Voltage Proﬁle and Sensitivity Analysis for a Grid Connected Solar, Wind and Small Hydro Hybrid System

: Due to increase in integration of renewable energy into the grid and power quality issues arising from it, there is need for analysis and power improvement of such networks. This paper presents voltage proﬁle, Q-V sensitivity analysis and Q-V curves analysis for a grid that is highly penetrated by renewable energy sources; solar PV, wind power and small hydro systems. Analysis is done on IEEE 39 bus test system with Wind power injection alone, PV power injection alone, with PV and wind power injection and with PV, wind and micro hydro power injection to the grid. The analysis is used to determine the buses where voltage stability improvement is needed. From the results, it was concluded that injection of the modeled wind power alone helped in stabilizing the voltage levels as determined from voltage proﬁles and reactive power margins. Replacing some of the conventional sources with PV power led to reduction of voltages for weak buses below the required standards. Injection of power from more than one renewable energy source helped in slightly improving the voltage levels. Distribution Static compensators (D-STATCOMs) were used to improve the voltage levels of the buses that were below the required standards.


Introduction
The demand for electric energy is rapidly increasing and putting pressure on utilities to expand their generation. This coupled with the need for clean energy has led to energy demand growth. Because of this, the researchers are envisaging the power generation technique from the renewable energy sources such as solar, hydro and wind. These energy sources are preferred for distributed generation because of their abundance, cleanliness and low cost [1,2] Solar PV and Wind power systems are getting popular because of their availability and reducing cost. However, they are intermittent in nature [3][4][5][6] and cannot satisfy power requirements alone throughout the year. Small hydro systems are also getting interest to generate electrical power in remote areas. The limitation to small hydro power is its poor voltage and frequency regulation. Therefore, a reliable technique is required to maintain constant voltage and frequency irrespective of the load and load types [7].
Grid interconnection of these renewable energy sources come with many advantages such as [8][9][10]: • Less environmental pollution because of increased use of non-polluting generation sources. • Low cost because of non-consumption of fuel.

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The power capacity of connected grids increase to meet the increase in demand. • Improved supply security.

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Cheaper power for consumers due to increase in power supply from cheaper sources.
unified power quality compensator (UPQC) where DVR is used to supply series voltage in the event of voltage sag or swell while STATCOM is used to supply or absorb reactive power to maintain constant DC-link voltage. Distribution FACTS devices are popularly used nowadays because they are smaller and less expensive than conventional FACTS devices [43,44]. STATCOM devices were used by [4,45] to support reactive power demand and improve voltage profile for a wind integrated grid. The performance of FACTS devices is done in literature [41]. Literature [42] compares the performance of STATCOM and SVC in improvement of the voltage profile after wind power integration. STATCOM is concluded to give better performance than SVC.
This paper analyzes the effects of connecting three renewable energy sources (solar PV, Wind and micro hydro) to the grid voltage levels. The sensitivities of the grid buses are also analyzed. A method for mitigating these effects is implemented and conclusions made. Solar PV system was connected to the grid through voltage source inverter to convert the DC power to AC power. Wind power was connected to the grid through voltage source converters, one to convert wind power from AC to DC for ease of control mechanisms and the other from DC to AC because the grid used was AC. Small hydro system was connected directly to the grid system.
Due to the effects of these renewable energy sources on the grid voltages and bus sensitivities, distribution static compensator (D-STATCOM) devices were connected to the affected grid buses in order to ensure the voltage levels are within the required standards as stated in IEEE standards. According to this standard, the voltage levels should always be within 5% above or below the nominal voltage value [46]. Figure 1 show the three renewable energy sources connected to the grid.

Solar PV
The equivalent circuit of a PV cell is shown in Figure 2 [47]. The current source Iph represents the cell photocurrent. Rsh and Rs are the intrinsic shunt and series resistances of the cell, respectively. Usually the value of Rsh is very large and that of Rs is very small, hence they may be neglected to simplify the analysis [48]. Practically, PV cells are grouped in larger units called PV modules and these modules are connected in series or parallel to create PV arrays which are used to generate electricity in PV generation systems. The equivalent circuit for PV array is shown in Figure 3 [49].

