# Combined PV-Wind Hosting Capacity Enhancement of a Hybrid AC/DC Distribution Network Using Reactive Control of Convertors and Demand Flexibility

^{1}

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## Abstract

**:**

## 1. Introduction

#### 1.1. Motivation

#### 1.2. Literature Review

#### 1.3. Contributions and Organization

- Proposing a stochastic and linearized model for the HC problem of HRES (PV-WT) (sizing in multi-candidate locations) in the hybrid AC/DC distribution network.
- Utilizing the reactive power control of VSCs (QSVC) as an ANM scheme for increasing the HC and reducing the network energy losses.
- Including the DFP in the proposed formulation in order to achieve the objectives of the problem.
- Presenting a multi-objective, multi-source, and multi-period optimization framework (increasing HC and reducing energy losses) based on ɛ-constraint and fuzzy satisfying methods.

## 2. Structure of a Hybrid AC/DC Distribution Network

## 3. Uncertainty Modeling

#### 3.1. Modeling of RESs Uncertainty

#### 3.2. Two-Stage Stochastic Optimization Modeling

## 4. Problem Formulation

#### 4.1. Objective Functions

#### 4.2. Constraints

#### 4.2.1. Power Flow Equations of AC Distribution Network

#### 4.2.2. Power Flow Equations of DC Distribution Network

#### 4.2.3. DFP Equations

#### 4.2.4. Modeling of VSC

#### 4.3. Linearization

- (1)
- The typical power flow equations in AC and DC distribution networks that are illustrated in (9), (10), and (29), are nonlinear and non-convex. Reasonably, utilizing these power flow terms in the optimization problems is difficult. Therefore, they are linearized by taking into consideration two practical assumptions. The first one is regarding the bus voltage magnitudes, in an AC and DC distribution system, to be close to the nominal value ${V}_{nom}$ The second assumption is that the voltage angle difference ${\theta}_{ij}$ through the AC line is tiny, leading to the trigonometric estimates, i.e., $\mathrm{sin}({\theta}_{ij})={\theta}_{ij}$ and $\mathrm{cos}({\theta}_{ij})=1$ [37]. In addition, the voltage magnitude at bus i and id can be represented as the summation of the nominal voltage and a minor deviation $\mathsf{\Delta}{V}_{i/id}$, i.e., ${V}_{i/id}={V}_{nom}+\mathsf{\Delta}{V}_{i/id}$.
- (2)
- The modulation index (M) of each VSC should be limited in order to prevent over-modulation and excessive harmonics. The upper limit of M can be selected as ${M}^{max}=1$ and the lower limit as ${M}^{min}={V}_{ac,pu}^{min}/{V}_{dc,pu}^{max}$, which is usually the upper and lower voltage limits, i.e., 0.95 p.u and 1.05 p.u, respectively. By defining the variable $H={M}^{-1}$, the upper and lower limits of H are considered equal to 1.1 and 1. Additionally, by defining ($H=1+dH+\mathsf{\Delta}H$) and dH equal to 0.05, the value of the new variable, i.e., $\mathsf{\Delta}H$, is limited to $\pm 0.05$. So, we have $M={H}^{-1}$ [37].
- (3)
- The variables $\mathsf{\Delta}H$, $\mathsf{\Delta}V,$ and θ have small values and therefore their multiplication can be considered to be zero [37].

#### 4.4. Multi-Objective Optimization

#### 4.5. Solution Procedure

## 5. Simulation Results

^{®}Core™ i7-4790k CPU @ 4.00GHz PC with 16 GB RAM.

