Congestion and Workflow Management in Energy Systems Using Adaptive Generation Rescheduling Techniques

Currently, energy demand is growing at an alarming rate worldwide hence creating pressure to the power systems to find ways of enhancing its efficiency and effectiveness in delivering electricity to consumers cheaply. More often power systems involve extensive coupling, and integration of numerous energy types, while imposing severe operational limitations [1]. Such dynamics pose certain difficulties, especially related to congestion and work flow which are central for system stability, costs containment and efficiency.

Nowadays, OPF is one of the main approaches to deal with these challenges. OPF has since its initial use in the 1960s, grown into an essential tool for system operators [2, 3]. It is mainly used to define the secure and efficient operation of a power system in steady-state by providing the lowest value of cost, for example, cost of fuel or loss cost under the juris of set of constraints so as to maintain the system secure with feasible operational conditions. Nevertheless, the fact that OPF is inherently a non-linear, non-convex and large-scale optimisation predicament renders its solution both computationally intensive and complex [4, 5].

Congestion, with regard to energy systems, is the situation in which the flow of power through some of the channels of its transmission gets to a point where actual physical and thermal limitations or forces have to be coordinated. This condition is usually experienced due to unpredicted load fluctuations, generation malfunctions or problems with transmission network [6, 7]. Congestion contributes to system unreliability and hikes operational costs and threatens to skew the supply of energy for fair use.

To select the appropriate management strategies, their aims are to regulate demand and generation by awaiting their proven overload and making sure that the existing transmission capacity is used in the most effective way possible [8, 9]. There has been the development of adaptive generation rescheduling techniques; the approach provides the operators with the ability to reschedule the flows of generations depending on the congestion levels in the system. Regarding the challenges of OPF, numerous techniques has been proposed throughout the years, starting with fundamental mathematical programming, and including heuristic and metaheuristic methods. These methodologies positively affect system reliability and efficiency, not only in integrating renewable energy sources but also in Flexible AC Transmission Systems (FACTS) devices as shown in Figure 1.

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Figure 1. Classification of FACTS devices

In power systems workflow management can be defined the process of integration and management of all the various components and the procedures which control the capability of generating, transmitting and distributing electricity. Its objectives include process rationalisation, minimisation of wastage, and improvement of structures and systems [10-12]. With the incorporation of renewable energy capitals and sophisticated modern grid infrastructure, the overall working patterns have enhanced the more challenging aspects of workflows, making use of sophisticated optimization tools and methods are inevitable.

OPF offers power system’s supply and demand a mathematical model where it seeks to find the most efficient way of operating the system from economic dispatch to voltage control [13]. In adaptive generation rescheduling, the OPF is used to determine how the rescheduling of generator outputs can alleviate the congestion problem without violating the constraints of the systems [14]. It is especially valuable in real-time application environments because context changes occur continually and synchronous responses are expected.

Opposed to this, the OPF problem can be defined as an optimisation problem with an independent function and restrictions. Normally, the aim function comprises terms such as generation cost, transmission losses or both which must both be minimized [15-17]. Constraints in OPF are classified into:

• Equality constraints: Coarse-grained stochastic activities meant to represent the relationships between substations in terms of power physics laws for example; real power = reactive power.
• Inequality constraints: Comprises generator output constraints, voltage restraints, and transmission line thermal constraints.

Adaptive rescheduling techniques makes use of enhanced resource allocation models to solve the OPF problem in varying power system conditions [18]. These methods use actual real-time data to balance generation schedules with hour-by-hour constraints and in this regard, costs are minimized while meeting system constraints.

However, mixed results show that solving OPF problems has several difficulties. Due to the nature of the OPF formulation which is non-convex and non-linear nature, the solution space has many local minimums hence making the determination of the global solution difficult. However, the incorporation of distributed renewable resources like wind and solar energy sources has WSM ACC, and variability and uncertainty complications that amplify the difficulties of OPF problems [19].

First-generation optimization procedures such as the LP, QP, and Newton type methods have been harnessed to solve OPF problems. However, these methods encounter difficulties in the convergence of solutions and the computational load increases rapidly for extensive systems [20]. To overcome these limitations, optimization heuristics and metaheuristic algorithms are advanced techniques that have been proposed by the researchers.

• Metaheuristic algorithms: Methodology like GA, PSO, SA has showed a promising result in handling with complex OPF issues [21]. These algorithms can easily solve multimodal and non-convex OPF problem with high degree of accuracy and provide solutions from whole universe.
• Hybrid optimization techniques: That is why the combination of methods based on the algorithms’ iterative application with heuristic optimization has been shown to enhance both the speed of convergence to the solution as well as the quality of the solution. For instance, the optimization of OPF solutions in congested systems has in the past been accomplished by combining TLBO with PSO.
• FACTS: FACTS devices, including TCSC and SVC, utilize power flow and voltage profile for controlling congestion. Further, the incorporation of these devices into OPF formulations increases flexibility and stability in the power system.
• AI-based techniques: OPF has recently been shown to be tractable using AI and ML. These procedures are very useful in real-time systems where decision making has to be done in real-time mode.

