Genetic Algorithm-Based Optimization of Regional Power Scheduling Problem and Provincial Electricity Market Bidding Mechanism

With the development of economy and increasing social demand, the complexity of power system operation is increasing. As an important part of power system management, cross-regional scheduling plays a key role in the safety and stability of power grid operation [1-3]. Cross-area scheduling in the power system refers to the scheduling and management of power exchanges between different regions to realize the balance of supply and demand and stable operation of the power grid. Inter-regional scheduling needs to consider many factors, including grid load, power supply, market demand, etc. [4-7]. Through reasonable inter-regional scheduling, the optimization of power system in terms of economy, security and stability can be achieved. In inter-regional scheduling, optimizing the scheduling scheme to improve the scheduling efficiency and economy is an important issue faced by power system operators [8-11].

Electricity market refers to the activities of both supply and demand sides of electric power under governmental management to carry out transactions by market mechanism. In this market, the supply subject provides electricity, the demand subject buys electricity, and both parties play the price game through the market mechanism, and the price formed is the bidding mechanism of the market [12-15]. Competitive bidding mechanism refers to the price will be generated in the market in accordance with the principle of competition, by the market participants bid to obtain. There are generally two forms of competitive bidding mechanism, one is a single round of bidding: that is, the participants of the goods (services) to provide a specified price, and ultimately the highest bidder to purchase the goods (services), the price of the price of the price they bid [16-19]. The second is multi-round bidding: i.e., in multiple rounds of bidding, participants can modify their offers in the next round based on the results of the previous round of bidding until they finally obtain the auction item or give up their participation [20-22].

In this paper, a regional power dispatch optimization model including market bidding based on genetic algorithms is designed. Firstly, the main constraints, such as branch flow constraints and standby constraints in each region, are modeled, and a preliminary solution method for hierarchical distributed computing is proposed. Then the genetic algorithm is applied to the provincial power market bidding to satisfy the constraints based on predicting the market-clearing tariffs in the future time period or accepting the information released by the market. The advantages and disadvantages are evaluated through the objective function, and the poorly adapted ones are eliminated, and finally the optimal solution is obtained and the bidding strategy tariff power curve is generated. The model is applied to a specific short-term optimal dispatch problem of hydropower, based on scenario revenue risk penalties or risk constraints, to validate the optimal regional power dispatch model.

2

Optimization model for regional power dispatch taking into account market bidding

2.1

Multi-objective function and constrained mathematical modeling

2.1.1

Basic assumptions

1) The principle of “price priority” was adopted for the day-ahead transactions, with the generating unit with the lowest offer being given priority in power generation;

2) In order to prevent the manipulation of the electricity market, the offers of thermal power units during the start-up process, which are subject to the minimum start-up time restriction, do not participate in the market clearing;

3) The coverage of the secondary electricity market is divided into N regions, and the regional grids are interconnected through contact lines. The market contains a superior trading center and N primary trading centers.

2.1.2

Objective function

The objective of day-ahead trading in the secondary electricity market is to reduce the cost of power purchases across the system while satisfying various constraints on system operation, and the objective function can be expressed as follows: (1) $\min \sum_{i \in G} \sum_{t = 1}^{T} I_{i, t} \cdot f (P_{i, t}) \cdot P_{i, t}$ \[\min \underset{i\in G}{\mathop \sum }\,\underset{t=1}{\overset{T}{\mathop \sum }}\,{{I}_{i,t}}\cdot f({{P}_{i,t}})\cdot {{P}_{i,t}}\]]

Where: G is the set of system-wide generating units; T is the total number of time periods; I_i,t is the start-stop state variable of unit i in time period t, with I_i,t = 1 denoting start-up and I_i,t = 0 denoting shutdown; f(P_i,t) is the offer function of unit i in time period t; and P_i,t is the generating power of unit i in time period t.

The objective function does not consider the unit startup and shutdown costs separately because the unit startup and shutdown costs can be reflected in the unit offer.

2.1.3

Main constraints

The main constraints on the objective function include:

1)

System active balance constraints:

(2)

\sum_{i \in G} P_{i, t} \cdot I_{i, t} = \sum_{n = 1}^{N} D_{n, t}, t = 1, 2, \dots, T

\[\underset{i\in G}{\mathop \sum }\,{{P}_{i,t}}\cdot {{I}_{i,t}}=\underset{n=1}{\overset{N}{\mathop \sum }}\,{{D}_{n,t}}\;,t=1,2,\cdots ,T\]]

Where: G is the set of system-wide generating units.