#### 5.1. Input Data

#### 5.2. Case Studies

#### 5.3. Case Study 1: Maximizing Hybrid PV-WT HC without DFP and with/without QVSC

_{1}. For the WT-only mode, high voltages level and voltage violations during the spring are more than in other seasons due to the high generation of WT. For PV-only, the high voltages level similarly tracks its source pattern, but the case is not as extreme as WT-only. In other words, despite the higher capacity of PV compared with the WT, the high voltages level in the PV-only mode is lower than in the WT-only mode and the voltage violations in the WT-only mode are more severe. This is due to the fact that WT sources generate noticeable power most of the time, leading to more effective utilization of the network capacity. However, the voltages level and violation of the hybrid PV-WT mode are more severe than the individual WT and PV modes, representing that the network HC is enhanced significantly.

_{1}. The high lines loading in PV-only mode follows its source pattern. The high lines loading and the line capacity violations in WT-only mode are more than in the PV-only mode. In addition, the case is more severe in the spring season. This is due to the same reason explained for the voltage levels. Besides this, the high lines loading and the lines capacity violation in hybrid PV-WT mode are more than individual WT and PV modes, which is due to the increased HC of the system.

_{9}–t

_{15}) in this area, the active power flows in reverse to the upstream grid and VSC helps to control the voltage of the buses by absorbing the reactive power. This is one of the advantages of VSC, i.e., controlling the voltage of the distribution network by injecting/receiving reactive power leading to the HC enhancement.

#### 5.4. Case 2: Maximizing Hybrid PV-WT HC with DFP and with/without QVSC

#### 5.5. Case Study 3: Minimization of Losses for Hybrid PV-WT with/without DFP and QVSC

#### 5.6. Case Study 4: Optimization of Hybrid PV-WT HC and Losses with the DFP and QVSC

#### 5.7. Economic Analysis

#### 5.8. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Indices | |

$i$: $j$ | Indices of the AC buses. |

$id$, $jd$ | Indices of the DC buses. |

$t$ | Index of the hours. |

$s$ | Index of the scenarios. |

$l$ | Index of the feeders. |

Sets | |

${\mathsf{\Omega}}_{sb}$ | Set of substation buses in the network. |

${\mathsf{\Omega}}_{s}$ | Set of scenarios in the operation period. |

${\mathsf{\Omega}}_{T}$ | Set of hours in the operation period. |

${\mathsf{\Omega}}_{pv}^{ac/dc}$ | Set of candidate AC/DC buses for installing PV. |

${\mathsf{\Omega}}_{w}^{ac/dc}$ | Set of candidate AC/DC buses for installing WT. |

${\mathsf{\Omega}}_{cvt}^{ac/dc}$ | Set of candidate AC/DC buses for installing the VSC. |

${\mathsf{\Omega}}_{n}^{ac/dc}$ | Set of AC/DC distribution buses. |

${\mathsf{\Omega}}_{d}^{ac/dc}$ | Set of demand buses in AC/DC network. |

${\mathsf{\Omega}}_{DF}^{ac/dc}$ | Set of distribution buses participating in the DFP in AC/DC network. |

Variables | |

${C}_{i}^{\left(w/pv\right),ac}$ | WT/PV installed capacity in the bus i of the AC network (MW). |

${C}_{id}^{\left(w/pv\right),dc}$ | WT/PV installed capacity in bus id of the DC network (MW). |

${\left(P,Q\right)}_{i,t,s}^{\left(w/pv\right),ac}$ | Active/reactive power of WT/PV in the bus i at time t and scenario s in AC network (MW/MVAR). |

${P}_{id,t,s}^{\left(w/pv\right),dc}$ | Active power of WT/PV in bus id at time t and scenario s in DC network (MW). |

${P}_{i,t,s}^{\left(cw/cpv\right),ac}$ | Curtailed power of WT/PV in the bus i at time t and scenario s in AC network (MW). |

${P}_{id,t,s}^{\left(cw/cpv\right),dc}$ | Curtailed power of WT/PV in the bus id at time t and scenario s in DC network (MW). |

${\left(P,Q\right)}_{i,t}^{dac}$ | Active/reactive demand of bus i considering DFP at time t in AC network (MW/MVAR). |

${P}_{i,t}^{ddc}$ | Active power demand in the bus id considering DFP at time t in DC network (MW). |