Solar PV
The equivalent circuit of a PV cell is shown in Figure 2 [47].  The current source I ph represents the cell photocurrent. R sh and R s are the intrinsic shunt and series resistances of the cell, respectively. Usually the value of R sh is very large and that of R s is very small, hence they may be neglected to simplify the analysis [48]. Practically, PV cells are grouped in larger units called PV modules and these modules are connected in series or parallel to create PV arrays which are used to generate electricity in PV generation systems. The equivalent circuit for PV array is shown in Figure 3 [49].    (2) where; q = electron charge, =1.6 × 10 −19 C; Voc = open circuit voltage (V); Ns = number of cells connected in series; n: the ideality factor of the diode; K: Boltzmann's constant, =1.3805 × 10 −23 J/K.
The module saturation current I0 varies with the cell temperature, which is given by:  The voltage-current characteristic equation of a solar cell is provided in [50]: Module photo-current I ph : where: I ph = photo-current in Amperes, I sc = short circuit current in Amperes, K i = shortcircuit current of cell at 25 • C and 1000 W/m 2 , T = operating temperature in Kelvin, I r = solar irradiation (W/m 2 ). Module reverse saturation current I rs : where: q = electron charge, = 1.6 × 10 −19 C; V oc = open circuit voltage (V); N s = number of cells connected in series; n: the ideality factor of the diode; K: Boltzmann's constant, =1.3805 × 10 −23 J/K. The module saturation current I 0 varies with the cell temperature, which is given by: where: T r = nominal temperature = 298.15 K; E g0 = band gap energy of the semiconductor = 1.1 eV; The current output of PV module is: and I sh = V * N p /N s + IR s R sh (6) where: N p = number of PV modules connected in parallel; R s = series resistance (Ω); R sh = shunt resistance (Ω); V t = diode thermal voltage (V). The output power of PV panels depends on the current produced due to irradiation of solar rays on the module. Thus the output power can be written as a function of insolation which is the power produced per unit square meter of the panel. Considering panels of size 1 m 2 , total power is the product of insolation, number of panels and the efficiency of the panel to effectively convert the solar irradiation into electric power. Thus the output power of PV panels can be mathematically expressed as: where: η = energy conversion efficiency, I = Current produced due to irradiation and S n = generating power per 1 m 2 for 1 MJ/m 2 .
In this paper, three PV systems were modeled with the aim of replacing three conventional generators in the IEEE 39 bus system. The PV parameters are shown in Table 1.

Doubly Fed Induction Generator (DFIG) for Wind Power
DFIGs have separate active and reactive control mechanism, hence they are the mostly used generators in wind farms as more than 85% of wind turbines utilize them. Furthermore, DFIG's converter rating is only 30% of the total generator rating which makes it attractive in the economic point of view [51,52]. The stator voltage and flux of a DFIG can be expressed as [53]; V s = R s I s + dψ s dt ψ s = L s I s + L m I r (8) where V s is the stator voltage, R s = stator winding resistance, I s is the stator current, ψ s is the stator flux linkage, L s is the stator inductance, L m is the maximum mutual inductance and I r is the rotor current. The rotor voltage (V r ) and rotor flux (ψ r ) are given by; where ω m is the rotor mechanical speed and L r is the rotor inductance. From Equations (8) and (9), the following expressions can be obtained: The magnitudes and parameters are all referred to the stator [53]. The angular stator frequency and rotor frequency are related by: where ω r is the rotor electrical speed and ω s is the electric synchronous speed. The rotor and stator voltages in the stationary reference frame are given by: V r = R r I r + sjω s L σr I r + sjω s L m (I r + I s ) V s = R r I s + sjω s L σr I s + sjω s L m (I r + I s ) (12) where L σr is the rotor leakage inductance?
The three phase active power losses for the stator (P s ) and rotor (P r ) of the DFIG machine are given by; The active power for the stator and rotor are given by; The mechanical power of DFIG is given by; The parameters used in modeling the DFIG are shown in Table 2.

Small Hydro System
The hydraulic power from a hydro system is given by [54]; where W = water discharge through the turbine in m/s, ρ = density in Kg/m 3 , H = Head in meters and g = gravitational acceleration = 9.81 m/s 2 .
Since the density of water is 1000 Kg/m 3 then the power is given by; Total potential of water can be calculated from; where: P h is the hydraulic power, n t is the turbine efficiency and n g is the generator efficiency.

