Control Structures Implementation to Allow High Penetration of a VSC within an Isolated Power System

: Recently, the increasing occurrence of power instability caused by alternative energy sources has attracted the possibility of implementing Energy Storage System (ESS), capable of supplying the energy necessary to improve the energy quality within the grid. Therefore, the attention of researchers has been drawn on the behaviour that has the connection of the ESS, based on internal controllers such as Virtual Synchronous Machine (VSM) and a Classical Control Cascade (CCC), for different ESS power ranges. In this context, this paper deals with the implementation of an ESS represented by a Voltage Source Converter (VSC) employing control techniques of VSM and CCC simulated in PScad environment in three cases: in the first case, the power system in the steady-state is seen during the description of the controls; in the second case, the power system in the presence of a fault; in the third case, the power system with a load at the PCC. Finally, a fusion CCC-VSM using a grid impedance estimator is implemented with different current reference controls considering Short Circuit Ratio (SCR) values that represent the weak and robust grid


INTRODUCTION
From the last decade, Renewable Energy Sources (RES) are increasing the rated power capacity concerning the Conventional Power Plants (CPP), generating a deficit in the energy quality and grid stability [1]. Due to the intermittent and aleatory RES production, the electrical grid can be exposed to sudden changes of active and reactive power flowing [2][3] [4]. To limit this issue, the adoption of Energy Storage System (ESS) was proposed as active power support for the grid. In [5], the possibility to incorporate the ESS through a Voltage Source Converter (VSC) was investigated, considering flexible AC transmission systems devices such as a Static Synchronous Compensator (Statcom) [6]. Some authors reported valuable studies on Statcom connected to energy storage units [7], [8]. In the following, the integration of a Statcom and an ESS is expressed as E-Statcom. As examples, the E-Statcom topology is investigated to support energy production from wind turbines [9] and photovoltaic panels [10]. Traditionally, VSC is used for applications that involve sinusoidal voltage with a variable output. In [11], a VSC generates a set of alternating voltages that can be controlled in amplitude and phase as it happens for the synchronous machines but, unlike them, E-Statcom has no inertia, since it has a virtually instantaneous response and it does not alter the system impedance significantly.
The control topology plays an essential role in the robustness of the converter formation. A Classical Control Cascade (CCC) is an internal loop that feedbacks among themselves. In [13], a Virtual Synchronous Machine (VSM) is proposed and fused to a classical CCC. Control algorithms for gridconnected converters in a simulated grid environment are validated considering a load connected to the Point of Common Coupling (PCC). Besides, the grid information is implemented by the algorithms; a grid impedance used to give stability and quality for the energy produced at the VSC output. To make the control model real, delays are introduced through delay compensation techniques to increase the quality power and reduce the output current oscillations. The relation between the grid and the VSC is expressed by the Short Circuit Ratio (SCR), that is the ratio between the grid short IOP Publishing doi:10.1088/1757-899X/1045/1/012046 2 circuit power and the converter rated power. The SCR, the grid characteristics and the voltage value are part of the facility's control requirements [14]. In this paper, the proposed controls are tested on an ideal grid representing an isolated power system of a small island. The simulations are carried out in the presence of a fault and a load at PCC for different values of SCR, to study both cases of weak and strong grids. The control is examined in the case of voltage regulation and power quality, as a function of the active power regulation, is also assessed by considering the effect of the ESS; simulations are performed in the PScad software. The remaining part of the paper is organised as follows: Section 2 gives the working principle of the power system model; Section 3 reports the control design of CCC, VSM and the fusion CCC-VSM; Section 4 provides the results obtained from the models implemented in PScad and, finally, Section 5 contains the conclusion of this paper.

