\theta) = \mathcal{L}(\theta\_0) + \left(\theta - \theta\_0\right) \cdot \frac{\mathcal{L}(\theta\_1) - \mathcal{L}(\theta\_0)}{\theta\_1 - \theta\_0} \tag{5}$$

(5)

The coupled-circuit model can easily be implemented in Matlab-Simulink that provides many numerical methods to solve the set of differential equations. A variable-step solver like a fifthorder ode15s is efficient in terms of simulation time, accuracy, and stability. The simulation time is also improved using the rapid accelerator mode of Simulink. The linear interpolation in a table of discrete values is easy to implement with the Simulink tools. Using an identification of inductance curves with 2D FEM, the coupled-circuit model has the advantage of combining the precision of the finite element spatial representation for the magnetic couplings, with high efficient variable-step solvers. From the inductance curves, we can evaluate their first and second derivatives curves [18]. Linear interpolation in these curves is an efficient method to estimate the inductance value and its derivative value for any rotor position. Knowing the inductance values of two discrete rotor positions (0 and 1), one can compute the inductance value for any rotor position between 0 and 1 using (5): 1 0 () () for () ( ) *L L L L*

One can notice that the assumption related to the proximity and skin effects is not a constraint in this model. Indeed, it is always possible to divide a massive conductor into several elemen‐ tary circuits carrying different currents [18]. The order of the model is increased, but the simulation of transients is still faster than with the finite element method. This approach is 1 0 The coupled-circuit model can easily be implemented in Matlab-Simulink that provides many numerical methods to solve the set of differential equations. A variable-step solver like a

fifth-order ode15s is efficient in terms of simulation time, accuracy, and stability. The simulation time is also improved using the rapid accelerator mode of Simulink. The linear interpolation in a table of discrete values is easy to implement with the Simulink tools. Using an identification of inductance curves with 2D FEM, the coupled-circuit model has the advantage of combining the precision of the finite element spatial representation for the similar to the one used in finite element simulation to simulate the currents in massive conductors as the current density in a cell area is constant.

It seems not practicable to estimate the magnetic losses with this kind of model. However, the user can add some search coils in the different parts of the machine, which can be used as flux sensors. With that information, one can evaluate the magnetic losses with the Bertotti formula. The addition of search coils does not make the study more difficult as all the magnetic couplings are calculated with the finite element method. This increases slightly the order of the model.

### **4.2. Coupled-circuit model application**

To evaluate the inductance curves of the generator under study, we used a 2D finite elements software (Flux 2D of Cedrat [15]). To reduce the size of the study domain, and reduce the simulation time required for inductance identification, the magnetic periodicity is considered. In this case, users should control the multiplying factors and calculate the inductances for a machine part only. This management of multiplying factors is simple to integrate in the coupled-circuit model. This allows more options for the winding connections between different parts of the machine.

The generator under study has a magnetic periodicity on half of its domain. Consequently, we have to identify 16 coupled circuits: 3 circuits for the stator phases, 1 circuit for the field, and 12 circuits for the damper bars. Thus, the skin effect in the damper bars is neglected. The number of rotor positions should be chosen high enough to allow the representation of the noload voltage harmonic content. The influence of the discretization of the inductance curves with different numbers of rotor positions (20, 10, and 5 rotor positions per stator slot pitch) is analyzed in [18]. The use of 20 rotor positions within one stator slot pitch allows a very precise prediction of the harmonics due to the slot pulsation field. However, the shapes are quite well preserved even with five rotor positions per stator slot pitch. The higher harmonic content can be readily seen on the curve of the field self-inductance.

### **4.3. Validations**

This section compares the waveforms obtained with the coupled-circuit model to the experi‐ mental ones.

The no-load voltage of the generator has an important harmonic content (third harmonic in the line-neutral voltage waveform and slot harmonic). The model is able to reproduce the shape of the curves accurately, but there is a small difference on the signal amplitude caused by the linear permeability used in the FE model (Figures 12 and 13).

When all phase ends are short-circuited with themselves, the phase current is trapezoidal (Figure 14) because of the third harmonic of the no-load voltage. Figure 15 presents the current waveform of a sustained three-phase short circuit, with a star connection and without the neutral–ground connection. In that case, the harmonic current multiples of three cannot circulate and the shape of the short-circuit current becomes more sinusoidal. The simulated waveforms are similar to the experimental data for both cases.

**Figure 12.** No-load voltage (*VLN* ) (field-winding current: 0.22 A; speed: 914 rpm)

**Figure 13.** No-load voltage (*ULL* ) (field-winding current: 0.22 A; speed: 914 rpm)

Here, we compare the sudden short-circuit response of every phase with itself. To compare the transient responses, we have synchronized the signals and imposed the experimental speed and field voltage. Prior to the sudden short circuit, the machine is operated at 914 rpm without load and the field current is 0.22 A (0.44 pu). At this point of operation, the magnetic saturation is negligible. Figure 16 compares the response of the phase and field current during the transient. The waveforms are well reproduced by the simulation. The current overshoot is around 2 pu for the stator winding and 8 pu for the field winding.

**Figure 14.** Steady-state current with each stator phase shorted to itself

**Figure 15.** Steady-state current with shorted star connection

Figure 17 compares the results of a three-phase short circuit without the neutral connection. The currents and the time constant are nearly the same as in Figure 16, but the shape of the phase current is more sinusoidal.

A phase-to-phase short circuit is presented in Figure 18. This short circuit generates a negative sequence current in the stator that induces an alternative voltage at twice the stator electrical frequency in the rotor winding. This explains the field current oscillations at the end of the transient period.

**Figure 15: Steady-state current with shorted star connection**

Here, we compare the sudden short-circuit response of every phase with itself. To compare the transient responses, we have synchronized the signals and imposed the experimental speed and field voltage. Prior to the sudden short circuit, the machine is operated at 914 rpm without load and the field current is 0.22 A (0.44 pu). At this point of operation, the

current during the transient. The waveforms are well reproduced by the simulation. The

current overshoot is around 2 pu for the stator winding and 8 pu for the field winding.

 **Figure 16: Transient currents when each stator phase is short-circuited to itself Figure 16.** Transient currents when each stator phase is short-circuited to itself

Figure 17 compares the results of a three-phase short circuit without the neutral connection.

negative sequence current in the stator that induces an alternative voltage at twice the stator

electrical frequency in the rotor winding. This explains the field current oscillations at the end  **Figure 17: Transient currents for a three-phase short circuit without neutral connection Figure 17.** Transient currents for a three-phase short circuit without neutral connection

of the transient period.

