# Optimizing Water-Light Complementary Systems for the Complex Terrain of the Southwestern China Plateau Region: A Two-Layer Model Approach

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Research Methodology

#### 2.1. Summarize

#### 2.2. Economic Scheduling Model Based on Robust Optimization

_{1}and c

_{2}are both uncertain parameters; d is a constant; π is a subset of a given set R

^{2}.

#### 2.2.1. Photovoltaic

_{s}denotes the actual photovoltaic value, and P

_{f}denotes the predicted value obtained through the simulation fitting of historical data from a photovoltaic power station. The photovoltaic prediction error is denoted by e.

_{f}parameter. The correlation coefficient diagram between this model and each actual curve in Figure 4b is shown in Figure 4c, indicating a minimum R

^{2}of 93.03%, well above 80%, confirming the excellence of the simulated and fitted model, making it a suitable pf parameter. Assuming the prediction error e follows an unbiased, normal distribution, the study utilizes discrete probability distributions to generate various photovoltaic output scenarios and their corresponding occurrence probabilities. This study considered only three error scenarios to streamline subsequent stochastic planning computations: exceedingly large prediction (e

_{1}), reasonable prediction (e

_{2}), and exceedingly small prediction (e

_{3}). With the probability of the prediction error falling in the interval (u − 3σ, u + 3σ) being 99.73%, the interval is divided into three equal parts, resulting in three discrete scenarios, as illustrated in Figure 4d. The simulation fitting model is expressed in Equation (2):

_{11}, ρ

_{22}, and ρ

_{33}represent the probabilities corresponding to a significant prediction, a reasonable prediction, and a small prediction.

_{1}= 0.1574, ρ

_{2}= 0.6852, and ρ

_{3}= 0.1574.

#### 2.2.2. Hydropower Modeling

#### Objective Function

_{m,n,t}denotes the amount of flow in the i-th hydropower unit over period t in the m-th photovoltaic scenario; $\mathsf{\Delta}t$ is the stepsize (scheduling period length); and n,t representss the on/off state of the unit; n is a 0–1 variable (1 for unit on, 0 for unit off).

#### Constraints

- (a)
- Crew dynamics limitations

_{NHQ}(.) represents the functional relationship between the generating flow, output, and head of the unit; ${P}_{m,n,t}^{h}$ denotes the hydroelectric unit output; h

_{m,t}represents the generation of clean water head.

- (b)
- Head constraints

- (c)
- Reservoir characterization constraints

_{m,t}and v

_{m,t+}

_{1}represent the beginning- and end-reservoir capacities at period t, respectively; WP

_{m,t}represents the outgoing flow after deduction of the cited flow for power generation

- (d)
- Hydropower unit output constraints

- (e)
- Water balance constraints

_{m,t+}

_{1}and v

_{m,t}represent the initial and final storage capacities of the hydropower plant at time t, respectively. I

_{t}represents the average incoming flow for period t.

- (f)
- Hydropower plant flow constraints

- (g)
- Hydropower plant hydraulic linkage constraints

_{t+}

_{1}and B

_{t+}

_{1}represent the predicted values and error analysis of regional small hydropower plants at time t + 1, respectively.

- (h)
- Reservoir capacity constraints

- (i)
- Load balancing constraints

_{t}represents the load required for the off-grid grid.

- (j)
- Rotating space constraints

_{t}represents the load required for the rotating spare margin.

- (k)
- Constraints on unit output rise and fall

- (l)
- Minimum start/stop constraints

_{n}and SD

_{n}are the minimum online time and offline time of the unit, respectively; su

_{n,k}denotes unit power-on action (1 indicates power-on, and 0 indicates power-off); sd

_{n,k}denotes unit power-off action (1 indicates power-off, and 0 indicates power-on).