2)

Standby constraints for each region

(3)

\sum_{i \in G n} P_{i}^{\max} \cdot I_{i, t} + E_{n, t} \geq D_{n, t} \cdot (1 + R_{n}^{+} %), t = 1, 2, \dots, T n = 1, 2, \dots, N

\[\underset{i\in Gn}{\mathop \sum }\,P_{i}^{\max }\cdot {{I}_{i,t}}+{{E}_{n,t}}\ge {{D}_{n,t}}\cdot (1+R_{n}^{+}%),\quad t=1,2,\cdots ,T\quad n=1,2,\cdots ,N\]]

(4)

\sum_{i \in G n} P_{i}^{\min} \cdot I_{i, t} + E_{n, t} \leq D_{n, t} \cdot (1 - R_{n}^{-} %), t = 1, 2, \dots, T n = 1, 2, \dots, N

\[\underset{i\in Gn}{\mathop \sum }\,P_{i}^{\min }\cdot {{I}_{i,t}}+{{E}_{n,t}}\le {{D}_{n,t}}\cdot (1-R_{n}^{-}%),\quad t=1,2,\cdots ,T\quad n=1,2,\cdots ,N\]]

Where: $P_{i}^{max}$ $P_{i}^{max}$] is the maximum active output of unit i; $P_{i}^{\min}$ $P_{i}^{\min }$] is the minimum active output of unit i; E_n,t is the net input power of region n in time period t; $R_{n}^{+}$ $R_{n}^{+}$] is the positive reserve ratio of region n; $R_{n}^{-}$ $R_{n}^{-}$] is the negative reserve ratio of region n [23].

Considering that the contact line may be blocked in the actual trading plan, a certain percentage of standby should be reserved for each region separately.

3)

Constraints on the upper and lower limits of generator output:

(5)

P_{i}^{\min} \cdot I_{i, t} \leq P_{i, t} \leq P_{i}^{\max} \cdot I_{i, t}, t = 1, 2, \dots, T

\[P_{i}^{\min }\cdot {{I}_{i,t}}\le {{P}_{i,t}}\le P_{i}^{\max }\cdot {{I}_{i,t}}\;,\quad t=1,2,\cdots ,T\]]

4)

Minimum unit start-up duration and minimum shutdown duration constraints:

(6)

(T_{i, t}^{o n} - T_{\min, i}^{o n}) (I_{i, t - 1} - I_{i, t}) \geq 0, t = 1, 2, \dots, T

\[(T_{i,t}^{on}-T_{\min ,i}^{on})({{I}_{i,t-1}}-{{I}_{i,t}})\ge 0\;,\;t=1,2,\cdots ,T\]]

(7)

(T_{i, t}^{o f f} - T_{\min, i}^{o f f}) (I_{i, t} - I_{i, t - 1}) \geq 0, t = 1, 2, \dots, T

\[(T_{i,t}^{off}\;-T_{\min ,i}^{off})({{I}_{i,t}}-{{I}_{i,t-1}})\ge 0\;,\quad t=1,2,\cdots ,T\]]

Where: $T_{i, t}^{o n}, T_{i, t}^{o f f}$ $R_{n}^{-}$] is the continuous start-up duration and continuous shutdown duration of unit i in time period t, respectively; $T_{\min, t}^{o n}, T_{\min, t}^{o f f}$ $T_{\min ,t}^{on},T_{\min ,t}^{off}$] is the minimum start-up duration and minimum shutdown duration of unit i, respectively.

5)

Unit climbing constraint:

(8)

P_{i, t - 1} - Δ P_{i}^{d o w n} \leq P_{i, t} \leq P_{i, t - 1} + Δ P_{i}^{u p}

\[{{P}_{i,t-1}}-\Delta P_{i}^{down}\le {{P}_{i,t}}\le {{P}_{i,t-1}}+\Delta P_{i}^{up}\]]

Where: $Δ P_{i}^{d o w n}, Δ P_{i}^{u p}$ $\Delta P_{i}^{down},\Delta P_{i}^{up}$] is the rate of decline and rate of rise of the power of the unit or power plant i during a time period, respectively.

6)

Branch current constraints:

(9)

| P_{l, t} | \leq P_{l, t}^{\max}, l = 1, 2, \dots, L t = 1, 2, \dots, T

\[|{{P}_{l,t}}|\le P_{l,t}^{\max }\;,\;l=1,2,\cdots ,L\quad t=1,2,\cdots ,T\]]

Where: P_i is the active current power of line l; $P_{l}^{\max}$ $P_{l}^{\max }$] is the upper limit of active current of line l; l is the branch number; L is the total number of branches.

Where: P_i is the active current power of line l; $P_{i}^{m a x}$ $P_{i}^{max}$] is the active current limit of line l; l is the branch number; L is the total number of branches.

7)

Nodal voltage inequality constraints:

(10)

V_{n}^{\min} \leq V_{n} \leq V_{n}^{\max}, n = 1, 2, \dots, N

\[V_{n}^{\min }\le {{V}_{n}}\le V_{n}^{\max }\;,\;n=1,2,\cdots ,N\]]

Where: V_n is the voltage magnitude of node n; $V_{n}^{\max}$ $V_{n}^{\max }$] is the upper limit of voltage magnitude of node n; $V_{n}^{\min}$ $V_{n}^{\min }$] is the lower limit of voltage magnitude of node n; n is the node serial number; N is the total number of nodes.

2.2

Distributed Solution Methods

2.2.1

General idea

When carrying out the calculation of the day-ahead trading plan for the secondary power market, the computer systems of the two-level power dispatching and trading centers constitute a hierarchical distributed computing platform to complete the day-ahead trading plan for the whole system through collaborative computation. [24] The calculation process is mainly divided into three steps:

1) Before the start of the transaction calculation, the higher-level power dispatch and trading center forwards the unit offer data reported to the center to the corresponding grassroots power dispatch and trading centers separately by region. The objective function of the calculation is: (11) $\min \sum_{t = 1}^{T} S M P_{n, t} \cdot D_{n, t}$ \[\min \underset{t=1}{\overset{T}{\mathop \sum }}\,SM{{P}_{n,t}}\cdot {{D}_{n,t}}\]] (12) $S M P_{n, t} = \max_{i \in G n} {I_{i, t} \cdot f (P_{i, t})}, t = 1, 2, \dots, T$ \[SM{{P}_{n,t}}={{\max }_{i\in Gn}}\{{{I}_{i,t}}\cdot f({{P}_{i,t}})\},\quad t=1,2,\cdots ,T\]]

Where: T is the total number of time slots; SMP_n, is the regional marginal price of region n in time slot t; G_n is the set of generating units in region N.