Adaptive generation rescheduling offers several benefits for congestion and workflow management in energy systems:

• Enhanced system reliability: Where generation produces a quantity of energy that varies over time, adaptive rescheduling balances the energy so produced in a way that the flow through transmission lines does not overload them as well as stabilizing the voltage.
• Cost efficiency: Reducing the fuel utilisation in generator schedules bring down the fuel cost and transmission losses thus a great saving.
• Integration of renewable energy: variable renewable energy sources are easily incorporated into the approach, which improves the grid related resilience and sustainability.
• Scalability and flexibility: These techniques make it possible to analyse different layouts of systems and as such they are applicable for both small and big power systems.

Technological advancement in renewable power and smart grid, among other factors, make it important to adopt new more elaborate congestion, and the flow of work. Generation rescheduling technologies which adapt with human beings are in the list of potential contenders to guide future energy systems powered by new optimization and artificial intelligence concepts [22]. Algorithms are still being developed for these methods as the scope of the techniques is anticipated to grow with future uses including microgrid control, demand response, and energy storage.

Congested transmission line is a major constraint in electrical power system, more especially, in deregulated system. Congestion management (CM) ensures maximum utilization and economic dispatch of power by controlling the flow of power within the network constraint limit. In case of conventional methods involving OPF and PSO, additional complexity and restrictions-specifically in terms of computational algorithms-are observed. The MTLBO algorithm is a new parameter less and efficient approach to solve the CM problems for minimizing rescheduling costs, system losses and line overloads in this research. The subsequent sections in Figure 2 describe the definition, realization and verification of MTLBO algorithm, and the mathematical models and numerical simulations applied in the present work.

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Figure 2. Flow illustration of the MLTBO

The CM problem is a big problem, containing several objectives, but for easier calculation it is reduced to one. The key objectives are:

•Minimizing congestion cost.

•Minimizing system losses.

•Maintaining power flow within safe limits.

This objective function reduces congestion management costs as the schedules of the generators are optimized as written in Eq. (1). It accounts for active power adjustments and associated costs:

$F=\sum_{i=1}^M\left(C_i^{+} \Delta P_i^{+}+C_i^{-} \Delta P_i^{-}\right)$         (1)

This leads to economic dispatch while achieving system stability without incurring congestion costs.

Here $M=$ total generators, $F=$ total congestion management cost, $\Delta P_i^{+}$ = active power outcome increment, $\Delta P_i^{-}$ = active power outcome decrement, $C_i^{+}$ = cost coefficient for increasing power generation, $C_i^{-}$ = cost coefficient for decreasing power generation.

It is because of this that the total power produced corresponds to the load demand plus the system losses as shown in Eq. (2):

$\sum_{k=1}^m P_{G_k}=\sum_{l=1}^N P_{D_l}+P_{\text {loss }}$       (2)

It balances between supply and demand and this is very important in grid operations during different situation.

Where $P_{G_k}=$ active power outcome of generator $k$, $P_{D_l}=$ active power demand of load $l, P_{\text {loss }}=$ total power loss, $m=$ total generators, $N=$ total loads.

It is essential that the fluxes in transmission lines do not above their temperature or safety limitations.

$\left|P_{k l}\right| \leq P_{k l}^{\max }$      (3)

This eliminates cases of line, overloading while at the same time providing system security against cascaded faults because of high-power flow.

Where $P_{k l}=$ active power flow among $k$ and $l$ as shown in inequality (3), $P_{k l}^{\max }=$ limit of the power that is allowed to pass through a transmission line linking buses $k$ and $l$.

To maintain quality and stability, the magnitudes of the bus voltage must stay within the stipulated maximums:

$v_k^{\min } \leq v_k \leq v_k^{\max }$       (4)

This prevents problems such as voltage collapse, and retains functional reliability at the interconnected system.

Where $\nu_b=$ voltage magnitude at bus $k$, $v_k^{\min }=$ minimum voltage magnitude at bus $k, v_k^{\max }=$ maximum voltage magnitude at bus $k$ as shown in inequality (4).

The electrical power of every generator has to be maintained within the range of its lowest and highest capacities:

$P_{G_k}^{\min } \leq P_{G_k} \leq P_{G_k}^{\max }$       (5)

This helps manage operations risks and prevents instances where some generation units may be used more than they should or conversely not used enough.

Where $P_{G_k}=$ active power outcome of generator $k, P_{G_k}^{\min }=$ minimum active power outcome of generator $k, P_{G_k}^{\max }=$ maximum active power outcome of generator $k$ as mentioned in inequality (5).

3.1 Modified TLBO

The MTLBO algorithm is an advanced form of the standard TLBO algorithm. In contrast to standard procedures, there are no control parameters for MTLBO and therefore the method is less sensitive to the choice of the algorithm. Innovative and problem-focused, this hybrid design makes for efficient consideration of the solution space in addition to the exploitation, most important considering the non-linear nature of congestion management problems.