Voltage Stability
Voltage stability analysis can be done using time simulations that capture the events that lead to instability or by use of static methods that examine the viability of a balance point that is represented by specified parameters of the power system. There are 4 static methods for voltage stability analysis: V-Q Sensitivity Analysis, Q-V Modal Analysis, V-Q Curves and P-V Curves. These static analysis methods allow examination of a wide range of system conditions can provide information about the nature of the problem and can identify the key contributing factors [55].
This paper utilizes the static methods to assess the effects of connecting solar PV, wind power and small hydro into the grid.

Q-V Sensitivity Analysis
This method calculates the relationship between voltage change and reactive power change [56]; where: ∆U = incremental change in bus voltage magnitude (vector), ∆Q = incremental change in bus reactive power injection (vector), J R = reduced Jacobian matrix. The V-Q sensitivities are found from the elements of the inverse of the reduced Jacobian matrix J R while the diagonal components are the self-sensitivities given by; The non-diagonal elements are the mutual sensitivities The sensitivities of voltage controlled buses are equal to zero since their voltages are assumed to be constant. V-Q sensitivities can either be; Positive or negative. Positive sensitivities shows that the system is under stable operation, the smaller the sensitivity, the more stable the system. As stability decreases, the magnitude of the sensitivity increases, becoming infinite at the stability limit. Negative sensitivities show unstable operation. At this region, the system is uncontrollable.

Q-V Modal Analysis
This modal analysis approach provides more information regarding the mechanism of instability. Voltage stability characteristics of the system are identified by determining the eigenvalues and eigenvectors of the reduced Jacobian matrix J R [56].
where: Λ = diagonal eigenvalue matrix, ξ = right eigenvector matrix, η = left eigenvector matrix, ξ i = the i th right eigenvector, i th column of right eigenvector matrix, η i = is the i th left eigenvector, ith row of left eigenvector matrix. Using modal analysis techniques Equation (19) becomes; where: u = η•∆U is the vector of modal voltage variations, q = η•∆Qq = η ∆Q is the vector of modal reactive power variations. The inverse transformation of (23) is given by; For U-Q modal analysis, Positive eigenvalue shows that the system is voltage stable. The smaller the magnitude, the closer the i th modal voltage is to being unstable. The magnitude of the eigenvalues can provide a relative measure of the proximity to instability. Zero eigenvalue shows that the i th modal voltage collapses because any change in that modal reactive power causes infinite change in the modal voltage. Negative eigenvalue shows that the system is voltage unstable. Zero reactive power is assumed for buses without load elements.
Bus participation factors give the relative participation of a bus in a certain mode. They are used to determine voltage weak areas or unstable (not controllable) areas. The sum of all the bus participations for each mode is equal to unity. The size of bus participation in a given mode indicates the effectiveness of remedial actions applied at that bus in stabilizing that mode [56].

Q-V Curves
Reactive-Voltage (Q-V) curve is one of the methods used in determining the stability of an electrical system. From Q-V curves, reactive power margin is measured as a distance between the lowest MVAr point and Voltage axis as shown in Figure 4 [57].  Therefore, reactive power margin indicates how further the loading on a particular bus can be increased before its loading limit is exhausted and voltage collapse takes place [58]. Literature [59] used reactive power margins to evaluate voltage instability problems for coherent bus groups. These margins are based on the reactive reserves on generators, SVCs and synchronous condensers that exhaust reserves in the process of computing a Q-V curve at any bus in a coherent group or voltage control area. This paper uses Q-V curves to analyze how the reactive power margins change with integration of different renewable energy sources to the grid.

Distribution Static Compensator (D-STATCOM)
D-STATCOM is a static synchronous generator operating as a Static Var Compensator (SVC) connected in parallel with the output current (capacitive or inductive) that can be controlled independently of the AC voltage network. The principle functions of a D-STATCOM are to mitigate the impact of voltage dips and voltage peaks of sensitive loads, voltage regulation, harmonic compensation and reactive power control. Its function in compensating reactive power and therefore regulating the bus bar voltage where it is connected is applied in this research paper. The basic structure for a static compensator is depicted in Figure 5 [60,61]. Therefore, reactive power margin indicates how further the loading on a particular bus can be increased before its loading limit is exhausted and voltage collapse takes place [58]. Literature [59] used reactive power margins to evaluate voltage instability problems for coherent bus groups. These margins are based on the reactive reserves on generators, SVCs and synchronous condensers that exhaust reserves in the process of computing a Q-V curve at any bus in a coherent group or voltage control area. This paper uses Q-V curves to analyze how the reactive power margins change with integration of different renewable energy sources to the grid.