2) On the basis of the data reported by each grass-roots power dispatch and trading center, the higher-level power dispatch and trading center will finely weave and coordinate each grass-roots power dispatch and trading center to carry out inter-regional trading by iterative calculation time by time, and carry out the grid security calibration at the same time of iterative calculation in a hierarchical manner.

3) When the calculation of the inter-regional trading plan for all time periods is completed, on the basis of not changing the results of this calculation, each grass-roots power dispatch and trading center will re-calculate the intra-regional trading plan, with the goal of calculating the lowest cost of purchasing power, and with the constraints including the various constraints mentioned above.

2.2.2

Algorithm design

The calculation process of the day-ahead trading plan for the secondary power market is shown in Figure 1. When all the information from each grassroots power dispatching and trading center reaches the higher-level power dispatching and trading center, the inter-regional transaction calculation is carried out from time period 1 on a time period-by-time period basis, and the iterative calculation steps for each time period are as follows:

1) The higher-level power dispatching and trading center performs regional classification. If the number of tradable regions is less than two, or if there is no power shortage region and the marginal price of each tradable region is equal (or differs only by the smallest offer unit), then it proceeds to the iterative calculation of the next time period (or goes to step 5 if the calculation of all time periods is completed), otherwise the higher-level power dispatch and trading center performs the following steps:

(1) Group the tradable regions according to the level of regional marginal price SMP_n, SMP_n,t the same region into the same group (here GMP indicates the marginal price of the group), and then sort the groups in accordance with GMP, so that GMP₁ < GMP₂ < … < GMP_p(p ≤ n), each group may have only one region, or there may be more than one region;

(2) Designate the power purchase region and the power sale region: the power purchase region is the region with the highest marginal price in the shortage region or the group with the highest marginal price and prioritize the shortage region to be designated as the power purchase region; the power sale region is the region in the group with the lowest marginal price. The transmission channel between the selling area and the purchasing area must be unblocked.

2) The Basic Power Dispatch Trading Center of the selling region calculates the power P_out that can be sold in this transaction and reports it P_out must meet the following conditions:

(1) The offer price is higher than and equal to the marginal price of the region, but not higher than the marginal price GMP₂ of the next lower region; if there are only two groups of regions in total, the offer price is not higher than GMP₁ + (GMP₂ – GMP₁)/2;

(2) It can be sent through the contact line in the direction of the power purchasing region after the security calibration of the grid in the region.

The primary trading center of the power purchasing region calculates the power that can be bought in this transaction p_in and reports it. If the power purchasing region is a power shortage region, then p_in it is a power shortage, otherwise p_in the following conditions are met:

(1) Offer not lower than the next highest marginal tariff GMP_p–1; or GMP₁ + (GMP₂ – GMP₁)/2 if there are only two groups of regions in total;

(2) After the intra-regional network security calibration can be fed through the contact line in the direction of the power selling region.

3) After receiving the data reported by the power purchasing region and the power selling region, the higher-level power dispatch and trading center calculates and determines the power for this transaction. The calculation method is as follows:

(1) If there are only two regions conducting transactions, the higher-level power dispatch and trading center searches for an interregional grid transmission channel from the power selling region to the power purchasing region and calculates the current maximum allowable transmission capacity of this channel P_trans, then the power for this transaction Δp = min(P_out,P_in,P_trans).

(2) If there are more than two regions conducting the transaction, it first calculates (P = min(∑P_out,∑P_in) and distributes P among several regions to obtain the tradable power for each region.

4) The higher-level power dispatching and trading centers are based on the actual traded power in each region. Modify the inter-regional grid currents, while the basic-level trading centers are based on the actual traded power.

5) Each grass-roots power dispatch and trading center coordinates the calculation of the intra-regional trading plan.

2.3

Genetic algorithm optimization solution process

2.3.1

Genetic Algorithm Solution Principles

From a mathematical point of view, genetic algorithm is essentially a search for optimization. Specific steps include. Coding, forming the initial population, calculating the fitness (including the determination of the fitness function), performing genetic operations (selection, crossover, mutation), terminating operations, etc. The basic flow chart is shown in Fig. 2 [25].

1)

Encoding

Since the genetic algorithm does not act directly on the variable to be solved, and its object of operation is a string, the objective function and variables of the problem should be determined first, and then the variable to be solved should be encoded.

2)

Formation of initial population

The initial population is the starting point of genetic algorithm search and optimization. The population size is the number of individuals contained in the population.

3)

Calculate the degree of adaptation

The fitness is a measure of individual merit, which is the basis for the implementation of the genetic algorithm “survival of the fittest”. Genetic algorithms basically do not need external information in the evolutionary search process, and only use the fitness function as the basis for searching using the fitness value of each individual in the population.

