Abstract
Most available long-term operation models for hydropower stations use deterministic historical data as inputs but cannot be employed to update the decision scheme in real time according to the actual solar radiation and inflow conditions, resulting in a disconnect between the given plan and actual decision-making process. In this study, a multistage rolling reservoir decision model considering the uncertainties in solar radiation and inflow is proposed to guide the formulation of long-term operational schemes for hydro-PV systems. We adopt the solar radiation and inflow series generated by the scenario tree (ST) method as inputs of the reservoir optimal operation model and use a genetic algorithm (GA) to solve the model. In the solution process, the scheme is adjusted according to the actual solar radiation and inflow conditions. Typical wet, normal, and dry years are analysed. The results illustrate that the model can better inform the design of long-term operational schemes for hydro-PV stations relative to the actual operational scheme and the traditional deterministic model.
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Data Availability
The data that support the findings of this study are available from corresponding author upon reasonable request.
Abbreviations
- \(Count\{\cdot \}\) :
-
Number counting function
- \({D}_{i,\xi }\) :
-
Euclidean distance between two randomly chosen series
- \({D}_{{i}{\prime},{\zeta }{\prime}}\) :
-
Euclidean distance between \({S}_{\mathrm{i}}\) and the historical series \({\zeta }{\prime}\)
- \({E}_{H}\) :
-
Hydro PG
- \({E}_{PV}\) :
-
PV PG
- GA:
-
Genetic algorithm
- \({H}_{\xi ,t}\) :
-
Node value of the series ξ at stage t
- \(h({O}_{i},\lambda (j))\) :
-
Adaptation function
- \({H}_{x,t}\) :
-
Randomly selected value from the historical series \(x\) at stage t
- \({I}^{t}\) :
-
Inflow in the \({t}^{\mathrm{th}}\) month
- \(j\) :
-
Iteration time from 0 to \({j}_{\mathrm{m}}\)
- \({j}_{m}\) :
-
Maximum iteration time
- \(K\) :
-
Comprehensive output coefficient of the hydropower station
- \(L\) :
-
Reservoir water level
- \({L}_{max}^{t}\) :
-
Maximum permissible reservoir water level during the \({t}^{\mathrm{th}}\) time period
- \({L}_{min}^{t}\) :
-
Minimum permissible water reservoir level during the \({t}^{\mathrm{th}}\) time period
- \(m\) :
-
Current decision-making stage
- \({N}_{i,t}\) :
-
Node value of scene \(i\) at stage t
- NG:
-
Neural gas
- NREL:
-
National Renewable Energy Laboratory
- \({O}_{i}\) :
-
Distance rank of scene \(i\)
- \(P\) :
-
Number of scenes
- PG:
-
Power generation
- \({P}_{H}\) :
-
Power of the hydropower station
- \({P}_{h}\) :
-
Total number of scenes of the streamflow ST
- \({P}_{Hmax}\) :
-
Maximum installed capacity of hydroelectric power
- \({P}_{PV}\) :
-
Actual output power
- \({P}_{PV}^{\prime}\) :
-
Installed capacity of the PV power station
- PV:
-
Photovoltaics
- \({P}_{PVmax}\) :
-
Maximum installed capacity of PV power
- ξ:
-
Initial scene \(i\)
- \({P}_{R}\) :
-
Total scenes of the solar radiation ST
- \(Q\) :
-
Discharge flow of the reservoir
- \({Q}^{t}\) :
-
Discharge flow of the reservoir in the \({t}^{\mathrm{th}}\) month
- \({Q}_{max}^{t}\) :
-
Maximum permissible water release of the reservoir during the \({t}^{\mathrm{th}}\) time period
- \({Q}_{min}^{t}\) :
-
Minimum permissible water release of the reservoir during the \({t}^{\mathrm{th}}\) time period
- \({R}_{STC}\) :
-
Solar irradiance under the standard test conditions
- \({R}_{T}\) :
-
Actual solar irradiance
- ST:
-
Scenario tree
- \(T\) :
-
Tailwater elevation
- \({T}_{air}\) :
-
Air temperature provided by the weather station
- \({T}_{s}\) :
-
Number of stages
- \({T}_{P}\) :
-
Actual temperature of the solar cell module
- \({T}_{STC}\) :
-
Temperature under the standard test conditions
- \({T}_{noc}\) :
-
Normal operating temperature of the solar cell module
- \({V}^{t}\) :
-
Water storage volume in the \({t}^{\mathrm{th}}\) month
- \(X\) :
-
Total number of historical series
- \(\Delta H\) :
-
Net water head of the hydropower station
- \(\Delta t\) :
-
Length of period \(t\)
- \({\alpha }_{P}\) :
-
Temperature coefficient of the power output of the solar cell module
- \({\beta }_{Hi}\) :
-
Probability of scene \(i\) in the streamflow ST
- \({\beta }_{i}\) :
-
Probability of \({S}_{\mathrm{i}}\)
- \({\beta }_{Rj}\) :
-
Probability of scene \(j\) in the solar radiation ST
- \({\lambda }_{f}\) :
-
Final adaptation parameter
- \(\lambda \left(j\right)\) :
-
Another step size function
- \({\lambda }_{0}\) :
-
Initial adaptation parameter
- \({\varepsilon }_{f}\) :
-
Final step size parameter
- \(\varepsilon \left(j\right)\) :
-
Step size function
- \({\varepsilon }_{0}\) :
-
Initial step size parameter
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (51979276), the Project of Sanya Yazhou Bay Science and Technology City (SCKJ-JYRC-2022-100), the Integration Program of the Major Research Plan of the National Natural Science Foundation of China (91847302), and the Key R&D program of Science and Technology Department of Tibet under Grant (XZ202101ZY0003G).
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Highlights
• In this paper, a long-term operational scheme is proposed for hydro-PV complementary power stations.
• The uncertainties in solar radiation and inflow are considered by applying the scenario tree method in reservoir operation.
• According to actual solar radiation and inflow data, the scheme is updated and adjusted to obtain a rolling solution.
• Compared with the actual operational scheme and the traditional deterministic model, our model can better guide the formulation of operational schemes for hydro-PV stations.
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Cao, H., Qiu, J., Zuo, HM. et al. A Long-Term Operational Scheme for Hybrid Hydro-Photovoltaic (PV) Systems that Considers the Uncertainties in Reservoir Inflow and Solar Radiation Based on Scenario Trees. Water Resour Manage 37, 5379–5398 (2023). https://doi.org/10.1007/s11269-023-03609-7
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DOI: https://doi.org/10.1007/s11269-023-03609-7