# Achieving an Optimal Decision for the Joint Planning of Renewable Power Supply and Energy Storage for Offshore Oil–Gas Platforms

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- The first stage is capacity optimization for WT and PV. After obtaining the forecasting of wind and solar resources based on the prediction model of the LightGBM network, the WT/PV-connected capacity at each node of the distribution network is optimized, with the goals of power-flow stability and economy.
- The second stage is cluster partition. Sensitivity analysis is carried out on the distribution network after WT/PV planning. The voltage and line-loss sensitivity of each node is calculated and nodes with similar impacts are grouped into sub-clusters.
- The third stage is the optimization of ES planning. Taking each sub-cluster as a unit, the optimal location of ES is determined according to the sensitivity-analysis method and, then, the optimal capacity planning of ES is carried out with the goals of minimizing voltage fluctuation, reducing active power loss, and achieving optimal capacity.
- An algorithm based on a PSO algorithm and a power-flow calculation are used to solve the optimal planning of WT/PV ES following the methods of gas-turbine power constraints and economical constraints for an existing offshore oil-gas platform distribution network. The feasibility of offshore WT/PV ES for an offshore oil-gas platform is assessed.

## 2. Modeling of Offshore Oil and Gas Platform Cluster System

#### 2.1. Wind-Turbine Model

_{w}is the output power of the wind turbine, x is the actual wind speed, M is the maximum power of the WT, α and β are linear parameters, and v

_{ci}, v

_{co}, and v

_{r}denote the cut-in wind speed, cut-out wind speed, and rated wind speed, respectively.

#### 2.2. Photovoltaic Model

_{s}and P

_{pv}are the PV-output power and the actual PV-output power under standard conditions (illumination intensity of 1000 W/m

^{2}, temperature of 25 °C), respectively; G

_{s}and G

_{a}are the illumination intensity and the actual illumination intensity under standard conditions, respectively; T

_{r}and T

_{a}are the nominal temperature (25 °C) and the actual temperature of PV, respectively; and k is the power–temperature coefficient.

#### 2.3. Energy Storage Model

_{c}and η

_{d}are the charging and discharging efficiencies of ES, respectively; E

_{ess}is the ES capacity; t is the time; Δt is a scheduling cycle; and P

_{ch}and P

_{dis}are the charging and discharging powers of ES, respectively.

#### 2.4. Topology Model

_{G1}is the apparent power of the upper distribution network, Z

_{i−1},i denotes the line impedance from node i − 1 to node i, U

_{i}is the voltage of node i, S

_{i−1},i is the line-flow power from node i − 1 to node i, Si is the apparent injection power of node i, and S

_{Li}is the sum of the load power P

_{l}/Q

_{l}of node i and the connected power of the distributed generation units. WT/PV ES and other distributed generation units are connected to the local line through the power electronic converter and supply power to the load of the offshore oil–gas platform, together with the distribution network. The excess renewable energy can also be transmitted through the distribution network to supply power for other loads.

_{i}is the power loss of the line, which can be expressed as follows:

_{i}is the voltage amplitude of node i; P

_{i}and Q

_{i}are the injected active and reactive powers, respectively, of node i; and R

_{i}

_{−1,i}and X

_{i}

_{−1,i}are the resistance and reactance, respectively, between nodes i − 1 and i.

#### 2.5. Prediction of Typical Output of Wind/Sunlight

_{w}

_{/pv}refers to the prediction model of wind-power or PV-power generation based on LightGBM, and X

_{i}is the i-th meteorological sample point for wind-power or PV-power generation. ${\widehat{P}}_{i}$ is the predicted generation power corresponding to the i-th sample point.

_{i}is the real power generation corresponding to sample i and N is the number of samples.

_{w}and the PV-power-generation prediction model f

_{pv}were used, respectively, to predict the wind-power generation and the PV-power generation on a typical day.

_{wind}and X

_{pv}denote the meteorological weather forecasting data used to predict the wind- and solar-power generation of a typical day, respectively, and their corresponding power predictions are determined by the following equations:

_{w,i}and X

_{pv,i}are the i-th sample points of meteorological wind power and meteorological solar power of a typical day, respectively.

_{G}and P

_{P}are the dispatching output power of the gas-turbine and power grids, respectively, P

_{e,i}is the ES dispatching output power, P

_{L}is the load-power forecasting, and n

_{pv}/n

_{w}/n

_{e}are the total numbers of PV/WT ES, respectively. The ideal planning operation results are shown in Figure 2.

## 3. Stability Analysis and Cluster-Partition Principles of Offshore Oil–Gas Platform Cluster System

#### 3.1. Stability Analysis

_{ij}of the branches between nodes i and j is as follows:

_{i}is the voltage amplitude of node i; P

_{j}and Q

_{j}are the injected active power and reactive power, respectively, of node j; and R

_{ij}and X

_{ij}are the resistance and reactance, respectively, between nodes i and j. When L

_{ij}< 1, the branch power flow is solvable and stable. The smaller the value of L

_{ij}, the greater the stability margin of the branch. When L

_{ij}> 1, the branch power flow has no solution and the power flow is unstable.