MODEL OF THE POWER SYSTEM
In [15], an E-Statcom regulates the PCC voltage within the specified limit with reactive power support. A simple model is represented in Figure 1 with two VSC: the first is E-S.1, based on VSM, using controls that provide virtual inertia and damping; the second is E-S.2, based on CCC, using feedback current control through coordinate transformation. The controllers have as the main goal to generate an AC-voltage through internal control loops. These are connected at the PCC through an RL-filter, composed of a resistance and an inductance , connected with a grid impedance g, modelled by a resistance and inductance (see Figure 1). The CPP is modelled as an ideal grid with a total rated power of 24.5 MVA, a rated phase to phase voltage of 10 kV, rated frequency of 50 Hz and an E-Statcom, having the characteristics of a VSC. On the other hand, the power delivered by the transmission line is studied for the following reference active power of E-Statcom: 0.2, 0.5, 0.7, 1 p.u. based on E-S.1/E-S.2 internal controls. The relation between the ideal-grid and the VSC is expressed by the Short Circuit Ratio = / where, is the grid short circuit power and is the converter rated active power. Therefore, varying the SCR value from 1 to 10 it is possible to analyse the behaviour of .

CONTROL DESIGN
This section provides a brief overview of the controls.

3.a VSM-Structure:
This control allows a compatible grid integration of E-Statcom even in a weak, isolated grid since it mimics a Synchronous Generator (SG) [16] [17]. The goal is to create the VSM-  (1) allowing the choice of the oscillation damping and the inertia support that will be used by the converter [18] [19]. (1) In Equation (1), is the input active power, is the VSC output active power, is the virtual mechanical time constant (measured in seconds), is the virtual mechanical damping, is the VSM angular frequency, is the power angle of VSM and is the rated angular frequency.
Simulations are performed for VSC active power references of 20% and 100% (dashed line). The following parameters are considered: constant inertia levels H 0.5 s (red line), 3 s (light blue), 7 s (medium blue), 10 s (raised blue), damping levels (D= 30, 50, 100).  Figure 2 shows that waveform improves with high damping values. Note that the damping is opposed to the inertial response. Therefore, the mean value of inertia is a good compromise.
Below, in Table 2 the analysis of overshoot % and settling time Τ ℇ is shown. Indeed, Table 2 verifies the similarity of the dynamic response of VSM with an average D between 50 to 100. It is possible to obtain a low power fluctuation. Therefore, the phase of the oscillatory component is estimated 70, thus providing active damping. According to the preliminary results from simulations, the average value of inertia 7s is adopted. In the following, the paper is mainly focused on optimal strategy from the mix of active power 0 from Equation (2) in steady-state and Equation (1). (2) In Equation (2), and g are respectively the magnitude voltage of the converter and of the grid in p.u., Xf is the converter reactance in p.u. The input and output ratio of the power imbalance transfer function is named . To find this, it is necessary to study the response of the controller after a small variation of the reference power Δ around the steady-state condition, based on Equations (1) and (2) can be expressed as: (3) (4) after some mathematical passages: (5) where the poles from Equation (5) are: −ℶ ± √ℶ2−1 , where ℶ is the damping ratio and is the natural frequency. Next, the VSM improvement is simulated as a function of a disturbance, considering that a step active power of 0.7 p.u. at the instant t = 5 s is activated. Virtual inertia of 7 s, it would be a good compromise among the three possibilities of inertia previously studied. The smallperturbation is a double-phase short circuit applied at the instant t = 10 s with values of short-circuit resistance =0.5 Ω.   [29]. Figure 4 shows the electrical circuit of the power system. Where is AC-voltage source represents the VSC and is grid voltage. The dynamic Equation that describes Figure 4 can be given in the stationary reference frame by (6) where subscript dq represent the multi-system variability due to two inputs and two outputs. represents the grid voltage. ( ) represents the current output of the VSC in dq coordinates. and are the filter resistance and inductance, respectively. 0 represents the natural frequency. Equation  6 in terms of the Laplace domain as (7) where represents the inputs. Equation (7) is resolved through the following transfer matrix. (8) Assuming that: (9) Figure 5 represents the block diagram, where ( ) is a transfer function. Respectively, the structure has input reference denominated as and output denominated as . It is doesn't see but is formed from references currents in dq and is given in terms of voltage in dq. Respectively, ̂( ) is an internal transfer function parallel to the system controller ( ). In other words, (10) Applying matrix properties (11) where is the identity matrix of ( ); ( ) and ̂( ) are internal transfer functions. Figure 6 is necessary to maintain the entire closed-loop stable, which means that all transfer functions must be permanent. On the other hand, to avoid the errors in steady-state should be used as an integral action; therefore, it is necessary that ̂( )= ( ). In [30] a calculation method of ( ) through an H2 optimisation procedure is proposed to achieve the condition of stability according ( )= ( ) ( ). In this case ( )= ( )−1, giving ( )= . This result should be readjusted adding a detune for the optimal controller with a low-pass filter represented as ( )= ( +⁄ ), where represents the CVC bandwidth. The ( ) is used in all diagonal elements of the matrix. Then, considering matrix properties maybe select ( )=( +⁄ ) . ( ) represents replaced in Equation (9).
Feedback controllers are based on PI controllers [31].
In [28], [29], two block diagrams represent the dq input of the CVC: the first one is an active power close loop with the RC tuning in Equation (14), and the latter is a reactive power close loop with the RC tuning in Equation (15).
where is a first-order low-pass filter with a cut off frequency − ; therefore, the bandwidth will be represented as ∝ = − . To improve the system dynamically, it is necessary a ∝ value like 10 ⁄. On the other hand, is a first-order low-pass filter with a cut off frequency − =∝ ⁄. It is essential to know that is evaluated on the greatness of the grid. Therefore, it is necessary to choose a value within the range of oscillations required by the controls. The fast-responding feedforward power controller assumes that the PLL angle always aligns with the . 3c) CCC-VSM: [32] proposes a fusion between VSM and CCC as shows in Figure 7. The block diagram has seven internal controllers, which are: a swing equation denominated as SC, used to create ; a damping controller denominated as DC, used to improve the response of active power of the VSC as function of the pole transfer function; a current control denominated as CVC, used to protect the converter from overcurrent; a reference control denominated as RC, used to obtain the converter input of the current control and coordinate change controls abc / dq and dq / abc. On the other hand, according to the diagram , , are firstly measured. The input of controls abc/dq and dq/abc are consequently evaluated. Note that these controllers use for generate and , which are the input of CVC. Moreover, is used as input of SC. Therefore, in the diagram, two types of variables are observed. First, variables denominated as complementary, are: , and 0. Secondly, variables denominated as reference are: , .  Figure 7. VSM-CCC fusion.