4)

Execution of genetic operations

From the point of view of optimization search, genetic operation can optimize the solution of the problem and approach the optimal solution. Genetic operations include the following three basic genetic operators: selection, crossover and mutation. Selection and crossover basically fulfill most of the search function of the algorithm, while mutation increases the ability of the algorithm to find near-optimal solutions:

(1)

Selection

The purpose of selection is to select good individuals from the current population so that they have a chance to act as parents and produce offspring individuals. The criterion for judging the goodness of individuals is their respective fitness.

(2)

Crossover

Crossover is the main means of generating new individuals by genetic algorithm, which refers to the operation of replacing and reorganizing some of the structures in the parent individuals and dusting them into new individuals.

(3)

Mutation

Mutation operation simulates the phenomenon of mutation of a gene at a certain position on a chromosome in the evolutionary process of natural organisms, thus changing the structure and physical traits of the chromosome.

5)

Termination

There are three ways to make a genetic algorithm terminate:

(1)

Specify the maximum number of iterations N

Once the number of iterations of the genetic algorithm reaches N, the operation is stopped and the results are output. In addition, due to the influence of many random factors in the genetic algorithm, the result of the last generation may not necessarily contain the optimal individual.

(2)

Specify the minimum deviation

For genetic algorithms where the fitness objective is known, such as the curve fitting problem where the variance is used as the fitness calculation, the termination condition can be formulated with a minimum deviation of δ, i.e.: (13) $| \begin{matrix} f_{\max} - f \end{matrix} | \leq δ$ \[|\begin{matrix} {{f}_{\max }}-f \\ \end{matrix}|\le \delta \]]

where f is the known fitness target and f_max is the fitness of each generation.

(3)

Observe the trend of adaptation degree.

At the beginning of the genetic algorithm, the fitness of the optimal individual as well as the average fitness of the population are relatively small, and later the fitness value increases with the operations of replication, crossover and mutation.

2.3.2

Solving for regional power dispatch with market bidding in mind

The process of using genetic algorithm to find the optimal for regional power dispatch taking into account market bidding can be understood as follows: the unit, under normal operating conditions, satisfies the constraints based on the prediction of the market clearing tariff in the future time period or accepts the information released by the market, and evaluates its advantages and disadvantages through the objective function. The poorly adapted ones are eliminated, and only the well-adapted ones have the chance to inherit their characteristics to the next round of solutions, and finally obtain the optimal solution to produce their own offer strategy tariff power curve.

Setting the coding, constructing the fitness function, generating the initial population, and performing the genetic operation according to the characteristics of the specific problem are the keys to optimizing the genetic algorithm. Appropriate coding can reduce the scope of the search space, and at the same time, the genetic operation will not produce ineffective individuals: effective fitness function is to realize the evolutionary principle of “survival of the fittest”; the reasonable selection of the initial population embodies the concepts of parallelism and global search of genetic algorithms; genetic operation is an important part of the genetic algorithm to obtain the best individuals and to avoid evolutionary stops and premature convergence. Genetic operation is a significant method for genetic algorithms to obtain good individuals and prevent evolutionary cessation and premature convergence. In summary, the optimization process for genetic offers is shown in Figure 3.

1)

Parameter coding

According to the market trading rules, 4 to 10 quotation points are selected to form a chromosome, i.e. an initial quotation scheme. Since the price is continuous in its definition domain, the use of real number coding can more accurately represent price changes than binary coding; moreover, real number coding does not require the process of compilation and decoding, so it is also faster than binary in terms of computing speed.

2)

Generating the initial offer program

Based on the predicted system marginal electricity price, an initial population of offer programs is constructed under the condition of satisfying the technical constraints of the generating unit. The selection of the initial population is generally carried out randomly, and this paper determines that it is appropriate to control the initial population at 20 to 40.

3)

Adaptation function

The fitness value of the bidding scheme is a principle in genetic algorithms to measure the merit of the bidding scheme. Considering the impact of constraints on the bidding scheme, a penalty function is introduced. If the value of the objective function is large and the violation of constraints is small, the scheme is good and its corresponding offer scheme should be assigned a large adaptation value. The adaptation value F_K can be calculated for Individual k according to the following equation: (14) $F_{k} = A + E - ϕ_{v} \sum_{v = 1}^{3} V_{v}$ \[{{F}_{k}}=A+E-{{\phi }_{v}}\underset{v=1}{\overset{3}{\mathop \sum }}\,{{V}_{v}}\]]

Violations are calculated as follows: (15) $V_{1} = \max {0, R - E (p, λ)}$ \[{{V}_{1}}=\max \{0,R-E(p,\lambda )\}\]] (16) $V_{2} = \max {(p_{\min} - p), \max (0, p - p_{\max})}$ \[{{V}_{2}}=\max \{({{p}_{\min }}-p),\max (0,\;p-{{p}_{\max }})\}\]] (17) $V_{3} = \max {λ_{\min} - λ), \max (0, λ_{\min} - λ)}$ \[{{V}_{3}}=\max \{{{\lambda }_{\min }}-\lambda ),\max (0,\;{{\lambda }_{\min }}-\lambda )\}\]]

A is a positive number, which ensures that the individual adaptation value is positive; E is the objective function, which is W_i(λ,p_i) = ζ_i·P_i – C_i(p_i) for this paper; ϕ_ν is the penalty coefficient of constraint ν, with an initial value of 1. In the algorithm evolution, if the constraint is violated, the penalty coefficient is gradually increased to ensure that the constraint is satisfied. p is the unit output, and λ is the electricity price.