If we add a neutral connection to the ground, current harmonic multiples of three can circulate and the shape of the phase current is trapezoidal (Figure 19). This is also true for a

These results show that the coupled-circuit model is very performant to simulate various transient responses by taking into account the time and space harmonics of the machine. The assumptions that neglect the magnetic saturation and the skin effect in the damper circuit appear to be valid with a low field current (044 pu). Comparisons with a higher field

 **Figure 18: Transient currents for line-to-line short circuit without neutral connection**  If we add a neutral connection to the ground, current harmonic multiples of three can circulate and the shape of the phase current is trapezoidal (Figure 19). This is also true for a

These results show that the coupled-circuit model is very performant to simulate various transient responses by taking into account the time and space harmonics of the machine. The assumptions that neglect the magnetic saturation and the skin effect in the damper circuit appear to be valid with a low field current (044 pu). Comparisons with a higher field

**Figure 20: Phase current with one**

**phase shorted to the neutral**

 **Figure 18: Transient currents for line-to-line short circuit without neutral connection Figure 18.** Transient currents for line-to-line short circuit without neutral connection

current (1 pu) are presented in section 7 for all the proposed models.

current (1 pu) are presented in section 7 for all the proposed models.

single-phase short circuit (Figure 20).

single-phase short circuit (Figure 20).

**Figure 19: Line-to-line short circuit**

**with neutral connection**

If we add a neutral connection to the ground, current harmonic multiples of three can circulate and the shape of the phase current is trapezoidal (Figure 19). This is also true for a single-phase short circuit (Figure 20).

These results show that the coupled-circuit model is very performant to simulate various transient responses by taking into account the time and space harmonics of the machine. The assumptions that neglect the magnetic saturation and the skin effect in the damper circuit appear to be valid with a low field current (0.44 pu). Comparisons with a higher field current (1 pu) are presented in section 7 for all the proposed models.

**Figure 19.** Line-to-line short circuit with neutral connection

**Figure 20.** Phase current with one phase shorted to the neutral

## **5. Finite element model**

The electromagnetic field computation based on Maxwell's equations using the finite element method is the state of the art in high-precision modeling of electrical machine. While being precise, it is the highest time-consuming simulation method. For the simulation of electrical machines, it is generally assumed that the displacement currents can be neglected and the electromagnetic problem can be studied with magnetostatic or magnetodynamic simulations [12]. This section discusses the modeling method and compares the simulation results of generator under study to the experimental measurements.

## **5.1. Modeling method**

Most electrical machines can be studied with a 2D approximation [12]. That approximation is valid when the geometry of a machine section does not change along the axial direction. The problem is solved using the magnetic vector potential that has only one component in the *z* direction. Some boundary conditions (Dirichlet, Neumann, periodicity, etc.) also minimize the size of the study domain. Finite element simulation can consider the movement of the rotor, *B*(*H*) curves of nonlinear magnetic materials, and massive conductor (proximity and skin effects). The conductors can be connected to each other's with an external electrical circuit. The currents in all conductors and the copper losses can be calculated with greater precision. For a given rotor position, it is also possible to calculate the torque by the Maxwell stress tensor or the virtual works and to estimate the magnetic losses in the machine. Time-stepping computations are based on Euler method using a fixed time step. More details on the finite element method applied to electrical machines are provided in [12].

### **5.2. Model application**

We used a commercial software, Flux 2D of Cedrat [15], for the finite element modeling of the generator. Figure 21 shows the periodic 2D sketch of the resolution domain. Massive conduc‐ tors of the damper winding are modeled using the copper conductivity. The external circuit links the damper bars with constant resistances that represent the contact resistances and the shorting ring.

### **5.3. Validations**

To consider the magnetic saturation, we used an analytic saturation curve [15]. This is a combination of a straight line and an arc tangent curve made with two parameters (*μ*r = 4000, *B*s = 1.5 T). The stator and rotor are made of the same magnetic material. The simulations are made in magnetodynamic with a fixed time step of 0.25 ms (135 pts per electrical period at 30 Hz). The experimental speed variations and the field voltage are imposed as inputs. Experi‐ mental stator voltage waveforms are also imposed after the sudden short circuit.

The steady-state waveforms of no-load electromotive force (emf) and short-circuit phase current with or without neutral connection are very close to the experimental results, and that is true for all points of operation; the saturation is well represented. We compare the same Simulation Methods for the Transient Analysis of Synchronous Alternators http://dx.doi.org/10.5772/61604 279

**Figure 21.** 2D transverse sketch

**Figure 22.** Flux densities (if = 0.22 A)

results as for the previous models using the experimental waveforms with a field current of 0.22 A (0.44 pu). The phase current transient responses during a three-phase short circuit (Figure 23) and a two-phase short -circuit (Figure 24) are compared to the experimental measurements. By comparing these results with the ones obtained with the previous models, it can be seen that the shape of the signals (peak value, time constant, oscillations) is always well reproduced. The most significant difference is observed on the oscillation amplitude of the field current during a line-to-line short circuit (Figure 24b).

(Figure 23) and a two-phase short -circuit (Figure 24) are compared to the experimental

is always well reproduced. The most significant difference is observed on the oscillation

amplitude of the field current during a line-to-line short circuit (Figure 24b).

**Figure 8: Phase current of a sudden three-phase short circuit without neutral Figure 23.** Phase current of a sudden three-phase short circuit without neutral

**Figure 8: Phase current of a sudden three-phase short circuit without neutral**

b) Field winding current

 **Figure 24: Transient currents for line-to-line short circuit without neutral Figure 24.** Transient currents for line-to-line short circuit without neutral

#### In synchronous machines, the magnetic saturation is clearly visible on the no-load characteristic. It is possible to approximate the no-load characteristic with the air gap line **6 Improved circuit models considering magnetic saturation 6. Improved circuit models considering magnetic saturation**