${\gamma}_{i/id,t}^{ac/dc}$ | DFP in the bus i/id of AC/DC network at time t. |

${\left(P,Q\right)}_{i,t,s}^{netac}$ | Net active/reactive power injection to the bus i at time t and scenario s (MW/MVAR). |

${P}_{id,t,s}^{netdc}$ | Net active power injection to the bus id at time t and scenario s (MW). |

${\left(P,Q\right)}_{i,t,s}^{cvtac}$ | Active/reactive power of VSC connected to bus i at time t and scenario s (MW/MVAR). |

$Plos{s}_{i,t,s}^{cvt}$ | Active power losses of VSC connected to bus i at time t and scenario s (MW). |

${P}_{id,t,s}^{cvtdc}$ | Active power of VSC connected to bus id at time t and scenario s in DC network (MW). |

${\left(P,Q\right)}_{ij,t,s}^{ac}$ | Active/reactive power flowing line ij in AC network at time t and scenario s (MW). |

${P}_{id.jd,t,s}^{dc}$ | Active power flowing line id.jd in DC network at time t and scenario s (MW). |

${\left(PL,QL\right)}_{ij,t,s}^{ac}$ | Active/reactive losses of AC lines connected between i and j at time t and scenario s (MW/MVAR). |

$P{L}_{id.jd,t,s}^{dc}$ | Active losses of DC lines connected between id and jd at time t and scenario s (MW). |

$Plos{s}_{t,s}^{ac/dc}$ | Active power losses of AC/DC network at time t and scenario s (MW). |

${\left(v,\delta \right)}_{i,t,s}^{ac}$ | Voltage magnitude/angle of bus i at time t and scenario s in AC network. |

${v}_{id,t,s}^{dc}$ | Voltage magnitude of bus id at time t and scenario s in DC network. |

$\mathsf{\Delta}{H}_{i.id,t,s}$ | Variable used in the linearization process for the DC network. |

$\mathsf{\Delta}{V}_{i/id,t,s}$ | Deviation of Voltage magnitude at bus i and id in AC/DC network. |

Parameters | |

${{\rm Y}}_{ij},{\theta}_{ij}$ | Magnitude/angle of the element ij of the admittance matrix of AC network. |

${g}_{ij}/{b}_{ij}/{S}_{ij}^{max}$ | Conductance/susceptance/ MVA rating of the line connecting bus i and j. |

${G}_{id.jd}^{dc}/{P}_{id.jd}^{max}$ | Conductance/ MW rating of the line connecting between bus id and jd in DC network. |

${P}_{min/max}^{sb}$ | Min/ Max active power imported from the upstream grid (MW). |

${Q}_{min/max}^{sb}$ | Min/ Max reactive power imported from the upstream grid (MVAR). |

${\varsigma}_{t,s}^{w/pv}$ | WT/PV power generation at time t and scenario s (percentage of the full capacity). |

${Q}_{i,min/max}^{w/pv}$ | Minimum/Maximum reactive power generation by WT/PV sources in the bus i (MVAR). |

$\mathrm{cos}{\left(\varphi \right)}_{i,t,s}$ | Power factor of WT and PV located in the bus i at time t and scenario s. |

${\alpha}_{i/id}^{ac/dc}$ | The upper limit for acceptable generation energy curtailment at bus i/id in AC/DC network. |

${\lambda}_{i/id}^{ac/dc}$ | A binary parameter that indicates the participation of bus i/id in DFP in the AC/DC network. |

${P}_{id.t}^{ddco}$ | Base (without DFP) active power in the bus id for time t in DC network (MW). |

${\left(P,Q\right)}_{i.t}^{daco}$ | Base (without DFP) active/reactive power in the bus i at time t (MW/MVAR). |

${\gamma}_{i/id}^{max/min}$ | Upper/lower boundary of DFP at bus i/id in AC/DC network. |