4)

The main process of genetic operation

(1)

Selection operator

The selection probability of chromosomes is adopted by the method of sorting the fitness function, m chromosomes in the population of the same generation are arranged according to the value of the fitness function from small to large, and these chromosomes are noted as 1 to m according to the value of the fitness function from small to large.The distribution probability is taken directly:

(18)

g (i) = \frac{2 i}{m (m + 1)}, 1 \leq i \leq m

\[g(i)=\frac{2i}{m(m+1)}\;,\;1\le i\le m\]]

Individuals with large fitness values are directly copied to the next generation instead of individuals with small fitness values.

(2)

Crossover operator

For some two parents, using the conventional method may result in identical parents and offspring, which will inevitably affect the convergence speed and search range. Therefore, from the beginning, their identical genes are first compared, and the crossover sites are randomly selected from different gene positions by the conventional method. General crossovers have the potential to disrupt monotonically rising offer curves, so arithmetic averages can be adjusted for hybrid progeny, e.g., λ₁,λ₂ crossover with progeny behaving as $λ_{1}^{*} = a λ_{1} + (1 - a) λ_{2}; λ_{1}^{*} = a λ_{1} + (1 - a) λ_{2}$ $\lambda _{1}^{*}=a{{\lambda }_{1}}+(1-a){{\lambda }_{2}};\lambda _{1}^{*}=a{{\lambda }_{1}}+(1-a){{\lambda }_{2}}$] as a uniformly distributed random number between 0 and 1.

In order to improve the convergence speed and search range, the crossover algorithm set in this system is as follows: firstly, according to the crossover rate (P_c) determined by the test, select the offer programs that need to perform the crossover operation, and then one by one, compare the same tariff one output combination of each two offer programs, and randomly select the crossover position points from different combination positions in accordance with the conventional method, i.e., from this point onwards to the last set of combinations, to exchange the combination methods of the two offer programs.

(3)

Mutation operators

Variation diversifies the individuals of the solution, allowing free movement away from the local optimum during the search for a better solution. A general variation is likely to disrupt the monotonically increasing offer curve, so it is adjusted to the offer constraints, i.e., it is carried out by using a single parent uniformly mutated to produce a single offspring, e.g., λ(λ₁,λ₂,…,λ_n) is chosen to be mutated at point k, then:

When k ≠ 1 or k ≠ n, $λ_{k}^{*}$ $\lambda _{k}^{*}$] takes a random number distributed with uniform probability between [λ_min,λ_k+1; when k = n, $λ_{k}^{*}$ $\lambda _{k}^{*}$] takes a random number distributed with uniform probability between [λ_min,λ_k+1]; when k = n, $λ_{k}^{*}$ $\lambda _{k}^{*}$] takes a random number distributed with uniform probability between [λ_k–1,λ_max].

5)

Conclusion

Genetic operations are performed on the resulting new generation of populations until the convergence end condition is satisfied.

3

Simulation experiments on optimization effects

3.1

Simulation experiments of short-term optimization algorithms for hydropower

The algorithm in this paper is used to solve the short-term optimal scheduling problem of hydropower based on scenario revenue risk penalty or risk constraint. The basic parameters of the optimization algorithm in this paper are: the population size is 120; the maximum number of evolutionary generations is 500; the crossover probability is 0.8; the penalty scaling factor of the terminal reservoir capacity constraint is 120; the scaling factor in the calculation of the individual standard variance in the variation operation is 0.1; the number of competing individuals in the competitive selection mechanism is 60; the target return is set as 14.8 million yuan; the penalty coefficient in the risky great penalty method is 10000; the acceptable risk level in the risk constraint is set as 8300 (RMB). is 10000; the acceptable risk level in the risk constraint is set to 8300 (RMB).

Figure 4 shows the evolutionary convergence process of this paper's optimization algorithm in terms of fitness value when maximizing the expected return under risk neutrality. Fig. 5 shows the evolutionary convergence process expressed in terms of expected return under risk neutrality. Figure 6 shows the evolutionary convergence process of the risk faced by the hydropower vendor under risk neutrality.

As can be seen from the figure, the value of the expected return is higher and the risk is lower in the initial stage of the evolutionary search, but this comes at the cost of a very large terminal reservoir constraint, which is violated up to the level of 105m3. As the iterative search proceeds, the constraint on the terminal reservoir capacity is gradually strengthened, enabling this constraint to be better approximated to be satisfied, and the violation of the constraint at the time of convergence is within the level of 102m3, with the expected benefit and risk reaching a stable equilibrium state.

Since the optimal dispatch strategy of hydropower station should comprehensively consider the fluctuation of electricity price under each scenario, and this fluctuation of electricity price has an inherent regularity, only the dispatch scheme that increases the power generation in the high electricity price period and reduces the power generation in the low electricity price area, and at the same time controls the violation of the terminal capacity constraint to be as small as possible, can achieve the maximization of the expected return and at the same time minimize the risk.