4.a No load at the PCC:
A perturbation is applied to the grid, represented by a double-phase short circuit at the instant t = 15s, with a short-circuit resistance ℎ=10 Ω. The following assumptions are made: • A step reference active power of 0.7 p.u. is active at the instant t = 5 s. In this context, it would be a good compromise among the three possibilities examined in Section 3. • and frequency: a step reference of 1 p.u. is active at the instant t = 5 s. • E-S.2 is analysed with the inclusion of a compensation angle introduced by PWM using synchronous sampling [32]. The is given by 0 , where the time delay is =1.5 and represents a sampling time. • E-S.1 is analysed with VSM-CCC with =7 ,ℶ=0.707, =70. The initial active power reference is zero and at the instant t = 0.5 s.
• the following delays are introduced: one sample delay between the calculation and the VSC-Voltage sending values; half sample between the calculation and VSC active power transmitting values. Regarding the delay values, they depend on the sampling rate of the converters: the modern converters for E-Statcom work with a sampling rate of about 1 or 5 kHz. • Both controllers are analysed in the case of a robust grid (SCR = 10) and weak grid (SCR = 5). • In both controllers, to improve power oscillation, a lead-lag is added to the measure of .  Figure 8. Controllers response. Figure 8 shows that: • E-S.2 control has the same VSC's active power trend for different SCR values.
• E-S.1 control has a variable VSC's active power trend that depends on grid condition SCR.
• E-S.1 control response speed is slower than E-S.2.
• E-S.2 is the best choice for an ideal-grid.
• The power responses at the time of failure are E-S.2. an overshoot of 0.2 p.u., while E.S-1 an overshoot of 200 p.u. • PCC-voltage is 12% over the allowed range for the E-S.1 with SCR = 5. For the rest of the simulations, it remains without a problem during the small-disturbance. • In the case of SCR, E-S.1 is not capable of supporting a weak grid. Therefore, PCC voltage is more significant than 1.15 p.u.