- (m)
- Restraint of the vibration zone of the unit

#### 2.3. Double-Level Nested Optimization Algorithm Based on Economic Dispatching Model

#### 2.3.1. Outer Layer Optimization (Economic Operation Modeling to Address the “Electricity to Water” Problem)

_{1}, x

_{2}…x

_{n}] and the velocity vector v = [v

_{1}, v

_{2}…v

_{n}]. Additionally, each particle has a memory function. The population’s global optimal particle location is P = [P

_{i}

_{1}, P

_{i}

_{2}…P

_{id}], and the historical optimal particle position of the ith particle is G = [G

_{1}, G

_{2}…G

_{3}]. Each particle progresses toward the current optimal particle position in the solution space while iteratively updating its position and velocity vectors using Equation (18).

_{1}and c

_{2}represent the self and population learning factors, respectively; r

_{1}and r

_{2}are random numbers in the interval [0, 1]; v

_{i}represents the velocity of the i-th particle; and w denotes the inertia weight represented by the inertia vector of the particle population.

**Innovative points:**

- (1)
- A recorder is introduced to the original model to distribute initial particles uniformly in space D rather than having random particle positions, effectively preventing optimization from falling into local optima.
- (2)
- To balance the global exploration and local development ability of PSO, this study proposes an improved PSO algorithm with inertia weights. It transforms the linearly decreasing variable of inertia weights into a nonlinear inertia weight, as depicted in Figure 6.

_{min}and w

_{max}represent the minimum and maximum values of w, respectively, and w

_{min}= 0.3; t is the number of current iterations; and T is the maximum number of iterations.

#### 2.3.2. Inner Layer Optimisation (Optimisation of Hydroelectric Units)

#### Hydroelectric Power Plant Output Scenarios and Time Sequences

_{th}sample scenario, respectively.

_{th}unit in the stepsize of the hydropower plant.

#### The Inner-Layer Optimization Models for Hydroelectric Power Plants Incorporate Specific Strategies

- (1)
- The inner layer optimizes the load distribution strategy across units using SOAT Operational. Unit load distribution is modeled with a stepwise optimization algorithm (SOA), treating each unit as a stage, and the input unit number represents the stage variable (d = 1, 2,…, N) for the facing stage of the residual phase. The output after the stage can be considered the unit’s overall output. Consequently, the state transfer equation of the SOA model is as follows:

- (2)
- When considering hydropower units, the unit on/off state variable (us) constitutes a two-dimensional coding, altering the conventional coding strategy of optimizing only the number of units. This change involves optimizing the time nodes and the number of units when the hydropower unit models are not the same as signified by:

_{1}, ou

_{2}, …, and ou

_{T}represent the online units in each scheduling period during the entire T period. The number of online units in each T scheduling period is the number of online units in each scheduling period.

- (3)
- The load factor η
_{i}of the hydropower plant is calculated, linking to the planned daily power generation ${E}_{i}^{c}$ and the maximum output of the hydropower plant, ${P}_{i}^{max}$:

- (4)
- The objective function of the unit combination model is established following the Bellman optimization principle. The recursive form, as shown in Equation (33), is employed:

_{t}.

#### Trial Operational

_{t}and generation referral flow q

_{t}are determined based on the hydropower plant’s output characteristics graph and the provided initial water level/reserve after the outer layer optimization. The daily planned generation load is subtracted as the initial output of the hydropower plant optimized in the inner layer, representing the target output to be achieved by each unit’s combination.

_{trm}and the corresponding output of each unit satisfy the prohibited operation area constraint (17) and the minimum start-stop constraint (16). If the results are positive, the process stops, and the optimal generation flow is acquired, leading to the calculation of the end water level/reservoir capacity entering the optimization plan for the period. If not, the process is reiterated until both constraints are fulfilled.

## 3. Case Studies

#### 3.1. Partial Parameterization of the Power Station and Multi-Scenario Settings

- 1.
- River hydro units (UNIT#1–4) output sequence from 1 March 2016 to 31 March 2016, at a 1-h resolution.
- 2.
- Sequence of PV output from PV power plants in the region spanning 1 April 2013 to 1 April 2014, with a 15-min resolution.
- 3.
- Output sequence on 15 June 2016, at a 1-min resolution for the water-photovoltaic (WPV) power plants in the region, consisting of 1200 MW of hydropower and 200 MW of photovoltaics.
- 4.
- Reservoir inflow runoff sequence from January 1956 to December 2011 at a monthly resolution.