Ψ_{i} | Power factor angle of VSC connected to bus i in AC network. |

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**Figure 3.**Normalization of the objective functions; (

**a**) maximization (HC), (

**b**) minimization (energy losses).

**Figure 5.**Single line diagram of the hybrid AC/DC distribution network and the candidate WT and PV buses.

**Figure 7.**Capacity of RESs in different locations of the network without DFP and with QVSC; (

**a**) WT-only and PV-only, (

**b**) hybrid PV-WT.

**Figure 8.**(

**a**) Highest voltage of the network (at any location), (

**b**) Difference between high lines loading (any line in the network) and its maximum allowable power flow; vs. time period in scenario s

_{1}without DFP and with QVSC.

**Figure 9.**(

**a**) Active power of VSC connected between buss ac62 and dc4 (hybrid mode), (

**b**) Reactive power of VSC connected between buses ac62 and dc4 (hybrid mode), (

**c**) Active power flow from bus ac1 to bus ac51 (hybrid mode), (

**d**) Reactive power of PV connected to bus ac55 (hybrid mode); without DFP and with QVSC.

**Figure 10.**Capacity of RESs in different locations of the network with DFP and QVSC; (

**a**) WT-only and PV-only, (

**b**) hybrid PV-WT.

**Figure 11.**Percentage of the hours that the parameters have reached the allowed limits in different scenarios with/without DFP and with QVC; (

**a**) voltages issue, (

**b**) lines loading issue.

**Figure 13.**Capacity of WT-only, PV-only, and hybrid PV-WT in different locations; (

**a**) without DFP and with QVSC, (

**b**) with DFP and with QVSC.

**Figure 15.**The capacity of (

**a**) PV and (

**b**) WT at the selected buses vs. the HC considering DFP and QVSC.

MILP Model | Multi Objectives Framework | Hybrid RESs | RESs Uncertainty | Stochastic Model | Hybrid AC/DC Network | Tools | |||
---|---|---|---|---|---|---|---|---|---|

DFP | ANM (QVSC) | ANM (Others) | |||||||

[6] | ✘ | ✓ | ✘ | ✓ | ✓ | ✘ | ✘ | ✘ | ✓ |

[11] | ✘ | ✘ | ✓ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[12] | ✘ | ✘ | ✘ | ✓ | ✓ | ✘ | ✘ | ✘ | ✓ |

[13] | ✓ | ✓ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[14] | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[15] | ✘ | ✓ | ✘ | ✓ | ✘ | ✘ | ✘ | ✘ | ✓ |

[16] | ✓ | ✓ | ✘ | ✓ | ✓ | ✘ | ✘ | ✘ | ✓ |

[17] | ✘ | ✓ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[19] | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[20] | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ |

[25] | ✘ | ✘ | ✓ | ✓ | ✘ | ✘ | ✘ | ✘ | ✓ |

[26] | ✘ | ✓ | ✘ | ✘ | ✘ | ✘ | ✓ | ✘ | ✓ |

[27] | ✘ | ✘ | ✘ | ✘ | ✘ | ✘ | ✓ | ✘ | ✓ |

Current paper | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

**Table 2.**Specifications of case studies based on the types of RESs, objectives, and tools used in each case.

Case Study | Stochastic (Uncertainties) | RESs | Objectives | Tools | ||||
---|---|---|---|---|---|---|---|---|

WT Only | PV Only | Hybrid PV-WT | Max HC | Min Losses | DFP | ANM (QVSC) | ||

1 | ✓ | ✓ | ✓ | ✓ | ✓ | ✘ | ✘ | ✓✘ |

2 | ✓ | ✓ | ✓ | ✓ | ✓ | ✘ | ✓ | ✓✘ |

3 | ✓ | ✓ | ✓ | ✓ | ✘ | ✓ | ✓✘ | ✓✘ |

4 | ✓ | ✘ | ✘ | ✓ | ✓ | ✓ | ✓ | ✓ |

**Table 3.**HC, energy of sources, curtailment, losses, and energy exchange by VSC without DFP and with QVSC.

RESs | WT Capacity (MW) | PV Capacity (MW) | Total HC (MW) | Energy of Sources (GWh) | Energy Curtailment (GWh) | Energy Losses (GWh) | Energy Exchange by VSC (GWh) |
---|---|---|---|---|---|---|---|