When it comes to power systems analysis, where fine-tuning the compromise between runtime and solution quality is critical, this extension is useful. MTLBO on the other hand achieves this balance through introduction of dynamic adaptability into the teaching and learning activities.

3.2 Steps of the MTLBO algorithm

Step 1: The solutions generated in the MTLBO algorithm correspond to a generator schedule. To do so, it is encoded as a vector of power outputs of m generators that satisfy operational constraints. For example:

Step 2: Initialization

•The space can be defined by limiting the generator parameters to operating levels.

•In a random manner the initial population of N solutions are to be set within this range.

Step 3: Fitness evaluation: The criteria that must be assessed concerning the applicability of each solution is the objective function F. The set with the lowest F represents is the best candidate for some solution.

Step 4: Teaching phase

•The one characteristic that works best for the present generation serves as the ‘teacher’.

•Make sure that every learner (answer) is updated in order to get closer to the viewpoint of the instructor, as specified by Eq. (6):

$a_{\text {new }}=a_{\text {old }}+r *\left(a_{\text {teacher }}-T_f * \bar{a}\right)$        (6)

This step increases the convergence by amplifying solution space in the neighborhood of teacher.

Step 5: Learning phase

Students learn through the interaction with each other and therefore come up with a diverse solution space.

For each solution, changes based on its interaction with a randomly chosen peer are made as shown mathematically in Eq. (7).

$a_{\text {new}}=\left\{\begin{array}{c}a_{\text {old}}+r *\left(a_{\text {peer}}-a_{\text {old}}\right), if\,\, f \left(a_{\text {peer}}\right)<f\left(a_{\text {old}}\right) \\ a_{\text {old}}+r *\left(a_{\text {old}}-a_{\text {peer}}\right), \text { otherwise}\end{array}\right.$         (7)

Step 6: Constraint handling

Infeasible solution candidates considering constraint such as power flow limits are made costly through this approach. A common penalty method modifies the fitness function as:

$F_{\text {penalized }}=F+\lambda * C V$       (8)

Here, λ = penalty factor, and CV = quantifies the magnitude of the violation mentioned in Eq. (8).

Step 7: Stopping criteria

It is possible for the algorithm to end when either:

•The convergence criteria set for the algorithm have been achieved or, more precisely, a highest number of repetitions is beaten.

•The enhancement in the best solution is less than the pre-designated level.

Step 8: Outcome: Management of congestion through the best generator schedule is found on the best solution at termination.

3.3 Advanced features of MTLBO

• Parameter-free design: While MTLBO does not contain any user-defined parameters (such as mutation rate in GA, inertia weight in PSO) this makes it a more straightforward and flexible method for application to numerous problem domains.
• Enhanced convergence: The teaching phase guarantees fast convergence in this strategy as the attention is on the teacher solution. The remaining part of learning phase is involved with the immediate operation of retaining diversity in order to make it avoid converging to local optima.
• Scalability: MTLBO is capable of solving large systems and more constraints, the results for MTLBO for real world power systems like IEEE-57 and IEEE-118 bus systems confirm this.
• Applicability to non-linear problems: The algorithm is non-sensitive to non-linearity since it does not require the evaluation of derivatives, like the gradient-based optimization techniques.

3.4 Algorithm pseudocode

Step 1. Start the generation of solutions from the population.

Step 2. Using Eq. (7) assesses the fitness of the genetic string every solution within the population to the objective function.

Step 3. Repeat until stopping criteria are met:

  a. Teaching Phase:

   i. Detect the teacher (sharpest value in the sample).

   ii. Teach every student using the teaching equation.

  b. Learning Phase:

   i. Now, for each student choose one of the peers randomly.

   ii. Modify the student as a result of peer interaction.

  c. Handle constraints by using penalty.

  d. Consider again how well each solution can fit in the approach.

Step 4. The best solution is the optimal generator schedule.

Power system congestion control can be efficiently dealt with the help of the MTLBO that has no parameters. Incorporation of dynamic teaching and peer-learning phases allows the optimization of the generator scheduling and reduces the costs of the rescheduling and system losses and enhances the stability of the grid. The versatility of MTLBO to handle non-linear constraints, along with faster convergence over conventional optimization algorithms including PSO and TLBO, proves MTLBO to be an optimum solution for most real-life problems. When applied to the IEEE bus systems, the proposed method resulted in the mean congestion cost reduction and operational improvement. They also emphasize its versatility and simplicity as a selling point, especially for future contingent as flexible solution for the more dynamic and liberalized day-ahead energy markets.

MTLBO improves TLBO by refining the exploration-exploitation balance, incorporating adaptive learning phases, and eliminating parameter dependency. Unlike standard TLBO, MTLBO accelerates convergence, enhances accuracy, and optimizes power rescheduling with minimal loss, making it a more effective tool for congestion management in modern power grids.