#### 3.2. Program Parameter Design

#### 3.3. Effectiveness Analysis of Double Nested Algorithms

^{3}/s due to improved Weight Coefficients. After 51 iterations and 20 statistical runs, the optimal flow rate stabilizes at 573 m

^{3}/s, indicating stable and convergent optimization results. Compared to the actual scheduling of 585.6 m

^{3}/s, water consumption decreases by 2.2% after optimal scheduling.

## 4. Comparison of Three Dispatch Scenarios for Individual Cases

^{2}, with more than 2719 h of sunshine annually and a sunshine percentage between 55% and 80%, signifying ample solar energy resources (Figure 21) [40]. Characteristics include microgrids, small power stations, and significant load (runoff) fluctuations.

^{3}of water in a single day. Additionally, based on the operating efficiency of the supplemental system in the area (3 m

^{3}= 1 kWh), power generation would increase by 21,000 kWh in a day and by 7.665 × 106 kWh annually. The station’s annual power generation benefit would also rise by 1,533,000 Yuan, resulting in a substantial economic advantage. This economic benefit is noteworthy at 1.533 million yuan, especially considering the context of a microgrid with small hydropower and a tiny photovoltaic power station. If the non-steady state strategy is applied to a large terraced multi-energy complementary system, the economic benefits become even more remarkable. Calculations reveal that the electricity consumption of 6,017,025 kWh would result in carbon emissions of 6,017,025 kg. The combustion of 1 ton of standard coal energy produces approximately 2.6 tons of carbon dioxide. Therefore, by emphasizing energy conservation and emission reduction, there is potential to reduce carbon dioxide emissions by 15,644.265 tons annually. This approach aligns with the principle of sustainable development, aiming to balance economic growth with the preservation of critical environmental resources such as the atmosphere, fresh water, oceans, land, and forests. Adopting sustainable practices presents needs without compromising the ability of future generations to meet their own needs, ensuring harmonious and peaceful coexistence while experiencing the positive impacts of sustainable development.

## 5. Conclusions

- (1)
- In a complementary system, the uncertainty in photovoltaic output and inflow runoff can complement each other by optimizing and adapting in a double-layer nested model.
- (2)
- The water head range, output range, and vibration range of the hydropower station influence the adjustable range of the unit. A small change in water consumption can bring about a significant change in the adjustable range. The proposed two-dimensional coding strategy effectively handles the continuous start/stop constraints of the unit, significantly reducing the number of optimization variables and achieving dimensionality reduction.
- (3)
- The proposed double-layer nested optimization algorithm effectively generates an economic operation plan within a short time. By trial-computing the inner-layer optimization results, a daily dispatch plan with 384 optimized variables can be obtained in just 5 min.
- (4)
- Compared with historical dispatch simulation scenarios, the deterministic optimization and stochastic optimization scenarios reduced water consumption by 1.7% and 1.2% respectively. This not only confirms the superiority of the model but also demonstrates the advantages of coupling photovoltaic and runoff prediction for short-term water dispatching, resulting in a complementary gain effect for water and light.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Glossary

IPSO-SOAT | Improved Particle Swarm Optimization Algorithm with Weight Coefficients-Stepwise Optimization Algorithm Trial Operational Model |

PV | Photovoltaic |

HES | Hybrid Energy System |

UC | Unit Combination |

RO | Robust Optimization |

BNOA | Bilayer Nested Optimization Approach |

p_{n} | Photovoltaic prediction, Uncertain Characterization of PV Output Force (MW) |

p_{f} | Typical daily values after clustering of photovoltaic historical data (MW) |

e | Optical prediction error values, following a normal distribution (MW) |

F | Objective function for economic dispatch operations (m) |

μ_{n,t} | On/off status of the unit, n is a 0–1 variable (1 for unit on, 0 for unit off) |

r_{m,n,t} | Consumption rate of the nth PV unit at time slot t for the mth PV scenario (m) |