**6 Improved circuit models considering magnetic saturation**

have shown that this approximation is valid for the transient simulation of the generator with a field current equal to 44% of its nominal value. When the saturation takes effect, that approximation is no longer true [20]. The no-load voltage amplitudes are greatly overestimated with a linear model, and this leads to incorrect steady-state and transient simulation results. Figure 25 compares the field current response characteristic. It is possible to approximate the no-load characteristic with the air gap line and neglect the saturation phenomenon for machine operations with a low field current. We have shown that this approximation is valid for the transient simulation of the generator with a field current equal to 44% of its nominal value. When the saturation takes effect, that approximation is no longer true [20]. The no-load voltage amplitudes are greatly overestimated with a linear model, and this leads to incorrect In synchronous machines, the magnetic saturation is clearly visible on the no-load character‐ istic. It is possible to approximate the no-load characteristic with the air gap line and neglect the saturation phenomenon For machine operating under a low field current. We have shown that this approximation is valid for the transient simulation of the generator with a field current equal to 44% of its nominal value.

and neglect the saturation phenomenon for machine operations with a low field current. We

In synchronous machines, the magnetic saturation is clearly visible on the no-load

steady-state and transient simulation results. Figure 25 compares the field current response of both circuit models (d-q and coupled circuits) during a three-phase short circuit at the nominal field current (0.5 A). The current waveforms obtained are less damped than the experimental result. This overestimation of the currents leads to incorrect prediction of losses and transient torques. When the saturation takes effect, that approximation is no longer true [20]. The no-load voltage amplitudes are greatly overestimated with a linear model, and this leads to incorrect steadystate and transient simulation results. Figure 25 compares the field current response of both circuit models (d-q and coupled circuits) during a three-phase short circuit at the nominal field

current (0.5 A). The current waveforms obtained are less damped than the experimental result. This overestimation of the currents leads to incorrect prediction of losses and transient torques.

**Figure 25.** Overestimation of field current without considering the saturation

Many methods are proposed to take into account the magnetic saturation in the d-q model [7, 20-22]. It is generally assumed that the leakage inductance does not vary regarding the level of saturation. Only the magnetizing inductances (*B*(*H* ), *L* ad) are affected. It is also assumed that the stator armature reaction has no influence on the magnetic saturation. Consequently, the magnetic saturation can be deduced from the machine no-load operation.

The simplest method uses two saturation factors (*L* aq, *k*sd) to modify the value of the magnet‐ izing inductances (*k*sq, *L* ad) (6). The factor (*L* aq) is function of the excitation current (*k*sd). It is computed from the no-load characteristic and the air gap line. For a given field current, we compute the ratio between the no-load voltage (*i f* ) and the equivalent voltage on the air gap line: *E*v(7).

$$\begin{cases} L\_{\text{adsat}} = k\_{\text{sd}} (\dot{\mathbf{i}}\_{\text{f}}) \cdot L\_{\text{ad}} \\ L\_{\text{aq},\text{sat}} = k\_{\text{sq}} (\dot{\mathbf{i}}\_{\text{f}}) \cdot L\_{\text{aq}} \end{cases} \tag{6}$$

$$k\_{\rm sd}(i\_f) = \frac{E\_{\rm v}(i\_f)}{E\_{\rm linear}(i\_f)}.\tag{7}$$

For the salient pole machine, the coefficient (*k*sd(*i f* )= *E*v(*i* f ) *E*linear(*i* f ) .) is usually set equal to 1 for all operating conditions as the path of *q*-axis flux is mostly in the air [7]. In the case of round rotor alternator, the coefficient (*k*sq) is often assumed equal to (*k*sq) as the *q*-axis saturation data are usually not available. In reality, magnetic saturation creates a cross-coupling between *d*- and *q*-axes [22]. However, the differences in stability performance when considering crossmagnetization have not been demonstrated for large generators [7]. In the case of the coupledcircuit model, we have applied the same simplified method using only one saturation coefficient equal to (*k*sd). All parameters of the inductance matrix have been multiplied by this coefficient.

For the generator under study, we computed the variations of (*k*sd) using the no-load charac‐ teristic up to twice the nominal field current. When the field current is greater than this value, the saturation coefficient is kept constant at its smallest value.

Figure 26 presents the simulation results when the magnetic saturation is taken into account. The d-q model current response is improved, but it is the coupled-circuit model that provides the best results. This improvement is impressive as the magnetic saturation is roughly taken into account.

**Figure 26.** Field current when considering the saturation

Note that the field current peak reaches 16 times its nominal value. At that specific moment, the finite element analysis shows that the magnetic saturation is predominantly located in the stator and rotor tooth tips because of the magnetic stator reaction (Figure 27).

**Figure 27.** Magnetic flux densities at 0.055 s (field current peak)

## **7. Sudden short-circuit comparisons**

This section compares the ability of the d-q, coupled-circuit, and finite element models to reproduce the current responses during sudden short circuits. We consider four kinds of short circuits: the sudden two-phase and three-phase short circuits without neutral connection, a two-phase short circuit with neutral–ground connection, and a single-phase short circuit with neutral–ground connection. We also compare several waveforms that have not been measured like the damper bar currents, the electromagnetic torque, and the damper circuit losses.

### **7.1. Three-phase short circuit without neutral connection at full voltage**

Right before both sudden short circuits, the machine is at 900 rpm without load and at rated field current. Solely for the purpose of comparing the current waveforms, the experimental rotor field voltage waveform and the experimental speed are used as inputs in the simulations. In addition, at the moment of the short circuit and until the end of the simulation, the measured voltage at the short circuit (at the breaker terminals) is applied in the simulation. The initial values for the rotor position and field current are imposed to the experimental ones. The time required for the simulation is of a few seconds for the d-q model, 15 second for the coupled circuit, and 2 hour 45 minute for the FE simulation. Figures 28 to 30a compare the phase current during the three-phase short circuit.

The experimental phase current peaks at 7 pu during this short circuit. The response of the dq and the coupled-circuit models are similar, and the differences with the experimental waveforms appear to be related to the speed variations and the precision on the initial conditions. Other factors could cause this difference such as magnetic saturation and skin effect. The finite element simulation is more accurate to consider these phenomena, but there is no significant improvement on the phase current response. The fixed step, the simple Euler method, and the precision of material properties could explain the discrepancies. The moment of the short circuit is between two time steps of 0.25 ms. Figure 30b shows the field current waveform that can be compared to Figure 26.

When comparing the waveforms of damper bar currents (Figure 31), it can be seen that the result of the coupled-circuit model matches closely with those of the finite elements. The d-q model does not provide that information. The experimental damper bar currents were not measured on the generator.

A comparison of simulated electromagnetic torque is shown in Figure 32. Figure 33 is a comparison of total copper losses in the damper bar circuit.