Distribution Static Compensator (D-STATCOM)
D-STATCOM is a static synchronous generator operating as a Static Var Compensator (SVC) connected in parallel with the output current (capacitive or inductive) that can be controlled independently of the AC voltage network. The principle functions of a D-STATCOM are to mitigate the impact of voltage dips and voltage peaks of sensitive loads, voltage regulation, harmonic compensation and reactive power control. Its function in compensating reactive power and therefore regulating the bus bar voltage where it is connected is applied in this research paper. The basic structure for a static compensator is depicted in Figure 5 [60,61]. The amount of the reactive power is proportional to the voltage difference between t V and sh V . The variation of the output voltages amplitude is achieved by varying the direct voltage across the capacitor. The D-STATCOM can deliver a capacitive or inductive current independent of the network voltage. So it can provide the maximum capacitive current even at low voltage values. Its ability to support the supply voltage is better than the SVC. The advantage of this device is in its ability to exchange energy nature (capacitive or inductive) only with an inductor. Unlike SVC, there is no capacitive element that can cause resonances with inductive elements of the network. The structure and operational characteristic is shown in Figure 6. The D-STATCOM smoothly and continuously controls voltage from 1 V to 2 V . However, if the system voltage exceeds a low-voltage (  The voltage of D-STATCOM, V sh is injected in phase with the line voltage V t , and in this case there is no exchange of energy with the active network, but only reactive power to be injected (or absorbed) by the D-STATCOM.
The reactive power exchange with the network is done by varying the amplitude of the output voltages [61].
The output voltage of the gate turn-off thyristor (GTO) converter (V sh ) is controlled in phase with the system voltage (V t ). The output current of the D-STATCOM (I q ) varies depending on V sh [61]. If V t < V sh then the phase angle of I q is leading with respect to the phase angle of V t by 90 degrees. This leads to reactive power flowing from the D-STATCOM (capacitive mode). When V t > V sh then the phase angle of I q is lagging with respect to V t by 90 degrees; the D-STATCOM consumes reactive power. When V t = V sh then no reactive power is delivered to the power system. As a result, lagging reactive power flows into the D-STATCOM (inductive mode).
The amount of the reactive power is proportional to the voltage difference between V t and V sh . The variation of the output voltages amplitude is achieved by varying the direct voltage across the capacitor. The D-STATCOM can deliver a capacitive or inductive current independent of the network voltage. So it can provide the maximum capacitive current even at low voltage values. Its ability to support the supply voltage is better than the SVC.
The advantage of this device is in its ability to exchange energy nature (capacitive or inductive) only with an inductor. Unlike SVC, there is no capacitive element that can cause resonances with inductive elements of the network. The structure and operational characteristic is shown in Figure 6. The D-STATCOM smoothly and continuously controls voltage from V 1 to V 2 . However, if the system voltage exceeds a low-voltage (V 1 ) or high voltage limit (V 2 ), the D-STATCOM acts as a constant current source by controlling the converter voltage (V 1 ) appropriately [61]. The equivalent circuit for D-STATCOM is shown in Figure 7. The equivalent circuit for D-STATCOM is shown in Figure 7. The equivalent circuit for D-STATCOM is shown in Figure 7.
The current injected to the busbar by the STATCOM is given by; When all the quantities are in three phase;  (27) The power injected to the busbar is given by; Taking V sh = V sh ∠δ sh as the reference phase and the fundamental component of the voltage source converter as V s = V s ∠0. The active and reactive power exchanged with the bus is given by; The current injected to the busbar by the STATCOM is given by; When all the quantities are in three phase; The power injected to the busbar is given by; The active and reactive power injected by the D-STATCOM is given by;

Sizing and Placement of D-STATCOM
There are various criteria for determining the required size of STATCOM devices [62] and [63]. STATCOM devices can be sized considering the ratings of the renewable energy systems connected to the gridas presented in [64]. In this study, the amount of reactive power needed for compensation is assumed to be equal to the sum of Wind turbine systems, PV systems and Small hydro systems ratings' depending on which one is integrated at a given time. Table 3 shows STATCOM sizes connected for different connections of renewable energy types. Literature [65] made comparisons of placement of STATCOM devices at the weakest buses of a network. The comparison is made on aggregated placement and dispersed placement at the weakest buses. The dispersed placement is preferred over the aggregated placement since it results to both lowest power losses and increase loadability of the network. Thus, considering this, this paper places the designed STATCOM devices on the weakest buses of the IEEE 39 bus test grid to improve the voltage stability with influx of the power from the renewable energy sources.