In the hydropower optimal dispatch model based on scenario revenue risk penalties or risk constraints, the risk is identified by the target revenue value. Since the scheduling plan for each scenario is deterministic, the adjustment of each scheduling plan has the same impact on each scenario, and thus the reduction of risk is consistent with the increase of expected return. Since this chapter uses an evolutionary class of optimization algorithms, this consistency such that penalizing risk or adding risk constraints will facilitate the algorithm's optimality search. This management of risk can thus be considered as a special kind of evolutionary operator that will have an impact on both the expected return, the risk, and the scheduling strategy, and this chapter verifies this regularity through an example analysis.

Figure 7 shows the comparison of the benefits of each scenario under the three models of risk-neutral, extremely penalized approach to risk and risk-constrained approach. Table 1 shows the comparison of expected return, risk, and end-pool constraint violation under the three modes.

From Fig. 7 and Table 1, it can be seen that since the risk-neutral evolution process considers both maximized expected return and terminal reservoir constraint, it can achieve a very small terminal reservoir constraint violation when the evolution process converges, but its search optimization mode does not achieve a good match with the fluctuation law of the electricity price in each scenario, which restricts its ability to get the maximum expected return, making the final value of the expected return obtained relatively The expected return value is relatively small, while the risk value is large. The maximized risk penalty approach emphasizes the adjustment of the overall scheduling strategy in the search mode throughout the evolution process so that each scenario can get a higher return value, thus obtaining a better balance between the expected return and the risk, but it weakens the treatment of the terminal capacity constraints, resulting in a more serious violation of the terminal capacity constraints. The risk-constrained approach, on the other hand, relaxes the penalty of risk so that the evolutionary process can be carried out in a broader space, while taking into account the treatment of the end-capacity constraints, so that the final optimization solution can obtain a higher expected return and a smaller value of risk, and the violation of the end-capacity constraints is less.

Table 1.

The comparison of the income, risk and the end capacity of the next period

Time/hour	Risk neutrality	Risk aversion
Time/hour	Risk neutrality			Maximum risk punishment	Risk constraint method
Expected earnings/(10⁴rmb)	1473.78	1527.86	1506.63
Risk/(rmb)	104839	573.47	8194.7
The end volume constraint violation quantity/m³	8.03	12918.5	-2084.6

The corresponding hydropower dispatch strategies will be different for different risk management approaches. Table 2 shows the comparison of hydropower scheduling strategies under the risk-neutral, risk-penalized and risk-constrained approaches.

Table 2.

Comparison of hydropower discharge strategy

Time/hour	Risk neutrality	Risk aversion
Time/hour	Risk neutrality	Maximum risk punishment	Risk constraint method
1	1318.89	1042.24	1303.68
2	1270.24	870.99	989.23
3	1737.69	1586.34	1394.63
4	1461.38	1162.51	857.49
5	1559.17	1669.25	1513.11
6	1125.75	2010.26	1300.64
7	1605.75	2232.08	1622.93
8	1601.97	2036.33	1773.61
9	1311.5	2019.03	1533.9
10	1441.86	2209.13	1350.8
11	1748.88	2184.71	1858.63
12	1721.71	1983.37	1687.42
13	1356.63	843.19	1682.64
14	1494.16	1775.52	1502.11
15	1502.81	1076.39	1282.53
16	1584.27	639.99	1505.81
17	1447.01	1367.85	1573.06
18	1657.18	1146.57	1228.48
19	1647.96	901.84	1810.7
20	1480	2266.34	1912.85
21	1130.18	1483.59	1826.94
22	1690.53	1737.49	1850.16
23	1197.21	554.44	1115.34
24	1230.88	548.75	869.68

3.2

Regional Power Dispatch Costs and Optimization Effectiveness

In order to analyze the energy-saving effect of implementing energy-efficient generation scheduling in the regional power grid and the impact on the cost of purchased power of the provincial company, we took one typical day in winter and one typical day in summer of the Central China Power Grid for simulation. The average coal consumption of power purchase in a province refers to the average coal consumption of power generation to supply the power demand in the province, and if the power generation comes from outside the province, the coal consumption of power generation in the outside province will be converted to the province. The average purchase price of electricity is calculated in the same way: if the electricity is generated from outside the province, the coal consumption of electricity generation from outside the province will be converted to the province, and the inter-provincial transmission fee will be added.

The following assumptions are made in the calculation:

1) According to the order stipulated in the Measures, high-quality energy sources, such as hydropower, are generated first, so the generation demand of the province will be subtracted from the generation capacity of high-quality energy sources, such as hydropower, and the remaining will be the generation demand of thermal power. Our measurement is only for conventional coal power units.

2) Design coal consumption is used for unit coal consumption values.

3) Safety constraints within the province are replaced by zonal limits and minimum start-ups.

4) Cross-provincial transmission must meet the transmission capacity constraints of the cross-provincial liaison line.

5) The combination of start-up units is determined first, and all start-up units use equal proportional peaking.