As the d-q model neglects all voltage and slotting harmonics, the high-frequency torque oscillations are filtered (Figure 32). The torque calculation methods of the two other models (FE and coupled circuit) lead to similar waveforms. It suggests that the electromagnetic torque peaks at 180 Nm (6.4 pu) compared to 110 Nm for the d-q model. One can also conclude that the assumptions used in the coupled-circuit model are valid. The finite element method takes account of the skin effect in the bars. This explains that the damper losses are near twice larger than the other models' estimations (Figure 33).

**Figure 28.** d-q model/experiment

### **7.2. Two-phase short circuit without neutral connection at full voltage**

The same conditions are used for the simulation of the sudden two-phase short circuit as for the previous section on the sudden three-phase short circuit.

From Figures 34 to 36, the phase and field currents are compared. A similar error can be seen on the evaluation of the first current peak. The possible advantage of a finite element simulation in obtaining these current waveforms is not entirely clear.

 **Figure 12: Two-phase short circuit; finite element model vs experiment Figure 30.** Three-phase short circuit; finite element model vs experiment

 **Figure 30: Three-phase short circuit; finite element model vs experiment**

 **Figure 13: Two-phase short circuit; damper bar currents**

When comparing the waveforms of damper bar currents ( Figure ), it can be seen that the

 **Figure 31: Three-phase short circuit; damper bar currents Figure 31.** Three-phase short circuit; damper bar currents

**Figure 9: Electromagnetic torque Figure 33: Total copper losses of**

As the d-q model neglects all voltage and slotting harmonics, the high-frequency torque oscillations are filtered (Figure 9). The torque calculation methods of the two other models (FE and coupled circuit) lead to similar waveforms. It suggests that the electromagnetic torque peaks at 180 Nm (6.4 pu) compared to 110 Nm for the d-q model. One can also conclude that the assumptions used in the coupled-circuit model are valid. The finite

**damper circuit**

**Figure 32.** Electromagnetic torque

conclude that the assumptions used in the coupled-circuit model are valid. The finite

losses are near twice larger than the other models' estimations (Figure).

**Figure 33.** Total copper losses of damper circuit seen on the evaluation of the first current peak. The possible advantage of a finite element simulation in obtaining these current waveforms is not entirely clear. element method takes account of the skin effect in the bars. This explains that the damper

 **Figure 34: Two-phase short circuit; d-q model with saturation vs experiment Figure 34.** Two-phase short circuit; d-q model with saturation vs experiment

 **Figure 34: Two-phase short circuit; d-q model with saturation vs experiment**

 **Figure 35: Two-phase short circuit; coupled circuit model vs experiment Figure 35.** Two-phase short circuit; coupled circuit model vs experiment

 **Figure 36: Two-phase short circuit; finite element model vs experiment Figure 36.** Two-phase short circuit; finite element model vs experiment

Comparing the waveforms of the damper bar currents shows that the coupled-circuit model provides results very close to the finite element model (Figure 37). Comparing the waveforms of the damper bar currents shows that the coupled-circuit model provides results very close to the finite element model ( Figure ).

Figure 38 shows a comparison of the electromagnetic torque, and the general pattern is the **Figure 37.** Two-phase short circuit; damper bar currents However, the waveforms of the finite element and coupled-circuit models are very similar after several periods when the current is lower (Figure 39). Some local magnetic saturation

bar losses.

same for all simulation methods. The two first periods are detailed on the second figure. The torque oscillations of high slotting frequency are overestimated by the coupled-circuit model. However, the waveforms of the finite element and coupled-circuit models are very similar after several periods when the current is lower (Figure 39). Some local magnetic saturation could explain this attenuation of torque oscillations, but the numerical methods used may be also involved. Figure 40 presents the damper circuit losses. The highest peak value (7 kW) is obtained with the finite element method, during the first period, according to the skin effect. The d-q Figure 38 shows a comparison of the electromagnetic torque, and the general pattern is the same for all simulation methods. The two first periods are detailed on the second figure. The torque oscillations of high slotting frequency are overestimated by the coupled-circuit model. However, the waveforms of the finite element and coupled-circuit models are very similar after several periods when the current is lower (Figure 39). Some local magnetic saturation could explain this attenuation of torque oscillations, but the numerical methods used may be also involved. could explain this attenuation of torque oscillations, but the numerical methods used may be also involved. Figure 40 presents the damper circuit losses. The highest peak value (7 kW) is obtained with the finite element method, during the first period, according to the skin effect. The d-q model underestimates these losses, but the differences are reduced afterward. We conclude that a simple magnetic saturation modeling method provides valid current waveforms, and the skin effect has little influence on the current waveforms. The largest

 **Figure 37: Two-phase short circuit; damper bar currents**

torque oscillations of high slotting frequency are overestimated by the coupled-circuit model.

model underestimates these losses, but the differences are reduced afterward. We conclude that a simple magnetic saturation modeling method provides valid current waveforms, and the skin effect has little influence on the current waveforms. The largest Figure 40 presents the damper circuit losses. The highest peak value (7 kW) is obtained with the finite element method, during the first period, according to the skin effect. The d-q model underestimates these losses, but the differences are reduced afterward. differences between the models are related to the electromagnetic torque and the damper bar losses.

differences between the models are related to the electromagnetic torque and the damper

 **Figure 10: Electromagnetic torque (general pattern and detail 1)**

bar losses.

We conclude that a simple magnetic saturation modeling method provides valid current waveforms, and the skin effect has little influence on the current waveforms. The largest differences between the models are related to the electromagnetic torque and the damper bar losses. model underestimates these losses, but the differences are reduced afterward. We conclude that a simple magnetic saturation modeling method provides valid current waveforms, and the skin effect has little influence on the current waveforms. The largest differences between the models are related to the electromagnetic torque and the damper

Figure 40 presents the damper circuit losses. The highest peak value (7 kW) is obtained with the finite element method, during the first period, according to the skin effect. The d-q

 **Figure 37: Two-phase short circuit; damper bar currents** Figure 38 shows a comparison of the electromagnetic torque, and the general pattern is the same for all simulation methods. The two first periods are detailed on the second figure. The torque oscillations of high slotting frequency are overestimated by the coupled-circuit model. However, the waveforms of the finite element and coupled-circuit models are very similar after several periods when the current is lower (Figure 39). Some local magnetic saturation could explain this attenuation of torque oscillations, but the numerical methods used may be

 **Figure 10: Electromagnetic torque (general pattern and detail 1) Figure 38.** Electromagnetic torque (general pattern and detail 1)

**Figure 39.** Torque (detail 2)

### **7.3. Two-phase short circuit with neutral–ground connection**

The neutral connection to the ground changes the current waveform because the harmonics multiple of three have high amplitudes in the phase emf voltage. It should be noted that the Matlab d-q model cannot simulate short circuits with neutral connection because the emf harmonics and homopolar current are neglected.

