# Hosting Capacity of the Power Grid for Renewable Electricity Production and New Large Consumption Equipment

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## Abstract

**:**

## 1. Introduction

- i)
- New types of electricity production. There is a shift from large production units connected to the transmission grid to small units connected to the distribution grid, sometimes even connected at low voltage on the customer side of the electricity meter. Driven by the need for a more sustainable energy system, this new production is often of the renewable type and connected through a power-electronics interface. This shift in production, including the expected future developments, is rather well documented in papers, books, and government reports [1,2,3,4].
- ii)
- Changes in electricity consumption. The electricity consumption is where societal changes often have the first impact. There is since many years a general increase in the number of electric devices used. The transition to a sustainable energy system is driving a shift towards more energy-efficient equipment, equipment with a power-electronics interface, and the introduction of new types of equipment. Examples of the latter are electric vehicles [5,6,7] and heat pumps (as a replacement of either gas heating or as a replacement for resistive electric heating) [8]. The replacement of incandescent lamps by compact fluorescent and LED lamps should be mentioned specifically [9]. In developing countries, an increase in wealth is strongly correlated to a growth in electricity consumption.
- iii)
- Changes in the grid. A combination of technical developments on the one hand and societal, environmental and regulatory requirements on the other hand is leading to new types of solutions being used as part of the power grid. The shift from overhead lines to underground cables is one example, but also the slow but on-going introduction of a range of technology that comes under the term “smart grids” [10,11,12]. This new technology is obviously intended to offer better and/or more cost-effective solutions, but unintended consequences of the new technology may still pose a challenge. An overview of some of the unintended consequences for power quality of smart-grid technology is presented in [13].

- i)
- The large-scale introduction of active power electronics, in production as well as consumption equipment, results in additional phenomena becoming of importance: interharmonics; DC components and low-frequency subharmonics (“quasi-DC”); and components above 2 kHz (“supraharmonics” [21]).
- ii)
- The amount of capacitance connected to the grid is expected to increase at all voltage levels. This will result in a shift of resonances to lower frequencies. The increased emission at higher frequencies may be (partly) compensated by the shift in resonance to lower frequencies. However, at the same time, the transfer of disturbances will become less predictable.

## 2. Hosting Capacity

#### 2.1. Definition and Aim of Hosting Capacity

#### 2.2. Uncertainties

- i)
- Which customers will have a PV installation and how big will these installations be?
- ii)
- Will these installations be three-phase or single-phase connected?
- iii)
- With single-phase connection: to which phase will it be connected?
- iv)
- What will be the direction and tilt of the panels?
- v)
- Will any of the panels follow the sun through single-axis or double-axis mounts?
- vi)
- What type of inverter will the installation have? Will it be one large inverter or a number of smaller inverters?
- vii)
- Will the installation have on-site storage or not? When it has on-site storage, what will its size be, which control algorithms will it use, and will the owner use the storage to participate in day-ahead and balancing markets?
- viii)
- Will the inverter be equipped with voltage and reactive power control?

#### 2.3. Impacts on the Hosting Capacity

## 3. A Hosting-Capacity-Based Planning Approach

- i)
- Estimate the no-load voltage variations in the low-voltage distribution network during those hours of the year that the production from solar power may be high. These are the voltage variations originating from the medium-voltage network.
- ii)
- Estimate the range of the lowest consumption during those hours of the year that the production from solar power may be high.
- iii)
- Estimate the production per installation, during the 10-min period with the highest impact from all installations together. This is not the same as the maximum production per panel, but it can be referred to as an “after diversity maximum production”, next to an “after diversity minimum consumption”.
- iv)
- Add solar power installations in a random way and calculate the distribution of worst-case voltage with increasing amount of solar power.
- v)
- Define a performance index for the network, an appropriate limit for this index, and determine the hosting capacity.

- i)
- The approach fits closely to existing planning approaches used by distribution companies.
- ii)
- A limited amount of input data is needed.
- iii)
- The results are such that they can be interpreted relatively easy by distribution companies.
- iv)
- Different kinds of uncertainties can be added without changing the basic approach.
- v)
- Any power-system analysis tool can be used to perform the actual calculations.