3.2.1

Energy efficiency analysis

The average coal consumption of each province under different modes is shown in Table 3. From the table, we can see that the average coal consumption in the energy-saving dispatch mode is much lower than the equivalent utilization hours, which fully reflects the energy-saving and emission reduction effect of energy-saving dispatch. In this mode, the average coal consumption in summer is lower than the average coal consumption in winter, because of the hydropower in Sichuan, Hunan, and other areas. is very large in summer, and the demand of thermal power units is reduced, according to the principle of giving priority to the large units with low coal consumption, the small units can't enter into the combination of units, so the average coal consumption in summer is lower. In the bidding transaction, each unit is quoted in accordance with the fixed cost plus variable cost, and large units with low coal consumption and relatively low variable cost are generally quoted at a lower price than small units, so some energy saving effect can also be achieved under this mode. However, since certain small units have been in operation for many years, and most of the large units are newly built units with high pressure of loan repayment, there is also a bidding advantage for some small units. Due to this reason, its energy-saving effect is less than that of the energy-saving scheduling mode.

Table 3.

Comparison of average coal consumption rate among different modes

The average winter day in the winter is the average electricity consumption
Province	Service hour	Energy saving dispatching	bidding	Juggling pattern
Hupei	335.1	327.6	330	327.6
Henan	342.3	328.5	334.7	327
Hunan	327.9	320.9	324.5	322.3
Jiangxi	339.2	332.2	333.3	331.5
Sichuan	343.8	330.2	329.7	330.2
Chongqing	333.1	326.8	331.6	329.7
The average Summer day in the winter is the average electricity consumption
Province	Service hour	Energy saving dispatching	bidding	Juggling pattern
Hupei	331.4	324.3	325.6	324.9
Henan	342.1	332.3	333.5	331
Hunan	325.2	316.9	323.9	317.5
Jiangxi	338.3	335.3	338.6	336.7
Sichuan	346.2	325	322.8	323.4
Chongqing	332.6	325.9	329.2	323.7

Table 4 shows the comparison of energy savings in different modes. The coal saving effect of using energy-saving dispatching is the most significant, and the whole region can save 4,305,175,000 tons of coal for the whole year; followed by the concurrent mode, which can save 3,976,675,000 tons of coal.

Table 4.

Comparison of coal-saving among different modes

Market model	Typical day	Mean coal consumption/ (g/kwh)	Depletion of coal (g/kWh)	Daily charge (GWh)	Daily reducing coal WT	Per Year reducing coal WT
Service hour	Typical Winter day	334.9	0	1218	0	0
Service hour	Typical Summer day	332.7	0	1269	0
Energy saving dispatching	Typical Winter day	323.8	10.2	1218	1.201	430.5175
Energy saving dispatching	Typical Summer day	323.1	9.1	1269	1.158
Bidding	Typical Winter day	326.5	6.5	1218	0.804	303.4975
Bidding	Typical Summer day	325.6	6.7	1269	0.859
Juggling pattern	Typical Winter day	324.7	8.4	1218	1.048	397.6675
Juggling pattern	Typical Summer day	323.9	9.7	1269	1.131

3.2.2

Analysis of the cost of power purchases by provincial companies

For energy-saving dispatching to be successfully implemented, it is necessary to take into account the interests of all parties to achieve a multi-win situation, so we did a comparative analysis of the average power purchase cost of the provincial companies. Table 5 shows the data on the average power purchase price for each province under different modes. In the measurement, the power purchase price under the equal utilization hour and energy-saving dispatch mode adopts the approved power price of each power plant, and the bidding mode and the balancing mode adopts the power generation offer of each enterprise. From the table, we can see that after the implementation of energy-saving scheduling, the average power purchase cost of grid enterprises has increased, which is due to the fact that most of the small units are not equipped with desulfurization equipment, so the approved tariffs are slightly lower. In contrast, with the adoption of competitive bidding and trading and the balanced model, the power purchase cost of grid enterprises has been reduced, and a good social benefit has been achieved.

Table 5.

Comparison of average purchasing cost among different modes

The average purchase price of electricity prices in the typical days of winter
Province	Service hour	Energy saving dispatching	bidding	Juggling pattern
Hupei	439.4	442.1	406.8	432.5
Henan	390.7	393.5	381.1	383.1
Hunan	427.6	435	403.7	419.6
Jiangxi	416.5	427.2	394.4	408.1
Sichuan	379.2	375.9	379.9	365.2
Chongqing	373	375.5	365.7	366.5
The average purchase price of electricity prices in the typical days of Summer
Province	Service hour	Energy saving dispatching	bidding	Juggling pattern
Hupei	428.6	433.2	395.7	406.8
Henan	388.6	397.1	380.4	384.3
Hunan	402.5	414.1	384.1	392.5
Jiangxi	419	420	388.8	409.1
Sichuan	358.9	357.6	346.2	358.4
Chongqing	363.6	369.7	361.7	365.6

3.2.3

Cross-provincial transaction volume analysis

We compared and analyzed the inter-provincial transactions of the energy-saving scheduling mode and the balancing mode, and the results are shown in Tables 6 and 7. From Table 6, we can see that the volume of inter-provincial transactions in winter is not large, and the recipient provinces are Jiangxi and Sichuan. Jiangxi is mainly due to the large number of small units in the province, while Sichuan is a large hydropower province with small hydropower output during dry periods. From Table 6, we can see that the volume of inter-provincial transactions in summer is significantly larger than that in winter. At the same time, we can also find that the energy-saving scheduling mode, Central China Power Grid in the summer appeared in the phenomenon of coal and power backward delivery, that is, Hunan, Chongqing and other provinces of power to the coal-producing province of Henan backward delivery. The reason for this phenomenon is that in summer, the hydropower in Hubei and other provinces is fully generated and supplied for local use, so that the marginal unit capacity of thermal power rises, forming a competitive advantage compared with Henan. While the adoption of the eclectic model takes into account the cost of power generation for enterprises, Henan Province has a low coal price, which gives it a competitive advantage compared to other provinces, so the phenomenon of energy backflow can be avoided under this model. From Table 6 and Table 7, we can also see that by adopting the balancing model, the volume of interprovincial transactions increases, which is conducive to optimizing power resources in the entire region.