**Figure 40.** Copper losses of damper circuit

Figures 41 and 42 compare the two-phase short-circuit responses at low field current (0.22 A– 0.44 pu). The results are better with the finite element model (Figure 42) than the coupledcircuit model (Figure 41). Explanations are provided in section 7.1.

Figure 43 shows that the damper current waveforms calculated by the finite element model are close to the ones provided by the coupled-circuit model. Again, the coupled-circuit model underestimates these currents.

 **Figure 11: Two-phase short circuit; coupled circuit model vs experiment Figure 41.** Two-phase short circuit; coupled circuit model vs experiment

### **7.4. Single-phase to ground short circuit**

The same conditions are used for the simulation of the sudden single-phase short circuit as for the previous section. In this case, there is a difference of 20 A on the first cycle of the phase

 **Figure 12: Two-phase short circuit; finite element model vs experiment**

 **Figure 13: Two-phase short circuit; damper bar currents**

 **Figure 12: Two-phase short circuit; finite element model vs experiment Figure 42.** Two-phase short circuit; finite element model vs experiment

 **Figure 12: Two-phase short circuit; finite element model vs experiment**

 **Figure 13: Two-phase short circuit; damper bar currents Figure 43.** Two-phase short circuit; damper bar currents

current between the coupled-circuit model and the experimental measurements (Figure 44a). However, the field current waveforms are close (Figure 44b). **7.4. Single-phase to ground short circuit**  The same conditions are used for the simulation of the sudden single-phase short circuit as **7.4. Single-phase to ground short circuit**

 **Figure 45: Single-phase short circuit; finite element model vs experiment**

 The d-q model is widely used for protection, control, and stability studies. This model is available from Matlab-Simulink library. One way to identify the d-q model parameters without short-circuit tests is to carry out a test of standstill frequency response (SSFR). This test may be performed using an experimental setup or a finite element method in complex. This model is fast and represents accurately the

 The coupled-circuit model is a high-order circuit model that considers all space harmonics in the machine and all winding configurations. We presented a method that uses a 2D finite element method to compute the magnetic couplings and evaluate discrete inductance variations according to the rotor position. This model is easy to implement in Matlab-Simulink. It has the advantage of combining the precision of the finite element spatial representation for the magnetic couplings, with efficient variable time-step solvers. It is a bit slower than the d-q model, but

waveforms of the currents in the stator and the field winding.

 **Figure 44: Single-phase short circuit; coupled circuit model vs experiment Figure 44.** Single-phase short circuit; coupled circuit model vs experiment

We have presented three electrical machine models:

**8 Conclusion**

The results of FE model show a good agreement with the experimental phase current wave‐ form (Figure 45a). The field current response of the FE model appears to be filtered (Figure 45b). This phenomenon may be related to the discretization chosen during simulation.

 **Figure 45: Single-phase short circuit; finite element model vs experiment Figure 45.** Single-phase short circuit; finite element model vs experiment

### We have presented three electrical machine models: **8. Conclusion**

**8 Conclusion**

 The d-q model is widely used for protection, control, and stability studies. This We have presented three electrical machine models:

electrical generator. Comparisons were made with a laboratory generator by performing various types of short circuit at various excitation levels. It was shown that the magnetic

saturation must be taken into account for a generator in normal operation.

analysis requires a perfect knowledge of the machine's geometry and material properties. The main drawback of this method is the simulation time. This model is the most accurate with regard to the local magnetic saturations and the damper bar losses with the skin effect. It also gives the best estimation of magnetic losses.

We showed that all three models are efficient to estimate the transient response of an electrical generator. Comparisons were made with a laboratory generator by performing various types of short circuit at various excitation levels. It was shown that the magnetic saturation must be taken into account for a generator in normal operation.

## **Acknowledgements**

This research was supported by the National Sciences and Engineering Research Council (NSERC) of Canada and Alstom Énergies Renouvelables Canada Inc.

## **Author details**

Jérôme Cros\* , Stéphanie Rakotovololona, Maxim Bergeron, Jessy Mathault, Bouali Rouached, Mathieu Kirouac and Philippe Viarouge

\*Address all correspondence to<EMAIL_ADDRESS>
LEEPCI, Laval University, Quebec, Qc, Canada

### **References**

## **Photovoltaic Power Plant Grid Integration in the Romanian System–Technical Approaches**

Dorin Bică, Mircea Dulău, Marius Muji and Lucian Ioan Dulău

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62739

### **Abstract**

Technical issues of the integration of distributed generation (GD) in distribution net‐ works are related to effects on power service quality (supply reliability, network voltage changes), power flows and network losses. The aim of this chapter is to perform a techni‐ cal and economic evaluation of the impact that the connection of a Photovoltaic (PV) Power Plant has upon the electric energy distribution network in the distribution opera‐ tor (DO) area. Additionally, the study also examines the effects on final consumers. The approach starts from general considerations and it continues with their practical applica‐ tion in a case study.

**Keywords:** impact on the electric grid, power flow, power quality, PV Power Plant, relia‐ bility

## **1. Introduction**

Over the past decades, worldwide interest in renewable energy sources has risen significantly. Limitation of fossil fuels (oil and gas), such as the increasing cost of these primary energy sources and their impact on the climate change have stimulated interest in the area of alter‐ native electrical energy supplies. Currently, the share of decentralized power systems in the electricity infrastructure has increased considerably [1-8].

The alignment of Romania's legislation to the European energy policy is achieved by invest‐ ments mainly focused on building photovoltaic plants with megawatts generation capacities. The need to maintain the performance standards in electricity supply to consumers by distribution operators (DO), to which most of photovoltaic (PV) power plants are connected, requires an analysis of the impact that they have upon power distribution network.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The chapter aims to perform a technical and economical impact that the connection of a PV power plant has upon the electric energy distribution network in the DO area.

Other researches in this field are focused on integration, design or impact [1-7] of PV power plants [1-7].

## **2. Photovoltaic (PV) power plants situation at the Romania national level**

Nationally, until 21 January 2014, according to Transmission and System Operator (TSO) - TRANSELECTRICA records, the PV power plants in use in our country are connected to the electrical distribution network with a maximum injection power of 835,076 MW, while those connected to the electrical transport network have an injection power of 24,562 MW. The PV power plants have a geographical distribution that covers most of the country, except for the mountain areas or the north and northeast parts of the country (Figure 1).

