By increasing the penetration level of photovoltaic systems, the distribution networks and their components are more likely to face operational problems. The extent of problems that arise depends directly upon the size (penetration level) of PV and location (siting) of the installation [5].

In utility-scale electricity generation, the so-called duck curve shows the timing disparity between peak demand and renewable energy production over a day. In many energy markets, the highest demand occurs after sunset, when solar power is no longer available. For areas where a large amount of solar energy has been installed, the amount of power to be produced from sources other than solar or wind shows a rapid increase around sunset and peaks in the mid-night hours, creating a graph that resembles the outline of a duck. At any given time of the day, the duck curve indicates the demand for electricity [12]. Electricity firms produce the least amount of electricity overnight, then it ramps up in the morning (due to increase in demand), then at sunset, energy demand peaks as shown in Figure 1.

Figure 2 shows the solar production and variation of demand curve over the day. The change in demand curve is shown with the increase in solar deployment over years. Maximum solar panel deployment is taking place and it is found that the sun produces most of the energy at the mid-day. New solar plants are being constructed yearly which makes mid-day demand drop substantially. This drop in the mid-day demand explains the formation of the “Belly of the Duck Curve” [12].

The stiffness ratio is determined at the Point of Common Coupling (PCC) for the solar PV Integration. The PCC is where Solar Plant is connected to the Distribution network. Stiffness Ratio (SR) is the ratio of the anticipated short circuit capability (in MVA) at the PCC to the PV plant output [13]. It is given as:

Stiffness   ratio = SC PCC / PV output

where SC_PCC is the maximum Short Circuit level at the Point of Common Coupling and the PV_output is the power output or rating of the solar PV.

Stiffness ratio gives a measure of the ability of a Distribution network to prevent voltage violations or deviations caused by Solar PV integration into the Grid. As best practice in the industry, S.R > 5 is considered to be adequate [13].

At one point, if the PV array (as after sunset) produces no real power, an inverter will supply only reactive power Q (kVAR). On the other hand, when the PV array generates its maximum rated real power, the inverter has no ability to produce reactive power unless it is deliberately over dimensioned or a part of active power output is truncated. Under such constraints, the PV inverter’s reactive power can be regulated by its power factor in such a way that the Solar PV inverter does not exceed its kVA rating. However, reactive generation of power by a PV inverter is not free, and comes at a cost [14]. The power factor of the inverter is therefore a key factor in determining the quantum of real and reactive power to be produced by the solar PV plant.

The viability of any solar PV installation at any location depends, to a large extent, on the availability of solar radiation at that location. To determine the availability of solar radiation at any location, the global horizontal irradiance (GHI) is measured. The GHI refers to the power per unit area received from the Sun in the form of short wavelength electromagnetic radiation measured perpendicular to the incoming sunlight. GHI is expressed in W/m² and comprises of direct normal irradiance and diffuse horizontal irradiance. Direct normal irradiance refers to the part of the GHI that falls in a straight line at its present location in the atmosphere from the direction of the sun. Diffuse horizontal irradiance refers to the GHI portion that does not come from the sun on a direct path, but has been dispersed through clouds, particles of dust, vapor molecules etc. Various national and international bodies collate the GHI for various locations throughout the world all year round. The collated GHI is used to plot solar maps for the various locations and countries (see Figure 3).

The solar maps provide information on grid cells on a month or annual average daily total of solar resources.

Figure 4 shows the climatic and solar irradiation data for Prestea, a town in the environs of Tarkwa. From Figure 4, it is evident that the seasonal variation

in the country impacts the GHI measured in the Prestea-Tarkwa area. From November to May, the GHI is above the annual average of 4.64 kWh/m²/d with the peak GHI of 5.23 kWh/m²/d recorded in February and March. During the rainy season, the GHI recorded for the area is below the annual average with the lowest GHI of 3.87 kWh/m²/d recorded in September. The recordings are within acceptable limits.

In Ghana, due to the equatorial location and tropical climate, a typical solar PV plant’s generation occurs during daytime hours starting from around 6:00 GMT. The power generated by the PV plant increases gradually until it peaks during the noon hours and gradually reduces to zero in the evening around 18:00. Figure 5 shows the generation profile of an existing Solar PV plant in ECG’s network. This study considers the load profile of the selected network from 7:00 to 17:00 in order to select the optimum size of the PV plant [6].

For the optimization study, analysis of the load profile of the network under study is critical. The solar PV plant must generate adequate electric power to meet the load demand and prevent power flow into the sub-transmission system.

In Ghana, owing to its equatorial location and tropical climate, a typical solar PV plant’s generation occurs during daytime hours starting from around 6:00. The power generated by the PV plant increases gradually until it peaks during the noon hours and gradually reduces to zero in the evening around 18:00 (see Figure 5). Thus, this study considers the load profile of the selected network from 7:00 to 17:00 in order to select the optimum size of the PV plant.