4.b Load at the PCC:
in this case, the scheme in Figure 1 is assumed, considering a shunt load connected at the PCC through a grid impedance composed by a resistance and an inductance . Then, Equation (11) in continuous time is (16) where * is the reference current calculated with Equations (14) and (15); is the measures of current in dq coordinates; − ℎ is a transfer function of a proportional-integral PI circuit where, − ℎ=∝ ( ℎ) is the proportional gain and − ℎ=∝ ( ℎ) is the integrator gain, indicating ∝ ( ℎ) as the closed-loop bandwidth of the CVC. Based on these criteria, the simulation is carried out in the presence of a perturbation located between the R-l filter and ℎ. The setting parameters are: a step active power of 0.7 p.u., activated at the instant t = 5 s, is set to 7 s, D to 70 p.u., and ∝ − ℎ to 1215 rad/s, with a perturbation of a double-phase short circuit applied at the instant t = 15 s, with ℎ=0.5 Ω,010 Ω and SCR=10.  • second, an effect on the power imbalance given at the time of the small-perturbation is that the d-axis inductance variation is small. However, cross-saturation may affect the q-axis inductance; as a consequence, the voltage grid had a variation of about 30%. It causes the daxis current a variation of 3% in the q-axis and of about 5% in the d-axis. Because of this, efforts should be made to improve the dynamic robustness of CVC and RC.

4.c Controller performance utilising a Grid Impedance Estimator GIE:
The grid impedance estimator consists of an indirect modification of the PCC that adds greater dynamic stiffness near the synchronous frequency. On the other hand, it is shown in Subsection 3b that the VSC's output power deteriorates due to coupling in the dq coordinates. In search of a solution, Equation (13) is rewritten in terms of an equivalent impedance ( , ) where is the sum of the VSC filter inductance and the estimated grid inductance and is the sum of the VSC filter resistance and the estimated grid resistance [13]. For the improvement of control with VSM-CCC is proposed to change RC for RC-2 as a function of Equation (6). (17) where is VSC voltage, ( ) is the measured VSC output voltage in dq-frame, the transfer function based on Equation (17). A simulation to test the internal control utilising GIE with an RC2 is proposed in Figure 10. The fault is located between ℎ and ℎ in this case. The setting parameters are the same as in Figure 9. The trends in Figure 10 reveal the following aspects: • The settlement time Taε of the PCC-voltage trend was evaluated as the time taken by the response to definitively enter a band between ±3% of the steady-state value after the step voltage; in this case, it is set ε% = 0.3 of the steady-state value that corresponds to 0.3 kV. These values are not placed in tables because after the fault the voltage is within this range. • The controller response in the previous Sections shows that the mix between E-S1 and E-S2 with the strategy based on virtual impedance is an exciting proposal because it allows implementing virtual inertia and damping in the isolated micro-grid leading to advantages for grid stability. • The simulation results show that the virtual impedance has a visible improvement. System stability and current sharing ability are strongly enhanced. • The controls require almost 15 s to stabilise in the event of extreme failure resistance.
• E-S.2 allows the VSC to produce only 78% of the reference at 26 s means that it is slower than E-S.1.

CONCLUSION
The dynamic response of the two controls is good at steady state. In particular, CCC is faster than VSM. Below, Table 3 reports a comparison of the two internal controls within the VSC. In case of a short-circuit, when an overcurrent is observable within the grid, it is necessary to implement a new control strategy. Therefore, various CRs, current limiters and some low-pass filters are studied to obtain the best internal collegiate controls. Considering the above results, the second RC option is chosen for the VSM-CCC model with the Load on the PCC, because it allows implementing virtual inertia and damping in the isolated micro-grid leading to advantages for grid stability.
The results of this study will be used for facing the issue of enhancing the penetration of RES-based generators in small islands, a very hot topic, as demonstrated by the recent literature [33]- [36].