**Figure 1.** Transmission grid and PV power plants map.

During winter, for the National Power System (NPS), the consumption is considered as peak load, so according to data from TSO on 21 January 2014, the consumption at national level was in the range of 8212 MW to 8762 MW, a value of cumulative electricity generation of all producers, resulting in a surplus of 549 MW of power.

These readings are instantaneous values recorded at 1:04 p.m., the time when the production of electric power from PV power plants has the highest relevance, being this particular time of a winter day when the PV power plants produce the maximum power reported of installed capacity.

Figure 2 represents the production of electricity for the timeframe 9:00 a.m. to 7:00 p.m., according to generating technology types.

**Figure 2.** Generation-consumption instantaneous values for 21 January 2014.

Considering the entire winter period, when annual consumption is at maximum level and the PV power plants electricity production is 30% lower than the installed power, the PV power plants contribution to the total power compared to other types of producers is small: PV power plants – 0.33%, coal – 30.95%, hydrocarbons – 24%, hydro power plants – 14%, nuclear power plants – 16.2%, wind power plants – 14% and biomass – 0.52%.

The situation during the summer, when consumption is considered as base load, the differ‐ ences are not significant, PV power plants operating at full capacity, noting that national consumption drops to an average of about 6000 MW.

Because a significant number of PV power plants, with an installed capacity of around 5500 MW, are not in use, their impact on the overall National Power System (NPS) cannot be analyzed in conjunction with the impact of other producers in the system.

Currently, in the Mureş County there are 15 PV power plants in operation, with a total installed power (*Pi* ) of 25,626 MW, of which 13 are connected to the (DO) - medium volt‐ age network (20 kV) - and 2 PV power plants are connected to the low voltage network of the same DO (Table 1).

**Table 1.** Number of PV power plants in Mureş County and installed capacity

## **3. Minimal technical requirements of PV power plants for safe operation**

The PV Power Plants, in addition to the Technical Norms governing the conditions for connecting the users to public electricity distribution ("Technical Code of Transport Network" [9] and "Technical Code of Electrical Distribution Networks" [10]), should also comply with the Technical Standard: "Requirements for the Connection to Public Electricity Networks for Photovoltaic Power Plants" [11] issued by Regulatory Authority for Energy (ANRE).

To ensure the safety operation of both the NPS and the PV power plants, the PV power plants fall into two categories, depending on the installed power: non-dispatchable power plants (NDPV) (that complies with the installed power *Pi* ≤ 5 MW) and dispatchable power plants (DPV) (*Pi* > 5 MW). Their connection to public electricity networks requires mandatory compliance with certain technical requirements before putting them into service and after‐ wards.

The following necessary requirements must to be respected by DPV power plants:

	- **◦** To remain connected to the network and run continuously, in the frequency range 47.5-52 Hz;
	- **◦** To remain connected to the main electrical network when a variation of up to 1 Hz/second of frequency occurs;
	- **◦** Continuous operating voltage in the range of 0.9-1.1 of nominal voltage;

**Figure 3.** Magnitude of voltage drops for safety operation of DPV power plants and inverters.

**Figure 4.** Active power and frequency deviations.

## **4. Case study: Chirileu PV power plant 3.2 MW**

As a particular case study we analysed the impact of a photovoltaic power plant on the grid to which it is connected. For this study we selected the Chirileu PV Power Plant with an installed capacity of 3.2 MW connected to the 20 kV overhead electric line (OEL), Ungheni-Cipău and supplied from 220/110/20 kV Ungheni station system [12].

### **4.1. General data of Chirileu PV power plant**

The PV power plant is located on an area of approximately 56,000 m2 in the Chirileu village, Mureş County. The plant is located 9.6 km from 220/110/20 kV Ungheni station and 12.7 km from Cipău supply point.

The general technical data of the photovoltaic power plant are as follows:

To emphasize the production capacity of the PV Plant, a power and energy production report for 11 July 2013 (Table 2) cumulative for the entire plant and of all inverters operating at full capacity, was generated. The total energy production was 22.27 MWh with operation at nominal power (3.2 MW).

The daily power and energy production graphics of the Chirileu PV Power Plant are presented in Figures 5 (summer) and 6 (winter).

**Figure 5.** PV power plant energy production chart – Summer.

**Figure 6.** PV power plant energy production chart – Winter.

**Table 2.** Energy/power recorded data of PV power plant (11 July 2013).

### **4.2. Network topology and characteristics**

### *4.2.1. Network topology and characteristics of 20 kV Ungheni-Cipău OEL*

The 20 kV OEL Ungheni-Cipău, 20.7 km long, comprises a conductor AlOl 70/12 mm2 (between towers 1 and 127) and AlOl 50/5 mm2 (between towers 128 and 239) (Figure 7).

The power transport capacity of the 70 mm2 OEL cross-section conductor is 7.8 MVA, and the economic power transport capacity is 7.2 MVA. The power transport capacity of the 50 mm2 and OEL cross-section conductor is 6.1 MVA and the economic power transport capacity is 5.8 MVA.

The 20 kV OEL parameters (Ungheni-Cipău) are as follows:

Photovoltaic Power Plant Grid Integration in the Romanian System–Technical Approaches http://dx.doi.org/10.5772/62739 303

**Figure 7.** 20 kV OEL Ungheni-Cipău.

### *4.2.2. Loads for 220/110/20 kV Ungheni station and 20 kV Ungheni-Cipău OEL*

In 220/110/20 kV Ungheni system station from Figure 8 (that belongs to TSO), 110/20 kV, 25 MVA transformer (Transformer 1)- had, in January 2013, a 13.91 MW (winter peak load-WPL) and a 11.43 MW (summer base load-SBL) in July 2013. The 20 kV Ungheni-Cipău OEL had a 2.74 MW (WPL) in January 2013 and 1.94 MW (SBL) in July 2013.

**Figure 8.** Ungheni system station and OEL 20 kV Ungheni-Cipău.

At 20 kV, Ungheni-Cipău OEL is connected to 39 consumers with a total installed apparent power 9.89 MVA.

The power dispatcher of the DSO provides that the nominal voltage on 20 kV Ungheni-Cipău station should be maintained at around 20.6 kV. This value is imposed so that the voltage drop should not exceed (-5%) the nominal value of the standard voltage.