Δt | Stepsize (scheduling time slot length) (min) |

${P}_{m,nt}^{h}$ | Hydroelectric unit transient output at time period t of the mth scenario (MW) |

h_{m,t} | Head at time period t of the mth scene (m) |

${h}_{m,t}^{loss}$ | head loss (m) |

${z}_{m,t}^{up}$ | Water level before runoff to hydroelectric plants (m) |

${z}_{m,t}^{down}$ | Water level after runoff from hydroelectric plants (m) |

v_{m,t} | Storage capacity at the beginning of time period t (m^{3}) |

v_{m,t+}_{1} | Storage capacity at the end of time period t (m^{3}) |

I_{t} | Average incoming flow in time period t |

${Q}_{t}^{min}$ | Upper limit of the flow rate into the reservoir of the hydropower plant in time period t (m^{3}/s) |

${Q}_{t}^{max}$ | Lower limit of the flow rate into the reservoir of the hydropower plant in time period t (m^{3}/s) |

Q_{t} | Incoming flow at hydroelectric power station at time period t (m^{3}/s) |

v^{−} | Lower limit of hydroelectric power plant capacity (m^{3}) |

v^{+} | Upper limit of hydroelectric power plant capacity (m^{3}) |

LP_{t} | spinning reserve margin (MW) |

ΔP | Upper speed limit for unit raising/lowering (MW) |

k | Time code |

SU_{N} | Minimum on-line time of the unit |

SD_{N} | Maximum online time of the unit |

su_{n,k} | Unit power-on action (1 for power on, 0 for power off) |

sd_{n,k} | Unit shutdown action (1 for shutdown, 0 for power on) |

${P}_{n}^{low}$ | Lower limit of unit vibration zone (MW) |

${P}_{n}^{up}$ | Upper limit of unit vibration zone (MW) |

${v}_{i}^{d}$ | The velocity of the ith particle in the d-dimension (m/s) |

${x}_{i}^{d}$ | Position of the ith particle in d-dimension (one solution of the objective function) |

w | Inertia weighting factor |

r_{1} | Self-learning factor |

r_{2} | Group Learning Factor |

${HP}_{t}^{n}$ | Hydroelectric power output at time t in the nth sample scenario (MW) |

${\Delta hP}_{t}^{n}$ | Hydroelectric output fluctuations at time t in the nth sample scenario (MW) |

H_{pe} | Hydroelectric Power Plant Expected Output Scenario Set (MW) |

${HP}_{t}^{up}$ | Upper boundary value of hydroelectric power plant output in Stepsize t (MW) |

${HP}_{t}^{low}$ | Lower boundary value of hydropower plant output in Stepsize t (MW) |

NT | The algorithm optimizes the total number of variables |

ou_{T} | Number of units on-line in each dispatch period during the entire dispatch period T |

so | Total number of consecutive periods during the scheduling period in which the number of units in operation remains unchanged |

tn_{so} | Indicates the time node at which the state of the unit is about to change |

su_{so} | Indicates the number of online units for each stabilization period. |

${R}_{d,t}^{*}$ | total output |

f_{rph}(p_{d,t},h_{t}) | Generation water consumption flow rate of unit j when net load is p_{d,t} and net head is h_{t} |