_{ij}of all branches:

#### 3.2. Sensitivity Analysis

#### 3.2.1. Voltage Sensitivity

#### 3.2.2. Loss Sensitivity

#### 3.3. Cluster-Division Principle Based on Voltage and Loss-Sensitivity Index

_{Sm}of the voltage-active power-sensitivity matrix and the column vector L

_{Sm}of the loss-sensitivity matrix:

_{Sm}reflects the relationship between voltage and active power and L

_{Sm}reflects the relationship between loss and active power. The specific solving process of electrical distance is shown in the following equations:

_{min}and VS

_{max}are the minimum and maximum values of voltage-active power sensitivity matrix elements, respectively; LS

_{min}and LS

_{max}are the minimum and maximum values of loss-sensitivity matrix elements, respectively; x

_{vmk}is the k-th spatial coordinate of node m after the normalization of voltage-sensitivity matrix elements; x

_{lm}is the spatial coordinate of node m after the normalization of loss-sensitivity matrix elements; d

_{ij}is the electrical distance between nodes i and j; p and q are the weight coefficients of different indicators; and p + q = 1. Equations (23) and (24) unify the data of voltage sensitivity and loss sensitivity to one standard through minimum–maximum normalization transformation and combined with the Euclidean distance calculation method of Equation (25), the size of the electrical distance between nodes i and j can be solved when the degrees of influence of loss sensitivity and voltage sensitivity are different.

## 4. WT/PV ES Optimization Decision

#### 4.1. General Idea

#### 4.2. Stage 1: WT/PV Siting and Sizing

#### 4.2.1. Objective Function

- Power-flow voltage stability F
_{1}

- 2.
- Total investment cost F
_{2}

_{2}is defined as the total cost of offshore WT/PV investment and construction; that is:

_{1}and C

_{2}are the per-capacity purchase and construction costs of WT and PV units, respectively, and P

_{W}and P

_{PV}are the installed capacities of WT and PV units, respectively.

#### 4.2.2. Constraint Condition

- Power-flow constraint of distribution network

_{ij}and B

_{ij}are the conductance and susceptance, respectively, between nodes i and j and θ

_{ij}is the phase-angle difference between nodes i and j.

- 2.
- Node voltage constraint

_{i}

_{,min}and U

_{i}

_{,max}are the minimum and maximum allowable values of node voltage deviation, respectively.

- 3.
- Total capacity constraint of WT/PV access

_{DG}is the actual capacity of WT/PV connected to the distribution network and P

_{DG,}

_{max}is the maximal permitted connected capacity of renewable energy.

#### 4.3. Stage 2 and 3: Cluster Partition and ES Siting and Sizing

#### 4.3.1. Objective Function

- Voltage fluctuation f
_{1}

_{1}and U

_{i,t}are the amplitudes of node 1 (slack bus) and node i, respectively, at time t.

- 2.
- Line loss f
_{2}

_{i,t}and Q

_{i,t}are the active and reactive power injection of node i, respectively, at time t.

- 3.
- Capacity of storage system f
_{3}

_{j,s}is the starting time of continuous charge/discharge of the j-stage ES; t

_{j,e}is the end time of continuous charging/discharging of the j-stage ES; P

_{ch/dis,i}is the charge/discharge power of the i-th ES period; SOC

_{max}and SOC

_{min}are the upper and lower limits of the SOC of ES, respectively; and N

_{e}is the amount of ES.

#### 4.3.2. Constraint Condition

- SOC constraint

_{i}

_{,max}and SOC

_{i}

_{,min}are the upper limit and lower limit of the SOC of the i-th ES, respectively.

- 2.
- Charging and discharging constraints of ES

- 3.
- ES energy balance constraint

#### 4.4. Multi-Objective Interactive Decision-Making Model

_{1}(x), f

_{2}(x), and f

_{n}(x) are different objectives. The satisfaction function can be obtained by normalizing the optimal solutions f

_{1, min}, f

_{2, min}, …, f

_{n,}

_{min}of multiple objectives ξ

_{1}, ξ

_{2}, …, ξ

_{n}:

_{1}ξ

_{2}… ξ

_{n}]

^{T}be the overall satisfaction function, where ξ

_{1}, ξ

_{2}, …, ξ

_{n}are the best expectations of objective function 1,…,n, with a theoretical value of 1. The best expected value of ξ(x) is ξ

^{*}(x

^{*}) = [ξ

^{*}

_{1}ξ

^{*}

_{2}… ξ

^{*}

_{n}]

^{T}. To solve the decision vector solution x

^{*}, the overall equilibrium decision function f is defined as follows:

#### 4.5. An Algorithm Based on a PSO Algorithm and Power-Flow Calculation

#### 4.5.1. Method I: Single-Objective Power-Limited Mode of Gas Turbine

- Step 1

- 2.
- Step 2

- 3.
- Step 3

- 4.
- Step 4

- 5.
- Step 5

- 6.
- Step 6

- 7.
- Step 7

#### 4.5.2. Method II: Multi-Objective Economic-Limited Mode

- Step 1

- 2.
- Step 2

- 3.
- Step 3

- 4.
- Step 4

- 5.
- Step 5

- 6.
- Step 6

## 5. Example Analysis

#### 5.1. Example Conditions

#### 5.2. Results and Analysis of Siting and Sizing

#### 5.2.1. Original Working Condition

_{1}was 0.094, the penetration indicator was 0, the voltage fluctuation indicator f

_{1}was 11.96, and the total loss in 1 day was 103.2 MWh.

#### 5.2.2. Scheme I: Power-Limited Mode of Gas Turbine

_{1}(x) and ξ

_{2}(x) were each assumed to be 1. When the gas-turbine output decreased by 50%, the optimization curve of the overall WT/PV was as shown in Figure 7. With the increase in the number of iterations, the overall balance decreased, and the optimal scheme which was acceptable to each optimization goal was reached. Considering the different capacities at each node, the WT/PV planning results obtained, based on varying output curves for WT/PV systems, are shown in Figure 8.

#### 5.2.3. Scheme Ⅱ: Economical Customization

## 6. Conclusions

- The optimal planning method of WT/PV ES proposed in this paper can effectively improve the power-flow stability of offshore oil–gas platform distribution networks, improve the penetration of renewable energy, reduce the burden of the distribution network and gas turbines, and improve the economic indicators.
- The cluster-partition principle and the ES connection method proposed in this paper can effectively improve the impact of the uncertainty of WT/PV output power on the distribution network and reduce the distribution network loss and voltage fluctuation.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 13.**Distribution of power flow in distribution network with gas-turbine output power reduced by 50%: (

**a**) one-day total loss optimization; (

**b**) voltage-fluctuation optimization.

**Figure 14.**WT/PV planning results: (

**a**) WT/PV planning results after 30% reduction in gas-turbine output power; (

**b**) WT/PV planning results after 70% reduction in gas-turbine output power.

**Figure 15.**Distribution of power flow in distribution network with gas-turbine output power reduced by 30%: (

**a**) before ES connection; (

**b**) after ES connection.

**Figure 16.**Distribution of power flow in distribution network with gas-turbine output power reduced by 70%: (

**a**) before ES connection; (

**b**) after ES connection.

**Figure 17.**Optimization of ES connection when the output power of the gas turbine is reduced by 30%: (

**a**) one-day total loss optimization; (

**b**) optimization of total voltage fluctuation of all the nodes.

**Figure 18.**Optimization of ES connection when the output power of gas turbine is reduced by 70%: (

**a**) one-day total loss optimization; (

**b**) optimization of total voltage fluctuation of all the nodes.

Various Indicators | Original Working Condition | Reduction of Gas Engine Output | |||
---|---|---|---|---|---|

30% | 50% | 70% | |||

Power and capacity permeability/% | 0 | 55.43 | 62.80 | 99.40 | |

Energy permeability/% | 0 | 34.84 | 39.42 | 61.10 | |

Stability index | 0.094 | 0.053 | 0.057 | 0.073 | |

Loss/MWh | Before storage connection | 103.2 | 53.5 | 49.4 | 44.6 |

After storage connection | 46.2 | 41.0 | 35.1 | ||

Voltage fluctuation/p.u. | Before storage connection | 11.76 | 7.58 | 9.23 | 9.57 |

After storage connection | 6.17 | 8.04 | 8.18 |

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## Share and Cite

**MDPI and ACS Style**

Hu, C.; Deng, J.; Liu, C.; Luo, S.; Li, X.; Lu, H.
Achieving an Optimal Decision for the Joint Planning of Renewable Power Supply and Energy Storage for Offshore Oil–Gas Platforms. *Appl. Sci.* **2023**, *13*, 8833.
https://doi.org/10.3390/app13158833

**AMA Style**

Hu C, Deng J, Liu C, Luo S, Li X, Lu H.
Achieving an Optimal Decision for the Joint Planning of Renewable Power Supply and Energy Storage for Offshore Oil–Gas Platforms. *Applied Sciences*. 2023; 13(15):8833.
https://doi.org/10.3390/app13158833

**Chicago/Turabian Style**

Hu, Changbin, Jufu Deng, Chao Liu, Shanna Luo, Xuecheng Li, and Heng Lu.
2023. "Achieving an Optimal Decision for the Joint Planning of Renewable Power Supply and Energy Storage for Offshore Oil–Gas Platforms" *Applied Sciences* 13, no. 15: 8833.
https://doi.org/10.3390/app13158833