## 4. Overvoltage and Undervoltage

#### 4.1. Two Swedish Low-Voltage Networks

#### 4.2. Risks Due to Single-Phase Equipment

#### 4.3. Single-Phase PV in a Rural Network—Overvoltage

- i)
- Each installation is connected single-phase and each installation produces 6 kW.
- ii)
- The consumption per customer per phase, during the worst case, is uniformly distributed between 0 and 250 W. This range was obtained from measurements of 10-min values of two customers (one in the rural network and one in the suburban network) and the study of hourly consumption from other customers. The worst case, when considering the risk of overvoltage, is when consumption is low and production is high. High production will likely last a period of one or two hours around noon. The regulation in most European countries sets limits to 10-min values of rms voltage. The lowest 10-min consumption values during one or two-hour periods were considered to obtain the range from 0 to 250 W. Only measurement values around noon during the summer months were used here.
- iii)
- The no-load voltage in the low-voltage network, during the worst case, is uniformly distributed between 238 V and 242 V. The highest 10-min values during one or two-hour periods around noon in the summer months (as obtained from the same measurements) were used to obtain this distribution.

#### 4.4. Single-Phase PV in a Rural Network—Undervoltage

- i)
- Consumption: 1000 W–2500 W per customer per phase. Note again that this is not a typical consumption but an estimation of the amount of consumption that may occur during a worst case for undervoltage due to PV.
- ii)
- No-load voltage: 232 V–236 V.

#### 4.5. Single-Phase PV in a Suburban Network—Overvoltage

#### 4.6. Single-Phase Electric Vehicle Chargers in the Suburban Grid

- i)
- Active-power consumption: uniformly distributed between 1500 W and 3000 W.
- ii)
- No-load voltage: uniformly distributed between 230 V and 234 V.
- iii)
- Charging power: 2300 W, 3680 W, 4600 W and 5750 W (corresponding to 10 A, 16 A, 20 A and 25 A).

#### 4.7. Discussion

#### 4.7.1. Reactive Power

#### 4.7.2. Probability Distributions

#### 4.7.3. Time Series

#### 4.7.4. Need for Data Collection

#### 4.7.5. Generality of the Results and of the Method

#### 4.7.6. Production per Installation during the Worst Case

#### 4.7.7. Choice of Performance Indices and Limits

## 5. Other Phenomena

- i)
- A generally accepted performance index.
- ii)
- A limit for the performance index that forms a border between “acceptable performance” and “unacceptable performance”.
- iii)
- A method for calculating the value of this index, either deterministically or in a stochastic way, as a function of the amount of new production or consumption.

#### 5.1. Overcurrent

#### 5.1.1. Performance Indices

#### 5.1.2. Limits

#### 5.1.3. Calculation Methods

#### 5.1.4. Planning Example

#### 5.2. Fast Voltage Magnitude Variations

#### 5.2.1. Performance Indices

#### 5.2.2. Limits

#### 5.2.3. Calculation Methods

#### 5.3. Voltage Unbalance

#### 5.3.1. Performance Indices

#### 5.3.2. Limits

#### 5.3.3. Calculation Methods

#### 5.4. Harmonic Voltage Distortion

#### 5.4.1. Performance Indices

#### 5.4.2. Limits

#### 5.4.3. Calculation Methods

- i)
- The emitted harmonic current is impacted by the voltage distortion at the terminals of the equipment. This phenomenon has been observed early for diode rectifiers like the ones used in televisions [77] and was explained and quantified by a model in [78]. That impact was shown to be limited and the emission for a clean supply voltage was in most cases the worst case and the one reasonably useable for harmonic studies. With modern power-electronic equipment, with an actively controlled interface, there are observations showing the contrary, the emission for a distorted supply voltage can be much higher than for a sinusoidal supply [79,80,81,82].
- ii)
- iii)
- The connecting of new production or consumption will change the impedance of the low-voltage customer and therewith the harmonic transfer impedance. There exist no acceptable models for new devices like PV inverters or EV chargers. Some measurements are presented in [86,87,88,89] but there are big variations between manufacturers and for future equipment guesses have to be made.
- iv)
- The statistical aggregation between different sources of harmonics is not known. This holds for the aggregation between different new devices (e.g., between different PV inverters) but also for the aggregation between the new devices and the background distortion. The aggregation between individual wind turbines has been studied by some authors [90,91,92] but it is not known if similar conclusions hold for PV inverters, EV chargers or other large low-voltage equipment like heat pumps [22,71,93].