## References

- Zhou, X.; Chen, S.; Lu, Z.; Huang, Y.; Ma, S.; Zhao, Q. Technology Features of the New Generation Power System in China. Proc. CSEE
**2018**, 38, 1893–1904. [Google Scholar] - Kober, T.; Schiffer, H.W.; Densing, M.; Panos, E. Global energy perspectives to 2060—WEC’s World Energy Scenarios 2019. Energy Strategy Rev.
**2020**, 31, 100523. [Google Scholar] [CrossRef] - Wang, D.D.; Sueyoshi, T. Climate change mitigation targets set by global firms: Overview and implications for renewable energy. Renew. Sustain. Energy Rev.
**2018**, 94, 386–398. [Google Scholar] [CrossRef] - Tafuni, A.; Giannotta, A.; Mersch, M.; Pantaleo, A.M.; Amirante, R.; Markides, C.N.; De Palma, P. Thermo-economic analysis of a low-cost greenhouse thermal solar plant with seasonal energy storage. Energy Convers. Manag.
**2023**, 288, 117123. [Google Scholar] [CrossRef] - Ma, X.; Zhai, Y.; Zhang, T.; Yao, X.; Hong, J. What changes can solar and wind power bring to the electrification of China compared with coal electricity: From a cost-oriented life cycle impact perspective. Energy Convers. Manag.
**2023**, 289, 117162. [Google Scholar] [CrossRef] - Guo, Y.; Ming, B.; Huang, Q.; Wang, Y.; Zheng, X.; Zhang, W. Risk-averse day-ahead generation scheduling of hydro–wind–photovoltaic complementary systems considering the steady requirement of power delivery. Appl. Energy
**2022**, 309, 118467. [Google Scholar] [CrossRef] - Tian, C.C. Function Remolding of Hydropower Systems for Carbon Neutral and Its Key Problems. Autom. Electr. Power Syst.
**2021**, 45, 29–36. [Google Scholar] - Nematollahi, O.; Hoghooghi, H.; Rasti, M.; Sedaghat, A. Energy demands and renewable energy resources in the Middle East. Renew. Sustain. Energy Rev.
**2016**, 54, 1172–1181. [Google Scholar] [CrossRef] - Luo, S.; Hu, W.; Huang, Q.; Han, X.; Chen, Z. Optimization of Photovoltaic/Small Hydropower/Pumped Storage Power Station System Sizing under the Market Mechanism. Trans. China Electrotech. Soc.
**2020**, 35, 2792. [Google Scholar] - Braff, W.A.; Mueller, J.M.; Trancik, J.E. Value of storage technologies for wind and solar energy. Nat. Clim. Chang.
**2016**, 6, 964–969. [Google Scholar] [CrossRef] - Guo, S.; Liu, Q.; Sun, J.; Jin, H. A review on the utilization of hybrid renewable energy. Renew. Sustain. Energy Rev.
**2018**, 91, 1121–1147. [Google Scholar] [CrossRef] - Yanmei, Z.; Shijun, C.; Guangwen, M.; Xiaoyan, H.; Liang, W. Short-Term Complementary Operation of Hydro-Photovoltaic Integrated System Considering Power Generation and Output Fluctuation. Trans. China Electrotech. Soc.
**2020**, 35, 2769–2779. [Google Scholar] - Ashok, S. Optimised model for community-based hybrid energy system. Renew. Energy
**2007**, 32, 1155–1164. [Google Scholar] [CrossRef] - Zou, S.; Zhang, N.; Wei, B. A capacity optimization and scheduling scheme of a multi-energy complementary power station considering energy trading. Front. Energy Res.
**2023**, 11, 1194139. [Google Scholar] [CrossRef] - Wang, S.; Jia, R.; Shi, X.; An, Y.; Huang, Q.; Guo, P.; Luo, C. Hybrid Time-Scale Optimal Scheduling Considering Multi-Energy Complementary Characteristic. IEEE Access
**2021**, 9, 94087–94098. [Google Scholar] [CrossRef] - Li, J.; Luo, G.; Li, T.; Gao, L.; Liang, X.; Hu, J.; Cao, Y.; Qi, L.; Liu, X.; Huo, M. Impact on traditional hydropower under a multi-energy complementary operation scheme: An illustrative case of a ‘wind–photovoltaic–cascaded hydropower plants’ system. Energy Strategy Rev.
**2023**, 49, 101181. [Google Scholar] [CrossRef] - Li, H.; Liu, P.; Guo, S.; Ming, B.; Cheng, L.; Yang, Z. Long-term complementary operation of a large-scale hydro-photovoltaic hybrid power plant using explicit stochastic optimization. Appl. Energy
**2019**, 238, 863–875. [Google Scholar] [CrossRef] - Yang, Y.; Zhou, J.; Liu, G.; Mo, L.; Wang, Y.; Jia, B.; He, F. Multi-plan formulation of hydropower generation considering uncertainty of wind power. Appl. Energy
**2020**, 260, 114239. [Google Scholar] [CrossRef] - Zhu, F.; Zhong, P.; Xu, B.; Liu, W.; Wang, W.; Sun, Y.; Chen, J.; Li, J. Short-term stochastic optimization of a hydro-wind-photovoltaic hybrid system under multiple uncertainties. Energy Convers. Manag.
**2020**, 214, 112902. [Google Scholar] [CrossRef] - Shayan, M.E.; Najafi, G.; Ghobadian, B.; Gorjian, S.; Mazlan, M. A novel approach of synchronization of the sustainable grid with an intelligent local hybrid renewable energy control. Int. J. Energy Environ. Eng.