Simulation and Results
After modeling the three renewable energy sources (Solar PV, wind and small hydro) their powers were injected into the IEEE 39 bus system for analysis of voltage profile, V-Q sensitivities and Q-V curves. Firstly, wind power was injected at bus 12 (15 MW) and bus 28 (15 MW) and analysis done. Secondly, three generators of the test system were replaced by solar power with varying insolation (from 1 kW/m 2 to 0.7 kW/m 2 ) at bus 30 (80 MW), at bus 32 (60 MW) and at bus 38 (100 MW) and analysis done. Thirdly, analysis was done with penetration of both wind power and solar power. Lastly, a small hydropower (10 MW) was injected at bus 03 and analysis done when the system is penetrated by all the three; solar power, wind power and small hydro power.
In order to improve the voltage levels to the required standards, the modeled D-STATCOM was connected to buses 12 and 07 and the results analyzed in comparison with those before compensation.
The IEEE 39 bus test system used in this work is shown in Figure 8.

Weak Buses of the IEEE 39 Bus System
The weakest buses of the IEEE 39 test bus system were determined using bus participation factors and are shown in Figure 9. The weakest buses are buses 12, 07 and 08.

Weak Buses of the IEEE 39 Bus System
The weakest buses of the IEEE 39 test bus system were determined using bus participation factors and are shown in Figure 9. The weakest buses are buses 12, 07 and 08.

Weak Buses of the IEEE 39 Bus System
The weakest buses of the IEEE 39 test bus system were determined using bus participation factors and are shown in Figure 9. The weakest buses are buses 12, 07 and 08.  Table 4 while the percentage voltage levels for the weakest buses of the system are depicted in Figure 10.  Table 4 while the percentage voltage levels for the weakest buses of the system are depicted in Figure 10.
From the Table 4 and Figure 10, the voltage profile for the weak buses are seen to reduce when the system is penetrated with PV solar power then slightly improve with the connection of wind power and small hydro power into the system. The buses with the highest voltage drops when PV power is used to replace the three IEEE 39 bus test system were, bus 5 from 100.53% to 93.54%, bus 6 from 100.77% to 93.57%, bus 7 from 99.7% to 92.77% and bus 8 from 99.6% to 92.89%. Considering the weakest buses of the system (12 and 07) the voltage levels percentages for bus 12 are seen to change from 100.02% to 99.96% to 94.67% to 94.84% and 94.95% in the presented order while for Bus 07, the voltage profile percentages change from 99.7%, to 99.7% to 92.77% to 92.99% to 93.93% in that order.

Voltage Profile When Reactive Power on Bus 07 Is Varied
The reactive power consumed by the load on bus 07 was varied and voltage profile analyzed. Table 5 and Figure 11, show the voltage profile for the system when the reactive power of the load at bus 07 is increased from 84.0 MVAR to 100.0 MVAR.

Voltage Profile When Reactive Power on Bus 12 Is Varied
The reactive power consumed by the load on bus 07 was varied and voltage profile analyzed. Table 6 shows the voltage profile for the system when the reactive power of the load at bus 07 is increased from 84.0 MVAR to 100.0 MVAR. Figure 12 shows the voltage profile for the weakest buses of the IEEE 39 bus system.     From the Table 4 and Figure 10, the voltage profile for the weak buses are seen to reduce when the system is penetrated with PV solar power then slightly improve with the connection of wind power and small hydro power into the system. The buses with the highest voltage drops when PV power is used to replace the three IEEE 39 bus test system were, bus 5 from 100.53% to 93.54%, bus 6 from 100.77% to 93.57%, bus 7 from 99.7% to 92.77% and bus 8 from 99.6% to 92.89%. Considering the weakest buses of the system (12 and 07) the voltage levels percentages for bus 12 are seen to change from 100.02% to 99.96% to 94.67% to 94.84% and 94.95% in the presented order while for Bus 07, the voltage profile percentages change from 99.7%, to 99.7% to 92.77% to 92.99% to 93.93% in that order.

