Stochastic Power Grid Dispatching via Hyperbolic Tangent Approximation
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Solution Overview
Problem
Conventional methods for active power rolling dispatch in power systems face challenges due to the volatility and randomness of renewable energy sources, such as wind and photovoltaic power, which lead to inaccurate forecasting and difficulties in applying deterministic dispatching methods, resulting in suboptimal dispatching strategies and high costs.
Innovation Solution
A two-side stochastic dispatching method is developed, transforming two-side chance constraints into deterministic convex constraints using a Gaussian mixture distribution approximated by a hyperbolic tangent function, allowing for the creation of a cost-minimized stochastic dispatching model that effectively limits uncertainty and reduces dispatching costs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional deterministic or robust dispatching methods are applied, then system operation risk is considered, but the volatility and randomness of renewable energy make it difficult to achieve optimal dispatching results
Solution Approach 1:
The patent transforms the two-side chance-constrained stochastic dispatching problem into a deterministic convex optimization problem by changing the parameter representation of renewable energy power. Specifically, it uses the cumulative distribution function (CDF) to transform random variables into deterministic equivalent constraints, where the chance constraints are converted into deterministic constraints through probabilistic transformation. This parameter transformation enables the use of efficient deterministic optimization algorithms while maintaining the statistical characteristics of renewable energy volatility.
2Loss of energy
If two-side chance-constrained stochastic dispatching is used, then the lowest-cost dispatching strategy is obtained, but the solution is extremely difficult with conventional sampling methods having large calculation amounts and poor convergence
Solution Approach 1:
The patent extracts the stochastic nature of renewable energy from the complex two-side chance-constrained optimization problem and separates it into a deterministic equivalent form. By taking out the probabilistic elements and transforming them into deterministic constraints using CDF, the method removes the computational complexity of sampling-based approaches while preserving the essential uncertainty handling capabilities. This extraction allows the use of standard deterministic optimization algorithms.
Solution Approach 2:
The patent substitutes the mechanical sampling-based solution approach with a mathematical transformation approach. Instead of using computational sampling methods that require extensive iterations and have poor convergence, the invention replaces the sampling mechanism with an analytical transformation using cumulative distribution functions. This substitution transforms the problem from a computational search process to a direct mathematical equivalence, dramatically reducing solution complexity.
3Reliability
If single-side chance-constrained dispatching is applied, then system operation risk and power generation cost are considered, but the independent modeling of upper and lower bound constrain results in optimization results being too slack and unable to meet preset safety level
Solution Approach 1:
The patent merges the independent upper and lower bound chance constraints into a unified two-side chance-constrained framework. Instead of treating reserve capacity constraints separately (which leads to overly conservative results), the invention combines both upper and lower bounds into a single optimization model with coordinated chance constraints. This merging allows the simultaneous consideration of both safety limits while maintaining optimization precision, as the constraints are solved together rather than independently.
Data Source
AI summary
The disclosure relates to a two-side stochastic dispatching method for a power grid. By analyzing historical data of wind power, the Gaussian mixture distribution is fitted by software. For certain power system parameters, a two-side chance-constrained stochastic dispatching model is established. The hyperbolic tangent function is used to analyze and approximate cumulative distribution functions of random variables in the reserve demand constraint and the power flow constraint, to convert the two-side chance constraint into a deterministic constraint. The disclosure can have the advantage of using the hyperbolic tangent function to convert the two-side chance constraint containing risk levels and random variables into the solvable deterministic convex constraint, effectively improving the solution efficiency of the model, and providing decision makers with a more reasonable dispatching basis.