**2023**, 14, 35–46. [Google Scholar] [CrossRef] - Shayan, M.E.; Najafi, G.; Ghobadian, B.; Gorjian, S.; Mamat, R.; Ghazali, M.F. Multi-microgrid optimization and energy management under boost voltage converter with Markov prediction chain and dynamic decision algorithm. Renew. Energy
**2022**, 201, 179–189. [Google Scholar] [CrossRef] - Shou-ren, Z. Development and utilization of hydropower resources in China: Opportunity and challenges. J. Hydraul. Eng.
**2007**, 1, 9350. [Google Scholar] - Yi, J.; Labadie, J.W.; Stitt, S. Dynamic Optimal Unit Commitment and Loading in Hydropower Systems. J. Water Res. Plan. Man.
**2003**, 129, 388–398. [Google Scholar] [CrossRef] - Anoune, K.; Bouya, M.; Astito, A.; Abdellah, A.B. Sizing methods and optimization techniques for PV-wind based hybrid renewable energy system: A review. Renew. Sustain. Energy Rev.
**2018**, 93, 652–673. [Google Scholar] [CrossRef] - Chen, L.; Ge, L.; Wang, D.; Zhong, W.; Zhan, T.; Deng, A. Multi-objective water-sediment optimal operation of cascade reservoirs in the Yellow River Basin. J. Hydrol.
**2022**, 609, 127744. [Google Scholar] [CrossRef] - Yuan, X.; Yu, H.; Liang, J.; Xu, B. A novel density peaks clustering algorithm based on K nearest neighbors with adaptive merging strategy. Int. J. Mach. Learn. Cybern.
**2021**, 12, 2825–2841. [Google Scholar] [CrossRef] - Salomon, S.; Avigad, G.; Fleming, P.J.; Purshouse, R.C. Active Robust Optimization: Enhancing Robustness to Uncertain Environments. IEEE Trans. Cybern.
**2014**, 44, 2221–2231. [Google Scholar] [CrossRef] [PubMed] - Jensen, M.T. Generating robust and flexible job shop schedules using genetic algorithms. IEEE Trans. Evolut. Comput.
**2003**, 7, 275–288. [Google Scholar] [CrossRef] - Wiesmann, D.; Hammel, U.; Back, T. Robust design of multilayer optical coatings by means of evolutionary algorithms. IEEE Trans. Evolut. Comput.
**1998**, 2, 162–167. [Google Scholar] [CrossRef] - Qiu, H.; Gu, W.; Xu, X.; Pan, G.; Liu, P.; Wu, Z.; Wang, L. A Historical-Correlation-Driven Robust Optimization Approach for Microgrid Dispatch. IEEE Trans. Smart Grid
**2021**, 12, 1135–1148. [Google Scholar] [CrossRef] - Mahdi, M.; Xueqian, S.; Gai, Q.; Basirialmahjough, M.; Yuan, H. Improving robustness of water supply system using a multi-objective robust optimization framework. Environ. Res.
**2023**, 232, 116270. [Google Scholar] [CrossRef] [PubMed] - Guo, Q.; Guo, T.; Tian, Q.; Nojavan, S. Optimal robust scheduling of energy-water nexus system using robust optimization technique. Comput. Chem. Eng.
**2021**, 155, 107542. [Google Scholar] [CrossRef] - Nag, K.; Pal, T.; Mudi, R.K.; Pal, N.R. Robust Multiobjective Optimization with Robust Consensus. IEEE Trans. Fuzzy Syst.
**2018**, 26, 3743–3754. [Google Scholar] [CrossRef] - San, L.C.; Fulong, L. Press Conference of the National Energy Administration on the Energy Situation in the First Half of the Year. In Proceedings of the China National Energy Administration Routine Press Conference, Beijing, China, 1 July 2022. [Google Scholar]
- Yousri, D.; Farag, H.E.Z.; Zeineldin, H.; El-Saadany, E.F. Integrated model for optimal energy management and demand response of microgrids considering hybrid hydrogen-battery storage systems. Energy Convers. Manag.
**2023**, 280, 116809. [Google Scholar] [CrossRef] - Prasanna, A.; Dorer, V.; Vetterli, N. Optimisation of a district energy system with a low temperature network. Energy
**2017**, 137, 632–648. [Google Scholar] [CrossRef] - Brentan, B.M.; Carpitella, S.; Izquierdo, J.; Luvizotto, E.; Meirelles, G. District metered area design through multicriteria and multiobjective optimization. Math. Method Appl. Sci.
**2022**, 45, 3254–3271. [Google Scholar] [CrossRef] - Liu, Y.; Wang, G.; Zhou, J.; Dai, R.; Yu, F. Optimal planning strategy for energy internet zones based on interval optimization. Energy Rep.
**2020**, 6, 1255–1261. [Google Scholar] [CrossRef] - Zhang, Y.; Lian, J.; Ma, C.; Yang, Y.; Pang, X.; Wang, L. Optimal sizing of the grid-connected hybrid system integrating hydropower, photovoltaic, and wind considering cascade reservoir connection and photovoltaic-wind complementarity. J. Clean. Prod.
**2020**, 274, 123100. [Google Scholar] [CrossRef] - Ming, B.; Liu, P.; Guo, S.; Zhang, X.; Feng, M.; Wang, X. Optimizing utility-scale photovoltaic power generation for integration into a hydropower reservoir by incorporating long- and short-term operational decisions. Appl. Energy
**2017**, 204, 432–445. [Google Scholar] [CrossRef]