### *4.2.3. Reserve loads for 20 kV OEL and Transformer 1 of Ungheni 110/20 kV Station*

The load reserves of both line and the Transformer 1 from the station are presented in Table 3, considering the maximum power supplied by Chirileu PV Power Plant and the admissible load. The OEL relates to economic transport capacity (70 mm2 cross section) and the optimal charging state (appropriate for minimum power losses) of transformer, considered at 75% of nominal apparent power (25 MVA).

**Table 3.** Load reserves of both line and the Transformer 1.

For the admissible load of 20 kV OEL, maximum load duration (*TM*) of 2000 hours/year was considered, which covers the *TM* duration required by the PV Power Plant, of 1332 hours/year.

### **4.3. Technical impact of PV Power Plant upon distribution power network**

### *4.3.1. Setting the voltage for the connection of the PV Power Plant*

As a first step for connecting the plant to a transmission or distribution electric network, the calculation of the voltage step at the connection point is required, and that is done by calcu‐ lating the moment of load, *Ml* .

$$\mathbf{M}\_{\text{A}}(MVAkm) = \mathbf{S}\_{\text{max}}(MVA) \cdot L(km) = \mathbf{3} \mathbf{3}.4(MVAkm) \tag{1}$$

For a moment of load *Ml* = 33.4 (MVAkm) and the maximum power supplied inside limits (2.5 -7.5 MVA), according to Table 4, the PV Power Plant is within Class C, so it can be connected to the MV network (20 kV).

**Table 4.** Voltage step levels at connection point according to the required power.

The technical standards establish important criteria that are taken into account for the connection of users to public electricity networks, which determine the voltage step level and the connection point:

### *4.3.2. Calculation of network safety level in connection point*

To calculate the reliability of equipments in the connection point, it is necessary to take into account the bus safety indicators of Ungheni 220/110/20 kV station (Table 5).

The parameter values of the reliability indicators for the equipments (cell line, measure, voltage transformer, current transformer) are presented in Table 6.

**Table 5.** Bus safety indicators of Ungheni 220/110/20 kV station

**Table 6.** Reliability indicators for the equipments

The calculation of the duration of interruption was performed according to the "Standard on Calculation Methods for Safety Operation of Power Plants and Devices" NTE 005/06/00 [13], using a specialized software (Figures 9 and 10).

**Figure 9.** Graphical use interface-Buses data.

**Figure 10.** Graphical use interface-Branches data.

The following main results are highlighted:

It can be concluded that the impact of Chirileu PV Power Plant connection to 20 kV Ungheni-Cipău OEL, in terms of reliability, is significant both in Ungheni station and in 20 kV Cipău connection point.

### **4.4. Load flow, power losses and voltage level analysis in steady-state conditions**

To evaluate the impact of Chirileu PV Power Plant on NPS (in particular upon the 220/110/20 kV Ungheni station, Ungheni-Cipău 20 kV OEL and consumers connected to the electric line), the following input data must be taken into account:

**•** Electrical energy production capacity of Chirileu PV Power Plant.

To perform the voltage drops, power flows and power losses, the maxim value of winter peak load (WPL) and summer base load (SBL), both in Ungheni station and 20 kV Ungheni-Cipău OEL, are considered in steady-state conditions.

Load flow studies for the power system's steady-state operation and development planning are performed to investigate MW and MVAR in the branches of the network and busbars (nodes) voltages [8].

In this case we analysed the evolution of voltage levels on the 20 kV Ungheni station bus, at the common connection point and at the end side of OEL, for two specific steady-state conditions:

Calculation of the power flow for 20 kV Ungheni -Cipău OEL is performed using NEPLAN software package [14] for the system (Figure 11), which allows for the design, simulation and management of electrical network. The solution of the power flow is obtained by means of the extended Newton-Raphson method due to the possibility of leading to an easier convergence process.

**Figure 11.** Line diagram of system in Neplan.

### *4.4.1. Power flow and power losses results*

The summary simulation results for the two regimes, winter peak load (WPL) and summer base load (SBL), for two cases, PV Power Plant out of service and PV Power Plant in service, are presented in Tables 7-10.

**Table 7.** WPL-PV Power Plant out of service

**Table 8.** WPL - PV Power Plant in service

**Table 9.** SBL-PV Power Plant out of service

**Table 10.** SBL-PV Power Plant in service

#### *4.4.2. Voltage level analysis*

According to the Performance Standard for Electricity Distribution Service, the voltage deviation and admissible limits are presented in Table 11.

**Table 11.** Voltage deviation limits

The results related to the voltage levels are presented in Table 12.

**Table 12.** Buses voltage magnitude results

The power flow results for the two regimes, winter peak load (WPL) and summer base load (SBL) are presented in Table 13.

**Table 13.** Power flow results

Due to transit of power produced by the plant, which is supplied on the 20 kV Ungheni Station bus, the power losses in the electric line increase, as presented in Table 14.

**Table 14.** Power losses results

### *4.4.3. Financial analysis - impact of Chirileu PV power plant*

The interruptions of electricity supply service result in financial losses, from the producer's point of view. According to the results of calculation of reliability indicators, the maximum duration of an interruption, in case of a fault to the point of connection, is about 20 hours.

According to the DSO performance standards, a specific quality indicator is calculated: EENS - electrical energy not supplied, defined as the total energy not supplied by the producer (PV Power Plant) to the users, due to interruptions:

$$EENS = \sum\_{i=1}^{n} \mathbf{p}\_i \cdot \mathbf{p}\_i = 1.4 \cdot 16 = 22.4 \text{(MWh)}\tag{2}$$

where:

*Pi* - non-delivered power, due to interruptions (the average of the active power non- generated by PV Power Plant (1.4 MW);

*Di* - interruption duration that is considered relevant during the time when PV Power Plant is out of service (e.g., summer, 16 hours/day).

The price of a green certificate is 130 Lei/MWh, and the producers receive two green certificates for each MW and an extra 170 Lei/MWh, the price of energy traded on the free market.

$$\text{Losses(Lei)} = \text{22.4} \\ \text{MMh} \cdot \text{(2} \cdot \text{130)} + \text{22.4} \cdot \text{170} = \text{9632(Lei / interception)} \tag{3}$$

## **5. Conclusions**

Electricity produced by conventional, large scale central generation requires HV transmission networks such as HV, MV and LV distribution networks to reach its consumers, while DG, often located at the MV busbars and closer to load, requires transporting facilities, may reduce network losses and increase service quality.