#### 5.5. Supraharmonics

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Hosting capacity approach, where the performance deteriorates already with small amounts of local generation.

**Figure 2.**Hosting capacity approach where the performance initially improves and only deteriorates with larger amounts of local generation.

**Figure 3.**Probability distribution (cumulative distribution function) for the highest voltage (worst-case voltage) for increasing amount of single-phase connected solar power in the 6-customer rural network. The different colours refer to the six different customers. The red dashed vertical line is the overvoltage limit at 110% of the nominal voltage.

**Figure 4.**90th percentile of the worst-case overvoltage as a function of the number of customers with PV in the 6-customer rural network.

**Figure 5.**90th percentile of the worst-case overvoltage as a function of the number of customers with PV in the 6-customer rural network; 4 kW production per PV installation.

**Figure 6.**75th percentile of the worst-case overvoltage as a function of the number of customers with PV in the 6-customer rural network.

**Figure 7.**Probability distribution (cumulative distribution function) for the lowest voltage (worst-case voltage) for increasing amount of single-phase connected solar power in the 6-customer rural network. The different colours refer to the six different customers. The black dashed vertical line is the nominal voltage.

**Figure 8.**Probability distribution (cumulative distribution function) for the highest voltage (worst-case voltage) for increasing amount of single-phase connected solar power in the 28-customer suburban network.

**Figure 9.**90th percentile of the worst-case overvoltage as a function of the number of customers with PV in the 28-customer suburban network.

**Figure 10.**10th percentile of the lowest voltage (worst-case voltage) as a function of the number of EV chargers in a 28-customer suburban network. A consumption of 5750 W (25 A) per charger has been used in the calculations.

**Figure 11.**Probability distribution (cumulative distribution function) of the highest single-phase current through the distribution transformer, with increasing number of customers with single-phase connected PV.

**Figure 12.**Four different percentiles (50th: red star; 75th: green circle; 90th: blue plus; 95th: black triangle) for the current through the transformer, as a function of the number of customers (out of 83) with single-phase connected PV.

**Figure 14.**Supraharmonics from a PV inverter connected alone (upper

**left**), the same inverter while neighbouring devices are connected (upper

**right**). A heat pump connected alone (lower

**left**), the same heat pump while neighbouring devices are connected (lower

**right**).

Case | Parameter | Default Value | New Value | Hosting Capacity |
---|---|---|---|---|

0 | 3 customers | |||

1 | Produced power per installation | 6 kW | 7 kW | 2 customers |

2 | 5 kW | 6 customers | ||

3 | 4 kW | 11 customers | ||

4 | Percentile | 90th | 95th | 1 customer |

5 | 85th | 5 customers | ||

6 | 75th | 8 customers | ||

7 | load per customer per phase | [0, 250 W] | [0, 150 W] | 3 customers |

8 | [0, 350 W] | 3 customers | ||

9 | No-load voltage | [238 V, 242 V] | [240 V, 244 V] | 2 customers |

10 | [239 V, 243 V] | 2 customers | ||

11 | [237 V, 241 V] | 4 customers | ||

12 | [236 V, 240 V] | 6 customers |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bollen, M.H.J.; Rönnberg, S.K.
Hosting Capacity of the Power Grid for Renewable Electricity Production and New Large Consumption Equipment. *Energies* **2017**, *10*, 1325.
https://doi.org/10.3390/en10091325

**AMA Style**

Bollen MHJ, Rönnberg SK.
Hosting Capacity of the Power Grid for Renewable Electricity Production and New Large Consumption Equipment. *Energies*. 2017; 10(9):1325.
https://doi.org/10.3390/en10091325

**Chicago/Turabian Style**

Bollen, Math H. J., and Sarah K. Rönnberg.
2017. "Hosting Capacity of the Power Grid for Renewable Electricity Production and New Large Consumption Equipment" *Energies* 10, no. 9: 1325.
https://doi.org/10.3390/en10091325