Voltage Profile when Reactive Power on Bus 07 Is Varied
The reactive power consumed by the load on bus 07 was varied and voltage profile analyzed. Table 5 and Figure 11, show the voltage profile for the system when the reactive power of the load at bus 07 is increased from 84.0 MVAR to 100.0 MVAR. Figure 11. Voltage profile when reactive power at the load at bus 07 is increased from 84 MVAR to 100 MVAR.  Figure 11. Voltage profile when reactive power at the load at bus 07 is increased from 84 MVAR to 100 MVAR. From Tables 5 and 6 and Figures 11 and 12, there is a reduction in the voltage levels when PV penetrates the grid and the voltage levels improve as wind and small hydro powers are injected to the grid. From  From Tables 5 and 6 and Figures 11 and 12, there is a reduction in the voltage levels when PV penetrates the grid and the voltage levels improve as wind and small hydro powers are injected to the grid. From Table 5, The buses with the highest voltage drops when PV power is used to replace the three IEEE 39 bus test system were,bus 4 from 100.28% to 94.88%, bus 5 from 100.37% to 93.32%, bus 6 from 100.61% to 93.35%, bus 7 from 99.46% to 92.46% and bus 8 from 99.4% to 92.62%. From Table 6, the buses with the highest voltage drops when PV power is used to replace the three IEEE 39 bus test system were, bus 4 from 100.31 to 94.91, bus 5 from 100.45% to 93.43%, bus 6 from 100.68% to 93.45%, bus 7 from 99.62% to 92.66% and bus 8 from 99.52% to 92.68% and bus 12 99.62% to 94.22%. Considering buses 04 and 05, from Table 5; the voltage levels changed 100.28% to100.26% to 94.86% to 95.04% to 95.16% for bus 04 and from 100.37% to 100.37% to 93.32% to 93.55% to 93.69% for bus 05 respectively. From Table 6 the voltage levels changed from 100.31% to 100.29% to 94.91% to 95.09% to 95.21% for Bus 04 and from 100.45% to 100.44% to 93.43% to 93.65% to 93.78% for bus 05 respectively.

Q-V Sensitivities before Varying Reactive Power
The bus sensitivities were determined using the standard loads of the IEEE 39 bus system and the results are shown in Table 7.
From Table 7, Q-V sensitivities increase with PV replacement of the conventional sources then start reducing as wind power and small hydro power are connected to the grid. Considering buses 12 and 07; the sensitivities change from 0.0332 to 0.0333 to 0.0369 to 0.0367 to 0.0366 for bus 12 and from 0.0150 to 0.10149 to 0.0191 to 0.0189 to 0.0188 for bus 07 respectively.

Q-V Sensitivities before Varying Reactive Power
The bus sensitivities were determined using the standard loads of the IEEE 39 bus system and the results are shown in Table 7.
From Table 7, Q-V sensitivities increase with PV replacement of the conventional sources then start reducing as wind power and small hydro power are connected to the grid. Considering buses 12 and 07; the sensitivities change from 0.0332 to 0.0333 to 0.0369 to 0.0367 to 0.0366 for bus 12 and from 0.0150 to 0.10149 to 0.0191 to 0.0189 to 0.0188 for bus 07 respectively.

Q-V Sensitivities when Reactive Power at Buses 07 Is Varied
The reactive power consumed by the load on bus 07 was varied and bus sensitivities determined. Table 8 shows the bus sensitivities for the system when the reactive power of the load at bus 07 is increased from 84.0 MVAR to 100.0 MVAR.

Q-V Sensitivities when Reactive Power at Buses 12 Is Varied
The reactive power consumed by the load on bus 12 was varied and sensitivities of the buses determined. Table 9 shows the bus sensitivities for the system when the reactive power of the load at bus 12 is increased from 88.0 MVAR to 100.0 MVAR.
From Tables 8 and 9 the V-Q sensitivities increase when the reactive power is increased compared to those on Table 4. The V-Q sensitivities are highest when PV alone is injected to the grid but reduce with wind and solar penetration. From Table 5, the highest sensitivities change from 0.0332 to 0.0333 to 0.0370 to 0.0368 to 0.0367. From Table 6, the highest sensitivities change from 0.0335 to 0.0336 to 0.0372 to 0.0371 to 0.0370 in that order.