The work presents and explores both of general and particular issues related to:

The results provide a complete overview of the situation from a technical (safety and power quality) and economical point of view. The results may be also be used as a basis for devel‐ opment plans of future Distributed Generation Sources.

## **Author details**

Dorin Bică1\*, Mircea Dulău1 , Marius Muji1 and Lucian Ioan Dulău2

\*Address all correspondence to<EMAIL_ADDRESS>
1 "Petru Maior" University of Tîrgu Mureş, Tîrgu Mureş, Romania

2 Technical University of Cluj Napoca, Cluj Napoca, Romania

## **References**

tional Journal of Photoenergy, Volume 2014, Article ID 321826, 7 pages, http:// dx.doi.org/10.1155/2014/321826.

## *Edited by Wenping Cao and Yihua Hu*

The development of renewable energy technologies (such as wind, solar, and biomass) has accelerated the establishment of a low-carbon society. This book provides a glimpse of some recent advancements in modelling, control, electrical generators and power converters, and social and political aspects of utilising these renewable sources of energy. It is aimed to provide some latest references for the readers who are interested in research work, energy policies, and social dimensions of renewable energy.

Renewable Energy - Utilisation and System Integration

Renewable Energy

Utilisation and System Integration

*Edited by Wenping Cao and Yihua Hu*

Photo by Grassetto / iStock


**2.6 Inorganic-based nanomedicines**

*Current and Future Aspects of Nanomedicine*

Lipid nanosystems including nanoemulsions and solid lipid-based nanoparticles are another form of nanomedicine, which are usually used to encapsulate hydrophobic cargos to improve permeation and control release profile. Usually, a surfactant is used to ensure a uniform dispersion. Lipid nanomedicine can also encapsulate some gene therapeutics such as siRNA or contrast agents used for imaging such as F-butane. Generally, lipid nanomedicine can improve the pharmacological effect by enhancing drug accumulation in targeted tissues beside its biocompatibility. However, there are several drawbacks like rapid clearance due to reticuloendothelial system (RES) uptake and some limitations for administration routes and challenges regarding system stability [5, 6]. Unlike liposomal-based nanomedicines, lipid-based nanomedicines are not limited for cancer diseases only. Some of the diseases that are treated by lipid-based nanomedicines are amyloidosis, hepatitis B, and hepatic fibrosis. Furthermore, several types of nanoemulsion were loaded with drugs like simvastatin, cinnarizine, coenzyme Q10, and cyclosporine, which used as antihyperlipidemia, antihistaminic, antioxidant, and immunosuppressants, respectively.

Albumin-based nanomedicines are another form of nanosystems, where albumin, especially human serum albumin (protein), is used as a carrier. Albumin nanosystems can be loaded with different cargos via a simple self-assembly procedure of albumin in aqueous solution with simple crosslinking step. The main advantage of albumin is biocompatibility. Despite that, only 2 out of the 29 listed approved nanomedicines and 2 out of the 65 nanomedicines under clinical trials are albumin-based. It is currently used in imaging and delivering drugs that treat

Micelles are self-assembled nanosystem by amphiphilic molecules that have a hydrophilic part and a hydrophobic one. They have several advantages like high permeability and solubility, which improve drug bioavailability. However, they still have some drawbacks like insufficient control to drug release and cytotoxicity due to amphiphilic molecule use, which interact with cell membrane [5, 7]. Although several reports used block copolymeric micelles to reduce clearance and increase bioavailability of chemotherapeutic agents and other types of drugs, there are no approved micelle-based nanomedicines. However, there are currently nine micellebased nanomedicines undergoing clinical trials. Majority of them are used for

Polymeric nanoparticles are one of the most commonly used nanosystems for drug delivery. Several polymers have been used like ethyl cellulose, poly(lacticco-glycolic acid), polylactic acid, cyclodextrin, alginate, and chitosan. Depending on the nature of the polymer, either hydrophilic or hydrophobic, there are several techniques that have been used to prepare polymeric nanoparticles. Several advantages like relative stability and prolonged duration of action make polymeric nanoparticles a promising platform for the market. However, there are no marketed products based on polymeric nanoparticles. Only three products are currently on

**2.2 Lipid-based nanomedicines**

**2.3 Albumin-based nanomedicines**

**2.4 Micelle-based nanomedicines**

**2.5 Polymeric-based nanomedicines**

cancer diseases.

cancer treatment.

clinical trials for cancer.

**6**

Inorganic-based nanomedicines have several subtypes. Due to degradability and biocompatibility issues, few types have been used for therapeutic purpose, while other types for diagnostic purpose like imaging agents. One of these subtypes are metal oxide nanoparticles such as hafnium oxide nanoparticles which enhance tumor cell death via electron production through their stimulation with external radiation. Another subtype is in the form of colloids such as iron dextran colloids, iron gluconate colloid, and other similar derivatives that are usually used for the treatment of iron-deficiency anemia. The last subtype mentioned is iron−/silica−/ gold-based nanomedicines, either as nanoparticles with drugs arranged on the surface for the treatment of cancer or as nanoshells/nanoparticles used for thermal ablation of tumors. There are 12 products in the market that belong to this type. Eight products used iron-replacement therapies. On the other hand, four products are currently on clinical trials for treating cancer.


*Edited by Hesham Abdeldayem*

The basic researches and clinical studies on biliary tree diseases continue to advance at a rapid pace. The articles in this book were written by recognized medical experts and researchers from North America, Europe, Asia, and Africa and aim to provide state-of-the-art reviews on the current knowledge and advances in the surgery of the biliary tree. It includes the most recent advances in that field, particularly cholangiocarcinoma, biliary tree injuries, and biliary cysts.

ISBN 978-1-78923-649-1

Topics in the Surgery of the Biliary Tree

Published in London, UK © 2018 IntechOpen © Ugreen / iStock


*Edited by Lee Roy Morgan*

A novel concept that is reviewed and discussed in several chapters in the book alludes to the transport of drugs bound to red blood cells into the highly vascular CNS tumors - both primary and metastatic. Such a transport mechanism is unique and of significant therapeutic potential. It is hopeful that the novel information presented in this book will result in new approaches to the treatment CNS tumors.

Photo by bestdesigns / iStock

Tumors of the Central Nervous System - Primary and Secondary

Tumors of the

Central Nervous System

Primary and Secondary

*Edited by Lee Roy Morgan*