The load profile of Tarkwa BSP for the year 2019 indicates a peak demand of 41.82 MVA with a corresponding power factor of 0.915 in the month of March. As a result, the average weekday and weekend daily demand was calculated from the 24-hour demand profile obtained from the ECG Automatic Meter Reading (AMR) online system for the month of March to enable us determine the penetration level of Solar PV plant to be connected to the Tarkwa BSP. Table 1 and Figure 8 show the average weekday demand profile for Tarkwa BSP, whereas Table 2 and Figure 9. show the average weekend demand profile for Tarkwa BSP for the month of March, 2019.

From Table 1 and Figure 8, the weekday peak demand of the average load readings in March was recorded as 31.34 MVA with a corresponding power factor of 0.921 at 21:00. From Table 2 and Figure 9, the weekend peak demand of the average load readings in March was recorded as 29.89 MVA with a corresponding power factor of 0.928 at 23:00.

The minimum demands recorded for weekday and weekend were 20.45 MVA with a power factor of 0.913 and 24.29 MVA with power factor of 0.912, respectively. The weekday demand profile was higher than the weekend demand

profile as can be seen from Figure 8 and Figure 9 respectively. Using an annual growth rate of 3.62%¹, the average weekday demand profile was projected to 2020. The weekday 2020 projected demand for Tarkwa BSP is shown in Figure 10.

The Tarkwa BSP serving the Tarkwa network recorded an average weekday and weekend load factors of 0.806 and 0.888 respectively. This shows a high utilization of power. The network is made up of a mix of industrial and residential customers. There is one significant peak which occurs in the evening and relatively flat demand profile during the daytime.

In this study, the existing Tarkwa BSP operational network was modelled using the CYME Power Engineering Software (Cyme 8.0 Rev 05). For the modelled network, three points of common coupling (PCCs) for the solar PV plant were considered. The PCCs selected from the Tarkwa BSP network were:

1) Interconnection at the source bus (Tarkwa BSP).

2) Interconnection at mid-way of the network (GAG Primary Substation).

3) Interconnection at the tail end of the network (Darmang Switching Station).

The following considerations were made in modelling the networks:

· Average behavior of the load type in the various networks was modeled as constant power loads.

· Based on data obtained from ECG Automatic Meter Reading (AMR) of Tarkwa BSP, the average power factor of the BSP of 0.903 lagging was used for all load points at the Tarkwa BSP.

· An operating voltage of 34 kV was used at the ECG end of the Tarkwa BSP as per ECGs specifications.

· Bus sectionalizers on 33 kV and 11 kV buses of primary substations were considered tied together respectively.

The 2018 projected demand for the Tarkwa BSPs was used as the base load for this study. The 12:00 pm reading of the average weekday profile of March, 2019 obtained from the ECG automatic meter reading (AMR) online system (24.27 MVA) was projected to 2020 (25.15 MVA) and used for the analysis. A corresponding average power factor of 0.903 was used for the load points in the network. The loads were allocated to the load points and substations within the networks.

The Solar PV was connected to the source of the 33 kV network of the Tarkwa (Old Atuabo) BSP. The detailed results of the study are presented in Table 4. The voltage profiles at the Source (Tarkwa PCC) and technical losses of the network for different Solar PV penetration levels are shown in Figure 11 and Figure 12, respectively.

As the PV penetration level increases at the Tarkwa PCC (Source), the voltage reduces, but nevertheless remains above ECG’s allowable voltage lower limit of 30.03 kV, as shown in Figure 11.

The 33 kV feeder losses, on the other hand, progressively increase, as the PV penetration level increases, with the minimum losses occurring at 40% penetration level corresponds to a capacity of 9 MWp as shown in Figure 12.

This implies that 40% PV penetration level optimizes the Tarkwa BSP network

with respect to loss reduction when the Solar PV plant is connected to the Source (Tarkwa BSP).

The Solar PV was connected midway of the network at the GAG Primary substation. The detailed results of the study have been presented in Table 5. The voltage profiles at the GAG PCC (midway) and technical losses for different Solar PV penetration levels are shown in Figure 13 and Figure 14, respectively.

As PV penetration level increases at the GAG PCC (midway of the network), voltage profile is improved, but nevertheless remains below ECG’s allowable voltage upper limit of 35.97 kV, as shown in Figure 13.

The network losses followed the usual U-Shape trajectory, as the PV capacities interconnected at the GAG PCC increases, with the minimum losses occurring at 40% penetration that corresponds to a capacity of 9 MWp as shown in Figure 14.

The Solar PV was connected at the tail end of the 33 kV-network at the Darmang

Switching substation. The detailed results of the study have been presented in Table 6. The voltage profiles at the Darmang PCC (tailend) and technical losses of the 33 kV at different Solar PV penetration levels are shown in Figure 15 and Figure 16, respectively.