**Figure 2.**Overall real-time-short-term framework for a regional multi-energy complementary system (MES).

**Figure 3.**China’s Installed PV Capacity, 2017–2022. (

**a**): National Cumulative/Newly Installed Capacity; (

**b**): Distributed/Centralized PV Installed Newly Installed Capacity [34].

**Figure 4.**Historical data processing of photovoltaic station output in the region. (

**a**): Simulation fitting function for historical data; (

**b**): Typical daily data obtained by clustering historical data of the complementary system; (

**c**): Heat map showing the correlation coefficient between the fitting function and typical daily data; (

**d**): Probability density map of e.

**Figure 8.**The first three intervals serve as temporal fluctuations of the hydroelectric plant at different confidence levels.

**Figure 9.**Characterization of uncertainty after optimization of hydroelectric power plant output region.

**Figure 12.**Expected incoming flows at the 83% confidence probability level for the hydroelectric power plant’s 33rd hour of trial calculations in the multi-generation program.

**Figure 16.**Typical June historical dispatch (simulation) for the region’s multi-energy complementary systems.

**Figure 17.**Graphs of unit efficiency curves at different heads: (

**a**) unit efficiency versus output; (

**b**) unit consumption flow versus output (Unit efficiency: electricity that can be generated per unit cubic meter of water).

**Figure 18.**(

**a**) Residual load process of the microgrid in the region; (

**b**) Uncertainty characterization of the generation of each hydropower plant after regional optimization.

**Figure 19.**Statistical graphs of twenty results for a typical day of optimization by the two-layer nested optimization algorithm: (

**a**) Iteration count and flow rate consumption optimization relationship; (

**b**) Iteration count and flow rate consumption box plots.

**Figure 22.**Reservoir Levels and Water Savings on Typical Days for Different Dispatch Scenarios. In calculating water savings for the two optimization scenarios, the simulated dispatch scenario (historical dispatch scenario for a typical day) is the baseline.