Table 6.

Comparison of trans-provincial power energy in winter

Energy saving mode
Direction	Extreme value		Peak		Normal segment		Trough		Total
Direction	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity
Hubei to Jiangxi	251	485	227	1386	217	2318	164	818	2018	5002
Hubei to Sichuan	101	201	104	623	106	1156	108	532	105	2478
Chongqing to Sichuan	605	1194	615	3691	617	6827	615	3056	617	14768
Total	957	1880	946	5700	940	10301	887	4406	2740	22248
The energy saving scheduling model of the power market
Direction	Extreme value		Peak		Normal segment		Trough		Total
	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity
Hubei to Henan	623	1247	583	3536	596	6572	478	2391	570	13850
Hunan to Henan	204	408	196	1142	195	5146	158	764	184	4478
Chongqing to henan	296	586	276	1667	287	3128	228	1135	283	6528
Sichuan to Hubei	251	504	254	1538	253	2768	249	1259	252	6003
Sichuan to Jiangxi	251	504	256	1538	253	2768	249	1248	252	6003
Sichuan to Chongqing	1587	3196	1208	7211	1385	15199	737	3679	1217	29395
Total	3212	6445	2773	16632	2969	35581	2099	10476	2758	66257

Table 7.

Comparison of trans-provincial power energy in summer

Energy saving mode
Direction	Extreme value		Peak		Normal segment		Trough		Total
Direction	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity
Henan to hubei	1596	3176	1477	8731	1408	15398	1153	5718	1386	33171
Henan to Jiangxi	247	508	285	1375	216	2347	167	836	215	5094
Sichuan to hubei	483	964	475	2609	417	4528	335	1695	407	9825
Sichuan to Hunan	74	147	76	438	75	796	72	357	76	1723
Chongqing to Hubei	1049	2135	988	5857	935	10318	768	3845	931	22039
Chongqing to Hunan	106	191	102	602	96	1059	95	489	97	2347
Total	3555	7121	3403	19612	3147	34446	2590	12940	3112	74199
The energy saving scheduling model of the power market
Direction	Extreme value	Peak	Normal segment	Trough	Total
	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity	Electric power	Electric quantity
Henan to hubei	1937	3861	1937	11871	2028	22276	1641	8177	1935	45863
Henan to Hunan	158	309	158	935	168	1819	151	748	162	3712
Chongqing to Hubei	472	954	472	2864	498	5463	408	2019	469	11309
Sichuan to Hubei	258	502	258	1536	259	2769	258	1283	258	6003
Sichuan to jiangxi	258	502	258	1536	259	2769	258	1283	258	6003
Sichuan to Chongqing	1536	3196	1207	7315	1368	15178	726	3696	1237	29247
Total	4619	9324	4290	26057	4580	50274	3442	17206	4319	102137

4

Conclusion

In this paper, we design an energy-saving scheduling model that takes into account the bidding and trading in the power market. Through the actual data of the Central China Power Grid, various models were analyzed, and it was proved that the scheduling model designed in this paper has a certain effect on energy saving. The annual coal saving is 3,976,675 tons. Its energy-saving effect is only second to the energy-saving scheduling, but also has the effect of reducing the cost of power purchase by provincial companies, increasing the volume of cross-provincial transactions, and optimizing the flow of resources between provinces, which is an energy-saving scheduling model that can be applied to the actual regional power grid. In the analysis of hydropower short-term optimization example, the model makes the constraints closer to be satisfied, and the violation of the constraints at the time of convergence is within the level of 10²m³, and the expected benefits and risks have reached a stable equilibrium state. The model in this paper achieves the objective of energy saving, reducing the cost of power purchase, and optimizing the allocation of resources.

Funding:

This research was supported by the Technology Project of the Guangdong Power Exchange Center (Project No.: GDKJXM20222659).

Idioma:: Inglés

Calendario de la edición:: 1 veces al año
Temas de la revista:: Ciencias de la vida, Ciencias de la vida, otros, Matemáticas, Matemáticas aplicadas, Matemáticas generales, Física, Física, otros

RSS Feed de revista

Genetic Algorithm-Based Optimization of Regional Power Scheduling Problem and Provincial Electricity Market Bidding Mechanism

Jinqing Luo

Kangan Shu

Qing Chen

Haohao Wang

Yun Xu

Publicado en línea: 21 mar 2025

Recibido: 03 nov 2024

Aceptado: 16 feb 2025

DOI: https://doi.org/10.2478/amns-2025-0609

Palabras claveElectricity market bidding, Objective function, Genetic algorithm, Regional power dispatching

© 2025 Jinqing Luo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Electricity market bidding, Objective function, Genetic algorithm, Regional power dispatching