As the PV penetration levels increase, the voltage profile improves, but nevertheless remains below ECG’s allowable voltage upper limit of 35.97 kV, as shown in Figure 15. The general improvement in the voltage profile with increasing PV penetration as evidenced in Figure 15, adds to the known and published facts in many journals that distributed PV injections in a power system is a useful tool for voltage regulation.

Besides, the network losses followed the usual a U-Shape trajectory, as the solar PV capacities at the Darmang PCC (tail end) were increased, with the minimum losses occurring at 40% penetration that corresponds to a capacity of 9 MWp, as shown in Figure 16.

It is noteworthy, that the U-shape trajectory nature of the network losses with increasing solar PV penetration levels at the PCC, is a feature that is well corroborated in other published works.

1) The average bus voltages recorded at Tarkwa (Old Atuabo), GAG and Darmang for the different penetration levels were 33.65 kV, 33.61 kV and 34.00 kV, respectively.

2) Since all these voltages fall within the acceptable ECG voltage range of between 30.03 kV and 35.97 kV, voltage was not used as a criterion for determining the optimum location and capacity of the Solar PV plant to be connected to the Atuabo BSP network.

3) The reduction in system losses was therefore the sole criterion considered for the determination of the optimum location and capacity of the Solar PV plant to be connected to the Tarkwa (Old Atuabo) BSP network. Figure 17

shows the comparison of reduction in 33 kV system losses with the Solar PV interconnected at Old Atuabo (Source), GAG (Midway) and Darmang (tail end) and at the different penetration levels.

4) From Figure 17, it is seen that significant loss reductions were obtained at the optimum penetration level of 40% (9 MW). At that penetration level, connecting the Solar PV plant at the GAG PCC (midway) and Darmang PCC (tail end) gave loss reductions (minus sign) of 7.76% and 6.84%, respectively. However, PV integration at the Atuabo BSP (source) rather gave an increment (positive sign) of 9.99%.

5) Beyond the optimum 40% value, it is generally seen that comparatively, the rate of increase in system losses is high.

6) Comparing the GAG and Darmang PCCs, it is noted that, the rate of increase in the system loss with increasing penetration level is far slower for the interconnection at GAG PCC (midway) as compared to Damang PCC (tail end).

7) From the above analysis, the optimum capacity of Solar PV plant to be connected to the Tarkwa (Old Atuabo) BSP network is 9 MWp and the optimum location is the Ghana Australia Gold (GAG) Primary Substation.

Power flow simulation was conducted for the optimum Solar PV capacity of 9 MWp connected to the GAG Primary Substation at varying power factors (0.85 - 1.0).

Figure 18 shows the percentage loss as a function of the power factor of the solar PV inverter.

From Figure 18, the optimum power factor of the 9 MWp Solar PV plant inverter to be interconnected at the GAG Switching Station is seen as 0.94. This is because, below and beyond this power factor, the losses in the network begin to increase.

The stiffness ratio (SR) at the Point of Common Coupling was determined to assess the impact of the connection of the optimum value of 9 MWp Solar PV plant at the optimum location of GAG PCC.

From Table 7, the stiffness ratio of the anticipated three phase fault capacity to the Solar PV Plant capacity is 41.9 which is far greater than the standard industrial minimum value of 5.

With reference to the international best practice, this higher value of 41.9 is an indication that there will not be any voltage control problems in the operation of the proposed Solar PV interconnection.

In this research work, simulation studies have been conducted using the CYME software (Cyme 8.0 Rev 05) to determine the optimum penetration level and location for solar PV integration into the Tarkwa (Old Atuabo) 33 kV BSP network in the Western Region of Ghana, and operated by the Electricity Company of Ghana (ECG). Besides, the stiffness ratio of the optimum location, as well as the optimum power factor of the solar PV inverter, has been determined.

Using losses reduction as the criterion, the optimum penetration level was determined as 40%, corresponding to 9 MWp solar PV plant output. For the three main PCCs, the Ghana Australia Gold (GAG) Substation was determined to be the optimum location for integration, yielding the highest system loss reduction. This GAG substation happens to be the midway PCC in the case study network.

Also, the stiffness ratio at the GAG Substation was determined as 41.9, a value far higher than the industrial standard minimum value of 5. This high value of SR indicates that the integration of the Solar PV Plant at the GAG Switching Station will create very few voltage regulation problems. In addition, the optimum power factor of the PV plant was determined to be 0.94 lagging.

Furthermore, increasing solar PV penetration levels generally resulted in improvement in the voltage profiles of the 33 kV network; the improvements were all nevertheless within the ECG’s allowable voltage range of between 30.03 kV and 35.97 kV. This upper value represents a 1.97% increase in the voltage profile of the 33 kV network.

A maximum of 7.76% system loss reduction was attained. Also, the network losses followed the usual U-shape trajectory with increasing solar PV penetration levels at the PCC, a feature that is corroborated in other published works.

It is recommended that stability studies be carried out on the Tarkwa (Atuabo) BSP network to further analyze the stability condition of the Tarkwa BSP with the integration of solar PV to it.