Q-V Curves
The Q-V curves for the system with standard IEEE 39 parameters, with wind power injection alone, with PV power injection alone, with PV and wind power injection and with PV, wind and small hydro power injections are shown in Figures 13-17 respectively.  Tables 8 and 9 the V-Q sensitivities increase when the reactive power is increased compared to those on Table 4. The V-Q sensitivities are highest when PV alone is injected to the grid but reduce with wind and solar penetration. From Table 5, the highest sensitivities change from 0.0332 to 0.0333 to 0.0370 to 0.0368 to 0.0367. From Table 6, the highest sensitivities change from 0.0335 to 0.0336 to 0.0372 to 0.0371 to 0.0370 in that order.

Q-V Curves
The Q-V curves for the system with standard IEEE 39 parameters, with wind power injection alone, with PV power injection alone, with PV and wind power injection and with PV, wind and small hydro power injections are shown in Figures 13-17 respectively Figure 13. Q-V curves before injection. Figure 13. Q-V curves before injection.  Tables 8 and 9 the V-Q sensitivities increase when the reactive power is increased compared to those on Table 4. The V-Q sensitivities are highest when PV alone is injected to the grid but reduce with wind and solar penetration. From Table 5, the highest sensitivities change from 0.0332 to 0.0333 to 0.0370 to 0.0368 to 0.0367. From Table 6, the highest sensitivities change from 0.0335 to 0.0336 to 0.0372 to 0.0371 to 0.0370 in that order.

Q-V Curves
The Q-V curves for the system with standard IEEE 39 parameters, with wind power injection alone, with PV power injection alone, with PV and wind power injection and with PV, wind and small hydro power injections are shown in Figures 13-17 respectively                Table 10 and Figure 18 show the voltage profile after connecting STATCOM on buses 07 and 12 in order to improve the voltage levels before varying reactive power.

After
Varying the Reactive Power on the Load at Bus 07 Figure 19 and Table 11 show the voltage profile of the IEEE 39 bus system when the reactive power of the load at bus 07 is changed from 84 MVar to 100 MVar.  Table 12 and Figure 20 show the voltage profile of the IEEE 39 bus system when the reactive power of the load at bus 12 is changed from 88 MVar to 100 MVar.
From Tables 10-12 and Figures 18-20, it can be seen that after connection of D-STATCOM at buses 07 and 12, all the voltage levels of all the buses were in the required standard i.e., within 5% above or below the nominal value for all the three cases; with PV penetration alone, with PV and Wind power penetration and with PV, wind power and small hydro penetration.   Table 11 show the voltage profile of the IEEE 39 bus system when the reactive power of the load at bus 07 is changed from 84 MVar to 100 MVar.   Table 12 and Figure 20 show the voltage profile of the IEEE 39 bus system when the reactive power of the load at bus 12 is changed from 88 MVar to 100 MVar.    From Tables 10-12 and Figures 18-20, it can be seen that after connection of D-STAT-COM at buses 07 and 12, all the voltage levels of all the buses were in the required standard i.e., within 5% above or below the nominal value for all the three cases; with PV penetration alone, with PV and Wind power penetration and with PV, wind power and small hydro penetration.

Conclusions
This paper has dealt with the analysis and mitigation of voltage stability on a grid highly penetrated by power from renewable energy sources. Determination of buses that need mitigation of voltage profile effects after integrating power from different renewable energy sources into IEEE 39 bus system network has been done. This has been done by analyzing voltage profiles, Q-V bus sensitivities and reactive power margins from Q-V curves. D-STATCOM was modeled and used to improve the voltage profiles. From the analysis, it was noted that connection of the modeled wind power alone while maintaining the conventional sources helped in stabilizing the system voltages as seen from the increase in reactive power margis from Q-V curves. When some of the conventional sources were replaced by PV systems the stability of the voltages in the grid was affected. It was further noted that connecting more than one energy source to the grid slightly improves the voltage levels and stability. In order to ensure that all the voltage levels meet the required standards, D-STATCOM was used. After connection of the D-STATCOM, the voltage levels for all the buses were improved to the required standards.