WT-only | 11.89 | - | 11.89 | 46.35 | 4.63 | 5.45 | 35.50 |

PV-only | - | 15.63 | 15.63 | 27.48 | 2.74 | 4.52 | 29.15 |

Hybrid PV-WT | 8.21 | 11.85 | 20.06 | 52.89 | 5.27 | 5.51 | 34.78 |

**Table 4.**HC, energy of sources, curtailment, losses, and energy exchange by VSC with DFP and with QVSC.

RESs | WT Capacity (MW) | PV Capacity (MW) | Total HC (MW) | Energy of Sources (GWh) | Energy Curtailment (GWh) | Energy Losses (GWh) | Energy Exchange by VSC (GWh) |
---|---|---|---|---|---|---|---|

WT-only | 12.83 | - | 12.83 | 50.01 | 5.00 | 6.08 | 30.81 |

PV-only | - | 18.25 | 18.25 | 32.08 | 3.20 | 4.79 | 32.64 |

Hybrid PV-WT | 8.69 | 15.69 | 24.39 | 61.47 | 6.14 | 7.55 | 44.46 |

**Table 5.**Energy losses in three modes: PV-only, WT-only, and Hybrid PV-WT with/without DFP and with QVSC.

RESs | Without DFP | With DFP | ||
---|---|---|---|---|

HC (MW) | Energy Losses (MWh) | HC (MW) | Energy Losses (MWh) | |

WT-only | 9.35 | 649.23 | 10.43 | 574.10 |

PV-only | 12.99 | 984.50 | 15.61 | 854.23 |

Hybrid PV-WT | 16.16 | 475.97 | 20.05 | 405.00 |

DFP | RESs | Additional Cost of Converters ($) | HC (MW) |
---|---|---|---|

Without DFP | WT-only | 0 | 11.89 |

PV-only | 101,595 | 15.63 | |

PV and WT in AC and DC network (multi-location/ hybrid mode) | 77,025 | 20.06 | |

PV in DC network and WT in AC network (single-location/ hybrid mode) | 0 | 19.37 | |

With DFP | WT-only | 4830 | 12.83 |

PV-only | 118,625 | 18.25 | |

PV and WT in AC and DC network (multi-location/ hybrid mode) | 101,985 | 24.39 | |

PV in DC network and WT in AC network (single-location/ hybrid mode) | 0 | 21.81 |

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**MDPI and ACS Style**

Taghavi, M.; Delkhosh, H.; Parsa Moghaddam, M.; Sheikhi Fini, A.
Combined PV-Wind Hosting Capacity Enhancement of a Hybrid AC/DC Distribution Network Using Reactive Control of Convertors and Demand Flexibility. *Sustainability* **2022**, *14*, 7558.
https://doi.org/10.3390/su14137558

**AMA Style**

Taghavi M, Delkhosh H, Parsa Moghaddam M, Sheikhi Fini A.
Combined PV-Wind Hosting Capacity Enhancement of a Hybrid AC/DC Distribution Network Using Reactive Control of Convertors and Demand Flexibility. *Sustainability*. 2022; 14(13):7558.
https://doi.org/10.3390/su14137558

**Chicago/Turabian Style**

Taghavi, Moein, Hamed Delkhosh, Mohsen Parsa Moghaddam, and Alireza Sheikhi Fini.
2022. "Combined PV-Wind Hosting Capacity Enhancement of a Hybrid AC/DC Distribution Network Using Reactive Control of Convertors and Demand Flexibility" *Sustainability* 14, no. 13: 7558.
https://doi.org/10.3390/su14137558