Power Plant | Regulating Capacity | Installed Capacity (MW) | Normal/Dead Water Level (m) | Maxi/Min Discharge (m^{3}/s) | Max/Min Head (m) | Unit Vibration Limit (MW) |
---|---|---|---|---|---|---|

power plants | year | 300 × 4 | 200/161.2 | 340 × 4/0 | 121.5/80.7 | (0–30) U (80, 180) |

Parameter Category | Symbol | Value | Unit |
---|---|---|---|

Min. start-up time | $S{U}_{n}$ | 1 | [h] |

Min. stopping time | $S{D}_{n}$ | 1 | [h] |

Climbing speed of output | $\Delta p$ | 10 | [MW/s] |

Spinning reserve | $L{R}_{t}$ | 80 | [MW] |

Vibration zone upper limit | ${p}_{j}^{up}$ | 30.180 | [MW] |

The lower limit of the vibration zone | ${p}_{j}^{up}$ | 0.80 | [MW] |

The upper limit of unit output | ${p}_{n}^{+}$ | 0 | [MW] |

The lower limit of the unit | ${p}_{n}^{-}$ | 300 | [MW] |

**Table 3.**Statistical results of 20 deterministic and stochastic optimizations in the region on a typical day in June 2016.

Statistical Counts | Deterministic Optimization | Stochastic Optimization |
---|---|---|

1 | 572.6 | 574.1 |

2 | 572.7 | 574.6 |

3 | 572.6 | 574.1 |

4 | 573.1 | 574.6 |

5 | 572.5 | 574.5 |

6 | 572.4 | 574.7 |

7 | 572.1 | 574.2 |

8 | 572.8 | 574.9 |

9 | 573.4 | 573.3 |

10 | 573.8 | 574.9 |

11 | 573.4 | 574.4 |

12 | 573.8 | 575.0 |

13 | 572.6 | 573.1 |

14 | 573.2 | 574.1 |

15 | 572.9 | 574.6 |

16 | 573.0 | 573.1 |

17 | 572.4 | 573.3 |

18 | 572.5 | 574.0 |

19 | 572.8 | 574.3 |

20 | 572.3 | 574.7 |

average | 572.8 | 574.2 |

statistics | 0.5 | 0.6 |

average ± statistics | 572.8 ± 0.5 | 574.2 ± 0.6 |

**Table 4.**Comparison of economic operation results for a typical day under different scheduling scenarios.

Evaluation Metrics | Historical Scheduling (Simulation) | Deterministic Optimization Scheduling | Stochastic Optimization Scheduling |
---|---|---|---|

Total water consumption (100,000 m^{3}) | 49.49 | 48.65 | 48.86 |

Probability of non-vibration zone operation (%) | 91.2 | 100 | 100 |

Load standby fulfillment probability (%) | 83.6 | 100 | 100 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hu, Z.; Luo, Z.; Luo, N.; Zhang, X.; Chao, H.; Dai, L.
Optimizing Water-Light Complementary Systems for the Complex Terrain of the Southwestern China Plateau Region: A Two-Layer Model Approach. *Sustainability* **2024**, *16*, 292.
https://doi.org/10.3390/su16010292

**AMA Style**

Hu Z, Luo Z, Luo N, Zhang X, Chao H, Dai L.
Optimizing Water-Light Complementary Systems for the Complex Terrain of the Southwestern China Plateau Region: A Two-Layer Model Approach. *Sustainability*. 2024; 16(1):292.
https://doi.org/10.3390/su16010292

**Chicago/Turabian Style**

Hu, Zhikai, Zhumei Luo, Na Luo, Xiaoxv Zhang, Haocheng Chao, and Linsheng Dai.
2024. "Optimizing Water-Light Complementary Systems for the Complex Terrain of the Southwestern China Plateau Region: A Two-Layer Model Approach" *Sustainability* 16, no. 1: 292.
https://doi.org/10.3390/su16010292